Individual-Based Model

Formulation for CutthroatTrout,

Little Jones Creek, California

Steven F. Railsback Bret C. Harvey

United States

Department

of Agriculture

Forest Service

Pacific Southwest

Research Station

General Technical Report

PSW-GTR-182
Publisher

Albany, California

Mailing address:

PO Box 245, Berkeley CA

94701-0245

(510) 559-6300

http://www.psw.fs.fed.us

June 2001

Pacific Southwest Research Station

Forest Service

U.S. Department of Agriculture

Abstract

Railsback, Steven F.; Harvey, Bret C. 2001. Individual-based model formulation for cutthroat

trout, Little Jones Creek, California. Gen. Tech. Rep. PSW-GTR-182. Albany, CA: Pacific

Southwest Research Station, Forest Service, U. S. Department of Agriculture; 80 p.

This report contains the detailed formulation of an individual-based model

(IBM) of cutthroat trout developed for three study sites on Little Jones Creek, Del

Norte County, in northwestern California. The model was designed to support

research on relations between habitat and fish population dynamics, the

importance of small tributaries to trout populations, and the usefulness of

individual-based models for forest management. The model simulates the full

trout life cycle at a daily time step; habitat is modeled at a resolution of several

square meters. The major trout activities simulated are spawning, habitat

selection (movement), feeding and growth, and mortality. Two feeding strategies

are simulated: drift feeding and searching for stationary food. Mortality risks

include starvation, aquatic predation, terrestrial predation, high temperature,

stranding, and high velocity. Movement maximizes the probability of surviving

and attaining reproductive size over a future time horizon. Risks to incubating

trout eggs include extreme temperatures, dewatering, and scouring by high

flows. The model design approach was adapted from complex adaptive systems

theory.

Retrieval Terms: cutthroat trout, habitat selection, individual-based model,

population model, salmonids

The Authors

Steven F. Railsback is an environmental scientist with Lang, Railsback

& Associates, 250 California Avenue, Arcata CA 95521; e-mail:

LRA@Northcoast.com.

Bret C. Harvey is a research fish biologist with the Pacific Southwest Research

Station, USDA Forest Service, 1700 Bayview Drive, Arcata CA 95521; e-mail:

bch3@humboldt.edu.

Acknowledgments

The Little Jones Creek cutthroat trout model was developed under Research

Joint Venture Agreement PSW-99-007-RJVA between the Pacific Southwest

Research Station, USDA Forest Service’s Redwood Sciences Laboratory, and

Lang, Railsback & Associates (LRA). Collaborative funding for software

development and model testing was provided to LRA by the Electric Power

Research Institute (EPRI). The trout model software is developed and maintained

by Steve Jackson, Jackson Scientific Computing, McKinleyville, California. Jim

Petersen, Columbia River Laboratory, U. S. Geological Survey, provided a

valuable review of a previous draft of this document. Tom Lisle, Pacific

Southwest Research Station, Arcata, California, helped develop the approach we

use for modeling redd scouring. The Swarm program at the Santa Fe Institute

(Santa Fe, New Mexico) has heavily influenced our approach to fish movement

and the overall modeling philosophy.
Pacific Southwest

Research Station

USDA Forest Service

General Technical

Report

PSW-GTR-182

June 2001

Contents

In Brief .....................................................................................................................iv

I. Introduction............................................................................................................. 1

 I.A. Fundamental Approach and Assumptions ............................................ 2

I.B. Study Site....................................................................................................... 3

I.C. Conventions.................................................................................................. 4

I.C.1. Units ................................................................................................. 4

I.C.2. Parameter and Variable Names .................................................. 4

I.C.3 Survival Probabilities and Mortality Sources........................... 4

I.C.4. Dates, Days, and Fish Ages ......................................................... 4

I.C.5. Habitat Cell Conventions............................................................. 4

II. Model Initialization ........................................................................................... 5

II.A. Habitat Initialization ................................................................................ 5

II.B. Fish Initialization ...................................................................................... 5

II.C. Redd Initialization .................................................................................... 6

III. Habitat Model...................................................................................................... 6

III.A. Cell Boundaries and Dimensions ........................................................... 7

III.B. Daily Flow, Temperature, and Turbidity ............................................. 7

III.C. Depth and Velocity ................................................................................... 7

III.D. Velocity Shelter Availability ................................................................... 8

III.E. Spawning Gravel Availability ................................................................ 8

III.F. Distance to Hiding Cover ........................................................................ 8

III.G. Food Production and Availability ......................................................... 8

III.G.1. Production.................................................................................... 9

III.G.2. Availability ................................................................................ 10

III.H. Day Length ............................................................................................... 10

IV. Fish Model.......................................................................................................... 10

IV.A. Spawning .................................................................................................. 11

IV.A.1. Determine Spawn Readiness .................................................. 11

IV.A.2. Identify Redd Location ............................................................ 11

IV.A.3. Make Redd ................................................................................. 12

IV.B. Movement................................................................................................. 12

IV.B.1. Departure Rules ........................................................................ 13

IV.B.2. Destination Rules...................................................................... 13

Individual-Based Model

Formulation for Cutthroat Trout,

Little Jones Creek, California
IV.C. Feeding and Growth............................................................................... 17

IV.D. Survival ..................................................................................................... 19

V. Redd Model ...................................................................................................... 20

V.A. Survival ..................................................................................................... 20

V.B. Development............................................................................................ 20

V.C. Emergence ................................................................................................ 21

V.C.1. Emergence Timing ..................................................................... 21

V.C.2. New Fish Attributes .................................................................. 21

V.D. Empty Redds............................................................................................ 22

VI. Model Schedules............................................................................................... 22

VI.A. Habitat Actions........................................................................................ 22

VI.B. Fish Actions.............................................................................................. 23

VI.C. Redd Actions............................................................................................ 23

VI.D. Observer Actions (Model Outputs) ..................................................... 24

VI.E. Complete Schedule ................................................................................. 24

VII.Calibration.......................................................................................................... 24

VII.A. Individual Actions ................................................................................. 25

VII.A.1. Fish Spawning......................................................................... 25

VII.A.2. Fish Growth and Survival ..................................................... 26

VII.A.3. Fish Movement ........................................................................ 27

VII.A.4. Redd Survival .......................................................................... 27

VII.A.5. Redd Development and Emergence .................................... 28

VII.B.Short-term Population Responses........................................................ 28

VII.B.1. Seasonal Changes in Habitat Use, Growth, and

 Survival ..................................................................................... 28

VII.B.2. Redd Scouring and Temperature-related

 Mortality................................................................................... 28

VII.C.Long-term Population Responses ........................................................ 28

VII.C.1. Redd Numbers and Incubation Success.............................. 28

VII.C.2. Long-term Abundance, Growth and

 Relative Abundance ............................................................... 28

VIII. Habitat Data Collection Methods ............................................................... 29

VIII.A. Reach Location and Length .............................................................. 29

VIII.B. Transects and Longitudinal Cell Boundaries ................................ 29

VIII.C. Lateral Cell Boundaries ..................................................................... 30

VIII.D. Depths and Velocities ........................................................................ 31

VIII.E. High-Flow Water Surface Elevations.............................................. 32

VIII.F. Spawning Gravel Availability.......................................................... 32

VIII.G. Velocity Shelter Availability............................................................. 32

VIII.H. Distance to Hiding Cover .................................................................. 33

IX. Method Details .................................................................................................. 33

IX.A. Criteria for Day of Spawning................................................................ 34

IX.A.1. Date Window............................................................................. 34

IX.A.2. Temperature Range .................................................................. 34

IX.A.3. Flow Limit................................................................................. 34

IX.A.4. Steady Flows............................................................................. 35

IX.A.5. Female Spawners ..................................................................... 35
IX.A.6. Minimum Length, Age, and Condition ................................ 35

IX.A.7. Not Spawned This Season....................................................... 36

IX.B. Spawning Habitat Suitability................................................................ 36

IX.C. Fish Feeding and Energetics ................................................................. 37

IX.C.1. Activity Budget ......................................................................... 37

IX.C.2. Food Intake ................................................................................ 38

IX.C.3. Respiration Costs and Use of Velocity Shelters .................. 42

IX.C.4. Other Energy Losses ................................................................ 44

IX.C.5. Feeding Strategy Selection, Net Energy Benefits, and

Growth........................................................................................ 44

IX.C.6. Feeding and Growth Calibration ........................................... 46

IX.D. Fish Survival Probabilities..................................................................... 48

IX.D.1. High Temperature .................................................................... 48

IX.D.2. High Velocity............................................................................. 49

IX.D.3. Stranding .................................................................................... 52

IX.D.4. Spawning.................................................................................... 52

IX.D.5. Poor Condition .......................................................................... 53

IX.D.6. Terrestrial Predation ................................................................ 54

IX.D.7. Aquatic Predation..................................................................... 58

IX.D.8. Total Survival: Parameter Estimation and Effects of

Fish Size, Depth, and Velocity................................................ 63

IX.E. Redd Survival Functions ....................................................................... 65

IX.E.1. Dewatering................................................................................. 65

IX.E.2. Scouring and Deposition ......................................................... 65

IX.E.3. Low Temperature ..................................................................... 68

IX.E.4. High Temperature .................................................................... 69

IX.E.5. Superimposition........................................................................ 69

X. Model Development Priorities and Research Topics ............................... 70

X.A. Imposed versus Emergent Behaviors .................................................. 70

X.A.1. Generalization of Movement Objectives .............................. 71

X.A.2. Readiness to Spawn and Spawning Location...................... 71

X.A.3. Allocation of Growth to Fish Length, Weight, and

Gonads ........................................................................................ 71

X.A.4. Diurnal Changes in Behavior and Hiding Cover

Limitations ................................................................................. 71

X.B. Habitat Model Issues.............................................................................. 72

X.B.1. Habitat Cell Sizes ...................................................................... 72

X.B.2. Accuracy of Hydraulic Simulations ...................................... 72

X.B.3. Variation in Velocity Shelter Availability ............................ 73

X.B.4. Spatial and Temporal Variation in Food Availability........ 73

X.C. Fish Model Issues .................................................................................... 73

X.C.1. Immigration and Emigration.................................................. 73

X.C.2. Movement Distances and Knowledge of Environment..... 73

X.C.3. Fitness Time Horizons for Movement .................................. 73

XI. Input Parameter Index ..................................................................................... 75

XII. References........................................................................................................... 77

In Brief . . .

Railsback, Steven F.; Harvey, Bret C. 2001. Individual-based model formulation for cutthroat

trout, Little Jones Creek, California. Gen. Tech. Rep. PSW-GTR-182. Albany, CA: Pacific

Southwest Research Station, Forest Service, U. S. Department of Agriculture; 80 p.

Retrieval Terms: cutthroat trout, habitat selection, individual-based model,

population model, salmonids

This report documents the formulation of an individual-based model (IBM)

of the cutthroat trout population of Little Jones Creek, Smith River drainage,

Del Norte County, in northwestern California. The model is being built as a

research joint venture of the USDA Forest Service’s Pacific Southwest Research

Station, Redwood Sciences Laboratory, and Lang, Railsback, & Associates,

using the California Individual-based Fish Simulation System (CIFSS). The

CIFSS is a modeling approach and software package for IBMs of stream fish.

The main objective of the Little Jones Creek cutthroat trout model is to evaluate

the IBM approach for management applications, such as predicting the

individual and cumulative effects of timber harvest, water diversion, and habitat

alteration on fish populations. The model will also be used to test hypotheses

about the mechanisms of habitat selection by stream salmonids over daily and

seasonal time scales and evaluate the importance of small tributaries to stream

trout populations.

The model uses a number of key features and assumptions, including a 1-

day time step for all model processes and a spatial resolution of several square

meters. Habitat is modeled as rectangular cells with dimensions typically in the

range of one to several meters across the stream and several meters in the

longitudinal direction. Stream flow, water temperature, and food availability

are the variables driving the model over time; food is the primary limiting

resource for trout; and trout have complete knowledge of the mortality risks

and food availability in a specific area of surrounding habitat. The model

simulates three kinds of objects: habitat cells, fish, and redds (nests created by

spawning trout).

We adapted a theoretical approach to IBM from the emerging science of

complex adaptive systems. Two key principles of this approach are that

IBMs are more powerful if realistic behavior patterns emerge from simple,

fitness-maximizing rules for individual behavior; and the modeled behavior

of individual fish is more realistic if the fish base their decisions on outcomes

predicted over some time horizon instead of on the immediate outcome.

Habitat cells determine their depth and velocity from the daily stream flow

rate; this calculation uses a lookup table imported from an external hydraulic

model. The popular Physical Habitat Simulation (PHABSIM) and River Habitat

Simulation (RHABSIM) hydraulic models can be used to create the lookup

tables. Habitat cells also track the availability of food, velocity shelters for driftfeeding fish, hiding cover, and spawning gravel.

The fish in our model conduct four major actions each day:

• Spawning: Adult fish spawn if they meet a number of readiness

criteria. Upon spawning, fish find appropriate habitat and create

a new redd, with the number and size of eggs depending on the

spawner’s characteristics.

• Movement: Each fish examines the surrounding area each day

and moves to the site with the best accessible habitat. Defining the

“best” habitat is crucial and has been a major focus of our research.

We assume fish move to habitat offering the highest probability of

surviving and growing to sexual maturity over a specified time
horizon (e.g., 90 days). Survival and growth to maturity are

functions of habitat-related mortality (e.g., extreme temperatures),

predation mortality, and food intake, which affect starvation

mortality, and growth.

• Feeding and growth: We simulate energy intake resulting from

both stationary drift feeding and active searching for benthic food

and overhead drop-in. Intake varies with depth, velocity, turbidity,

fish size, food availability, and food depletion by competing fish.

Energy costs of swimming also depend on the feeding strategy and

the availability of velocity shelters. We assume fish use the more

profitable of the two strategies, and calculate growth from energy

intake and consumption using standard bioenergetics methods.

• Survival: Daily survival is a function of high temperature, high

velocity, stranding by inadequate depth, spawning stress,

starvation, and predation. Our predation formulation includes

separate functions for terrestrial and aquatic predators, with

survival probabilities that vary with depth, velocity, hiding cover,

temperature, turbidity, and fish size.

Redds are modeled from when they are created until all eggs have died or

emerged as new fish, with the development rate a function of temperature.

Redds can suffer egg mortality due to dewatering at low flows, scouring at high

flows, high or low temperatures, and superimposition of new redds.
I. 

Introduction 

I. Introduction 

Because of concern about fish stocks at risk of extinction, such as stocks of 

Pacific salmon, many large-scale resource management efforts have been 

implemented, including the Northwest Forest Plan (NWFP). One significant 

weakness of existing information to support management efforts is the inability 

to link habitat conditions to the dynamics of populations. This situation is partly 

attributable to the historical tendency to view habitat requirements and 

population dynamics as separate research topics. Most previous research on the 

habitat requirements of Pacific salmonids has not been process-oriented and has 

not attempted to link the availability of habitat features to changes in population 

size. Conversely, existing population models for salmonids are too general to 

predict the effects of specific habitat changes on populations. One consequence 

of this failure to link habitat directly to population dynamics is that little or no 

guidance is available to managers attempting to prioritize activities for the 

conservation of threatened and endangered fishes. 

The recent development of individual-based models (IBM) for fish 

populations (Van Winkle and others 1993) could be a major step forward in 

guiding management decisions. In particular, spatially-explicit versions of these 

models directly predict the consequences for fish populations of changes in 

physical habitat and biological conditions. However, these models are at an early 

stage of development. Readily testable, useable models are urgently needed. 

Although the ultimate goal is to provide useful tools to managers, the Little 

Jones Creek cutthroat trout model serves as a prototype to allow testing of the 

IBM approach. In addition to evaluating the IBM approach for management 

applications, such as predicting the individual and cumulative effects of timber 

harvest, water diversion, and habitat alteration, the Little Jones Creek cutthroat 

trout model will be used to address hypotheses about the mechanisms of habitat 

selection by stream salmonids over daily and seasonal time scales, and to evaluate 

the importance of small tributaries to stream trout populations. Evaluating the 

effectiveness of the approach for a particular population will determine if it 

should be applied more broadly. 

The primary objective of this report is to fully document the methods and 

parameters that were implemented in the software of the IBM for Little Jones 

Creek cutthroat trout. The predictions of IBMs are potentially dependent on all 

of the detailed assumptions, equations, parameter values, and schedules used in 

the model, and on how these are implemented in computer code. This document 

describes how the model is initialized by defining the habitat and starting fish 

populations, then describes the methods used to simulate habitat, fish, and 

redds. The model schedule, which has an important effect on simulation results, 

is specified explicitly. The report also identifies topics for future model 

development and research. 

The report is organized to allow readers to develop a general understanding of 

the model before encountering all its details. Sections II through VI provide 

information on the major components of the model, but ignore some details for 

clarity. Section VII describes methods for calibrating the full model and calibration 

completed to date. Section VIII presents a description of field data collection methods 

appropriate for this model and how they differ from conventional instream flow 

modeling approaches. Section IX contains full descriptions of the more complicated 

details of the model. Priorities we have identified for future research related to this 

model are documented in Section X. The cutthroat trout model is built with the 

California Individual-based Fish Simulation System (CIFSS), a system for designing 

and coding individual-based fish models. The computer software that implements 

this formulation (including parameter and input file formats) is described in a 

separate user guide (Railsback and others 1999b). This formulation document uses 

the same input parameter names as the computer code and compiles them into a 

master list of model parameters (Section XI). USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 1 
I. Introduction 

I.A. Fundamental Approach and Assumptions 

This model is built around a theoretical approach to individual-based 

modeling that we have adapted from the emerging science of complex adaptive 

systems. A key principle of this approach is that IBMs are more powerful if 

realistic behavior patterns emerge from simple, fitness-maximizing rules for 

individual behavior. Most IBMs depend heavily on rules that impose specific 

behaviors on the model animals; these rules are often designed to force behaviors 

that have been observed in the field to be reproduced in the model. We prefer to 

avoid such “imposed behavior” rules, and instead try to give our model fish the 

freedom to make whatever choices maximize simple objectives that are clearly 

and directly related to their fitness. 

A second key principle we follow is that the modeled behavior of individual 

fish is more realistic if fish make decisions by maximizing a variable more closely 

related to evolutionary fitness, rather than focusing on factors such as 

instantaneous growth and survival rates. Other IBMs and much of the optimal 

foraging literature attempt to explain animal behavior by using only the 

immediate outcome of a decision (e.g., selecting habitat to maximize 

instantaneous food intake or survival probability). Instead, we assume animals 

base decisions on the consequences over some time horizon, which can lead to 

significantly different results. For example, maximizing instantaneous survival 

probability for most fish would result in merely hiding from predators, while 

maximizing survival over the next 90 days requires a fish to eat enough to avoid 

starvation risks. Because the ability to base decisions on predicted future 

outcomes provides a significant fitness benefit, it seems unreasonable to model 

behavior without considering how animals predict the consequences of decisions 

to their fitness over times much greater than 1 day. This principal has been 

explored and supported by Bull and others (1996), Mangel (1996), Railsback and 

others (1999c), Railsback and Harvey (2001), and Thorpe and others (1998). 

This IBM formulation is for resident coastal cutthroat trout. We use the 

following fundamental assumptions: 

•All model processes, such as stream flow and temperature, fish 

movement, foraging, growth, mortality, and spawning occur on 1-day 

time steps. 

•The spatial resolution is several square meters. Habitat is modeled as 

rectangular cells with dimensions typically in the range of one to several 

meters across the stream and several meters in the longitudinal direction. 

Cell borders are chosen to minimize the habitat variation within cells 

while capturing the stream’s natural variation among cells. 

•�The external variables driving the model over time are stream flow, 

water temperature, turbidity, and food availability. 

•Flow, temperature, and turbidity are constant over space. We assume 

that food availability parameters (the mass of drift food per volume of 

stream water and mass of stationary food per stream area) are constant 

over both space and time. (Simulating realistic spatial variation in food 

availability, and its effect on fish, is a long-term goal of our modeling 

program; Section X.B.4.) 

•Fish compete for food, not habitat space. We assume that the food 

intake of a fish is a function of the total food available in a habitat cell 

(a function of cell size, depth, and velocity) and the amount of food 

consumed by more dominant fish in the cell. This allows fish densities 

to vary realistically with food availability and the need to avoid 

mortality risks. 

2 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
I. Introduction 

•�The fish activities driving trout habitat selection are spawning and 

feeding. Only habitat characteristics related to these activities are 

simulated. We do not, for example, simulate use of habitat for hiding and 

resting when not feeding; we assume all fish can find such habitat. 

• Trout move in response to spatial variation in food intake and survival 

probability. We assume fish are “intelligent” enough to correctly 

predict their food intake and survival probabilities in different habitat 

cells and determine which cell offers the highest fitness (Section 

IV.B.2). We do not assume or simulate any learning by fish. (Note 

that, although we assume fish correctly perceive the actual food intake 

and survival probabilities at potential destinations, alternative 

assumptions are possible; e.g., Section X.C.2.) 

I.B. Study Site 

Little Jones Creek is a third-order tributary of the Middle Fork Smith River, in 

Del Norte County, northwestern California (fig. 1). Resident cutthroat trout are 

the only fish present; a barrier at the mouth of the creek prevents upstream 

migration of anadromous fish. Harvey (1998) provides a more complete 

description of the watershed. 

The trout model is being applied to three separate reaches of Little Jones 

Creek; these are approximately 1,000 m upstream of the mouth, 3,300 m 

upstream of the mouth, and a first-order tributary entering the creek at about 

3,300 m upstream. 

Figure 1 —Study site at the Little 

Jones Creek of the Middle Fork 

Smith River in Del Norte County, 

northwestern California. Modeled 

reaches are enclosed in rectangles. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 3 
I. Introduction 

I.C. Conventions 

I.C.1. Units 

This formulation and the CIFSS software use length units of centimeters 

(cm), weight units of grams (g), and temperature in Centigrade (°C). Stream flow 

is in units of cubic meters per second (m3/s). 

Because the model uses a daily time step, most time-based parameters use 

day as the time unit. However, there are several exceptions to this convention; 

for example, flow and velocity variables are per second. Most food intake 

calculations use hourly rates because the number of hours per day that fish feed 

is variable. 

Fish lengths are evaluated as fork lengths throughout this model formulation. 

All weight variables for fish and prey (food) use wet weight. 

I.C.2. Parameter and Variable Names 

So that the parameter names in this report match those in the model code’s 

input files, we follow the naming conventions used in the Swarm simulation 

software used to code the model (Railsback and others 1999b). Variable and 

parameter names typically are made by joining several words. The first word 

starts with a lower-case letter, and capital letters are used at the start of each 

subsequent word (e.g., “fishWeightParamA”; see the list of parameter names in 

Section XI). 

We use the convention of starting input parameter names with the kind of 

object that uses the parameter. These objects include fish, redds, habitat cells, fish 

mortality sources, and redd mortality sources. Consequently, most parameters 

start with the words “fish,” “redd,” “cell,” “hab,” “mortFish,” or “mortRedd.” This 

convention is not strictly followed for variables calculated by the model. 

I.C.3 Survival Probabilities and Mortality Sources 

A number of factors can cause fish or fish eggs to die in our model. We refer 

to these factors as “mortality sources.” (The term “mortality rate” typically is 

used to mean the daily probability of dying, equal to one minus the survival 

probability.) Although we use the word “mortality” in parameter names and our 

text, the model formulation bases all mortality-related calculations on survival 

probabilities. This convention simplifies computations and reduces the chances 

of error: the cumulative survival of several mortality sources is calculated simply 

by multiplying the individual survival probabilities together. 

I.C.4. Dates, Days, and Fish Ages 

This model uses input in the “MM/DD/YYYY” format (e.g.: 12/07/1999) for 

dates. The software converts this input to an internal date format that 

automatically accounts for leap years. 

Parameters that are days of the year (e.g., spawning is allowed to occur 

between April 1 and May 31 of each year) are input in the “MM/DD” day format. 

We follow the convention that fish are age 0 when born, and the age of all 

fish is incremented on January 1. 

I.C.5. Habitat Cell Conventions 

We developed our own conventions for describing the rectangular cells used 

to model habitat. These conventions were designed to correspond with computer 

graphics conventions (so that habitat is mapped correctly by our software) and to 

correspond with terms used in popular instream flow models. 

“Transects” and “Cells”— Habitat is modeled as rectangular, twodimensional, depth-averaged “cells”; depth and velocity are modeled for each 

cell and assumed uniform within the cell. Cells fall along a “transect,” a straight 

row of cells across the stream and floodplain perpendicular to the direction of 

flow. (The word “transect” also commonly refers to a line across the channel 

4 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
II. Model Information 

along which depth and velocity is measured. Because we do not necessarily use 

this data collection approach, we use “transect” to refer to a row of cells.) The 

number of habitat cells usable by fish varies with flow: cells on the stream 

margins may be dry at low flows. 

X and Y Dimensions—Because the hydraulic model we use is onedimensional, our model assumes the river is straight with all velocities in one 

direction. The X and Y values referred to here are coordinates (in cm) of cell 

boundaries. 

The X dimension is defined to be in the downstream-upstream direction. 

Because the origin (X = 0) is at the downstream end of a reach, water flows from 

right to left on an X-Y plot. The Y dimension is across the channel. To correspond 

with computer graphics, which place the origin (X,Y = 0,0) at the top left of the 

screen, we define Y to be zero on the left bank facing upstream. 

Distances between Cells—Some calculations in the model require values for 

the distance between two cells (e.g., for finding the cells that are within a fish’s 

maximum movement distance). Because cells are two-dimensional, there is no 

single distance between two cells; as a convention, we evaluate the distance 

between two cells as the straight-line distance between the centers of the cell. 

II. Model Initialization 

This section describes the methods used to initialize the habitat and fish 

populations when each new model run is started. Although this section mentions 

some of the input types and files, complete documentation of file and input types 

is provided only in the separate user guide (Railsback and others 1999b). 

II.A. Habitat Initialization 

A model run starts by reading in the habitat characteristics that do not change 

during the simulation. These characteristics are the location and dimensions of 

habitat cells, the values of habitat cell variables that do not change with time (the 

fractions of cell area with velocity shelters and spawning gravel, distance to hiding 

cover), and the lookup tables used to calculate daily depth and velocity in each cell. 

(Habitat cells and these variables are described in Section III.) 

II.B. Fish Initialization 

We build the initial fish population from input data giving the number, 

mean length, and variance in length for each age of each species. The input file 

for initial fish populations can provide data for multiple dates (e.g., all dates on 

which the population at the study site was censused so that the model can be 

started at any of these dates). For the Little Jones Creek study site, model 

simulations typically start around October to take advantage of the most accurate 

population estimates. (Fish population estimates are most accurate in the fall 

because low late-summer flows provide good counting conditions and youngof-year fish are relatively large and observable.) 

Lengths (cm) for each fish are drawn from a lognormal distribution, the 

mean and variance of which is provided as input. To avoid unrealistic values 

(e.g., negative lengths) when a high variance is specified, the lengths of initial 

fish are restricted to being greater than half the mean length for their age class. 

The weight (g) of each fish is calculated from its fork length using a lengthweight relation whose parameters are input. (This relation is also used to 

calculate growth in length from a change in weight; see Section IV.C.) 

fishWeight = fishWeightParamA fishLength fishWeightParamB 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 5 
III. Habitat Model 

Table 1—Parameter values for length-weight relation. 

Parameter Definition Units Value 

fishWeightParamA Length-weight relation multiplier 1g/cm3 0.0124 

fishWeightParamB Length-weight relation exponent none 2.98 

1Approximately; this is an empirical parameter in which units vary with fishWeightParamB. 

This is not a standard length-weight regression relationship. It is intended to 

be a site-specific length-weight relation for fish in good condition. 

Parameter values for this relation (table 1) were calculated from fish 

observations made at the Little Jones Creek study sites. They were based on 

observations of fish in relatively good condition, with weight per length that is 

slightly higher than average. We determined these parameter values using fish 

collected approximately monthly throughout 1998 and 1999. Standard condition 

factors (100,000 times weight over length cubed) were calculated for each observed 

fish. We used log-log regression to estimate the parameters from the length and 

weight of fish that had standard condition factors between 1.1 and 1.3. 

By initializing fish using the length-weight relation used in the growth 

routine, we build in the assumption that fish are initially in good condition. This 

assumption reflects observed low variation in condition among individuals and 

over time for cutthroat trout in Little Jones Creek. 

Each fish’s location is assigned randomly to one of the habitat cells. The first 

day’s movement simulation puts the fish in reasonable starting locations. 

However, we do not assign fish to cells where the depth is zero because some 

small fish may have a maximum movement distance (Section IV.B.2) too small to 

allow them to find reasonable habitat on the first move. 

We initialize fish assuming that no fish have recently spawned at the time 

they were initialized (Section IX.A.7). This assumption should be reconsidered if 

the model is initialized during a spawning season. 

II.C. Redd Initialization 

In this model we have not provided the capability to initialize the model 

with redds present. 

III. Habitat Model 

The habitat component of our model simulates hydraulic conditions (depth 

and velocity), temperature, and food availability (a function of food production 

and the number of fish competing for it). 

We follow the lead of preceding habitat models (Bovee 1982) and IBMs (Van 

Winkle and others 1998) by representing stream habitat as a collection of 

rectangular, two-dimensional, depth-averaged cells. However, we have made 

the important improvement of carefully designing the habitat cell sizes and 

placement to avoid scaling errors common in other models. In modeling habitat 

at our Little Jones Creek site, we considered these factors in representing habitat 

as cells: 

• Cell sizes should be appropriate for the scale over which fish use and 

select habitat. There is little conclusive literature on the most appropriate 

scale for fish-habitat interactions, but it seems clear that fish select 

habitat over longer distances than the spatial resolutions typically used 

in PHABSIM habitat suitability studies. 

•�The very small or narrow cells typically used in PHABSIM models likely 

would induce major edge-effect errors in an IBM where we model 

6 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
III. Habitat Model 

competition among multiple fish for the resources available within 

each cell. 

• Cells should be placed to capture the full range of hydraulic variation 

and complexity of the stream being modeled. Capturing this variation 

is more important to the model’s accuracy than any difficulties that 

may be encountered in calibrating the hydraulic model to such habitat 

(Railsback 1999). 

•� Cells should be placed to minimize habitat variation within each cell, 

because the model assumes habitat is homogeneous within cells. 

The methods we developed for implementing these considerations are 

provided in Section VII. 

III.A. Cell Boundaries and Dimensions 

All the cells on one transect have the same length in the X (upstreamdownstream) dimension, but vary in width, the Y (across channel) dimension. 

For each transect, the user provides the X coordinate for the upstream end of the 

cells. For each cell, the user provides the Y coordinate of the cell’s right boundary. 

These coordinates are measured in the field. This input allows the model to 

determine the extent of each cell in both dimensions. 

III.B. Daily Flow,Temperature, andTurbidity 

At the start of each daily time step, the model reads in the day’s river flow 

(m3/s), temperature (°C), and turbidity (nephelometric turbidity units, NTU). 

Flow is used only to calculate the depth and velocity in each cell, and for several 

criteria used to determine when fish spawn (Section IX.A). Turbidity data are 

used in the model of drift food intake (Section IX.C.2) and predation mortality 

(Sections IX.D.6 and IX.D.7). (We do not model the potential effects of turbidity 

on production of fish food.) 

We assume these parameters are constant over relatively short reaches that 

do not contain tributaries, including our sites at Little Jones Creek. We also 

neglect diurnal variation in them. Diurnal variation in water temperature at 

Little Jones Creek averaged only 1.1 °C (maximum 2.6 °C) between May 1998 and 

May 1999. 

III.C. Depth and Velocity 

The depth and velocity of each habitat cell (and the number of cells that have 

water) vary with the river discharge. The hydraulic models we currently use 

neglect changes in channel direction and cross-channel flows, so water velocity 

has only one component (downstream). 

To take advantage of existing stream hydraulic modeling software and avoid 

having to include hydraulic simulations in our model, we import lookup tables 

of depth and velocity, as a function of stream flow, for each cell. These depth and 

velocity lookup tables are generated by external hydraulic simulation software. 

This approach allows all the hydraulic model building, testing, and calibration to 

be conducted in specialized hydraulic software, prior to running our model. We 

used RHABSIM (TRPA 1998) to generate the depth and velocity look-up tables 

for Little Jones Creek, but any hydraulic model capable of providing data on the 

scale of habitat cells could be used in conjunction with the fish model. 

Daily velocities and depths for each cell are interpolated from the values in 

the lookup table. Because both depth and velocity are assumed by the hydraulic 

models to be logarithmically related to flow, we use log interpolation. To make 

this computationally efficient, we store the base-10 logarithm of the flows, depths, 

and velocities as they are read in from the lookup table. Then, when depths and 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 7 
III. Habitat Model 

velocities are needed for a daily flow rate, we use the log of daily flow and linear 

interpolation to find the corresponding log(velocity) and log(depth) for each cell. 

For zero depth and velocity values, in the lookup table, we set the log to -1. If the 

interpolated log value of depth or velocity is less than or equal to -1, then we set 

the value to zero. (Using values lower than -1 to represent the log of zero values 

causes unrealistic interpolation results when depths or velocities are very low 

but non-zero.) 

For any flows below the lowest in the lookup table, we extrapolate the depth 

and velocity downward from the lowest two flows. The need to make this 

extrapolation can be avoided by making sure the lookup table includes flows 

lower than any we need to simulate. RHABSIM can model depths and velocities 

down to zero flow. 

Likewise, for flows above the highest in the lookup table, we logarithmically 

extrapolate depth and velocity upward from the highest two flows. If this 

produces unrealistic results, the lookup table can be extended to higher flows 

using the hydraulic model or manually edited to put in extremely high flows. 

III.D.Velocity Shelter Availability 

We assume that a constant (over time) fraction of each habitat cell has 

velocity shelters available for use by drift feeding fish (Section IX.C.3); shelters 

also affect the high velocity mortality risk (Section IX.D.2). The user provides as 

input the fraction of each cell with velocity shelter (variable “cellFracShelter”). 

These fractions should include any part of the cell with complex hydraulics that 

could be used by trout to reduce their swimming energy. Boulders, cobbles, or 

other substrates that induce roughness in the bottom, woody debris, roughness 

in the banks or bedrock channel, or adjacent cells with near-zero velocities could 

provide such shelters. (We recognize that velocity shelter availability can vary 

with fish size and flow, but do not model such variation because of its complexity. 

Addressing this issue is one of our research priorities; Section X.B.3.) 

We assume each fish uses up an area of velocity shelter equal only to the 

square of its length (Section IX.C.3). This assumption is designed to maintain our 

overall assumption that fish compete for food, not space. A fish has access to 

shelter if the amount of shelter available in its habitat cell (the cell area times the 

fraction of the cell with velocity shelter) is greater than the area of the cell already 

used by more dominant fish. This means that a fish has access to shelter if there is 

any unused shelter space available for it. 

III.E. Spawning Gravel Availability 

Spawning gravel availability is described as the fraction of cell area with gravel 

suitable for spawning, assumed to be constant over time. This area includes small 

pockets of gravel behind boulders as well as more classic spawning beds. The user 

provides these spawning gravel fractions (variable “cellFracSpawn”) as input. 

III.F. Distance to Hiding Cover 

The model includes a habitat input variable that is an estimate of how far a fish in 

the cell would have to move to find hiding cover. This variable (cellDistToHide, m) is 

used in the terrestrial predation mortality model (Section IX.D.6). 

III.G. Food Production and Availability 

The amount of food available to fish is a very important habitat variable, 

probably more important than flow or temperature in determining fish 

population abundance and production except under extreme conditions. 

Unfortunately, the processes influencing food availability for stream salmonids 

are poorly understood. Although some studies (Morin and Dumont 1994, 

8 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
III. Habitat Model 

Railsback and Rose 1999) indicate that food availability and consumption can 

vary with factors, including flow, temperature, fish abundance, and physical 

habitat characteristics, there is little information available on how food 

availability varies over time and space at scales relevant to IBMs. Modeling food 

production is also complicated by the multiple sources of food available to fish. 

We assume all food is either “drift” food, moving with the current, or “search” 

food that is relatively stationary and must be searched out by the fish. Both drift 

and search food may originate with benthic (stream bottom) production or from 

terrestrial input. 

Our model assumes fish compete for the food available in each habitat cell. 

Therefore, the habitat model includes methods to determine for each cell: how 

much food is available each day, and how much is consumed by fish. 

III.G.1. Production 

In the absence of established models of trout food production, we developed 

models that are simple yet mechanistic and easily calibrated using observed 

trout growth and survival (Section IX.C.6). We make the simple assumption that 

the concentration of food items in the drift (“habDriftConc,” grams of prey food 

per cm3

 of stream water) and the production of stationary food items in the 

stream benthos or overhead drop-in available via the search feeding strategy 

(“habSearchProd,” grams of prey food produced per cm2

 of stream bottom per 

hour) are constant over time and space. 

(We considered trying to simulate how food is produced in specific habitats 

like riffles and depleted by fish as it travels downstream, as in the feeding model 

of Hughes (1992b). However, the model of Hughes (1992b) shows that simulating 

drift depletion over space would require a major increase in the complexity of 

our food production and availability model. Our approach appears to capture 

the general food competition dynamics in a much simpler model.) 

Our feeding formulation allocates the amount of drift and search food 

available per hour in each cell among fish (Section IX.C.5). These hourly rates are 

determined by the physical characteristics of habitat cells. The total amount of 

search food available (“searchHourlyCellTotal,” g/h) is simply the cell area 

multiplied by habSearchProd. 

The total drift food available in a cell (“driftHourlyCellTotal,” g/h) is a 

function of the cell’s cross-sectional area and average water velocity, the drift 

food concentration parameter habDriftConc, and a drift regeneration parameter 

“habDriftRegenDist”: 

driftHourlyCellTotal (g/h) = 3600 s/h cell width (cm) depth(cm) 

velocity (cm/s) habDriftConc (g/cm3

) 

[cell length (cm) / habDriftRegenDist (cm)]. 

The last term in this equation has two purposes. First, it simulates the 

regeneration of prey consumed by drift-feeding fish. Second, it makes the amount 

of drift food available per cell area independent of the cell’s length. Without this 

term, five transects with cells 2 m long would have five times the food availability 

of one 10 m-long transect. This term keeps the amount of food available (and the 

consequent density of fish) from being an artifact of how transects are spaced. 

The parameter habDriftRegenDist has units of centimeters and should 

theoretically have a value approximating the distance over which drift depleted 

by foraging fish is regenerated. This parameter is actually used to calibrate 

habitat selection and survival of starvation (Section IX.C.6). Smaller values of 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 9 
  

  

IV. Fish Model 

habDriftRegenDist provide higher amounts of food in a cell. The parameter 

habDriftConc also affects the amount of food in a cell, but unlike 

habDriftRegenDist, it also affects food capture rates of drift-feeding fish (Section IX.C.2). 

Estimation of preliminary values for these food parameters is discussed in 

Section IX.C.6, and calibration values are provided in Section VII.A. 

III.G.2. Availability 

When a fish is conducting its daily evaluation of potential movement 

destinations (Section IV.B), it considers how much food is available to it in each 

cell. We model food availability to a fish as the total food production, minus the food 

consumed by any other fish that have moved into the cell. Because fish movement 

occurs in descending order of fish size, larger fish have access to food before smaller 

fish do. Availability is tracked separately for drift and search food. 

At the start of each day, the total daily food availability is calculated for each 

cell, for both drift and search food. Total daily availability is equal to the hourly 

production rates described above (Section III.G.1) times the number of hours per 

day we assume fish feed (Section IX.C.1). 

Each time a new fish moves into a cell, its food consumption is subtracted 

from the food remaining available for additional fish. When a fish’s consumption 

is limited by the amount of food available in the cell (Section IX.C), its 

consumption will equal the remaining availability and no food will be available 

for additional fish. Any fish moving into a cell where all the food is consumed by 

larger fish will consequently have zero food consumption. 

III.H. Day Length 

Day length (“dayLength,” in hours) is used in the food intake routine and is 

calculated from the Julian date (day of the year, 1-365) and site latitude 

(habLatitude, an input parameter). We use equations modified from the Qual2E 

water quality model (Brown and Barnwell 1987): 

 12   × habLatitude  dayLength = 24 − 2   

arccos tan  

tan 

180  

where: 

 23.45   2   =  180  cos  .  365 (173 − date)  

For the Little Jones Creek site, habLatitude is 42 degrees. 

Day length is used to estimate the number of hours per day available for fish 

to feed. Although nocturnal feeding may be common in salmonids, Young and 

others (1997) observed primarily daytime feeding by Colorado River cutthroat 

trout during summer. 

IV. Fish Model 

This section describes the methods used by the model’s fish. We use the same 

methods for all fish (except incubating eggs and embryos) regardless of age or size. 

Fish carry out daily four sets of actions: spawn, move to maximize fitness, 

feed and grow, then survive or die according to survival probabilities that vary 

with habitat cell and fish characteristics. The order in which these actions are 

scheduled is discussed in Section VI.B. 

The coastal cutthroat trout ( Oncorhynchus clarki clarki) is closely related to the 

rainbow trout (O. mykiss), and they have similar life history characteristics 

(Stearley 1992). Because less laboratory and field information is available for 

10 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IV. Fish Model 

cutthroat than for rainbow trout, in many parts of the formulation we use 

equations and parameter values originally developed for the latter. 

IV.A. Spawning 

The objectives of this model require simulation of the full life cycle and I.A). 

Our long-term research goals include making the spawning methods more 

compatible with our mechanistic, fitness-based approach by letting fish select 

their spawning date on the basis of their energetic condition, predicted habitat 

conditions, and the consequent predicted spawning success (Section X.A.2). 

We make two major simplifying assumptions in the spawning formulation. 

First, we only track spawning actions for females. We also neglect the energetics 

of spawning: the energy costs of gonad production, weight loss upon spawning, 

etc., except for a spawning mortality function. 

IV.A.1. Determine Spawn Readiness 

Fish in the model can spawn only on days when a number of fish- and 

habitat-based criteria are met. These spawning criteria (described in Section 

IX.A) limit spawners to fish in good physiological condition and restrict 

spawning to times when physical conditions (dates, flows, temperatures) are 

likely to be successful. The criteria for readiness to spawn do not include a 

requirement that good spawning habitat be available; this formulation is guided 

by the assumption that trout will spawn whether or not “classic” spawning 

habitat is present. 

On the days when all the spawning criteria are met for a fish, then it has a 

random probability of spawning equal to the variable “fishSpawnProb.” This 

stochastic selection of spawning date gives the model user some control over what 

percent of spawning-sized fish actually spawn; if the value of fishSpawnProb is low 

compared to the number of days in the spawning period (e.g., 1/fishSpawnProb is 

greater than the number of potential spawning days), then some potential spawners 

will probably not spawn. It also imposes variation in the date fish spawn; without 

this probabilistic approach, an unrealistically large number of fish would spawn on 

the first day when spawning day criteria are met. 

Before calibration, we estimate the value of fishSpawnProb to be 0.016, the 

inverse of the number of days in the spawning period. This value was estimated 

from limited spawning observations in Little Jones Creek, which indicated that 

spawning occurs approximately from April 1 to June 1, a period of 62 days. 

IV.A.2. Identify Redd Location 

The model incorporates the observation that trout select specific ranges of 

depth, velocity, and substrate without attempting to simulate the mechanisms 

by which these variables affect redd success. We adopt a PHABSIM-like approach 

of weighting potential sites by their habitat suitability, then having the spawner 

select the best available cell of those within moving distance. Superimposition 

(Section IX.E.5) is likely to result from this formulation because fish actively 

search a large area for the best spawning habitat. However, the best cell for 

spawning can vary from day to day as flow varies. 

The spawner selects the cell that (a) is within moving distance and (b) has the 

highest value of variable “spawnQuality” where: 

spawnQuality = spawnDepthSuit spawnVelocitySuit spawnGravelArea. 

The variables spawnDepthSuit and spawnVelocitySuit are habitat suitability 

factors determined using methods described in Section IX.B. The value of 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 11 
IV. Fish Model 

spawnGravelArea is the cell area times its fraction with spawning gravel. The 

spawnGravelArea is included in spawnQuality because we assume a fish, even if 

it does not select for bigger patches of gravel, is more likely to spawn in a cell that 

has more area of gravel. 

We assume that spawners can move the same distance for spawning as they 

can each day to improve their food intake and survival probabilities (Section 

IV.B.2). This formulation does not allow long spawning migrations, which are 

not feasible anyway in the limited study reaches we model. (Spawning habitat 

appears ample in Little Jones Creek.) We assume that fish move to the cell that 

they select for spawning, even though they are likely to move from it during the 

same day’s movement process. When they have identified the cell in which to 

spawn, we set the fish’s location to this cell. 

Spawning movement overrides feeding habitat selection. To spawn, fish 

move into cells regardless of other fish in the cell. Multiple females can also 

spawn at the same site on the same day. 

IV.A.3. Make Redd 

Each spawner creates a redd. The number of eggs in the redd (the spawning 

female’s fecundity) depends on the spawner’s characteristics, according to this 

equation. 

numberOfEggs = fishFecundParamA × fishLengthfishFecundParamB 

We use the parameter values that Van Winkle and others (1996) obtained for 

brown trout from Avery (1985). These parameter values (table 2) result in 

fecundities of 60 eggs for a spawner of our minimum spawning size of 12 cm 

(Section IX.A.6), and 220 eggs for a spawner of 20 cm, corresponding well with a 

small number of observations of fecundity at and near the Little Jones study site 

and the findings of Carlander (1969). 

IV.B. Movement 

Fish movement is a very important process to simulate realistically because 

movement is probably the most important mechanism available to stream fish 

for adapting to short- and mid-term changes in habitat and fish state. Daily fish 

movement results in patterns of predicted habitat selection that are easily tested 

against observed patterns. For the model to meet its objectives, it must produce 

realistic habitat selection patterns. 

Modeling movement has been a primary focus of our research in developing 

this model. We reviewed methods used in previous models and developed our 

own approach, documented by Railsback and others (1999c). We developed the 

following principles for modeling movement: 

•The model will be most general and powerful if realistic movement 

emerges when we give fish simple decision rules for responding to the 

environment and realistic information about the environmental 

complexities to which they must respond. Restrictions that force the 

model to reproduce a specific observed behavior that is not ubiquitous 

(for example, territoriality) should be avoided. 

Table 2—Parameter values for fecundity. 

Parameter Definition Units1 Value 

fishFecundParamA Fecundity (eggs per redd) multiplier 11/cm3 0.11 

fishFecundParamB Fecundity exponent none 2.54 

1Approximately; this is an empirical parameter with variable units. 

12 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IV. Fish Model 

•Stream fish are generally aware of their surrounding environment and are 

able to make movement decisions in much less time than our 1-day time step. 

•In a model such as ours where both food consumption and mortality 

risks are spatially variable, realistic movement decisions must 

consider both food intake and mortality risks. 

•The simplest, most believable decision rules maximize some direct 

measure of an animal’s fitness. 

•To make realistic decisions, modeled animals must consider outcomes 

predicted over some upcoming time period. It is unreasonable to assume 

that an animal makes its decisions considering only the immediate, 

same-time-step outcome. 

Simulating fish movement involves two related steps: a fish determines 

whether to move each day (using the “departure rules”), and determines the 

destination it moves to (using the “destination rules”). Our formulation does not 

explicitly assume fish are territorial. Instead, the density of fish in each cell is an 

emergent property of how fish move to maximize their individual fitness. Each 

fish’s decision whether to move into a cell is a function of how much food the fish 

would get there and what its probability of survival would be. Fish move to 

maximize their fitness, where fitness is defined as the expected probability of 

surviving over a specified time horizon multiplied by the fraction of reproductive 

size attained over the time horizon. This formulation was selected following a 

detailed review of alternatives (Railsback and others 1999c). Our movement 

approach was successfully tested by demonstrating its ability to reproduce six 

important patterns of trout habitat selection. Not all of these habitat selection patterns 

were reproduced by alternative approaches, such as maximizing net energy intake 

or minimizing immediate mortality risk (Railsback and Harvey 2001). 

IV.B.1. Departure Rules 

We use a simple departure rule: fish examine potential destinations every 

day and move to a location offering higher fitness if one is available. This method 

assumes fish are aware of their surroundings and know when better habitat is 

available nearby (Hughes 1992a). This method allows fish to escape habitat that 

becomes poor (cells that go dry when flow decreases; excessive velocities during 

floods). The model therefore reproduces the observed ability of trout to move in 

response to events like flood flows (Harvey and others 1999). 

IV.B.2. Destination Rules 

We assume fish move to the habitat cell that is accessible, as limited by a 

maximum movement distance and exclusion of cells where depth is zero; and 

provides the highest value of the fitness measure used to evaluate destination 

cells. This approach is implemented by using the following steps. 

Move in Order of Dominance—The destination rules are dependent on fish 

moving in order of decreasing dominance, implementing the assumption (tested 

by Hughes 1992a) that stream salmonids rank feeding positions by desirability 

and the most dominant fish obtain the most desirable sites. The most dominant 

fish move first and cannot be displaced by smaller fish. Dominance in the model 

is determined by fish length; Hughes (1992a) showed that dominance is usually, 

but not always, proportional to length for arctic grayling. The significance of 

prior residence to territorial defense and movement of salmonids (Cutts and 

others 1999, Johnsson and others 1999) is not currently included in the model. 

(In determining the dominance of each fish, the model multiplies fish length 

by the parameter sppDomFactor. By using different values for different species, 

this parameter allows dominance to be a function of species as well as length. In 

single-species models like this cutthroat model, sppDomFactor has no effect on 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 13 
IV. Fish Model 

results, but the parameter must be included in the parameter input file and it must 

have a value greater than zero.) 

Identify Potential Destination Cells—A distance limitation, barriers, and depth 

can limit potential destination cells. The number of fish already in a cell does not limit 

its availability as a destination. Following our approach of having fish compare 

conditions between its current cell and destination cells, our term “destination cells” 

does not include the cell a fish is currently in. 

Distance limitation. A habitat cell is excluded as a potential destination if it is 

beyond a certain distance. The maximum movement distance should be considered 

the distance over which a fish is likely to know its habitat well enough to be aware 

when desirable destinations are available, over a daily time step. The maximum 

movement distance is not necessarily a function of the fish’s swimming ability. 

We assume the maximum movement distance is a function of length. Because we 

assume mobility and spatial knowledge increase rapidly with fish size, we use an 

exponential function. The parameters should be considered site-specific. For example, 

fish may explore larger areas in lower-gradient rivers. 

maxMoveDistance = fishMoveDistParamA × fishLength fishMoveDistParamB 

Our model lets fish follow a gradient toward better habitat if the gradient is 

detectable within the maxMoveDistance, but it does not give fish the ability to find 

and move toward some specific target if that target is beyond maxMoveDistance. For 

example, if habitat generally improves in an upstream direction, fish will have an 

incentive to gradually move upstream. However, if a very good location for some fish 

exists farther away than its maxMoveDistance, the fish will not be aware of it. 

Movement observations from the literature cannot be considered direct 

measurements of maxMoveDistance but can be useful for evaluating its parameters. 

Observed movement distances (Bowen 1996, Gowan and Fausch 1996, Harvey and 

others 1999) show how far fish actually move, not the distance over which they 

evaluate habitat. These observations are also potentially confounded by a number of 

factors. Small fish may actually move more than large fish, because they are less able 

to defend a location; this does not mean small fish have a larger maximum movement 

distance as defined for the model. Movement rates (m/d) reported in the literature 

are also potentially deceptive because they are generally not based on continuous or 

even daily observations of location. 

However, the literature observations do indicate that adult trout commonly move 

distances up to 300 m. Harvey and others (1999) showed fall and winter movements 

of adult (18-24 cm length) cutthroat trout of up to about 55 m in 1 day at the Little 

Jones Creek study site. Summer conditions (lower flows, higher metabolic rates and 

food requirements, higher population densities) may encourage greater movement 

distances. 

June (1981) observed little movement in newly emerged cutthroat trout < 3 cm; 

dispersal started after they exceeded 3 cm in length. 

We selected parameter values (table 3) to estimate maxMoveDistance as less than 

2 m for newly emerged trout with length of 3 cm, as 5 m for juveniles 5 cm long, as 30 

m for trout 10 cm long, and 80 m for trout 20 cm long. 

Table 3—Parameter values for fish movement distance. 

Parameter Definition Units1 Value 

fishMoveDistParamA Multiplier for maximum movement distance none 20 

fishMoveDistParamB Exponent for maximum movement distance none 2 

1 fishLength (fork length) and maxMoveDistance are both in cm. 

14 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
These move distance parameters could preclude very small fish from having 

any potential destination cells if cells are large. This artificial barrier to movement 

(an artifact of the model’s spatial scale) could be important, for example, by 

preventing newly emerged fish from moving from the cell where their natal redd 

was to habitat where survival probabilities are higher. In such a situation, 

competition among new fry for food would largely be an artifact of the cell’s size, 

which controls how much food is in it (Section III.G). To address this problem we 

always include as potential destinations four cells bordering the sides of a fish’s 

current cell. 

Movement distances vary among individuals and over time. This variation 

could be induced in the model by making the value of the parameter 

maxMoveDistance variable (Section X.C.2). 

This formulation provides another advantage to rapidly growing fish: they 

are able to look further for good habitat. 

Barriers. In one of the Little Jones Creek study sites (a small tributary) there 

are cascades large enough to block upstream movement of trout. These barriers 

affect the potential destinations available in movement. (We define “barrier” to 

mean a blockage to upstream, but not downstream, movement.) For cells 

upstream of a trout’s current cell, the effect is straightforward: if there is a barrier 

between the trout and an upstream cell, then the upstream cell is excluded as a 

potential destination. We do not simulate the possibility of barriers being 

passable to large trout but not to small ones; we assume no fish can pass 

upstream over a barrier. 

For cells downstream of a trout’s current cell, the effect is less 

straightforward. We assume fish consider as movement destinations those cells 

that they are familiar with, as determined by the variable maxMoveDistance. 

However, it does not seem reasonable to assume a fish would be familiar with 

the habitat in a cell that is downstream of a barrier; the barrier makes it impossible 

for the fish to have explored the cell and returned to its current cell. Fish 

movement downstream over barriers occurs, with the fish apparently making an 

uninformed assumption about the consequences of moving downstream. Making 

such “blind” movements seems most likely to be successful if they are undertaken 

only when the alternative of not moving downstream is very risky. Therefore, we 

model downstream movement over barriers in this way: 

•Cells that are within maxMoveDistance from a fish, but downstream of a 

barrier, are included as potential movement destinations. 

•We assume the fish is not familiar with the habitat at such cells and 

therefore cannot predict the “expected maturity” fitness measure used 

to evaluate destinations (Section IV.B.2). Therefore, we assume the fish 

will cross downstream over a barrier if, and only if, none of the 

alternative cells (which do not require crossing the barrier) have an 

expected maturity value greater than 0.5. (This means the fish will not 

cross a barrier unless its expected survival at alternative sites is very 

low, but when expected survival at alternatives is low, the fish always 

crosses the barrier.) 

•If a fish does cross downstream over a barrier, we place the fish in a cell just 

across the barrier and then repeat the whole movement process. This means 

a fish can cross several barriers in a day, and possibly (if conditions for 

survival are poor) move all the way down the modeled reach. 

Minimum depth. We exclude cells as destinations if they have depth 0. This 

rule is imposed only to reduce computer execution times. The fitness measure that 

determines movement gives fish a very strong incentive to avoid moving to dry 

cells, where the risk of mortality by stranding is very high. However, specifically 

excluding movement to dry cells significantly reduces the computations needed to 

select a destination cell, with very little anticipated effect on model results. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 

IV. Fish Model 

15 
IV. Fish Model 

We do not, however, require a fish to move if the depth in its current cell drops to 

zero. But in that situation, the fish must either move or suffer stranding mortality. In 

addition, if the flow decreases so that the nearest cell with non-zero depth is farther 

away than a fish’s maximum movement distance, then the fish suffers stranding 

mortality (Section IX.D.3). 

Evaluate Potential Destination Cells—A fish evaluates each potential destination 

cell to determine the fitness it would provide. We use the “expected maturity” fitness 

measure of Railsback and others (1999c). Each fish has to evaluate its potential fitness 

in each potential destination cell (and its current cell), because the fitness measure is a 

function of the fish’s size and species and of the cell characteristics. 

Individual fish select the potential destination cell providing the highest value of 

“expectedMaturity” where: 

expectedMaturity = nonstarvSurvival × starvSurvival × fracMature. 

The variable “nonstarvSurvival” is the calculated probability of survival for all 

mortality sources except poor condition, over a specified time horizon given by the 

variable “fishFitnessHorizon.” This probability of survival is calculated assuming 

that the current day’s survival probabilities will persist for the number of days 

specified by “fishFitnessHorizon.” The value of “nonstarvSurvival” is calculated as: 

nonstarvSurvival = (Si × Sii × Siii)

fishFitnessHorizon 

where Si, S ii, S iii, etc. are the daily survival probabilities (the unitless probability of 

surviving for one day) for various mortality sources (i,ii,...), evaluated for the current 

day, fish, and cell (Section IX.D). The value of nonstarvSurvival is determined for the 

fish’s size before the daily growth that would occur at the potential destination cell; 

this assumption is made to simplify the model’s software. (It would be more consistent 

with the rest of our model to calculate nonstarvSurvival by using the fish size after 

the growth it would obtain at the destination cell; however, we expect the effect of 

this assumption to be negligible in almost all cases.) 

The value of “starvSurvival” is the probability of surviving the risk of poor 

condition (closely related to starvation; Section IX.D.5) over the number of days 

specified by “fishFitnessHorizon.” This term introduces the effects of food intake to 

the fitness measure. The value of starvSurvival is determined by these steps (Railsback 

and others 1999c): 

•Determining the foraging strategy, food intake, and growth (g/d) for the fish 

and habitat cell in question, for the current day. The potential growth at a 

destination cell is determined by simulating how much food would be 

obtained and how much energy it takes to swim in the cell (Section IX.C). 

•Projecting the fish’s weight, length, and condition factor K that would result 

if the current conditions persisted for the number of days specified by 

“fishFitnessHorizon”. The daily growth is multiplied by fishFitnessHorizon 

to determine the change in weight; the corresponding change in length and K 

are determined using the methods described in Section IV.C. 

•Approximating the probability of survival over the fitness horizon by using 

the following equation, which estimates survival as the first moment of the 

logistic function of starvation survival vs. K (Section IX.D.5): 

T   aK  

starvSurvive =  

 1 ln 1 +e

( t +T + b) 

 

 a  1+e

(aKt + b)  

(Kt +T − Kt ) 

 

 

where Kt

condition factor at the end of the fitness horizon, T is equal to fishFitnessHorizon, and

is the fish’s condition factor at the current day and Kt+T is the projected 

16 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
I

V. Fish Model 

a and b are the logistic curve parameters determined (within the code, from the 

user-provided parameter values) for the poor condition mortality function (Section 

IX.D.5). This equation causes a divide-by-zero error when Kt+T equals Kt

, a common 

condition because K equals 1.0 whenever fish are well fed. This equation is also 

subject to significant errors due to the limits of computer precision when Kt+T is 

extremely close to K

t

. To avoid these problems, we set starvSurvival equal to the 

daily survival probability for Kt raised to the power “fishFitnessHorizon” whenever 

the difference between Kt+T and Kt is less than 0.001. 

The term “fracMature” represents how close to the size of sexual maturity a 

fish would be at the end of the fitness time horizon. It is simply the length the fish 

is projected to be at the end of the time horizon divided by the parameter 

“fishSpawnMinLength” (defined in Section IX.A.6). This term induces a 

movement gradient toward sites with higher growth for fish that have not yet 

reached the size allowing them to spawn. (Note that we assume both sexes have 

the same length at sexual maturity, an assumption that may not be valid for 

many populations of salmonids.) 

The time horizon variable “fishFitnessHorizon” is the number of days over 

which the terms of the expected maturity fitness measure equation are evaluated. 

The biological meaning of this variable is the time horizon over which fish 

evaluate the tradeoffs between food intake and mortality risks to maximize their 

probability of surviving and reproducing. It is discussed in the “unified foraging 

theory” literature (Mangel and Clark 1986). Smaller values of fishFitnessHorizon 

place less emphasis on food intake and avoiding starvation in movement 

decisions. Values of fishFitnessHorizon of 5-10 d caused expectedMaturity to 

vary almost exclusively with non-starvation survival, with very little effect of 

food intake and growth. Values of fishFitnessHorizon in the range of 100 d 

caused expectedMaturity to vary almost exclusively with growth rates when 

growth was less than the minimum needed to maintain a condition factor of 1.0. 

To our knowledge, only two studies address the issue of fitness time 

horizons. Bull and others (1996) used a model similar to ours and assumed 

overwintering juvenile salmon used the remaining winter period as a time 

horizon. Thorpe and others (1998) proposed using the duration of various 

salmonid life stages as time horizons. If we follow the lead of this literature and 

assume fish anticipate seasonal changes in habitat conditions and their life stage, 

it makes sense to assume they use a habitat selection time horizon of several 

months. We use “fishFitnessHorizon” equal to 90 d and include evaluation of 

alternative assumptions in our research priorities (Section X.C.3). 

Move to Best Destination—The fish identifies the cell that has the highest 

value of the expected maturity fitness measure and then moves there. We do not 

limit movement by territory size or otherwise restrict the number of fish that can 

be in a cell. When a fish moves into a cell, the resources it uses are subtracted 

from those available for subsequent fish (Sections III.D; III.G.2). These resources 

may include one of the two kinds of food and velocity shelter. Because fish may 

move into a cell even when none of these resources remain available to it, its 

consumption of them is zero. IV.C. Feeding and Gr

owth 

The model’s methods for determining the daily growth (change in weight, 

g/d) that a fish would obtain in a specific habitat cell are used both in the daily 

movement decision and to determine growth once a fish has moved. Growth is 

determined by using the foraging and energetics methods described in Section 

IX.C. Food intake and growth depend on fish size, habitat conditions, and food 

availability in the cell. Growth can be negative, a situation common in nature 

(Railsback and Rose 1999). 

We do not specify the exact kinds of food consumed by fish, but our feeding 

formulation and parameters generally represent invertebrate food. Even though USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 

17 
  

IV. Fish Model 

the model assumes small fish are vulnerable to predation by adult trout (Section 

IX.D.7), feeding studies at the Little Jones Creek study site indicate that fish make up a 

small part of the trout diet. Therefore, we do not represent piscivory in the feeding 

model. 

Unlike previous individual-based stream trout models, we assume that fish 

compete with each other for the available food instead of for feeding space. We assume 

each cell has a certain amount of food produced in it each day and the food available to 

a fish in the cell is limited by the cell’s food production and the amount of food eaten 

by other fish in the cell (Section III.G). In combination with our movement rules, this 

assumption makes fish density a property that emerges from food availability and 

mortality risks instead of being imposed by requiring territorial behavior. 

Our model includes two alternative feeding strategies. Drift feeding, in which the 

fish remains stationary and captures food as it is carried past by the current, is the most 

studied and often the most profitable strategy (Fausch 1984, Hill and Grossman 1993, 

Hughes and Dill 1990). We model drift food intake (Section IX.C.2) as a function of 

stream depth and velocity and fish length; intake peaks at an optimal velocity that is 

higher for larger fish. We model the effect of turbidity on drift intake, reducing intake 

as turbidity increases. Metabolic costs for drift feeding increase with water velocity, 

but use of velocity shelters reduces this cost. Actively searching for benthic food and 

food dropped into the stream from overhead is an alternate strategy that can be 

important when competition for food is intense, conditions for drift feeding are poor, 

or the abundance of benthic food is high (Nielsen 1992, Nislow and others 1998). We 

assume the energetic benefits of search feeding are mainly a function of food 

availability, with energetic cost depending on water velocity (Section IX.C). 

For both of these strategies, we model the potential food intake and metabolic costs 

a fish would experience in a cell; the fish then selects the strategy that provides the 

highest net energy (which often can be negative). Following standard bioenergetics 

approaches, we assume growth is proportional to net energy intake. 

From the daily growth, the model determines the changes in length and condition 

factor. No simple, realistic ways of modeling this have been established. We adopt the 

simplistic approach developed by Van Winkle and others (1996), but propose the 

development of alternative approaches that seem likely to be more realistic and in 

better accord with our modeling philosophy (Section X.A.3). 

The method for calculating daily change in length we adopt from Van Winkle and 

others (1996) also uses their nonstandard definition of a condition factor, K, a unitless 

index of how much weight a fish has relative to its length. This condition factor can be 

considered as the fraction of “normal” weight a fish is, given its length. The value of K 

is 1.0 when a fish has a “normal” weight for its length, according to a length-weight 

relation input to the model. Fish grow in length whenever they gain weight while their 

value of K is 1.0. Condition factors less than 1.0 indicate that the fish has lost weight. In 

this formulation, condition factors greater than 1.0 do not occur. 

Weight, length, and K are calculated in this way: 

• The fish’s weight is changed by the value of dailyGrowth (calculated using 

methods in Section IX.C; note that daily growth can be negative). 

• The length of a healthy fish with the fish’s new weight (“fishWannabeLength”) is 

calculated from the inverted length-weight relation (with the same parameters 

used to initialize new fish, Section II.B): 

 fishWeight  fishWannabeLength =  fishWeightParamA 

1 fishWeightParamB 

• If the fish’s actual length is less than fishWannabeLength (indicating that 

the fish is not underweight), then its length is set to fishWannabeLength. 

•� If the fish’s actual length is greater than fishWannabeLength (indicating the 

fish is underweight for its length), its length is not changed. 

18 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IV. Fish Model 

The new condition factor (unitless) is equal to the fish’s new weight divided 

by the “normal” weight for a fish its length: 

fishCondition = fishWeight 

fishWeightParamA × fishLength fishWeightParamB ( ) 

It is important to note several limitations of this formulation: 

• It does not allow fish to store a high-energy-reserve condition. Fish will 

have a condition of 1.0 only on those days when daily growth is positive. 

Even if a fish has eaten well for many days in succession, its condition 

factor can only be as high as 1.0 and one day of negative net energy 

intake causes condition to fall below 1.0. This could be a serious problem 

where short periods of high food intake are common. 

• This formulation locks in a length-weight relationship for growing fish. 

Calibration of growth to situations where this relationship is valid will 

be automatic, but calibration to situations where the relationship is not 

valid will be impossible. For example, our model cannot predict the 

existence of unusually fat fish. 

• The energetics of reproduction are not considered (Section IX.A). We do not 

model how the need to store energy for gonad development affects length 

and weight, nor how the loss of gonads in spawning affects weight. 

Our research objectives include addressing these limitations (Section 

X.A.3). 

IV.D. Survival 

Our survival simulations determine, each day, which fish die from what 

causes. Mortality sources are modeled using survival probabilities. (By “mortality 

source” we mean the individual processes we model that can cause mortality, 

e.g., predation, poor condition, high temperature.) Survival probabilities are the 

daily probability of not being killed by one specific mortality source. Survival of 

multiple mortality sources can be calculated simply by multiplying together the 

survival for each individual source. The mortality sources we model are: 

• High temperature 

• High velocity (representing exhaustion and inability to maintain 

position) 

• Stranding (including predation risk associated with extremely shallow 

habitat) 

• Spawning (occurring only to adults on the day they spawn) 

• Poor condition and starvation 

• Predation by terrestrial animals 

• Predation by fish. 

The survival probability functions used to determine whether a fish lives or 

dies depend on the fish’s state (length, condition) and its habitat (depth, velocity, 

temperature) (Section IX.D). 

Understanding and calibrating mortality in the model requires that we 

evaluate each potential mortality source separately; if we calculated one daily 

overall survival probability for each fish each day, we would not be able to 

attribute mortality to any particular source (Section VI.B). Therefore, we treat 

each mortality source as independent from the others. For each mortality source, 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 19 
V. Redd Model 

we obtain the survival probability from the fish’s mortality methods (Section IX.D) 

and obtain a random number from a uniform distribution between zero and one. If the 

random number is greater than the survival probability, then the fish dies as a result of 

the mortality source. 

V. Redd Model 

Redds are the nests laid by spawning salmonids. A redd is modeled as one object. 

We do not track individual fish until they emerge from redds. The model keeps track 

of the number of eggs remaining alive in each redd. Characteristics of the spawner 

determine a redd’s species and number of eggs. The eggs develop each day at a rate 

that depends on temperature. We do not explicitly simulate the changes in fish 

morphology and life stage that occur in the redd—all fish in a redd are considered 

eggs until they emerge as age-0 fish. 

Redds are modeled as having four daily actions—survival, development, 

emergence, empty redds—that determine the number of age 0 fish produced. 

Scheduling of these actions is discussed in Section VI.C. 

V.A. Survival 

Eggs in a redd are subject to five mortality sources: low and high temperatures, 

scouring by high flows, dewatering, and superimposition (having another redd laid 

on top of an existing one). 

Redd survival is modeled using redd “survival functions,” which differ from 

survival probabilities because they determine, for each redd on each day, the fraction 

of eggs that survive one particular kind of mortality. This fraction is then multiplied 

by the number of eggs in theredd to determine how many eggs survive. The number of 

eggs surviving is rounded to an integer. 

Most redd survival functions are straightforward functions of the daily depth, 

velocity, and temperature in the redd’s habitat cell (Section IX.E), but mortality due to 

“superimposition” is less straightforward. Superimposition can be important if 

spawning habitat is very limited compared to the number of spawners, or fish 

superimpose on existing redds more frequently than predicted by habitat availability 

alone (Essington and others 1998). 

We track how many eggs die of each mortality source by applying each redd 

survival function individually, updating the number of surviving eggs after each 

function is applied (Section VI.C). 

V.B. Development 

To predict the timing of emergence, the developmental status of a redd’s eggs is 

updated daily. We use the fractional development approach of Van Winkle and others 

(1996). The model accumulates the fractional development of the redd that occurs each 

day (reddDailyDevel), a function of temperature. This means the redd has a variable 

“fracDeveloped,” that starts at zero when the redd is created and is increased each day 

by the value of reddDailyDevel. When fracDeveloped reaches 1.0, then the eggs are 

ready to emerge. 

The daily value of reddDailyDevel is determined using this equation: 

reddDailyDevel = reddDevelParamA + (reddDevelParamB 

× temperature) + (reddDevelParamC × temperature 2

) 

In the absence of values specific to cutthroat trout, we use the rainbow trout parameter 

values of Van Winkle and others (1996; table 4). A simple degree-day model for cutthroat 

(emergence occurring 430 to 560 degree-days after spawning) was tested by June (1981). 

June observed the number of degree-days between spawning and emergence at his field 

site to range from 475 to 600, and the 430-560 model predicted emergence within 12 days. 

20 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
V. Redd Model 

Table 4—Parameter values for egg development rates. 

Parameter Definition Units Value 

reddDevelParamA Constant in daily redd development equation none -0.000253 

reddDevelParamB Temperature coefficient in daily redd 

development equation (°C)-1 0.001340 

reddDevelParamC Temperature squared coefficient in daily 

redd development equation (°C)-2 0.0000321 

We compared this degree-day approach to the equation and parameters of Van 

Winkle and others (1996), using temperatures measured at the lower Little Jones 

Creek study site in 1998 and assuming spawning on May 8. The Van Winkle and 

others equation predicted emergence on July 5 after 614 degree-days; this was 4 days 

after the threshold of 560 degree-days was met. It appears that these two methods 

produce similar results. 

V.C. Emergence 

When eggs in our model are fully developed, they “emerge” from the redd as 

new fish. (Real trout actually pass through a life stage known as “alevin” before 

emerging; however, we do not distinguish between eggs and alevins in the 

model.) New fish emerge over several days. The following steps are used to 

determine how many fish emerge each day. 

V.C.1. Emergence Timing 

We assume that no new fish emerge until the day upon which eggs are fully 

developed (the day when fracDeveloped reaches 1.0), and then the fish emerge 

over a period of several days after this. Causing emergence to occur over several 

days represents natural variation in emergence timing and can potentially have 

strong effects on survival of newly emerged trout. These fish compete with each 

other for food as soon as they emerge. If all emerged on the same day, without 

time for some to move, competition would probably be overestimated. As a 

simple (but artificial) way to spread emergence over about 9 days, we assume 

that the fraction of remaining eggs that become fish on each day is 0.1 the first 

day, 0.2 the second day, 0.3 the third day, etc. until all fish have emerged. 

V.C.2. New Fish Attributes 

For each egg that emerges as a new fish, the model assigns these attributes. 

• The fish is assigned its species from that of the redd 

• The fish is placed in the same habitat cell as its redd. 

• Sex is assigned randomly, assuming 50 percent of fish are each sex. 

• The length of each individual fish is assigned from a random normal 

distribution with mean equal to the parameter reddNewLengthMean 

and a variance equal to the parameter reddNewLengthVar. 

• Weight is calculated from length, using the same method used to create 

initial fish (Section II.B). 

We estimate length parameters for newly emerged fish (table 5) from a study 

of coastal cutthroat in Washington (June 1981). This study measured lengths of 

newly emerged fry found in a downstream trap. A few of these had lengths 

between 2.4 and 2.7 cm, but most were between 2.7 and 3.0 cm. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 21 
VI. Model Schedules 

Table 5—Parameter values for size of newly emerged fish. 

Parameter Definition Units Value 

reddNewLengthMean Constant for new fish length equation

reddNewLengthVar Variance in length of newly emerged fish cm2 0.04

cm 2.8 

From Elliott (1994), we assume that fish emerging from a redd vary slightly, but 

perhaps significantly, in size. This variation in starting size gives larger fish an 

advantage in dominance that is likely to persist and grow over time. Elliott (1994) 

observed a coefficient of variation of 0.07 in length at emergence for brown trout at 

several sites. We adopt this value by converting it to the variance in length (parameter 

reddNewLengthVar, cm2

); with a coefficient of variation of 0.07 and a mean length of 

2.8 cm, reddNewLengthVar is 0.04 cm2. 

We assume, by assigning weight this way that all fish are of normal condition 

when they emerge. Alternative assumptions (e.g., that initial condition is a random 

variable) are easily implemented, but we know of no basis for such assumptions. 

Previous models (Railsback and others 1999a, Van Winkle and others 1996) assumed a 

relation between the size of a spawning female and the size of its eggs and, therefore, the 

emergence size of its offspring. This variation may be very important for salmon and large 

trout where variation in spawner size is large. It is also a mechanism making the offspring 

of larger fish more likely to be successful. We assume, however, that variation in new fish 

size with spawner size is not important in resident cutthroat trout. 

V.D. Empty Redds 

Then number of eggs remaining in redds is reduced when eggs die or fish emerge. When 

the number of remaining eggs in a redd reaches zero, the redd is dropped from the model. 

VI. Model Schedules 

The schedule in which events occur is a key factor determining the outcome of 

individual-based models. This section defines the order in which trout model actions 

occur. 

We followed several guidelines in defining the schedule. In general, an action is 

placed in the schedule before any others that might be affected by it. The schedules for 

imposing mortality sources consider the fact that placing a mortality source earlier in 

the schedule makes it slightly more likely to cause mortality (a mortality source cannot 

kill a given fish on a given day if a preceding mortality source does so first). Therefore, 

we schedule widespread, less random mortality sources (e.g., high temperatures, high 

velocities) first; survival probabilities for these sources tend to be either negligible (1.0) 

or very low when some mortality event occurs. 

In this section, we consider the computer implementation of the model by 

scheduling the “observer” actions that allow us to observe the model’s state as it 

executes. This computer implementation is included because users of the model must 

understand how the observer schedule affects the model’s output. 

VI.A. Habitat Actions 

Characteristics of individual habitat cells (depth, velocity, temperature, turbidity, 

and food availability) are updated daily. The physical habitat is updated first because 

subsequent fish and redd actions depend on that day’s habitat conditions. 

22 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
VI. Model Schedules 

VI.B. Fish Actions 

Fish actions are scheduled before redd actions because one fish action 

(spawning) can cause mortality of eggs or fish in redds by superimposition. This 

order means that new fish emerging from a redd are not simulated as fish until 

the day after emergence. 

The four fish actions in the model are conducted in the following order: 

spawning, movement, growth, and survival. Actions are carried out one fish at a 

time, from the longest to the shortest individual. Each action is conducted for all 

fish before the next action is begun. 

We schedule spawning as the first fish action because we assume spawning 

is the primary activity of a fish on the day it spawns. Spawning also is scheduled 

before survival because a fish’s survival probability is reduced when it spawns. 

Movement is scheduled as the second fish action each day to allow fish to 

move in response to each day’s new habitat conditions before feeding and 

survival simulations. Movement strongly affects both growth and survival. 

Movement decisions are based in part on survival probabilities, which vary with 

fish size, and we base movement decisions on survival probabilities evaluated 

for the fish’s current size (before the current day’s growth, which depends on its 

movement destination). This assumption can be considered a shortcut that 

introduces an error expected to be negligible in almost all cases. 

Growth is scheduled before survival because changes in a fish’s length or 

condition factor affect its probability of survival. 

Fish survival includes evaluation of a number of mortality sources, and the 

number of fish killed by each mortality source depends on the order in which 

survival probabilities for each source are evaluated. 

The schedule of fish actions has subtle implications for testing the model 

software. Processes that affect fish movement and growth (e.g., food intake, 

swimming costs) can produce different results when executed during the 

movement action than they do when executed during the growth action. This is 

because these actions depend on how many other fish are in the fish’s cell, which 

changes as movement is executed. The availability of food and velocity shelters 

decreases as more fish are added to a cell during the movement action. For this 

reason, re-calculating net energy intake for a fish after the movement action is 

completed would produce a result that was not valid at the time the fish made its 

movement decision. Likewise, mortality risks evaluated during movement will 

differ slightly from those used in the survival action because the fish has acquired 

its daily growth after movement and before survival actions, and survival 

probabilities depend on fish size. Software tests must consider the availability of 

food and velocity shelters, and the fish’s size, that occurred at the time each fish 

made its movement decision. 

VI.C.Redd Actions 

Redd actions occur last each day because redds do not affect either habitat 

cells or fish (with the exception of creating new fish). 

Three model actions affect redds: survival, development, and emergence. 

Survival is scheduled first because the number of fish emerging is a function of 

survival. Also, if emergence were scheduled before redd survival, new fish 

would be subject to no mortality (either as fish or as eggs) on the day of their 

emergence. Development is scheduled before emergence because we assume 

new fish emerge on the same day egg development is complete (if development 

were scheduled after emergence, then fish would begin to emerge the day after 

development was complete). 

Redd survival includes several separate egg survival probabilities; the least 

random sources (dewatering, scouring) are first, and the most random 

(superimposition) is last. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 23 
VII. Callibration 

VI.D. Observer Actions (Model Outputs) 

We schedule observer actions as the last of the daily model actions. This 

means that the model’s graphical and file outputs represent the state of the model 

after all the habitat, fish, and redd actions have been completed for a time step. 

Intermediate states of the model (e.g., the number of eggs in a redd after some, 

but not all, survival functions have executed; the size of a fish at the time it made 

its movement calculations but before its simulated growth; the food availability 

in a cell before all its fish moved into it) can only be observed by specifically 

telling the software to save the desired values. 

Our software allows the model user to identify and “kill” individual fish via the 

graphical user interface. This observer-induced mortality (not otherwise described in 

this document) occurs during the observer actions at the end of a time step. 

VI.E. Complete Schedule 

The complete schedule of event execution in the model follows this order: 

1.Habitat Actions: Update flow, depth, velocity, temperature of cells 

2.Fish Actions 

a. Spawning 

b. Movement (move fish in order of decreasing dominance) 

c. Growth 

d. Survival 

i. High temperature 

ii. High velocity 

iii. Stranding 

iv. Spawning 

v. Poor condition 

vi. Terrestrial predation 

vii.Aquatic predation 

3.Redd Actions 

a. Survival 

i. Dewatering 

ii. Scouring 

iii. Low temperature 

iv. High temperature 

v. Superimposition 

b. Development 

c. Emergence 

4.Observer Actions: Model outputs 

VII. Calibration 

Calibration has the objectives of testing, demonstrating, and improving the 

model’s ability to reproduce observed phenomena. Calibration includes changes 

in parameter values and, possibly, revision of the model formulation. Calibration 

occurs in two major phases: 

•� Individual components of the model formulation (e.g., feeding and 

growth methods) are tested and calibrated as they are designed. In this 

document, discussion of such calibration is included in the sections 

describing individual formulation components. 

24 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
• The full model is calibrated after all model components have been 

designed and calibrated individually, the entire model has been 

implemented in computer code, and the code checked thoroughly. 

This section discusses full-model calibration methods that are useful only 

after individual model components have been tested and calibrated. Calibration 

to date has included empirically fitting food availability and survival probability 

parameters, and testing of the model’s ability to simulate movement and habitat 

selection realistically. 

Calibration of complex models requires a systematic approach. Because our 

model is designed to simulate the population level changes that result from 

individual fish behavior, the actions of individual fish must be calibrated before 

there can be any chance of successfully calibrating population-level 

characteristics. On the other hand, there are feedbacks from population-level 

characteristics to individual actions (e.g., when populations are high, growth of 

many individuals may be lower). In addition, individual characteristics may not 

be reflected in population-level statistics (e.g., many individual fish may have 

growth rates much less than the observed population average because they do 

not survive until population observations are made). Considering such 

complexities, we recommend the following approach to calibration: 

• Calibrate individual and short-term responses before attempting to calibrate 

population-level, inter-annual responses. The ultimate goal of the model is 

to predict population responses to environmental changes like altered 

discharge regimes, but there are an infinite number of ways to calibrate the 

model so that it reproduces observed population-level responses. 

• Focus calibration on underlying processes driving individual fitness 

instead of using “brute force” adjustments to match observed data. 

Models that produce realistic behavior and population responses as 

patterns that emerge from simple rules are more powerful than models 

where realistic behaviors are imposed by inflexible rules. For example, 

the relative abundance of two species in a model should emerge from 

the fitness of individuals of each species (e.g., fish that emerge from 

redds earlier may have an advantage over late-emerging fish because 

the former begin growing sooner) rather than from different imposed 

mortality rates that produce observed differences in abundance. 

• Establish appropriate calibration criteria, which vary among processes 

and need not always be numerical. In general, reproducing observed 

patterns in the response of fish to events is more useful than exactly 

reproducing observed data (Railsback 2001). 

• At each level of calibration, identify parameters (or equations) that 

appear most appropriate to change via calibration. These are generally 

parameters or equations that have strong effects on the model action 

being calibrated and are more uncertain. 

VII.A. Individual Actions 

The actions of individual fish and redds should be calibrated first. We 

identified the following criteria for fitting individual fish and redd actions to 

observations, and we identified the parameters that should be adjusted first 

during calibration. This section also describes calibration conducted to date. 

VII.A.1. Fish Spawning 

The predicted date of spawning can be compared to observed spawn timing 

(which is rarely known precisely). The habitat cells where model redds are 

placed can be compared to observed spawning habitat preferences. The models 

for timing and location of spawning are simple and closely constrained; they 

should require little if any calibration if the parameters were selected accurately. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 

VII. Callibration 

25 
VII. Callibration 

VII.A.2. Fish Growth and Survival 

Although pre-calibration values for important and uncertain food availability 

and survival probability parameters were estimated during model development 

(Section IX.C.9, Section IX.D.8), calibration of the full model is required to obtain 

realistic growth and survival of model trout. The preliminary growth and survival 

calibration described here produced food and survival parameters that have 

been used for a number of long-term simulation experiments. To calibrate food 

availability and predation risks at our Little Jones Creek study site, we developed 

the following criteria. 

Calibration was conducted over a 75-day period from July 19 to October 2, 

1998. The lower study site was used. We estimated the initial relative abundances 

of age classes (table 6) by using field data from July 1999. We doubled the total 

abundance of fish observed in 1999 to reflect data from three previous censuses 

of Little Jones Creek by other workers. 

The number of age 0 fish could not be estimated in July because some 

members of this age class were not large enough to census. Consequently, we 

calibrated survival for age 1 and older fish and then used the model to estimate 

the July 19 abundance of age 0 fish. 

The target ending (October 2) population characteristics (table 7) were 

estimated from field observations collected at the Little Jones study site at the 

end of September 1999, supplemented with rainbow trout data from a site on the 

Tule River, Sierra Nevada, California, from which field data for 11 years are 

available (Studley and others 1995, Railsback and Rose 1999). The Tule site 

(upstream of the Tule River diversion dam) is roughly similar to Little Jones 

Creek in habitat type and structure, but has higher summer temperatures and 

brown trout that compete with the rainbow trout. 

The ending average lengths for each age class were taken from the Little 

Jones Creek field data. The calibration targets for numbers of trout were 

developed from both Little Jones and Tule River data. The apparent mortality 

rates observed in Little Jones Creek in 1999 were quite low, whereas the Tule River 

data had average summer mortality rates (for a time period roughly equal to our 75-day 

calibration period) of 40 percent for age 1 and 2 trout. 

Table 6—Initial population characteristics for calibration. 

Age, y Number Mean Length, cm Variance in Length, cm 

0 unknown, > 450 50.0 0.67 

1 50 11.4 1.69 

2 and above 20 16.9 7.56 

Table 7—Ending population characteristics used as calibration targets. 

Age, y Number Mean Length, cm 

0 450 6.9 

1 40 12.8 

2 and above 15 19.0 

26 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
VII. Callibration 

Table 8—Calibration results. 

Output Run 1 Run 2 Run 3 Run 4 Run 5 Mean (SD) 

Age 0 abundance 472.0 446.0 451.0 429.0 444.0 448.0 (16.0) 

Age 1 abundance 39.0 35.0 38.0 39.0 32.0 37.0 (3.0) 

Age 2+ abundance 18.0 15.0 17.0 19.0 17.0 17.0 (1.0) 

Age 0 length 6.4 6.6 6.6 6.6 6.7 6.6 (0.1) 

Age 1 length 12.9 13.0 13.5 12.4 13.1 13.0 (0.4) 

Age 2+ length 18.6 18.2 18.8 18.5 18.2 18.5 (0.3) 

We calibrated growth (change in length) for age 1 and older fish by adjusting the 

food availability parameter that represents the concentration of drift food in the 

water column (habDriftConc). Because many age 0 fish used the active searching 

feeding strategy, we next used the density of search food (parameter habSearchProd) 

to calibrate age 0 growth. We assumed that aquatic predation is the most important 

(along with poor condition) and least certain mortality source for age 0 trout. The 

parameter mortFishAqPredMin was therefore used to calibrate age 0 survival. 

Similarly, we assumed that terrestrial predation is the most important and least 

certain mortality source for age 1 and older fish and used the parameter 

mortFishTerrPredMin for calibration of survival for these age classes. 

We did not attempt to calibrate survival and growth precisely, but we did try 

to ensure that rates and causes of mortality and growth rates were reasonable. 

The calibration process produced these values of the calibration parameters: 

•habDriftConc: 1.50E-10 

• habSearchProd: 7.0E-7 

•mortFishAqPredMin: 0.997 

•mortFishTerrPredMin: 0.99 

Terrestrial predators account for about 40 percent of mortality of age 0 fish in 

the calibrated model. The rest of the mortality was evenly spread among aquatic 

predation, stranding (which includes the extreme predation risk in shallow 

water), and starvation. 

We conducted five replicate model runs (initialized with different random 

number seeds; table 8). These can be compared to the calibration targets in table 7. 

VII.A.3. Fish Movement 

Because moving to different habitat is a primary way that stream fish adjust 

to changing conditions, testing the model’s ability to represent movement 

realistically is a key step in calibration. Movement, survival, and growth are 

closely linked: survival and growth rates are the factors that determine how fish 

move, and where fish move affects their survival and growth rates. After we 

conducted the calibration of survival and growth, we tested the model’s 

simulation of movement and habitat selection by trout. We identified six 

observed patterns of shift in habitat by trout in response to known stimuli; the 

model reproduces all of these patterns. This test is documented in a separate 

publication (Railsback and Harvey 2001). 

VII.A.4. Redd Survival 

Data allowing calibration of survival rates of eggs in individual redds will rarely 

be available. Calibration may be limited to making sure survival rates are reasonable 

for periods when redd mortality factors can safely be presumed to be low. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 27 
VII. Callibration 

28 

VII.A.5. Redd Development and Emergence 

Because redd development rates are dependent only on temperature, fullmodel calibration is not needed (Section V.B). 

VII.B. Short-term Population Responses 

Long-term population predictions are likely to be inaccurate if predicted 

responses to short-term events are not realistic. We recommend the following shortterm events be simulated and the model calibrated to reproduce observed responses. 

VII.B.1. Seasonal Changes in Habitat Use, Growth, and Survival 

Several changes in habitat use patterns with season and fish size are well 

documented (PG&E 1994, Vondracek and Longanecker 1993). These patterns 

include use of increasing depths in the first year of life and selection of lower 

velocities in winter. The model has been shown to predict changes in habitat 

selection with seasonal changes in temperature and day length (Railsback and 

Harvey 2001), but the magnitude of these habitat shifts have not been calibrated. 

The model’s seasonal patterns in habitat use, growth, and survival will be 

highly dependent on the assumptions made about how food availability varies. 

(Currently, we assume no seasonal variation in food availability.) One way to 

match such seasonal patterns is to adjust food availability by season or 

temperature, one of our research priorities (Section X.B.4). 

VII.B.2. Redd Scouring and Temperature-related Mortality 

There is strong evidence that scouring of redds and temperature-related 

mortality of incubating eggs are relatively common and have major 

consequences for trout populations. Historic data on recruitment success may be 

useful to calibrate the model to reproduce these important short-term events. 

VII.C. Long-term Population Responses 

A primary objective of the trout model is to predict long-term populationlevel responses to changes in flow and other conditions. These responses should 

be addressed in calibration only after it has been determined that simulations of 

individual actions and short-term responses are realistic. 

As with previous calibration levels, it is important to ensure that the model 

reproduces observed processes and relations, not just observed outcomes like 

abundance or average growth. For example, matching observed (or literaturebased) effects of driving variables like flow and temperature on predicted 

population should take priority over simply matching long-term mean 

population measures. 

The model should not be calibrated using field data strongly affected by processes 

not included in the model. Our model currently does not simulate emigration or 

immigration, stocking, or angler harvest; caution should be used when attempting 

calibration to data from periods when these processes may be important. 

VII.C.1. Redd Numbers and Incubation Success 

Because long-term patterns of spawning, redd numbers, and the number of 

fish produced per redd are difficult to observe, direct calibration of the number 

and success of redds is unlikely. In cases where redd counts are available from 

multiple years, calibration could include testing the model’s ability to predict 

trends between redd numbers and spawner abundance or flow. Because of the 

difficulty of field observations, we expect redd success can normally be 

calibrated only as one of the factors driving the abundance of age 0 trout. 

VII.C.2. Long-term Abundance, Growth, and Relative Abundance 

Once simulations of individual behavior simulations appear reasonable, 

long-term growth rates should be calibrated by adjusting the food availability 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
parameters, similar to the process of calibrating individual fish actions. (Small 

differences in calibration of daily growth of individuals can add up to large 

errors in long-term average growth of a population.) Keep in mind that survival 

rates affect growth because remaining individuals will have access to more food 

when populations are low, and size-dependent mortality (e.g., higher starvation 

or predation mortality in smaller individuals) changes the population-level 

growth rates. 

Long-term abundance is a cumulative result of survival rates (and 

reproduction rates). Because starvation can be an important mortality source, 

abundance cannot be calibrated precisely until feeding and growth simulations 

are relatively accurate. To calibrate non-starvation survival, we recommend 

using the parameters controlling aquatic predation risk (mortFishAqPredMin) 

and terrestrial predation risk (mortFishTerrPredMin) because these are generally 

less certain than other risk factors (high temperature, high velocity, stranding, 

and spawning). Variation in mortality with fish size can be used to guide 

calibration of these parameters; aquatic predation affects only small fish. 

VIII. Habitat Data Collection Methods 

Field data to depict habitat for this individual-based model should differ 

from the data typically used for habitat assessment models like PHABSIM. This 

is because the objective of habitat modeling in the IBM is to provide a map of 

habitat relevant for the model’s daily time step and spatial processes, whereas 

PHABSIM characterizes hydraulics in detail across a few selected transects. In 

general, habitat data for the trout model should be collected at more transects 

and fewer points across each transect than typically used for PHABSIM. Field 

data include cell size and location, depth and velocity at several flows to calibrate 

a hydraulic model, availability of spawning gravel and velocity shelter, and 

distance to hiding cover. In addition, water surface elevations at high flows help 

calibrate the hydraulic model. 

The following guidelines are intended to help modelers familiar with 

PHABSIM field techniques collect data appropriate for our trout IBM. 

VIII.A. Reach Location and Length 

The selection of a stream reach for modeling should consider the purpose of 

the modeling study. If the model is intended for research purposes, then the 

study design (e.g., testing the model against field observations, comparing 

predictions among different habitat types) should be a primary consideration in 

reach selection. Models intended to provide management information may best 

use reaches that represent habitat of the whole river, but should also include any 

habitats known to be important to the fish population (e.g., unique spawning 

areas or sites with very high fish densities). 

We do not yet have the experience to provide specific guidance on 

appropriate reach lengths. Considerations include how important fish movement 

is expected to be, locations of barriers to movement, and how much habitat 

varies along the river. Longer reaches with more fish require more computer 

time to execute, but this should not be considered a limitation. 

VIII.B.Transects and Longitudinal Cell Boundaries 

Our approach for defining cell boundaries in the longitudinal (upstreamdownstream) direction is simpler than that of PHABSIM. In PHABSIM, transects 

are the lines across the stream where depths and velocity are measured to 

calibrate the hydraulic model. The cell borders between transects are defined by 

the “transect weighting factor,” the percent of the distance to the next upstream 

transect. Instead, we treat a transect as a row of cells across the river and directly 

measure the location of the boundary between each pair of adjacent transects. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 

VIII. Habitat Data Collection Methods 

29 
VIII. Habitat Data Collection Methods 

Unlike PHABSIM conventions, we also measure the upstream and downstream 

extent of the cells on the upstream and downstream ends of the study reach. We 

measure all these distances from downstream to upstream, with zero being at the 

downstream end of the cells represented by the first (most downstream) transect. 

The transects and their boundaries are placed to capture the upstreamdownstream variation in habitat, using the following criteria: 

• Represent all the habitat types that are common in the reach; include the 

full range of variation in habitat. 

• Include habitat types known to be important to fish even if they are rare; 

for example, areas with high concentrations of large woody debris. 

• Do not exclude common habitat types even if they are not expected to be 

important to fish. 

• Do not place transects closer together than about 1 meter, to avoid cell 

boundary effects in simulations. There is no upper limit due to modeling 

considerations on distance between transects. 

The frequency of transects should reflect the longitudinal physically 

heterogeneity of the habitat, e.g., riffles with consistent depth and 

substrate may be represented by one or two transects. 

VIII.C. Lateral Cell Boundaries 

The best approach to placing cells across transects for this model does not 

follow standard PHABSIM methods. The PHABSIM approach was adopted from 

stream gaging techniques without giving adequate consideration to 

consequences for habitat modeling (Railsback 1999). In PHABSIM, “stations” 

(points where bed elevation, depth, and velocity are measured) are usually 

spaced evenly at a minimum of 20 points across the channel; cell boundaries are 

then automatically placed halfway between each station. Instead, we use fewer, 

less evenly spaced cells. 

The goal in placing lateral cell boundaries is to make variation in habitat 

(depth, velocity, velocity shelters) low within each cell, but high among cells. It 

helps to remember that because the fish model assumes the depth and velocity 

are uniform within each cell, it sees a transect as a series of level cells (fig. 2). 

The cell boundaries are the points along the transect where, in the model, the 

bottom elevation changes; the task in the field is to determine where these 

boundaries should be. They should be measured and recorded in such a way tha 

they can easily be relocated at different flows. These distances are entered into 

the model as distances across a transect from left bank to right bank, facing 

upstream, so it helps avoid errors to measure them in the same direction. The 

distance of each boundary from the end of the transect must be recorded. In 

addition, a bottom elevation representative of the cell average should be 

measured. In many cases, this representative elevation will be taken near the 

cell’s center (halfway between the boundary points), or the average of the 

elevations at each of the cell’s boundaries could be used. However, if the cell’s 

bottom elevations do not vary gradually or consistently (e.g., if they contain 

large boulders or the thalweg), then the representative bottom elevation may 

need to be measured at some other point. 

Figure 2 —Transect depicting cells 

with uniform depth. Left to right is 

the channel, looking upstream. 

30 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
The following criteria should be used to define cell boundaries: 

• On at least the lowest bank of the river, the first cells should be high 

enough to include some overbank habitat so that the model includes 

refuge habitat when flows are above bank-full. 

• Cell boundaries should be placed wherever there are significant, sudden 

changes in slope, depth, velocity, or substrate type across the transect. 

Where depth, velocity, and substrate type remain fairly uniform across 

the transect, there is no need to put cell boundaries close together—there 

is no recommended upper limit on cell width. 

• Where habitat varies steadily across the transect (e.g., the bed has a 

constant slope so that depth and velocity steadily increase), cell 

boundaries should be relatively close together. 

• Cell boundaries should not be less than about 1 m apart, to avoid 

undesirable boundary effects in the fish model. Cells should ideally be 

wider than 2 m to keep them large compared to the width of stream 

individual fish can search for drifting prey (Section IX.C.2). 

• If there is a well-defined thalweg, or a local elevation peak, it is probably 

best to place the boundary between two cells on it. This way the 

maximum (or minimum) depths and velocities will not be modeled, but 

the averages conditions around them will be represented. 

In the field, we find it useful to stretch a measuring tape across each transect 

then tie short pieces of surveyor’s flagging onto the tape at the boundaries 

between cells. The pieces of flagging are easily moved along the tape as 

alternative cell boundaries are considered. 

VIII.D. Depths and Velocities 

To calibrate the hydraulic model, we need to measure water depths and 

velocities that represent each cell. These measurements should be made at a 

minimum of three different flows. The location where measurements are made 

should be recorded. It is not essential that the representative depth and velocity 

be measured at the same place each time they are measured at different flows, 

but doing so may avoid some potential calibration problems. 

The velocity values should be mean column velocities. At water depths up to 

1 m, velocity can be measured once at 0.6 of the depth below the surface; at 

higher depths, or in highly variable velocities, measurements should be made at 

0.2, 0.6, and 0.8 of the depth and averaged. 

The model bases all velocity-dependent calculations on the velocity’s 

magnitude, not its direction. Therefore, all velocity measurements should be 

made with the meter facing directly into the cell’s local flow direction, even if the 

cell’s flow direction is not perpendicular to the transect. It is important to 

measure the velocity’s magnitude in its prevailing direction; no negative 

velocities should be recorded. (For example, if a cell is in an eddy and its velocity 

is 10 cm/s in the upstream direction, it should be recorded as +10 cm/s.) It does 

not matter if the velocity direction in a cell changes among the several different 

flows used for calibration; the velocity magnitude in its prevailing direction 

should be measured in each case. This practice may make conventional hydraulic 

model “calibration” methods more difficult, but provides a more meaningful 

depiction of stream habitat. (Recording the angle of flow with respect to the 

channel’s direction may help in calibrating the hydraulic model.) 

The following are criteria for determining where to measure depth and 

velocity in habitat cells: 

The overriding criterion is that the depth and velocity measurements need 

to represent the cell’s average conditions. Eddies, obstacles, rocks, etc. 

should be avoided if they appear to cause unrepresentative measurements. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 

VIII. Habitat Data Collection Methods 

31 
VIII. Habitat Data Collection Methods 

• For relatively simple, uniform cells it should suffice to measure depth 

and velocity at one point near the cell’s midpoint. 

• For complex cells, or cells containing a thalweg or local elevation peak, 

it may be best to measure depth and velocity at several places within 

each cell. For example, four measurements could be taken, one in each 

quadrant of the cell. These measurements would be averaged to 

represent the whole cell. 

• For cells that are dry at the time of measurement, it is necessary only to 

measure a representative ground elevation for the cell. 

VIII.E. High-Flow Water Surface Elevations 

For most applications, the individual-based model will need to adequately 

represent hydraulic conditions at flood flows. It is often dangerous and difficult 

to measure the depth and velocity in each cell at high flows. However, calibration 

of such flows can be accomplished adequately by measuring only the water 

surface elevation at each transect. Therefore, water surface elevations (and flow 

rate) should be measured at several high flows, up to and ideally above bankfull 

flow. These measurements are especially important for studies where high flow 

effects on fish and redds are important. 

VIII.F. Spawning Gravel Availability 

The model determines where fish spawn by using a parameter representing 

the percent of each cell’s area that has gravel substrate suitable for spawning. 

This parameter must be estimated in the field, using judgment of what 

constitutes usable spawning substrate. We make no attempt to rate the relative 

suitability of different gravels. These measurements may best be made at low 

flows because the substrate (especially in pockets behind obstacles) is more 

visible. There is no need for this parameter to be estimated to more than one 

significant figure. 

VIII.G.Velocity Shelter Availability 

The model’s formulation to determine the net energetic benefits of feeding 

locations includes the assumption that fish in a velocity shelter have negligible 

energetic costs for swimming. This formulation uses a parameter representing 

the percent of each cell’s area that offers velocity shelter for drift-feeding fish. 

Parameter values will be approximate, as velocity shelter availability cannot be 

measured precisely and varies with fish size and flow rate; estimates should be 

considered accurate to no more than one significant figure. 

The following criteria can be used in estimating how much velocity shelter 

area is available in a cell: 

•Area should be included as having shelter if there is turbulence offering 

the possibility of fish finding a spot with low velocity. All area with 

such possibilities should be included, not just the actual area with very 

low velocities. For example, all areas with large boulder substrate should 

be included. We assume the fish are much better at finding velocity 

shelters in such turbulence than we are. 

•Velocity shelters can be provided by bottom topography and substrate 

as well as by large obstacles in the water column. 

•Adjacent areas of slow water can also provide velocity shelters. A cell 

containing fast water that has an adjacent cell of slow water (e.g., along 

a steep, rough bank) should be considered to have velocity shelter along 

the side of the cell where the horizontal gradient in velocity occurs. (Our 

model assumes that a fish’s cell is where it feeds, not necessarily where 

it shelters while waiting for food.) 

32 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

• Areas where the mean cell velocity is low should not be included as 

velocity shelter. Shelters should be areas where velocities are 

significantly lower than the cell mean. (In the model, velocity shelters 

are unimportant in quiet cells like pools.) This means that a cell with 

very low velocity may provide velocity shelter for fish feeding in an 

adjacent high-velocity cell, but does not have velocity shelter itself. 

• It may be best to measure velocity shelter availability at higher 

calibration flows because the availability of shelter can vary with flow. 

For example, in a pool at low flow there may be no velocity shelter areas 

with velocities substantially less than the cell’s mean velocity because 

that mean velocity is very low; but velocity shelters may appear and be 

important at higher flows. Overestimating the availability of shelter at 

low flows and velocities does not cause major errors in model predictions 

(velocity shelters have little effect on results in cells with low velocity). 

Therefore, it is better to consider conditions under intermediate to high 

flows when evaluating velocity shelters. 

• According to the model’s formulation for metabolic costs, the energetic 

cost of swimming equals and exceeds standard respiration at swimming 

speeds of around 30 cm/s. Hill and Grossman (1993) also found that 

activity respiration was a negligible part of the energy balance at 

velocities at least up to 40 cm/s. Therefore, areas where local velocities 

are less than 30 cm/s clearly offer shelter if their velocities are also 

substantially lower than the mean column velocity. However, because it 

is unlikely that we can find the lowest velocity in a turbulent zone as 

well as a fish can, apparent shelters should not be excluded if we cannot 

measure velocities less than 30 cm/s there. 

VIII.H. Distance to Hiding Cover 

The daily probabilities of avoiding predation depend on the availability of 

hiding cover. The use of hiding cover appears to occur at spatial scales larger 

than our habitat cells: fish can hide using cover several meters away. Therefore, 

we evaluate cover for each cell as the distance (m) from the cell to the nearest 

available hiding cover, whether or not that cover is within the cell. 

Because cells can be fairly big, there will be no single value for the “distance 

to hiding cover” parameter that accurately fits the whole cell. Therefore, we 

estimate this parameter by using the distance from the center of the cell to cover. 

It should not be estimated to more than one significant figure. Values of zero are 

acceptable, for example if the cell has ample wood or undercut banks. 

The kinds of objects providing hiding cover are likely to vary among sites, 

and site-specific observations (especially using radiotelemetry) are useful for 

determining where fish hide. Possible cover types include: 

• Undercut banks and boulders 

• Cavities in the substrate 

• Wood and brush 

• Water that is deep or fast enough to provide concealment. 

IX. Method Details 

This section provides the formulation details for parts of the model that are 

too complicated to be explained in full in the preceding sections. The goal of this 

section is to unambiguously describe the model in sufficient detail for it to be 

implemented in computer code or otherwise reproduced. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 33 
IX. Method Details 

IX.A. Criteria for Day of Spawning 

Trout are assumed to spawn only on days when all of the following criteria 

are met (Section IV.A.1). The order in which these criteria are evaluated does not 

affect model results. These rules for determining when trout are ready to spawn 

force the model to reproduce observed spawning patterns. 

IX.A.1. Date Window 

Salmonids generally have well-defined spawning seasons. This is not 

surprising because time-of-year is an important predictor of factors that are 

critical to successful spawning. For example, early spawning may make eggs and 

fry more vulnerable to cold temperatures or streambed scour from high flows, 

but spawning too late may make offspring more vulnerable to high temperatures 

or reduce their ability to compete with other age 0 fish. We allow fish to spawn 

only on days within a user-specified date window. 

The date windows are input parameters with values estimated from the literature 

and site-specific field observations from the Little Jones Creek study site (table 9). 

June (1981) used redd surveys to estimate the time of spawning in a mixed population 

of anadromous and resident coastal cutthroat in Washington. Spawning was 

observed from mid-January through mid-May, with most redds formed in March. 

The May redds were apparently from resident trout, as anadromous fish were not 

present. Limited spawning observations in Little Jones Creek in 1999 found evidence 

of spawning between early April and late May. 

IX.A.2. Temperature Range 

To match observed behavior, we limit spawning to within a range of daily 

mean temperatures. Conceptually, it makes sense that spawners would use 

temperature as a cue to predict seasonal changes and avoid temperature-induced 

egg mortality (Section IX.E). We define the maximum and minimum 

temperatures for spawning, using parameter values estimated from the literature 

by Van Winkle and others (1996) for rainbow trout (table 10). 

IX.A.3. Flow Limit 

The maximum flow limit implements an assumption that fish will not spawn 

during high flows when the best spawning habitat is likely to be in river margins. 

Spawning during flood flow tends to place the redds at risk of dewatering 

mortality when flows drop. Because this parameter is highly site-specific and 

very difficult to measure, we estimate values for each model site (table 11) . 

Table 9—Parameter values for spawning date window. 

Parameter Definition Units Value 

fishSpawnStartDate Date at which spawning season starts (Day) 4/1 (April 1) 

fishSpawnEndDate Date at which spawning season ends (Day) 5/31 (May 31) 

Table 10—Parameter values for spawning temperature range. 

Parameter Definition Units Value 

fishSpawnMinTemp Minimum temperature at which spawning occurs °C 8 

fishSpawnMaxTemp Maximum temperature at which spawning occurs °C 13 

34 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Table 11—Parameter values for maximum flow for spawning. 

Modeling site Value of fishSpawnMaxFlow (m3/s) 

Little Jones Creek- Lower 4

4

Little Jones Creek- Tributary 2

Little Jones Creek- Upper 

Table 12—Parameter values for age, length, and condition limits on spawning. 

Parameter Definition Units Value 

fishSpawnMinAge Minimum age for spawning females Years1 1.00 

fishSpawnMinLength Minimum length for spawning females cm 12.00 

fishSpawnMinCond Minimum condition factor for spawning 

females none 0.95 

1An integer number of years. 

IX.A.4. Steady Flows 

We assume fish do not spawn when flows are unsteady because flow 

fluctuations place redds at risk of dewatering or scouring mortality. We adopt 

from Van Winkle and others (1996) the criterion that fish spawn only if daily 

flow has changed less than 20 percent from the previous day. We define this 

criterion with the parameter “fishSpawnMaxFlowChange” (unitless), which we 

give a value of 0.20. 

IX.A.5. Female Spawners 

Our model does not track any affect male fish may have on the spawning 

process. Therefore, we conduct the spawning simulations only for female fish. 

IX.A.6. Minimum Length, Age, and Condition 

Because we do not explicitly simulate the bioenergetics of reproduction, we 

use fish length, age, and condition to predict energetic readiness to spawn. 

Minimum values of these characteristics (table 12) are used to ensure that only 

fish with energy reserves comparable to those needed for gonad production can 

actually spawn. Length and condition are the primary indicators of spawning 

readiness as they are related to energy reserves, but the age minimum is useful in 

model runs where fish growth and condition are not well calibrated. Fish cannot 

spawn unless their age is at least equal to the value of the parameter 

fishSpawnMinAge, an integer number of years (following our convention for 

fish ages; Section I.C.4). We use 1 year for this parameter in the Little Jones Creek 

model. (Spawning in age 1 stream trout is rare but can occur.) 

The model’s fish cannot spawn until they attain a length equal to the 

parameter fishSpawnMinLength. (This parameter is also a key variable in the 

“Expected Reproductive Maturity” fitness measure used as a basis of movement 

decisions; Section IV.B.2.) This length is likely to vary among sites. We estimated 

parameter values for the Little Jones sites from site-specific observations and the 

literature. June (1981) observed spawning marks in nine resident coastal cutthroat 

trout and estimated their length at spawning. Five of these fish spawned at age 2, 

at lengths of 12.0 to 14.5 cm. These observations indicate a minimum spawning 

length of about 12 cm. 

A fish’s condition factor (Section IV.C) must exceed the minimum condition 

factor parameter fishSpawnMinCond (unitless). Keeping in mind our nonstandard definition of condition factor (Section IV.C), our growth formulation 

that makes it impossible that condition is equal to 1.0 on any days when fish did 

not obtain at least as much energy as expended for respiration, and that we do 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 35 
IX. Method Details 

not simulate the bioenergetics of reproduction, we assume that fish do not 

spawn unless they have a condition factor near, but not equal, to 1.0. 

IX.A.7. Not Spawned This Season 

We assume trout do not spawn more than once per annual spawning 

season. We give the fish a variable “dateLastSpawned.” If this date differs from 

the current date by a number of days less than the duration of the spawning 

date window, then the fish cannot spawn. When new fish are created, they are 

assigned a value of dateLastSpawned so that this criterion does not prevent any 

fish from spawning once in the first spawning season of a model run. 

IX.B. Spawning Habitat Suitability 

The spawning habitat selection method includes suitability factors for depth 

and velocity (Section IV.A.2). We interpolate a depth suitability factor 

(spawnDepthSuit; unitless) from the values in table 13 . These values provide a 

simplified PHABSIM-type depth criteria curve (fig. 3), estimated from a 

collection of rainbow and brown trout spawning criteria (PG&E 1994). The 

number of points in this suitability relationship is fixed at five. 

A velocity suitability factor (spawnVelocitySuit; unitless) is interpolated from 

the values in table 14, which produces the function shown in figure 4. These values 

were estimated from a collection of brown trout spawning criteria (PG&E 1994). 

The number of points in this relationship is fixed at six. 

Figure 3 —Spawning suitability 

function for depth. 

Table 13—Parameter values for spawning depth suitability. 

Parameter Name Depth (cm) Parameter Name spawnDepthSuit 

fishSpawnDSuitD1 0 fishSpawnDSuitS1 0.0 

fishSpawnDSuitD2 5 fishSpawnDSuitS2 0.0 

fishSpawnDSuitD3 50 fishSpawnDSuitS3 1.0 

fishSpawnDSuitD4 100 fishSpawnDSuitS4 1.0 

fishSpawnDSuitD5 1000 fishSpawnDSuitS5 0.0 

36 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

IX.C. Fish Feeding and Energetics 

The feeding and energetics methods determine the net energy benefits 

(joules of food energy per day available for growth) and growth (grams of fish 

mass per day) a fish would obtain if it were in a specific habitat cell. These 

methods are used both to evaluate potential destinations during movement 

(Section IV.B) and to simulate growth (Section IV.C). 

The energetics methods are a simplified version of widely used fish 

bioenergetics models (Hanson and others 1997). Net food energy benefits of a 

site are equal to the fish’s food intake (a function of food availability, depth and 

velocity, and fish size), minus respiration costs (a function of fish size, 

temperature, and swimming speed). Intake and costs differ between two 

foraging strategies: stationary drift feeding and active searching for food. Food 

availability can be limited by the consumption of food by other fish in a habitat 

cell. We assume fish select the more profitable of these two strategies. This 

approach is modified from that of Van Winkle and others (1996). 

Sections IX.C.1 through IX.C.4 describe input to the net energy intake and 

growth calculations, which are detailed in Section IX.C.5. Parameter estimation 

and calibration for food intake and growth are discussed in Section IX.C.6. 

IX.C.1. Activity Budget 

Energy intake and costs differ between feeding versus resting fish. To avoid 

the need for sub-daily simulations, we parameterize the fish’s daily activity 

schedule. Energetic calculations are based on hourly energy rates (j/h), and the 

daily energy totals depend on how many hours are spent feeding versus resting. 

We simply assume that the modeled fish spend all daylight hours feeding. 

Hill and Grossman (1993) observed that rainbow trout in a small stream spent 98 

Figure 4 —Spawning suitability 

function for velocity. 

Table 14—Parameter values for spawning velocity suitability. 

Parameter Name Velocity (cm/s) Parameter Name spawnVelocitySuit 

fishSpawnVSuitV1 0 fishSpawnVSuitS1 0.0 

fishSpawnVSuitV2 10 fishSpawnVSuitS2 0.0 

fishSpawnVSuitV3 20 fishSpawnVSuitS3 1.0 

fishSpawnVSuitV4 75 fishSpawnVSuitS4 1.0 

fishSpawnVSuitV5 100 fishSpawnVSuitS5 0.0 

fishSpawnVSuitV6 1000 fishSpawnVSuitS6 0.0 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 37 
  

�

IX. Method Details 

percent of daylight (including dusk and dawn) feeding, except that no feeding 

occurred at temperatures below 2 °C. We include 1 hour before sunrise and 

after sunset in the feeding period. Consequently, we calculate the time spent 

feeding as: 

feedTime (h/d) = daylength + 2; if temperature 

< fishMinFeedTemp, then feedTime = 0. 

This assumption is undoubtedly inaccurate for Little Jones Creek, where 

nocturnal activity and diurnal changes in activity have been documented (Harvey 

and others 1999). However, a more detailed depiction of activity budget would 

significantly complicate the model. (A strategy for doing so is outlined in Section 

X.A.4.) At this early stage in model testing we choose to use the simpler 

formulation. 

The input parameter fishMinFeedTemp is a temperature threshold below 

which trout do not feed. Using the observations of Hill and Grossman (1993), we 

use a value of 2 °C for this parameter. Temperatures this low have not been 

observed in Little Jones Creek. 

IX.C.2. Food Intake 

Drift Feeding Strategy—Drift feeding fish wait and capture invertebrates as 

they are carried within range by the current. Our drift feeding energy intake 

formulation is modified and simplified from that of Van Winkle and others 

(1996), which was based largely on the work of Hill and Grossman (1993), 

Hughes (1998), and Hughes and Dill (1990). This literature shows clearly that 

prey items at greater distance from a fish are less likely to be captured, and the 

distance over which fish can capture food increases with trout size and decreases 

with water velocity. Unlike previous models, we include the negative effect of 

turbidity on the distance over which trout can see and capture prey (Barrett and 

others 1992). Turbidity varies dramatically in streams we study, and 

incorporating its effects on trout feeding is fairly straightforward. To avoid 

additional complexity in the model, we currently neglect the effect of prey size on 

capture probability. 

We assume drift-feeding fish capture all food items that pass within a 

“capture area”—a rectangular area perpendicular to the current, the dimensions 

of which depend on depth, velocity, fish size, and temperature. A fish’s intake 

per hour is calculated as the mass of prey passing through the capture area: 

driftIntake (g/h) = habDriftConc (g/cm3) × velocity (cm/s) 

× captureArea(cm2) × 3600 s/h. 

In this equation, habDriftConc is a habitat cell variable (Section III.G.1), and 

captureArea is calculated using a reactive distance approach. 

We use the approach and parameter values of Van Winkle and others (1996) 

to identify a “reactive distance” at which 90 percent of prey items are captured 

(table 15). This equation and its parameters werederived from data reported by 

Hill and Grossman (1993) relating velocity to capture success of rainbow trout: 

reactDistance = fishLength 

 0.9   velocity  ln

1 − 0.9 − fishReactParamA − fishReactParamB fishLength −( fishReactParamC × temperature) 

fishReactParamD 

38 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Table 15—Parameter values for drift feeding reactive distance. 

Parameter Definition Units Value 

fishReactParamA Reactive distance constant none -5.91 

fishReactParamB Reactive distance velocity parameter none 0.847 

fishReactParamC Reactive distance temperature parameter 1/C° -0.0473 

fishReactParamD Reactive distance fish length parameter none 1.74 

fishTurbidMin Turbidity below which reactive distance NTU 5.0 

is unaffected 

fishTurbidParamA Multiplier in equation for turbidity effect NTU-1 -0.0227 

on reactive distance 

fishTurbidParamB Constant in equation for turbidity effect none 1.12 

on reactive distance 

At high velocities (e.g., 50 cm/s for fish 5 cm long; 155 cm/s for 15 cm fish), this 

equation produces negative values for reactDistance. We set such values to zero. 

This formulation has the advantage of being developed from the data of Hill 

and Grossman (1993), who used a wide range of fish lengths (5-12 cm) and velocities 

(between 0 and 40 cm/s) for rainbow trout, which are relatively similar to the 

cutthroat trout we are modeling; it also produces very reasonable results (Section 

IX.C.6). The temperature dependence was determined from data collected at 5 and 

15°C, approximately the range observed in Little Jones Creek. However, the 

approach has several potential limitations. Data were collected at reactive distances 

only up to 2.5 times the fish length were tested, whereas the model predicts reactive 

distances of more than four times the fish length. Because the data of Hill and 

Grossman (1993) were collected using only one size of prey (chironomids, which 

are small), the model may underestimate the distance over which fish capture 

larger prey. The model of Hughes and Dill (1990) has been used in several other 

models (Gowan 1995), but it has the disadvantage of having parameter values 

available only for arctic grayling; cutthroat trout may have significantly different 

swimming ability than grayling. 

Turbidity effects on reactive distance are simulated using the simple model 

developed by Barrett and others (1992) for 9-19 cm rainbow trout. Barrett and 

others (1992) found a somewhat noisy but highly significant linear effect of turbidity 

(NTUs) on reactive distance as a fraction of reactive distance in clear water. This 

relationship is implemented in the model as follows: 

• If turbidity fishTurbidMin(NTU) , then reactDistance is unaffected. 

• If turbidity fishTurbidMin (NTU ), then: 

reactDistance = reactDistance [(turbidity fishTurbidParamA) 

+ fishTurbidParamB] 

• If the resulting value of reactDistance is less than zero, then it is set to zero. 

The parameter values from Barrett and others (1992 ; table 15) cause 

reactDistance to reach zero at a turbidity of 49 NTUs. 

We define the width of the rectangular capture area as twice the reactive 

distance; this implements the assumption that fish are able to capture all drift that 

comes within the reactive distance to their left and right (as they face into the 

current). We compared the width of the capture area calculated by our drift-feeding 

method to the diameter of territories estimated by the field observations assembled 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 39 
  

IX. Method Details 

Figure 5 —Comparison of modelpredicted capture widths and 

observed territory diameters. 

by Grant and Kramer (1990), assuming negligible turbidity. The capture area 

varies with velocity as well as fish size (hence the three lines for velocities of 10, 

20, and 40 cm/s), but in general our model and the territory model of Grant and 

Kramer (1990) are very similar in how much stream width they allocate per fish, 

especially in the range of fish lengths (5-12 cm) used by Hill and Grossman (1993) 

to evaluate their parameters (fig. 5). Gowan (1995) independently developed a 

similar capture area approach. 

We define the height of the capture area to be the minimum of the reactive 

distance and the depth, as we assume fish are more likely to be near the stream 

bottom than at mid-depth when feeding. Our testing of this formulation indicates 

that the reactive distance is typically 3-5 body lengths in velocities of less than 50 

cm/s. Especially in shallow habitat and for large fish, the depth will be less than 

reactive distance. Thus, we must limit the height of the capture area by the depth: 

captureArea = [2 × reactDistance] × [min(reactDistance, depth)] 

Increasing velocities increase the rate at which prey items are carried past a 

fish but decrease the reactive distance. As a consequence, the value of driftIntake 

peaks at intermediate velocities and reaches zero at high velocities (see the graphs 

in Section IX.C.6). 

Active Searching Strategy—Actively searching for benthic or drop-in food is 

an alternative to the drift-feeding strategy. We simulate the food intake from this 

active searching strategy simply as: 

searchIntake = habBenthicProd × fishSearchArea × 

 maxSwimSpeed − velocity ×  maxSwimSpeed  

The value of searchIntake is set to zero if this equation produces a negative 

value. This equation assumes food intake rate for searching fish (searchIntake, g/ 

h) varies linearly with the rate at which search food becomes available to fish 

(habSearchProd, g wet weight/h-cm2; Section III.G.1). The proportionality 

constant (fishSearchArea, cm2

) can be loosely interpreted as the area over which 

the production of stationary (non-drifting) food is consumed by one fish. This 

40 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

search area, however, may not be a contiguous piece of stream area: a small fish 

searching a small area closely may obtain the same food intake as a big fish spotsearching over a much larger area. Because fishSearchArea would be very difficult 

to measure, it is a good parameter to use for calibration. Because we do not make 

searchIntake a function of fish size, except for the effect of size on maxSwimSpeed, 

active searching is more likely to be the desirable strategy for smaller fish. 

This equation also includes a term causing searchIntake to decrease linearly 

with the habitat cell’s mean velocity and reach zero when velocity equals the 

fish’s maximum sustainable swim speed (maxSwimSpeed). The equation for 

maxSwimSpeed is presented in the formulation for high velocity mortality 

(Section IX.D.2). This term is included to decrease the ability of a fish to see and 

search for food as velocity increases. (It does not represent the energetic cost of 

swimming at high velocities, which is considered in the respiration formulation 

in Section IX.C.3.) For habitat velocities above a fish’s maximum swimming 

speed, searchIntake is zero. 

Our estimation of habSearchProd and other growth parameters is discussed in 

Section IX.C.6. 

Maximum Consumption—As part of the net energy intake calculations, we 

check to make sure calculated intake does not exceed the physiological maximum 

daily intake (Cmax, g/d). Field bioenergetics studies (Preall and Ringler 1989, 

Railsback and Rose 1999) indicate that actual food intake does not approach Cmax 

under typical conditions. However, Cmax serves the purpose of restricting intake 

and growth during low temperatures, a function otherwise lacking in the model 

(except that the time spent feeding becomes zero at temperatures below a threshold; 

Section IX.C.1). Cunjak and others (1998) cite evidence that low food assimilation 

efficiencies and gut evacuation rates, which can be represented by Cmax, limit 

energy intake in cold temperature. 

There are a number of published equations for Cmax that include an allometric 

function, relating Cmax to fish size; and a temperature function. We use the 

equation: 

Cmax g ( d) = fishCmaxParamA ×[ fishWeight(g)]

( 1+ fishCmaxParamB) 

× cmaxTempFunction 

with the allometric parameters developed by Rand and others (1993) for rainbow 

trout (table 16 ). 

For the Cmax temperature function, our experience with lab studies indicates 

that only a simple approach is appropriate because Cmax is poorly defined and 

highly variable with fish condition, activity, food type, etc. (Myrick 1998, PG&E 

1997). We use a simplified temperature function (table 17), interpolating values 

between the points estimated from laboratory studies on rainbow trout (Myrick 1998). 

Table 16—Parameter values for allometric function of maximum consumption. 

Parameter Definition Units Value 

fishCmaxParamA Allometric constant in maximum 

intake equation none 0.628 

fishCmaxParamB Allometric exponent in maximum 

intake equation none -0.3 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 41 
IX. Method Details 

Table 17—Parameter values for temperature function of maximum consumption. 

Parameter Name Temperature (°C) Parameter Name maxTempFunction, 

cutthroat trout 

fishCmaxTempT1 0 fishCmaxTempF1 0.05 

fishCmaxTempT2 2 fishCmaxTempF2 0.05 

fishCmaxTempT3 10 fishCmaxTempF3 0.5 

fishCmaxTempT4 22 fishCmaxTempF4 1.0 

fishCmaxTempT5 23 fishCmaxTempF5 0.8 

fishCmaxTempT6 25 fishCmaxTempF6 0.0 

fishCmaxTempT7 100 fishCmaxTempF7 0.0 

Daily Food Availability—In determining the daily food intake rate for fish, 

our feeding formulation uses the total amount of drift (driftDailyCellTotal, g/d) 

and search (searchDailyCellTotal, g/d) food available each day in each cell. 

These daily food availability values are a function of the fish’s feeding time 

because we cannot count food produced during non-feeding hours as available 

to the fish. We obtain the daily food availability rates from the hourly food 

availability rates described in Section III.G.2. 

driftDailyCellTotal (g/d) = driftHourlyCellTotal (g/h)× feedTime(h/d) 

searchDailyCellTotal (g/d) = searchHourlyCellTotal (g/h) 

× feedTime (h/d) 

IX.C.3. Respiration Costs and Use of Velocity Shelters 

Conventional bioenergetics modeling approaches for fish (Hanson and others 

1997) model respiration as the energetic cost of metabolism and swimming. We 

adopt this approach, modeling standard respiration that is independent of the 

fish’s activity and an additional activity respiration that increases with the daily 

swimming speed. 

Swim Speeds —We assume drift-feeding fish swim at a speed equal to their 

habitat cell’s water velocity unless they have access to velocity shelter. Fish using 

the active search feeding strategy are assumed to swim at a speed equal to their 

cell’s mean water velocity. 

If a drift-feeding fish has access to velocity shelter, then we assume its 

swimming respiration is a fraction of its habitat cell’s mean water velocity, 

determined by the input parameter fishShelterSpeedFrac. A number of studies 

have shown that “focal” water velocities (the velocity measured as closely as 

possible to the location of a fish assumed to have been drift-feeding) are related 

to, but less than, the mean column velocity at the same location. For example, we 

plotted focal versus mean column velocity for rainbow trout using data from 

Baltz and Moyle (1984), Baltz and others (1987), and Moyle and Baltz (1985). The 

focal velocity is consistently about 77 percent of the mean column velocity for 

observations made at the microhabitat scale (fig. 6). 

Unfortunately, we are unaware of any studies that relate focal velocity to 

mean water velocities at scales approximating habitat cells in the model. In the 

absence of a reliable way to estimate the daily swimming speed of a trout using 

velocity shelter, we assume a value of 0.3 for the parameter fishShelterSpeedFrac. 

We also use this formulation and parameter in the high velocity mortality 

function (Section IX.D.2). 

42 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Figure 6 —Relation between 

observed focal velocities and 

mean column velocities for trout. 

Velocity Shelter Access—We use the following steps to determine whether 

each fish has access to shelter in a habitat cell: 

• Each cell has a limited area of velocity shelter; this area varies among 

cells but is constant over time (Section III.D). 

• Each drift-feeding fish is assumed to use up an area of velocity shelter 

equal to the square of its length. 

• A fish has access to velocity shelter only if the sum of shelter areas 

occupied by more-dominant fish in a cell is less than the cell’s total 

shelter area. 

We assume each fish uses only a small shelter area (the square of its length) to 

ensure that fish compete with each other for food, not for shelter area, unless 

velocity shelter clearly limits net energy intake. With our approach, fish will 

share velocity shelters in high densities if our movement rules indicate it is 

favorable for them to do so. 

Respiration Cost Model—We adopt the Wisconsin Model equation 1 for 

respiration (Hanson and others 1997), as modified by Van Winkle and others 

(1996), to apply the activity respiration rate only during active feeding hours 

(feedTime). We use the parameters that Rand and others (1993) developed for 

steelhead trout (converted from calories to joules; table 18). This formulation 

breaks respiration into two parts: standard respiration takes place 24 h/d and 

assumes no activity; activity respiration is the energy needed to swim during 

feeding. Total respiration is the sum of these two. Respiration costs are in j/d. 

The equations are: 

respStandard = ( fishRespParamA × fishWeight fishRespParamB ) 

× exp( fishRespParamC × temperature) 

and 

 feedTime  respActivity =  24 

 ×[exp( fishRespParamD × swimSpeed)− 1] 

× respStandard 

where swimSpeed is the fish’s swimming speed (cm/s) during feeding. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 43 
VI. Model Schedules 

Table 18—Parameter values for respiration. 

Parameter Definition Units Value 

fishRespParamA Allometric constant in standard 1(j/d) × g-0.78 30.0 

respiration equation 

fishRespParamB Allometric exponent in standard none 0.784 

respiration equation 

FishRespParamC Temperature coefficient in standard 1/°C 0.0693 

respiration equation 

fishRespParamD Velocity coefficient in activity s/cm 0.03 

respiration equation 

fishShelterSpeedFrac Swim speed reduction for fish using none 0.3 

velocity shelter 

1Empirical parameter with units that depend on fishRespParamB. 

The standard respiration formulation above overestimates the effect of temperature 

on respiration rates and does not account for an observed decrease in respiration at 

temperatures above 22° (Myrick 1998). These problems cannot be fixed by changing 

parameter values, because of the Wisconsin Model equation’s exponential temperature 

function. However, we have been able to make realistic calibrations of growth with 

this function. The decrease in respiration by inactive fish at high temperatures observed 

by Myrick (1998) in laboratory respiration chambers may not be applicable in many 

natural settings. 

IX.C.4. Other Energy Losses 

Most fish bioenergetic formulations include terms for energy losses due to egestion, 

excretion, and specific dynamic action. We do not include these terms because their 

effects are small compared to the large uncertainties in food availability and in the 

bioenergetics formulation and parameter values. These terms may be important at 

extremely low or high temperatures when the ability to digest food can limit growth, 

but we use the Cmax function to limit food consumption at extreme temperatures. 

IX.C.5. Feeding Strategy Selection, Net Energy Benefits, and Growth 

The feeding strategy selection, net energy, and growth methods calculate a fish’s 

daily growth for a specific habitat cell, using the variables described in previous 

sections. Total food intake is calculated and total losses subtracted, determining 

whether drift feeding or active searching is more profitable. Competition among fish 

for food is implemented in these rules and our movement approach, which causes each 

fish’s potential food intake in a cell to be limited by the food consumption of more 

dominant fish in that cell. 

“Food” variables are in grams of prey; “Energy” variables are in joules. Prey 

energy density is used to convert grams of prey eaten to joules of energy; we adopt the 

value of Van Winkle and others (1996) for habPreyEnergyDensity of 2500 j/g. The 

change in fish weight (g/d) is equal to the net energy intake (j/d) divided by the 

energy density of a fish (“fishEnergyDensity,” j/g). We use the energy density of Van 

Winkle and others (1996), 5900 j/g. 

The following steps are used: 

1. Determine the daily drift intake that would be obtained in the absence of more 

dominant fish in the cell. This “dailyPotentialDriftFood” is determined from the 

hourly intake rates and hours spent feeding: 

dailyPotentialDriftFood (g/d) = driftIntake (g/hr) feedTime (h/d). 

44 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
VI. Model Schedules 

2. Determine how much drift intake is really available after more dominant 

fish have consumed their intake: this “dailyAvailableDriftFood” is equal to 

driftDailyCellTotal minus the drift intake of all drift-feeding fish already in 

the cell (Section III.G.2). 

3. Calculate the actual drift intake, considering actual food availability and 

the physiological maximum intake, Cmax: 

dailyDriftFoodIntake = minimumof (dailyPotentialDriftFood, 

dailyAvailableDriftFood,Cmax). 

4. Convert daily drift intake in grams of food to joules of energy: 

dailyDriftEnergyIntake (j/d) = dailyDriftFoodIntake 

× habPreyEnergyDensity (j/g). 

5. Use the bioenergetics equation to get net energy intake for drift feeding, with 

activity respiration dependent on whether the fish has velocity shelter: 

dailyDriftNetEnergy (j/d) = dailyDriftEnergyIntake 

� respStandard � respActivity. 

6. Determine the daily active searching intake that would be obtained in the 

absence of more dominant fish in the cell; “dailyPotentialSearchFood” is 

determined from the hourly intake rates and hours spent feeding: 

dailyPotentialSearchFood (g/d) = searchIntake (g/hr) 

× feedTime (h/d). 

7. Determine how much search intake is really available after more dominant fish 

have consumed their intake: this “dailyAvailableSearchFood” is equal to 

searchDailyCellTotal minus the search intake of all search-feeding fish already 

in the cell (Section III.G.2). 

8. Calculate the actual search intake: 

dailySearchFoodIntake = minimum of (dailyPotentialSearchFood, 

dailyAvailableSearchFood, Cmax). 

9. Convert daily search intake in grams of food to joules of energy: 

dailySearchEnergyIntake (j/d) = dailySearchFoodIntake 

habPreyEnergyDensity (j/g). 

10. Conduct the bioenergetics energy balance to get net energy intake for search 

feeding (no search-feeding fish have velocity shelter): 

dailySearchNetEnergy(j/d) = dailySearchEnergyIntake 

� respStandard � respActivity. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 45 
IX. Method Details 

46 

11. Select the most profitable feeding strategy: 

bestNetEnergy (j/d) = maximum of (dailyDriftNetEnergy, 

dailySearchNetEnergy). 

12. Convert net energy intake to grams of growth: 

dailyGrowth (g/d) = bestNetEnergy / fishEnergyDensity (j/g). 

IX.C.6. Feeding and Growth Calibration 

Because many variables affect growth, it must be calibrated incrementally 

so that reasonable results are likely before trying to calibrate growth in the full 

model, where flow and movement are additional major factors affecting growth. 

We started the calibration process by estimating initial parameter values for the 

food intake and growth formulation after coding it in a spreadsheet. Parameter 

estimation concentrated on adjusting the search and drift food availability 

parameters so that feeding strategies and growth rates met criteria that we 

developed from field observations of habitat use and laboratory growth data. 

For this process, we ignored depletion of food by competing fish. 

We used the following criteria for initial estimates of food intake and 

growth parameters: 

• Daily food intake should be in the range of 20 to 50 percent of Cmax. 

Cmax should rarely if ever limit food intake. This criterion is based on 

field research in which food intake was estimated from observed growth 

and bioenergetics models (Preall and Ringler 1989, Railsback and Rose 

1999). (This criterion may not be valid in unusual situations where food 

is extremely abundant and trout growth rates very high, or at very low 

temperatures where Cmax is very low.) 

• Drift feeding should be more profitable than active search feeding, 

except at low velocities, when turbidity is high, or when benthic prey 

are extremely abundant. Trout are rarely observed feeding only with 

the search strategy; and where both strategies are available, drift feeding 

is probably more often preferred (Nielsen 1992, Nislow and others 

1998). 

• Growth under good conditions (high food intake, low swimming 

velocity) should not exceed growth rates observed in lab studies where 

fish were fed as much as they could eat (Myrick 1998, Myrick and Cech 

1996). These lab growth rates are in the range of 2 to 6 percent of body 

weight per day, varying with temperature. 

We estimated habDriftConc by assuming that, under ideal conditions, a 15 

cm trout can catch food at a rate equal to 50 percent of its Cmax. This assumption 

is based on field evidence that in summer, average trout get 30 to 35 percent of 

Cmax (Railsback and Rose 1999). Under assumed conditions of 15o C, 50 cm/s 

velocity (which provides maximum intake), and a mid-summer feeding time of 

16 h/d, 50 percent of Cmax is 0.19 g of food per hour. Our drift feeding method 

provides this intake when the value of habDriftConc is 2 × 10-10 g/cm3

. 

The value of habDriftRegenDist was estimated by assuming a cell that 

contains 15 cm trout, each having a square territory 150 cm on each side. This 

assumption is based on the observations collected by Grant and Kramer (1990), 

which indicate that 15 cm trout have an average territory diameter of 150 cm. 

Further, we assume that the fish get an intake of 30 percent of Cmax, or 0.13 g/ 

h, and that under these conditions drift food production equals consumption by 

the trout. To provide this level of drift food production, the value of 

habDriftRegenDist must be approximately 500 cm. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

The assumptions used to estimate search intake parameters are a search-feeding 

fish consumes the production of 2 square meters so that the value of fishSearchArea 

is 20,000 cm2; and a 5 cm trout can maintain zero growth by search feeding for 16 h/ 

d at 15° (an intake of 0.006 g/h). These conditions give a value of 3 × 10-7 g/cm2/h 

for habSearchProd. 

These parameter estimates provide the food intake levels (evaluated as the 

fraction of Cmax) and growth (evaluated as percent of body weight per day) shown 

in figures 7-8. For comparison to these parameter estimates, we did not locate any 

published estimates of the rate at which food becomes available, or is eaten by 

trout, at the stream bottom; published estimates of invertebrate production do not 

separate drift from any invertebrates eaten at the benthic surface. The rate at which 

food drops in from overhead (part of our search food production) is also rarely 

measured. Poff and Huryn (1998) report overall food production rates (in Atlantic 

salmon streams) in the range of 4 to 24 g dry weight per m2

 per year, which converts 

to 10 – 60 × 10-7 g/cm2

/h (assuming a typical ratio of 20 for dry:wet weight; Hanson 

and others 1997). Our estimate of habSearchProd appears reasonable compared to 

this value: we would expect habSearchProd to be a relatively small but not 

negligible fraction of the total production rate. 

We show food intake (fig. 7) and growth rates (fig. 8) for 5 and 15 cm trout, as a 

function of cell velocity. For these graphs, the temperature was 15°, depth was 50 cm, 

and feeding time was 16 h/d. Food intake is reported as the percent of Cmax, growth as 

percent body weight per day. 

Figure 7 —Variation in gross 

food intake with velocity for 

two sizes of trout, using drift or 

search feeding. 

Figure 8 —Variation in growth 

rate with velocity for two sizes 

of trout, drift and search 

feeding strategies. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 47 
IX. Method Details 

48 

Several patterns in these results are noteworthy in that they appear to reflect 

observed patterns of trout feeding: 

• Conditions providing high intake do not always provide high growth, 

due to the metabolic costs of swimming (especially for fish drift feeding 

without velocity shelters). 

• The use of velocity shelters for drift feeding is very beneficial. 

• Search feeding is a profitable strategy only for small fish in low 

 velocities. 

• The relative benefits of drift feeding increase with fish size. 

• Larger fish can drift feed profitably over a wider range of velocities, and 

at higher velocities, than can smaller fish. 

Calibration of the full model (Section VII.A) resulted in relatively minor 

changes in value for the parameters habDriftConc (1.5 × 10-10 g/cm 3

 instead of 

the preliminary estimate of 2 × 10-10) and habSearchProd (7 × 10-7 g/cm2/h 

instead of the preliminary estimate of 3 × 10-7). 

IX.D. Fish Survival Probabilities 

The survival probability methods determine the daily probability of a fish 

surviving individual mortality sources, typically as a function of habitat and fish 

size and condition. These methods are used for two purposes: they are used in 

the movement destination rules to evaluate each potential destination site (Section 

IV.B.2), and in survival simulations to determine if and how each fish dies each day 

(Section IV.D). We use the same survival probabilities for each of these purposes, 

assuming that fish are completely aware of actual mortality risks. 

We do not provide a calibration parameter for any risks except the two 

predation risk functions. A calibration parameter lets the user adjust the 

magnitude of the risk without changing how it is related to fish and habitat 

variables. To reduce the number of processes adjusted in calibration, we assume 

that survival probabilities for high temperature, high velocity, stranding, 

spawning, and poor condition are less uncertain than predation and should not 

be used for calibration. 

Users should be aware that seemingly high survival probabilities can result 

in low survival over time. For example, a survival probability of 0.99 results in 

mortality of 26 percent of fish within 30 days (0.9930 = 0.74). Survival probabilities 

should be well above 0.99 if they are not to cause substantial mortality. 

The survival probability formulations make extensive use of logistic 

functions, which are useful for depicting how many survival factors vary 

between 0 and 1 in a nonlinear way. We define these logistic curves by using 

parameters that specify the point at which the logistic function equals 0.1 and 

0.9. (These lower and upper logistic curve dependent variable values of 0.1 and 

0.9 are set via the fish parameters LOWER_LOGISTIC_DEPENDENT and 

UPPER_LOGISTIC_DEPENDENT.) 

We simulate seven mortality sources. Parameter estimation and calibration 

of survival is discussed at Section IX.D.8. 

IX.D.1. High Temperature 

This function represents the failure of physiological processes at high 

temperatures. It does not represent the effect of high temperatures on 

bioenergetics. Because the high temperature survival function is based on 

laboratory data collected (presumably) from disease-free fish, it does not 

represent the effect of disease even though fish are probably more susceptible to 

disease at high temperatures. Instead, we model disease as part of poor condition 

mortality: a fish able to maintain its weight is assumed to remain healthy at 

sublethal high temperatures. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Table 19—Parameter values for high temperature mortality. 

Parameter Definition Units Value 

mortFishHiTT9 Daily mean temperature at which high °C 25.8 

temperature survival is 90 pct 

mortFishHiTT1 Daily mean temperature at which high °C 30.0 

temperature survival is 10 pct 

Figure 9 —Survival probability 

function for high temperatures. 

Although input to the model includes only daily mean temperature, mortality 

is related to the daily maximum as well as the mean (although the relative 

importance of mean vs. maximum temperature is not clear; Dickerson and 

Vinyard 1999, Hokanson and others 1977). The survival probability function 

therefore includes an assumed difference between mean and peak temperatures. 

The temperature mortality parameters could be re-evaluated for sites with 

particularly high or low diurnal temperature variations. 

Because high temperature mortality is poorly known and variable (especially 

in relation to daily mean temperatures), we use a decreasing logistic equation 

defined by the temperatures where this survival probability is equal to 0.9 and 

0.1. Lethal temperatures appear similar among trout species (Behnke 1992). 

Recent laboratory data showed approximately 60 percent survival of golden 

trout (O. mykiss) juveniles over a 30-d period at a constant 24° (Myrick 1998), 

equivalent to a daily survival of 0.98. Dickerson and Vinyard (1999) measured 

survival of Lahontan cutthroat trout for 7 d at high temperatures, finding zero 

survival at 28°, 40 percent survival at 26° (equivalent to daily survival of 0.88), 

and 100 percent survival at 24°. Considering this literature and the low diurnal 

variation in temperature at our study sites, we fit parameters to provide survival 

of 0.98 at 24°, 0.88 at 26°, and < 0.5 at 28° (fig. 9; table 19). Lethal temperatures 

have not been observed at the Little Jones study sites. 

IX.D.2. High Velocity 

The high velocity survival function represents the potential for trout to suffer 

fatigue or lose their ability to hold position in a cell with high velocity. This 

function is included not because we expect it to kill fish often, but because it is a 

significant factor affecting fitness. Mortality caused by high velocities is not 

observed in nature because fish avoid them via movement. However, we must 

include this risk to cause such movement to occur in the model. Velocities posing 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 49 
IX. Method Details 

mortality risk are widespread at high flows. Our feeding model (Section IX.C.6) 

predicts that growth rates become negative at water velocities just below the 

onset of high velocity risk. 

The survival probability is based on the ratio of the swimming speed required 

to remain in a cell to a fish’s maximum sustainable swim speed, a function of fish 

size. Larger fish are better able to resist higher velocities than smaller fish are. We 

determine a fish’s swimming speed the same way we do for calculating 

respiration energy costs (Section IX.C.3). Fish are assumed to swim at the cell’s 

water velocity unless they are drift-feeding with access to velocity shelters. Fish 

using velocity shelters are assumed to swim at a speed equal to the cell’s velocity 

times the parameter fishShelterSpeedFrac. 

First, we estimate the fish’s maximum sustainable swim speed 

(maxSwimSpeed). As used in our model with its daily time step, this variable 

should be a speed that fish can swim for hours, not a burst or short-term maximum 

speed. Myrick (1998) measured “critical swimming speed,” a high estimate of 

sustainable speed; Myrick cites references indicating that trout may start to use white 

(fast-twitch) muscle fibers at 90 to 95 percent of the standard critical swimming 

speed. A better estimate of the speed fish can sustain for long periods is 90 percent of 

the critical speed (Myrick, personal communication). Myrick (1998) measured critical 

swim speed at temperatures between 10 and 19°C for four strains of O. mykiss.; he 

also cites other studies in which critical swimming speed has been measured for O. 

mykiss and cutthroat trout at similar temperatures. These measurements are subject 

to a number of potential errors, including that laboratory fish may not be in good 

exercise condition. These data show a lack of temperature dependence and good 

correspondence among studies (fig. 10). 

Griffiths and Alderdice (1972) made extensive measurements of swimming 

speed over temperatures between 2 and 26°C for juvenile coho salmon. These 

were the basis of the swimming speed model of Stewart (1980), which was also 

adopted in the individual-based model of Van Winkle and others (1996). These 

measurements showed gradual increase in sustainable swimming speed as 

temperature increased from 2 to about 20°, approximately doubling over this 

range. Swimming performance dropped off sharply at temperatures above about 

20°. However, the data presented by Griffiths and Alderdice (1972) do not allow 

the effect of fish length to be separated from temperature effects. It seems 

reasonable to conclude from all the evidence that temperature has a relatively 

small effect on sustainable swimming speed except at temperatures approaching 

a fish’s physiological tolerance limits. The model used by Van Winkle and others 

(1996) estimates swim speeds well above the critical swim speed measurements. 

Figure 10 —Observed critical swim 

speeds. 

50 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

We use a maximum sustainable swim speed equation that is a simple linear 

function of fish length: 

maxSwimSpeed = [fishSwimParamA fishLength] 

+ fishSwimParamB. 

It assumes sustainable swim speeds are 0.9 times the measured critical swim 

speeds, using linear regression on the data in figure 10 (excluding the outlier at 

fish length of 30.8 cm and critical speed of 54 cm/s). The predicted sustainable 

swim speeds for trout of 4, 10, and 30 cm length are 40, 51, and 88 cm/s. 

A decreasing logistic function relates survival probability to the habitat cell 

velocity divided by the fish’s maximum swim speed (fig. 11). The parameters for 

this function (table 20) are chosen so that high velocity mortality is negligible at 

cell velocities less than maxSwimSpeed, reflecting that the laboratory apparatus 

for measuring swim speeds does not have the kinds of turbulence and fine-scale 

velocity breaks that trout can use to swim at speeds less than the cell mean and 

that stream fish are likely to be in better condition than laboratory fish. 

Table 20—Parameter values for high velocity mortality. 

Parameter Definition Units Value 

fishSwimParamA 

fishSwimParamB 

mortFishVelocityV9 

mortFishVelocityV1 

Length coefficient in maximum swim 

speed equation 

Constant in maximum swim speed 

equation 

Ratio of mean column velocity to 

maximum swim speed at which high 

velocity survival is 90 pct 

Ratio of mean column velocity to 

aximum swim speed at which high 

velocity survival is 10 pct 

1/s 1.83 

cm/s 33.00 

none 1.4 

none 1.8 

Figure 11 —Survival probability 

function for high velocity. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 51 
IX. Method Details 

IX.D.3. Stranding 

We include a stranding survival probability factor to represent mortality 

of fish that are unable to move away from very low depths as flows decrease. 

Our movement rules provide a very strong incentive for fish to move from a 

cell that has zero depth, but there may be cases where a fish is limited by its 

maximum movement distance from reaching a cell with non-zero depth or no 

better habitat is available for other reasons. Our formulation was not designed 

for evaluation of stranding mortality from rapidly varying flows, as our time 

step of 1 day is too large. 

Our formulation makes survival of stranding an increasing logistic function 

of depth divided by fish length (fig. 12; table 21). Because our terrestrial predation 

function does not represent the greatly increased likelihood of predation 

mortality when depth is extremely low (Harvey and Stewart 1991), we include 

this risk as part of stranding mortality. The stranding survival function does not 

distinguish whether fish in very low or zero depths die from the lack of water or 

by predation. 

Our parameters do not cause survival to reach zero when depth is zero, 

reflecting that real habitat (as opposed to the model’s cells) has variation in 

bottom elevation—some water could remain even if a cell’s average depth 

becomes zero. Depth is divided by fish length to scale how the risks of low 

depths vary with fish size: shallow habitat that may be very valuable for 

small fish (protecting them from aquatic predation) may pose a stranding risk 

for large fish. 

IX.D.4. Spawning 

We adopt the approach of Van Winkle and others (1996) for modeling spawning 

mortality. On the day a female fish spawns, its spawning survival is equal to the 

input parameter mortFishSpawn. Otherwise, spawning survival is 1.0. 

Figure 12 —Survival probability 

function for stranding. 

Table 21—Parameter values for stranding mortality. 

Parameter Definition Units Value 

mortFishStrandD1 Ratio of depth to fish length at 

which stranding survival is 10 pct none -0.3 

mortFishStrandD9 Ratio of depth at which stranding 

survival is 90 pct none 0.3 

52 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

We found few data that address mortFishSpawn. Stearley (1992) states that 

survival of spawning for anadromous populations of cutthroat trout is 40 to 50 

percent, higher than the 5 to 40 percent survival estimated for steelhead. In the 

absence of spawning survival estimates for resident cutthroat trout, we use a 

value of 0.9. 

This approach only inflicts spawning mortality on females, since we do not 

keep track of which males spawn (Section IV.A). Therefore, caution should be 

applied if spawning mortality is used to calibrate the abundance of large adults. 

(If there is evidence that spawning mortality in males is important to model 

accuracy, it could be simulated by identifying a large male near the spawning site 

and imposing mortality on it.) 

IX.D.5. Poor Condition 

Fish in poor condition (low weight in relation to length) probably suffer 

higher mortality risks from starvation, disease, and predators. (We assume the 

separate predation mortality applies to healthy fish.) 

We use an increasing logistic function to represent survival probability as a 

function of condition (fig. 13; table 22). Parameters were selected to reflect that 

disease can occur (though is less likely) when condition is relatively good and 

our non-standard definition of condition factor (Section IV.C) that has a 

maximum of 1.0. These parameters result in a 4 percent probability of surviving 

for 30 days when condition is 0.6, a 50 percent probability when condition is 0.7, 

and 96 percent probability when condition is 0.9. 

In evaluating the condition-based survival parameters, it must be taken into 

consideration that these are daily survival probabilities and low condition factors 

are likely to persist for a number of days. Even apparently high survival values 

(e.g., 0.90) will result in a low chance of survival until weight can be regained. 

Figure 13 —Survival probability 

function for poor condition. 

Table 22—Parameter values for poor condition mortality. 

Parameter Definition Units Value 

mortFishConditionK1 Fish condition factor at which 

survival is 10 pct none 0.3 

mortFishConditionK9 Fish condition factor at which 

survival is 90 pct none 0.6 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 53 
IX. Method Details 

54 

IX.D.6. Terrestrial Predation 

Terrestrial predators are birds and mammals. Our formulation is designed to 

represent predation by a mix of such predators as otters, raccoons, snakes, 

herons, mergansers, kingfishers, and dippers. Characteristics of terrestrial 

predators affecting the survival probability function include that they are 

generally bigger than the trout, poorer swimmers than adult trout, warmblooded, and locate fish prey from the air. These characteristics vary among 

predators, but they lead to these generalizations about terrestrial predation: big 

trout are vulnerable, risks are year-round, and the ability to detect prey from the 

air is important to predator success. 

Our formulation assumes a minimum survival probability that applies when 

fish are most vulnerable to terrestrial predation and a number of “survival 

increase factors” that can increase the probability of survival above this 

minimum. We model survival increase factors as functions with values between 

zero and one, with higher values for greater protection from predation. Because 

we assume the survival increase factors act independently, we obtain the 

terrestrial predation survival by increasing the minimum survival (decreasing 

the difference between minimum survival and 1.0) by the maximum of the independent 

survival increase factors. This assumption is expressed mathematically as: 

terrPredSurv = mortFishTerrPredMin 

+ [(1–mortFishTerrPredMin) max 

(terrPredDepthF, terrPredTurbidityF, 

terrPredLengthF...)]. 

Using the maximum survival increase factor has several important numerical 

advantages over the alternative of multiplying all the survival increase factors 

together to adjust the overall predation risk. If we used the alternative of 

multiplying all the survival increase factors together, then the value of 

terrPredSurv could be several orders of magnitude less than the value of 

mortFishTerrPredMin, the input and calibration parameter; and the magnitude 

of terrPredSurv could be overly sensitive to small changes in a fish’s condition. 

These characteristics would make results difficult to understand and calibrate. 

Also, multiplying the survival increase factors together would make the value of 

terrPredSurv a function of the number of survival increase factors as well as the 

value of these factors; as a result, adding or removing a survival increase factor 

could significantly alter fish abundance and require re-calibration of predation 

survival. By using our approach, survival increase factors can be added or 

removed, and they will not make order-of-magnitude changes in the overall 

predation survival rate. 

The value of mortFishTerrPredMin is assumed to be the daily probability of 

surviving terrestrial predation under conditions where the survival increase 

factors are minimal (offering no reduction in risk). Because field data for 

estimating this minimum survival are unlikely to be available, we recommend 

estimating it by calibrating the model to observed abundance and habitat use 

patterns. The magnitude of this mortality source can vary with site conditions: 

e.g., rivers that have open, exposed banks are expected to have higher terrestrial 

predation rates. Before calibration, we assumed a value of 0.95 for 

mortFishTerrPredMin. Calibration of the full model (Section VII.A) resulted in a 

value of 0.99. 

Our model parameter values for terrestrial predation mortality include seven 

survival increase factors (table 23). These factors may vary among sites. 

Additional factors may be needed in some situations. (The effect of any factor 

can be turned off by setting its parameters to yield a constant value of zero.) 

Depth—Fish are more vulnerable to terrestrial predators when in shallow 

water (Harvey and Stewart 1991) likely because they are easier for predators to 

locate and catch. We model the depth survival increase factor as an increasing 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Table 23—Parameter values for terrestrial predation mortality. 

Parameter Definition Units Value 

mortFishTerrPredMin Daily survival probability due to none 0.99 

terrestrial predators under most (calibration 

vulnerable conditions (calibration value) 

constant) 

mortFishTerrPredD1 Depth at which survival is 10 pct cm 5 

of maximum 

mortFishTerrPredD9 Depth at which survival is 90 pct of cm 100 

maximum 

mortFishTerrPredL9 Fish length at which survival is 90 pct cm 3 

of maximum 

mortFishTerrPredL1 Fish length at which survival is 10 pct cm 6 

of maximum 

mortFishTerrPredF9 Feeding time with survival 90 pct of h 0 

maximum 

mortFishTerrPredF1 Feeding time at which survival is 10 h 18 

pct of maximum 

mortFishTerrPredV1 Velocity at which survival is 10 pct cm/s 20 

of maximum 

mortFishTerrPredV9 Velocity at which survival is 90 pct cm/s 100 

of maximum 

mortFishTerrPredH9 Distance to hiding cover at which cm -100 

survival is 90 pct of maximum 

mortFishTerrPredH1 Distance to hiding cover at which cm 500 

survival is 10 pct of maximum 

mortFishTerrPredT1 Turbidity with survival 10 pct of NTU 10 

maximum 

mortFishTerrPredT9 Turbidity with survival 90 pct of NTU 50 

maximum 

Figure 14 —Depth function for 

terrestrial predation mortality. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 55 
IX. Method Details 

logistic function: survival increases as depth increases (fig. 14). Power (1987) 

indicates that predation by birds is low at depths above 20 cm, although predators 

that are larger or better swimmers (herons, mergansers, otters) are likely effective 

at greater depths. (The very high risk of terrestrial predation that occurs when 

fish are in near-zero depths is included in stranding mortality; Section IX.D.3.) 

Turbidity—Turbidity makes fish less visible to terrestrial predators and, 

because detection from the air is key to terrestrial predation success, is assumed 

to be an important survival increase factor. We located no direct literature 

directly relating terrestrial predation to turbidity. Instead, we consider the 

observed effect of turbidity on the ability of fish to detect prey (Barrett and others 

1992, Vogel and Beauchamp 1999; Section IX.C.2), which shows the ability to 

detect drifting invertebrates unaffected at turbidities of 5 NTUs but declining to 

zero at 50 NTUs. Fish are likely more visible than invertebrates because of their 

size, but terrestrial predators must observe prey through greater lengths of water 

than must fish predators. We therefore assume that turbidity has little effect at 

values below 5 NTUs but reduces terrestrial predation risk almost completely at 

50 NTUs (fig. 15). 

Fish Length—Small fish are less vulnerable to terrestrial predation, 

presumably because they are less visible (Power 1987), less desirable, and 

possibly more difficult to capture than larger fish. However, because dippers 

(Cinclus mexicanus) prey on trout fry and other small fish (Thut 1970), very small 

fish are not invulnerable to terrestrial predation. We model decreasing survival 

of risk from terrestrial predators with fish length as a decreasing logistic function, 

with fish less than 4 cm in length being relatively protected (fig. 16). 

Figure 15 —Turbidity function 

for terrestrial predation mortality. 

Figure 16 —Fish length function 

for terrestrial predation mortality. 

56 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Feeding Time—Fish are assumed more vulnerable to predation when they 

are actively feeding instead of resting and hiding. (This factor is not designed to 

reflect how predation pressure changes diurnally; we assume terrestrial 

predators are present during both the day and night.) However, we assume a 

low level of predation can occur when fish are not feeding. We model the 

survival increase factor as a decreasing function of “feedTime” (h), a variable 

also used in calculating energy intake (Section IX.C.1). Parameters are chosen so 

that survival decreases nearly linearly with feedTime (fig. 17) . 

Velocity —We include a function that increases terrestrial predation survival 

as water velocity increases. This function is based on the assumption that 

predators are less able to see and capture fish in turbulent water. 

We model the survival increase factor as an increasing logistic function that 

provides nearly complete protection from terrestrial predators at velocities above 

100 cm/s (fig. 18). 

Temperature—We do not include a temperature-based survival increase 

factor because there are no clear mechanisms that would cause predation 

pressure to change with temperature. At our study sites, ice cover does not 

provide protection from predation in winter. There is not a good basis for 

assuming predator activity is lower in winter; most of the predators we represent 

are warm-blooded and do not hibernate. In fact, such predators need additional 

food to maintain their metabolic needs in winter. 

Figure 17 —Feeding time 

function for terrestrial 

predation mortality. 

Figure 18 —Velocity function for 

terrestrial predation mortality. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 57 
IX. Method Details 

Figure 19 —Distance to hiding 

cover function for terrestrial 

predation mortality. 

Distance to Hiding Cover —Fish can avoid mortality by hiding when 

predators are detected. The success of this tactic depends on the presence of 

hiding cover and the distance the fish must travel to reach it. The value of hiding 

cover is one habitat function that clearly occurs at a spatial scale different from 

our cell size; hiding cover several meters from a fish can provide at least some 

predation protection. 

We model a distance-to-hiding survival increase factor using field estimates 

of the distance from the center of the cell to hiding cover for adult fish (Section 

VIII.H). This increase factor reflects the importance of nearby cover; at the Little 

Jones study sites there is sufficient cover so that all fish can hide within 10-20 m. 

We assume that very short distances to cover (< 1 m) provide nearly complete 

protection from some predators, but do not protect fish from predators that strike 

very quickly (e.g., some birds) or that could be able to extract trout from hiding 

(e.g., otters). Cover several meters away is still valuable for escaping from 

terrestrial predators that have been detected. Therefore, we model distance-tohiding survival increase as a decreasing logistic function of the habitat input 

variable for distance to hiding cover (fig. 19). 

IX.D.7. Aquatic Predation 

Our aquatic predation formulation assumes that this risk results from adult 

trout, the only predator fish in our Little Jones Creek sites. Therefore, only 

juvenile trout are vulnerable to aquatic predation. We simulate the effect of adult 

trout density on aquatic predation risks, making this survival probability the 

only one with direct density dependence. 

The risk of predation by adult trout is generally highest for small fish in 

deeper water (Power 1987). As with terrestrial predation, we assume a minimum 

survival probability that applies when fish are most vulnerable to aquatic 

predation, and define a number of survival increase factors: 

aqPredSurv = mortFishAqPredMin 

+ [(1–mortFishAqPredMin) 

max(aqPredDepthF, aqPredLengthF, aqPredVelF ...)]. 

The value of mortFishAqPredMin (unitless) is assumed to be the daily 

probability of surviving aquatic predation under conditions where the survival 

increase factors offer no reduction in risk. As with terrestrial predation, because 

58 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

data for directly estimating aquatic risks are unlikely to be available, we 

recommend estimating mortFishAqPredMin by calibrating the model to 

observed abundance and patterns of habitat selection by juvenile fish. 

Diet data from the Little Jones Creek sites indicate that cannibalism by 

cutthroat trout occurs at a low rate: fewer than 1 percent of adult fish contained 

juveniles. However, even this low rate results in a significant mortality risk: 10 

adults catching fish on 1 percent of days results in 37 mortalities per year. The 

risk of predation also appears to be an important factor driving habitat selection 

(Brown and Moyle 1991): avoiding predation is likely a key reason why small 

fish prefer shallow water. In this section, we use a preliminary value of 0.95 for 

mortFishAqPredMin (Section IX.D.8). Calibration of the full model (Section 

VII.A) resulted in a value of 0.997. 

We do not include a factor for distance to hiding cover in computation of the 

risk from aquatic predators, as we do for risk from terrestrial predators (Section 

IX.D.6). This decision was made because only small trout are vulnerable to 

aquatic predators, and we assume small trout are capable of hiding almost 

anywhere in the complex substrate of our study sites. 

We include a survival increase factor for turbidity that is based on the 

experimental observations and citations provided by Gregory and Levings (1999). 

Turbidity appears to reduce the ability of piscivorous fish to detect prey fish and 

thus the encounter rate between predator and prey (Gregory and Levings 1999, 

Vogel and Beauchamp 1999). One mechanism that can offset this reduced encounter 

rate is that turbidity also reduces the vulnerability of adult trout to terrestrial 

predation, making them more likely to forage in shallow habitat where small fish are 

likely to be found (Section IX.D.6; Vogel and Beauchamp 1999). 

Our aquatic predation survival formulation includes six survival increase 

factors, and several parameter values were used (table 24). 

Table 24—Parameter values for aquatic predation mortality. 

Parameter Definition Units Value 

mortFishAqPredMin Daily survival probability due to aquatic 

mortFishAqPredP9 

mortFishAqPredP1 

mortFishAqPredD9 

mortFishAqPredD1 

mortFishAqPredL1 

mortFishAqPredL9 

mortFishAqPredF9 

mortFishAqPredF1 

mortFishAqPredT9 

mortFishAqPredT1 

mortFishAqPredU9 

mortFishAqPredU1 

predators under most vulnerable conditions

(calibration constant)

Predator density at which survival is 90 pct

of maximum

Predator density at which survival is 10 pct

of maximum

Depth at which survival is 90 pct of maximum

Depth at which survival is 10 pct of maximum

Fish length with survival 10 pct of maximum

Fish length with survival 90 pct of maximum

Feeding time with survival 90 pct of maximum

Feeding time with survival 10 pct of maximum

Temperature with survival 90 pct of maximum

Temperature with survival 10 pct of maximum

Turbidity at which survival is 90 pct of

maximum

Turbidity at which survival is 10 pct of

maximum

none 0.997 

(calibration 

value) 

cm-1 0.0005 

cm-1 0.004 

cm 10 

cm 20 

cm 4 

cm 8 

h 0 

h 18 

°C 2 

°C 6 

NTU 80 

NTU 5 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 59 
IX. Method Details 

Predator Density—The only aquatic predators in our Little Jones Creek sites 

are large trout. Considering observed predator–prey size ratios for salmonids 

(Amundsen and others 1995) and the size distribution of cutthroat trout in Little 

Jones Creek, we assume all trout age 2 are potential cannibals. (Compared to 

the alternative assumption of specifying a length at which trout become 

piscivorous, using age as the criterion makes the computer implementation 

easier and provides a buffer against effects of poorly calibrated growth rates.) 

The trout model tracks the abundance of trout ≥ age 2, allowing us to 

simulate the effect of predator density on survival probability. Post and others 

(1998) measured the mortality of tethered juvenile trout due to predation by 

adult trout in lakes. This study showed the risk to increase exponentially with 

adult trout density, rising very sharply between 8 and 10 predators per 1,000 m3

. 

This result supports a logistic-like relation between adult trout density and 

juvenile trout survival probability, but is not directly applicable because it was 

obtained in lakes where cover and other habitat complexities may mediate the 

effect of predator density, and because risks were evaluated over 1 hour periods, 

whereas our model uses a daily time step. 

There are three options for representing the density of predators: the total 

number of piscivores in the model reach, the number of piscivores per unit 

stream area, and the number of piscivores per unit stream length. The first 

alternative would make the survival function parameters highly site-dependent 

because the probability of piscivorous fish encountering prey becomes a function 

of the length of the reach being modeled. It is not clear whether the second or 

third alternative best reflects the mechanisms of piscivory; if we assume prey are 

likely to be in the stream margin habitat (where they are typically observed), then 

the number of predators per length of stream may be the best representation. The 

second option requires the minor computational burden of calculating stream 

area as it varies daily with flow. 

We model the survival increase factor for adult trout density using a 

decreasing logistic function of the number of age 2+ trout per cm of stream length 

(fig. 20). (We use trout numbers per cm to maintain our units conventions; Section 

I.C.1.) Parameters were chosen to reflect near-zero risk when predator density is 

zero and a steep decline in survival as predator density exceeds one adult trout 

per 6 to 8 m of stream length. These parameters should be re-evaluated for new 

modeling sites, considering stream width and the extent of shallow habitat. 

Figure 20 —Predator density 

function for aquatic predation 

mortality. 

60 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Model users should be aware that this survival increase factor eliminates 

aquatic predation risk if the model is run with no adult trout, and the absence of 

this risk can have a major effect on juvenile trout habitat selection. It should also 

be noted that the dependence of aquatic predation survival on the density of 

trout age 2 means this survival probability may decrease suddenly on January 

1, when the age of all fish is incremented; Section I.C.4. 

Depth—Aquatic predation is assumed to be low in water shallow enough to 

exclude large fish. We model the depth survival increase factor as a decreasing 

logistic function, with protection provided at depths less than 15 cm (fig. 21). 

Fish Length—Large fish are less vulnerable to aquatic predation because 

they can out-swim predators and because piscivorous cutthroat trout are unable 

to swallow large prey. The length survival increase factor is an increasing logistic 

function, with fish greater than 10 cm being very unlikely to be eaten by trout 

(fig. 22). Our parameter values reflect the relatively small size of the predators at 

our study site. Models of sites with larger predators should reflect the 

corresponding vulnerability of larger trout. 

Figure 21 —Depth function for 

aquatic predation mortality. 

Figure 22 —Fish length function 

for aquatic predation mortality. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 61 
IX. Method Details 

Feeding Time —This survival increase factor is the same for aquatic 

predation as it is for terrestrial predation. The survival increase is a decreasing 

logistic function of “feedTime,” the number of hours per day spent foraging. 

Low Temperature—This survival increase factor reflects how low temperatures 

reduce the feeding activity of predatory fish and therefore reduce predation 

pressure. We base this factor on the bioenergetics of the trout predators, using a 

decreasing logistic function (fig. 23) that approximates the decline in maximum 

food consumption (Cmax) with declining temperature (Section IX.C.2). 

We neglect the decline in aquatic predation risk that results from high 

temperatures; such a decline would result from predatory trout not feeding at 

extremely high temperatures. 

Turbidity—The turbidity factor represents how encounter rates between 

predator and prey fish decline as turbidity increases. In an experiment using 

tethered juvenile salmonids, Gregory and Levings (1999) observed predation 

rates two to three times higher in turbid habitat (27 to 108 NTUs) than in habitat 

where turbidity was negligible. Predation was reduced by not eliminated in 

turbid habitat. We estimated parameters that provide no protection from aquatic 

predation at low turbidities and a 50 percent reduction in risk at 40 NTUs (fig. 

24). As turbidity continues to increase toward extreme values, aquatic predation 

risk continues to decrease but is not eliminated. 

Figure 23 —Temperature function 

for aquatic predation mortality. 

Figure 24 —Turbidity function 

for aquatic predation mortality. 

62 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

IX.D.8. Total Survival: Parameter Estimation and Effects of Fish Size, 

Depth, and Velocity 

The total survival probability for a fish is calculated by multiplying together 

the probabilities of surviving separate mortality risks. Figures 25-28 illustrate 

the variation in total survival with fish size, depth, and velocity. They were 

created by plotting the total daily survival probability for four sizes of trout 

that all have a condition factor of 1.0, are at a temperature of 15°, feed for 16 h/ 

d, have a minimum survival probability for both terrestrial and aquatic 

predation (fishTerrPredMin, fishAqPredMin) of 0.95, and have the values for 

other parameters. Turbidity, distance to hiding cover, and adult trout density 

were assumed to have no effect on survival. The daily survival is shown on a 

scale of 0.8 to 1.0 because survival probabilities below 0.8 result in very high 

mortality over several days. 

The 3 cm trout (fig. 25) are vulnerable mainly to aquatic predators, and the 

10 (fig. 27) and 20 cm (fig. 28) trout are vulnerable mainly to terrestrial predators. 

The 5 cm trout (fig. 26) are vulnerable to both categories of predators. 

Survival rates in the modeled trout populations are not only a function of 

the survival probability formulation and parameters but also of the feeding 

and growth formulation and food availability. Food intake affects poor 

condition mortality and habitat selection; and because survival probabilities 

vary with habitat, habitat selection has a major effect on a fish’s survival. As 

a consequence, little parameter estimation can be conducted prior to 

calibration in the full model. 

Our approach to parameter fitting and calibration is to assume most of 

the uncertainty in the survival formulation is in the two base predation 

parameters (mortFishTerrPredMin and mortFishAqPredMin) and use only 

these two for calibration, and define the following criteria for calibrating 

survival in the full model: 

• When adult trout diet data are available, predicted aquatic predation 

mortality should match observed rates. 

Figure 25 —Total survivial 

probablity as a funciton of depth 

and velocity, 3 cm trout. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 63 
IX. Method Details 

•� The calibrated model should reproduce observed patterns of habitat 

use. Preferences for depth and velocity have been documented to vary 

with fish size, season, and competition. 

• The formulation should produce age-specific survival rates that 

reproduce observed age distributions. 

• The overall survival rate should be reasonably closed to observed 

survival rates. Calibration may be easier for time periods when habitat 

conditions are relatively stable. 

Figure 26 —Total survival 

probablity as a function of depth 

and velocity, 5 cm trout. 

Figure 27 —Total survival 

probablity as a function of depth 

and velocity, 10 cm trout. 

64 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

Figure 28 —Total survival 

probablity as a function of depth 

and velocity, 20 cm trout. 

IX.E. Redd Survival Functions 

The redd survival methods simulate each mortality source. For each such 

source, a survival function determines the daily fraction of eggs surviving (Section 

V.A). These fractions are each multiplied by the number of eggs remaining in a redd 

to calculate a new number of surviving eggs. 

We do not currently have a redd survival function related to spawning 

gravel quality. Although spawning gravel quality has several effects on redd 

success (Kondolf 2000), we currently choose not to simulate these effects to avoid 

additional complexity and data requirements. Our spawning site selection criteria 

(Section IV.A.2) allow a fish to spawn in a cell that has little or no gravel; we inflict no 

redd mortality penalty for doing so. The exception is that if superimposition occurs 

in a cell with little spawning gravel (which seems unlikely unless gravel is very 

rare), then superimposition mortality is likely to be high. In Little Jones Creek, 

spawning gravel appears abundant. 

IX.E.1. Dewatering 

Reiser and White (1983) did not observe significant mortality of eggs when 

water levels were reduced to 10 cm below the egg pocket for several weeks. 

However, they also cited literature indicating high mortality when eggs and 

alevins are only slightly submerged (which may yield poorer chemical conditions 

than being dewatered) and high mortality for dewatered alevins. Because we do 

not distinguish between eggs and alevins, we do not model these processes 

mechanistically or in detail. We simply assume that, if depth is zero, then the daily 

fraction of eggs surviving is equal to the input parameter “mortReddDewaterSurv.” 

We use a value of 0.9 for this parameter. 

For study sites where dewatering of redds is an important management 

issue, this formulation could be expanded to model the effects of dewatering and 

low velocities on eggs and alevins in more detail. 

IX.E.2. Scouring and Deposition 

Scouring and deposition mortality results from high flows disturbing the 

gravel containing a redd. Deposition of new gravel on top of a redd may make 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 65 
IX. Method Details 

water flow through the redd inadequate to transport oxygen and waste materials 

or may prevent alevins from emerging. 

This redd mortality source can be very important to trout populations. 

There is a fitness benefit to spawning early: offspring emerge earlier and have a 

competitive advantage over young-of-year fish that emerge later. However, this 

benefit is to some extent offset by greater risk of redds being scoured in streams 

(including Little Jones Creek) where high flows occur in winter and spring. 

There are methods for predicting the potential for scouring mechanistically 

as a function of shear stress and substrate particle size, but geologists now 

understand that scour and deposition at the scale of individual redds are highly 

stochastic processes. At least in gravel-bed streams like Little Jones Creek, it is 

virtually impossible to predict where scour and deposition will occur at various 

flows (Haschenburger 1999, Wilcock and others 1996). Consequently, we 

adapted an approach for predicting the probability of redd scouring or 

deposition from the empirical reach-scale work of Haschenburger (1999). This 

approach was developed for gravel-bed channels and may not be appropriate 

for sites where spawning gravels occur mainly in pockets behind obstructions. 

Haschenburger (1999) observed the spatial distribution and depth of 

scouring and deposition at a number of flow peaks in several study sites in 

gravel-bed rivers. The proportion of a stream reach that scoured or filled to a 

specified depth during a high-flow event was found to follow an exponential 

distribution, the parameter for which (scourParam) varies with shear stress. We 

assume that the probability of a redd being destroyed is equal to the proportion 

of the stream reach scouring or filling to depths greater than the value of the 

input parameter mortReddScourDepth (cm). Consequently, the probability of a 

redd not being destroyed (scourSurvival) is equal to the proportion of the 

stream scouring or filling to a depth less than the value of mortReddScourDepth. 

This scour survival probability is estimated from the exponential distribution 

model of Haschenburger (1999); the proportion of the stream scouring to less 

than a given depth is the integral of the exponential distribution between zero 

and the depth: 

scourSurvival =1- e scourParam mortReddScourDepth 

The value of scourParam is estimated by Haschenburger empirically: 

scourParam = 0.33e 1.52 (shearStress/0.045) 

The value of shearStress (a dimensionless indicator of scour potential) is 

estimated as: 

RS shearStress = ( s − )D 

where is the density of water (1 g/cm3); R is the reach-average hydraulic 

radius; S is the reach-scale energy slope; ρ is the density of sediment, s 

approximated as 2.7 g/cm3; and D is the mean substrate particle diameter. 

The model can calculate value of shearStress, as a function of flow rate, for 

the study site. This can be done by using the approximation that the hydraulic 

radius is equal to the average depth, which can be calculated each day as a 

function of flow, and by providing the slope as an input parameter. However, 

this method may introduce significant errors because it assumes that all the 

resistance to flow through the study site is a result of bed roughness (controlled 

by shear stress). In reality, the flow resistance in most river channels is partly 

due to “form roughness,” the effect of channel bends and large obstacles in 

backing up the flow. Using the above equation to estimate shear stress for our 

model reaches, which have numerous sharp bends and obstacles, would 

overestimate shear stress and the potential for scouring. 

66 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

We circumvented this potential problem by estimating a relation between 

shear stress and flow at a nearby stream reach that is relatively straight and 

obstacle–free and has low form roughness, with a slope and substrate diameter 

similar to the modeling reach. From this shear stress reference site, we obtained 

the following empirical relation between shear stress and flow (m3/s): 

shearStress = mortReddShearParamA flow mortReddShearParamB 

The distance down from the gravel surface to the top of a redd’s egg pocket 

appears to be an appropriate measure of mortReddScourDepth. Scour to this 

depth is almost certain to flush eggs out of the redd. Deposition of new material 

to this distance would double the egg pocket’s depth, likely to severely reduce 

the survival and emergence of its eggs. Deposition is especially likely to reduce 

survival if it includes fine sediment. The literature suggests 10 cm is a reasonable 

value of mortReddScourDepth for small trout like Little Jones Creek cutthroat 

(DeVries 1997). 

Our parameters (table 25) produce a decreasing relation between peak flow 

and survival of redd scouring (fig. 29). 

This model of scouring estimates the probability of a redd surviving scour in 

each high-flow event, not on a daily time step. The single survival probability is 

applied to all redds, assuming that if scouring occurs, then no eggs survive. 

Table 25—Parameter values for scour and fill redd mortality. 

Parameter Definition Units Value1 

mortReddShearParamA Multiplier for the relation between 

flow and shear stress s/m3 0.019 

mortReddShearParamB Exponent for the relation between 

flow and shear stress none 0.383 

mortReddScourDepth Depth of scour or fill assumed to 

destroy a redd cm 10 

1 Values determined at a site on Little Jones Creek about midway between the upper and lower 

modeling reaches. These values probably poorly represent the small tributary modeling site. 

Figure 29 —Scour and fill redd 

survival function. 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 67 
IX. Method Details 

Therefore, we apply this risk factor only once per cycle of rising then falling 

flows, using these steps: 

• The redd scour survival probability is calculated only on days when the 

flow is greater than both the previous day’s flow and the next day’s 

flow; this means the flow peaked on the current day. When this peak 

occurs, the following two steps are followed; on all other days, the 

fraction of eggs surviving is 1.0. 

• One value of scour survival probability (scourSurvival) is calculated for 

the whole model reach, using the above equations for the current flow. 

This probability is used for all redds. 

• For each redd, a uniform random number between zero and one is 

drawn. If the value of this number is greater than the value of 

scourSurvival, then the fraction of eggs surviving is zero. Otherwise, the 

fraction of eggs surviving is 1.0. 

IX.E.3. Low Temperature 

Both low and high temperatures cause mortality in eggs at temperatures 

much different than those causing mortality in fish. We model mortality caused 

by high and low temperatures separately and use logistic functions, which seem 

to represent the available data well. Because temperatures are moderate at the 

Little Jones Creek study site, both low and high temperature redd mortality are 

expected to be minor. 

We assume the fraction of eggs surviving low temperatures per day is an 

increasing logistic function of temperature. We estimated parameter values from 

data compiled by Brown (1974), keeping in mind that because eggs incubate 

slowly at low temperatures, even apparently high daily survival rates can result 

in low egg survival over the incubation period. 

The data compiled by Brown (1974) indicate that rainbow trout spawn at 

temperatures as low as 3 to 5°C and eggs have a 90 percent survival rate over a 

100-d incubation period at 3°C (egg survival = 0.999). We also assumed a daily 

survival rate of 0.9 at 0°C and found logistics parameters that reproduce these 

two points (fig. 30; table 26). We adopt these values for cutthroat trout. 

Figure 30 —Low temperature redd 

survival function. 

Table 26—Parameter values for low temperature redd mortality. 

Parameter Definition Units Value 

mortReddLoTT1 Temperature at which low temperature 

survival is 10 pct °C -3 

mortReddLoTT9 Temperature at which low temperature 

survival is 90 pct °C 0 

68 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
IX. Method Details 

IX.E.4. High Temperature 

We assume the fraction of eggs dying from high temperatures per day is an 

increasing logistic function of temperature (fig. 31). We adopt rainbow trout 

values that were based on interim results of lab studies conducted by the 

University of California at Davis (Myrick 1998). These data showed daily survival 

rates declining from about 0.9998 at 11°C to about 0.985 at 19°. Our parameters 

(table 27) appear to indicate high survival at high temperatures, but in fact cause 

low survival if temperatures are elevated for long periods. 

IX.E.5. Superimposition 

Superimposition mortality can occur when a new redd is laid over an existing 

one; females digging new redds can disturb existing redds and cause egg 

mortality through mechanical damage or by displacing eggs from the redd 

environment. For simplicity, our formulation currently assumes that 

superimposition is a random occurrence, with spawners not intentionally 

spawning over existing redds. The study by Essington and others (1998) indicates 

that stream trout may indeed intentionally superimpose their redds over existing 

ones, a practice that has the advantages of reducing the work necessary to clean 

redd gravels and the competition that the spawner’s offspring will face. Our 

formulation could easily be modified to study the complex effects that intentional 

superimposition might have. 

We assume that, if another redd is laid in the same habitat cell, the risk of 

superimposition mortality is a function of the area disturbed in creating the new 

redd and the area of spawning gravel available. We simulate superimposition by: 

1. Determining, for each redd on each day, if one or more new redds were 

created in the same cell. 

2. If so, the risk of superimposition mortality occurring (reddSuperImpRisk, 

unitless daily probability) is equal to the area of a redd divided by the area 

of spawning gravel. 

Figure 31 —High temperature 

redd survival function. 

Table 27 —Parameter values for high temperature redd mortality. 

Parameter Definition Units Value 

mortReddHiTT9 Temperature at which high temperature 

survival is 90 pct °C 21 

mortReddHiTT1 Temperature at which high temperature 

survival is 10 pct °C 30 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 69 
X. Model Development Priorities and Research Topics 

3. A random number (uniform distribution between zero and one) is drawn; if 

it is less than the value of reddSuperImpRisk, then superimposition 

mortality occurs. 

4. If superimposition mortality occurs, then the fraction of eggs surviving 

is a uniform random number (0-1). 

5. Steps 2-4 are repeated if more than one new redd was placed in the cell. 

The value of reddSuperImpRisk can be greater than 1.0 if cellFracSpawn is 

very small. In the event that cellFracSpawn is zero, we assume there is no risk of 

superimposition because there is no gravel to be disturbed by another spawner. 

Because of the way we use the parameter reddSize in this formulation, we 

define it to be the area that a spawner disturbs in creating a new redd. On the 

basis of field observations at Little Jones Creek, we assume reddSize to be 1200 

cm2 (the area of a circle with a diameter of 35 cm) for resident cutthroat trout. 

X. Model Development Priorities and Research 

Topics 

This section describes additional model development and research needs 

that we identified in designing this model formulation. The development and 

research needs include: 

• Ways to address potentially important ecological processes that are 

currently absent, simplified, or poorly quantified in the current 

formulation; and 

• Approaches that better match the modeling philosophy we attempt to 

follow (Section I.A). 

Some of these model development ideas would add complexity and 

computational burden to the model but may also add key elements of realism. 

An experimental approach can be taken to adding them, determining their 

relative costs and benefits. 

One general model development priority is to conduct an analysis of the 

sensitivity of model predictions to individual model components and parameters. 

A useful sensitivity analysis would focus on parameters and equations, which 

are not as well defined and supported by independent literature. 

X.A. Imposed versus Emergent Behaviors 

The trout model’s formulation includes both methods that force fish to 

behave in ways that have been observed in real trout populations (“imposed 

behaviors”) and those that let fish choose their behavior to maximize their 

fitness, producing “emergent behaviors.” An example of imposed behavior in 

some models of stream salmonids is that fish are forced to maintain territories, 

although there are times when doing so is not beneficial or realistic. Our feeding 

formulation does not impose territorial behavior; instead, our feeding and 

movement rules let fish select habitat to maximize their long-term fitness. Habitat 

selection patterns emerge from the combination of habitat dynamics and fitnessseeking behavior, sometimes producing behavior similar to territoriality but 

sometimes not. This approach is more appealing from a theoretical sense because 

we model the underlying causes of behavior instead of imposing behaviors that 

may not always be appropriate. 

We have found the “Unified Foraging Theory” and related approaches (Bull 

and others 1996, Mangel and Clark 1986, Thorpe and others 1998) for modeling 

decision-making to be especially valuable for individual-based modeling with 

emergent behaviors. In contrast to traditional foraging theory, these approaches 

make the critical and realistic assumption that fish base their decisions on the 

predicted mid- to long-term consequences. 

70 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
X. Model Development Priorities and Research Topics 

X.A.1. Generalization of Movement Objectives 

The model’s rules for movement (habitat selection) allow fish to select the 

destination that maximizes a simple measure of their fitness (“expected 

reproductive maturity”; Section IV.B.2). These rules can be generalized to provide 

more accurate and complete measures of fitness for fish to maximize. Some 

changes may give fish more realistic habitat selection behaviors. 

For instance, our movement rules let fish predict the effects of food intake 

on the risk of starvation and consider it in movement decisions. However, 

these rules currently do not consider the effect of predicted growth on other 

risks. For example, selecting a site that provides rapid growth would decrease 

a fish’s risk of being eaten by another fish. Including the effects of growth on 

all risks would give fish a more accurate measure of the fitness benefits of 

alternative destinations. 

The model’s current fitness measure has only the simplest representation of 

how fish size affects reproductive success: a length threshold for spawning. 

Providing a more general representation of how fecundity and offspring survival 

depend on spawner size in the fitness measure appears to be a simple yet 

important way to make habitat selection and growth more realistic. This change 

would encourage adult fish to continue growing after attaining the minimum 

reproductive size. 

X.A.2. Readiness to Spawn and Spawning Location 

One example of imposed behavior in this model is our approach for 

determining the day when a fish spawns: we prohibit the fish from spawning 

except when a number of predetermined criteria are met, then use a stochastic 

rule to impose variation in the dates that fish spawn. Both the predetermined 

spawning criteria and the variation in spawning dates are imposed to make the 

behavior of model fish match that of real fish. Similarly, we use observed habitat 

preferences to determine where a fish should spawn. 

A more mechanistic approach to these spawning decisions would be to 

model the fish’s readiness to spawn (e.g., by tracking its energy reserves), and let 

each fish decide if, when, and where it spawns so that it maximizes the 

probability of producing fry that can compete well in the critical first summer of 

life. Simple models of how a fish predicts the effect of spawning location and 

timing on expected redd survival and fry viability could be developed from our 

existing redd development and survival formulation. An even more complete 

approach would incorporate the effects of spawning versus not spawning on 

reproductive value. 

X.A.3. Allocation of Growth to Fish Length, Weight, and Gonads 

The approach we adopt from Van Winkle and others (1996) for 

determining how much a fish grows in length when it gains weight unrealistically locks the fish into a predetermined length-weight relationship. It does 

not, for example, let fish store energy reserves that can be used later (Section 

IV.C). We also currently do not simulate the important energetic effects of 

gonad development and spawning. 

A fitness optimization approach to allocation of growth seems feasible: let 

the fish allocate weight to length, muscle, fat, or gonads to maximize its expected 

fitness. This approach is similar to that tested successfully by Bull and others 

(1996). Such an approach could also contribute to a more mechanistic method for 

simulating readiness to spawn (Section X.A.1). 

X.A.4. Diurnal Changes in Behavior and Hiding Cover Limitations 

Fish vary their diel pattern of feeding and hiding (Heggenes and others 

1999). If hiding is specifically modeled (it is not included in the current model), 

then the potential limiting effects of hiding cover can be simulated. The 

availability of winter hiding cover appears to be low and potentially limiting at 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 71 
X. Model Development Priorities and Research Topics 

Little Jones Creek. Our current formulation is incapable of predicting seasonal 

(or habitat-related) changes in diurnal behavior; instead, we simulate only 

daytime feeding behavior (Section IX.C.1). 

A potentially viable approach to incorporating concealment behavior may be to: 

• Include the habitat cell’s area of hiding cover in the habitat model and 

make survival during hiding a function of competition for hiding cover. 

• Assume that hiding fish have no food intake and much lower mortality risk. 

• Simulate how survival probabilities and food intake for feeding fish 

differ between day and night. 

• Alter the model’s movement rules so that they maximize expected 

reproductive maturity using a daily optimal combination of feeding 

versus hiding. A fish could choose to feed in the day and hide at night, 

hide in the day and feed at night, hide day and night, or feed day and 

night. This decision would incorporate the effect of the availability of 

hiding cover on survival probabilities when not feeding and perhaps 

differential feeding success at night versus during the day. 

X.B. Habitat Model Issues 

Despite the many years that stream trout habitat models have been used, 

frustrating limitations remain. The first three of these habitat-modeling issues are 

relevant to conventional habitat index models like PHABSIM (Railsback 1999). 

X.B.1. Habitat Cell Sizes 

The spatial scales used in models have crucial effects on results. Despite the 

popularity of habitat models for stream fish, we found a dearth of literature on 

how the ability to predict such fish characteristics as behavior, survival, and 

growth varies with spatial scale. Currently, we select the spatial resolution of our 

model (cell size) to approximate the scale at which microhabitat varies at the 

study site. The resolution we use seems reasonable, but research on what spatial 

scales are most appropriate for stream fish models with daily time steps would 

be welcome. 

X.B.2. Accuracy of Hydraulic Simulations 

We identified two problems with our hydraulic simulation approach that 

uses PHABSIM hydraulic models. One problem is that PHABSIM hydraulic 

models cannot simulate zero or very low velocities well, even in shallow margin 

habitats and especially in eddies and backwaters. This makes it difficult to model 

fish that prefer low velocities and shallow water, like age 0 trout. A second 

problem is that standard PHABSIM calibration methods tend to reduce the 

natural variation in depth and velocity in complex habitats. Because such 

variation makes model calibration difficult and results in unrealistic hydraulic 

predictions, model users tend to take the variation out during calibration (if they 

do not avoid it by biasing where hydraulic data are collected; Railsback 1999). 

Using more appropriate calibration measures can reduce this problem. 

These two problems are largely due to the one-dimensional nature of the 

PHABSIM models and because they do not consider bedform roughness, even 

though bedform roughness often appears to be the most important process 

controlling stream velocities. 

Two approaches for avoiding these problems are being considered by 

instream flow researchers. Two-dimensional finite-element hydraulic models 

can do a better job of representing margin habitat and can (in some cases) better 

accommodate spatial variation. These models can also have lower field data 

costs when modern surveying technologies are employed. Several research 

groups have looked at this class of models for instream flow studies but a model 

ready for routine use has not yet appeared. 

72 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
X. Model Development Priorities and Research Topics 

The second alternative approach is using a statistical representation of 

habitat, treating field hydraulic measurements as point samples of a population 

instead of as a map of the stream environment (Dingman 1989). This approach 

has the disadvantages of being a less direct representation of the stream, not 

maintaining the spatial relations among habitats, and likely having burdensome 

requirements for collection of field data. 

X.B.3. Variation in Velocity Shelter Availability 

The drift-feeding component of our model indicates that velocity shelters are 

very important to trout energetics (Section IX.C.6). We currently assume that the 

area of a habitat cell with velocity shelters is constant (Section III.D). However, 

field observations indicate that the amount of velocity shelter varies with flow 

and is a function of fish size. For example, a small boulder may provide no 

velocity shelter during high flows, yet may provide abundant shelter for a 

juvenile fish during lower flows. Especially for sites where velocity shelters are 

limited, more realistic assumptions about velocity shelter may be valuable. 

However, modeling variation in shelter availability may introduce considerable 

computational burden and uncertainty. 

X.B.4. Spatial and Temporal Variation in Food Availability 

Food availability is a very important parameter that we currently simulate 

simply. Predictions of fish habitat use and population dynamics will be more 

accurate if we develop ways to simulate how food availability varies over space 

and time, and with habitat conditions (especially, with flow and temperature). 

One possibility is making the drift food regeneration parameter (Section III.G.1) a 

function of velocity, substrate type, or temperature. An example approach is the 

work of Morin and Dumont (1994) showing how aquatic insect production rates 

vary with temperature. 

X.C. Fish Model Issues 

X.C.1. Immigration and Emigration 

Immigration and emigration of healthy fish are commonly observed 

phenomena, and we plan to incorporate these processes in future versions of the 

model. We especially will focus on movement of juvenile fish out of a small 

tributary into the creek’s mainstem. We have not yet developed the methods for 

doing so. We will most likely develop approaches for simultaneously modeling a 

mainstem and tributary site and the movement of fish between them. 

X.C.2. Movement Distances and Knowledge of Environment 

We assume the distance over which a fish “knows” habitat conditions and 

considers potential movement destinations depends only on its length (Section 

IV.B.2). This approach seems simplistic. A more sophisticated approach to 

simulating how much habitat animals consider during movement decisions is to 

let each build its own map of the environment, with maps expanded via 

exploration. To maximize their predicted long-term fitness, animals can make 

random exploratory movements outside its known area that would improve its 

map of known habitat as an alternative to making fitness-maximizing movements 

within known areas. This approach has been used in the cowbird model of 

Harper and others (2000). A simpler but less mechanistic approach is to assume 

that the maximum distance over which fish can evaluate potential movement 

destinations varies randomly among individuals or over time. 

X.C.3. Fitness Time Horizons for Movement 

The fitness measure we use to evaluate movement destinations (Section 

IV.B.2) uses a fixed time horizon over which risks of starvation and other 

mortality sources are evaluated. There is little literature or evidence supporting 

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 73 
X. Model Development Priorities and Research Topics 

selection of a time horizon value. A similar modeling approach developed by 

Thorpe and others (1998) proposes time horizons reflecting a salmonid’s activity 

or life history stages; for example, the fitness horizon for a trout overwintering 

in a cold climate could be the time remaining before active feeding can resume. 

It seems reasonable for the time horizon of adult trout to be the time remaining 

before the spawning season, over which the fish can build spawning energy 

reserves and produce gonads. 

If the time horizon is variable, it could depend on the outcome of movement 

decisions: for example, the time horizon could be the time remaining before a 

fish achieves the length and weight needed for spawning. In this case, the time 

horizon would depend on net energy intake: cells providing higher growth 

reduce the time remaining before spawning size is achieved. The relative fitness 

offered by various habitat cells would depend not only on starvation and other 

risks but also on the time horizon resulting from the growth rate in the cell. 

There are a number of such research issues related to fixed or variable fitness 

time horizons. 

74 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
XI. Input Parameter Index 

XI.Input Parameter Index�

F 

fishCmaxParamA .....................41

fishCmaxParamB......................41

fishCmaxTempF1 .....................42

fishCmaxTempF2 .....................42

fishCmaxTempF3 .....................42

fishCmaxTempF4 .....................42

fishCmaxTempF5 .....................42

fishCmaxTempF6 .....................42

fishCmaxTempF7 .....................42

fishCmaxTempT1.....................42

fishCmaxTempT2.....................42

fishCmaxTempT3.....................42

fishCmaxTempT4.....................42

fishCmaxTempT5.....................42

fishCmaxTempT6.....................42

fishCmaxTempT7.....................42

fishEnergyDensity ..................44,

46

fishFecundParamA ..................12

fishFecundParamB ...................12

fishFitnessHorizon........ 16, 17

fishMinFeedTemp......... 38, 60

fishMoveDistParamA... 30, 31

fishMoveDistParamB ...... 30, 31

fishReactParamA......................62

fishReactParamB ......................62

fishReactParamC ......................62

fishReactParamD......................62

fishRespParamA.......................68

fishRespParamB .......................68

FishRespParamC ......................68

fishRespParamD.......................68

fishSearchArea......................... 65,

71

fishShelterSpeedFrac .............. 68,

69, 70

fishSpawnDSuitD1....................60

fishSpawnDSuitD2....................60

fishSpawnDSuitD3....................60

fishSpawnDSuitD4....................60

fishSpawnDSuitD5....................60

fishSpawnDSuitS1.....................60

fishSpawnDSuitS2.....................60

fishSpawnDSuitS3.....................60

fishSpawnDSuitS4.....................60

fishSpawnDSuitS5.....................60

fishSpawnEndDate ...................58

fishSpawnMaxFlowChange ....59

fishSpawnMaxTemp.................58

fishSpawnMinAge ....................59

fishSpawnMinCond..................59

fishSpawnMinLength............. 17,

35

fishSpawnMinTemp .................34

fishSpawnProb ..........................11

fishSpawnStartDate ..................34

fishSpawnVSuitS1.....................37

fishSpawnVSuitS2.....................37

fishSpawnVSuitS3.....................37

fishSpawnVSuitS4.....................37

fishSpawnVSuitS5.....................37

fishSpawnVSuitS6.....................37

fishSpawnVSuitV1 ....................37

fishSpawnVSuitV2 ....................37

fishSpawnVSuitV3 ....................37

fishSpawnVSuitV4 ....................37

fishSpawnVSuitV5 ....................37

fishSpawnVSuitV6 ....................37

fishSwimParamA ......................51

fishSwimParamB .......................51

fishTurbidMin............................39

fishTurbidParamA ....................39

fishTurbidParamB.....................39

fishWeightParamA .......... 4, 5, 6

fishWeightParamB ................ 5, 6

H 

habDriftConc ..............................9,

10, 27, 38, 46, 48

habDriftRegenDist .....................9,

10, 46

habLatitude ................................10

habPreyEnergyDensity .......... 44,

45

habSearchProd............................9,

27, 40, 41, 47, 48

L 

LOWER_LOGISTIC_DEPENDENT

48

M 

mortFishAqPredD1...................59

mortFishAqPredD9...................59

mortFishAqPredF1....................59

mortFishAqPredF9....................59

mortFishAqPredL1 ...................59

mortFishAqPredL9 ...................59

mortFishAqPredMin .............. 27,

29, 58, 59, 63

mortFishAqPredP1 ...................59

USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 75

XI. Input Parameter Index 

mortFishAqPredP9 ...................59

mortFishAqPredT1 ...................59

mortFishAqPredT9 ...................59

mortFishAqPredU1...................59

mortFishAqPredU9...................59

mortFishConditionK1 ..............53

mortFishConditionK9 ..............53

mortFishHiTT1 ..........................49

mortFishHiTT9 ..........................49

mortFishSpawn ................. 52, 53

mortFishTerrPredD1 ................55

mortFishTerrPredD9 ................55

mortFishTerrPredF1 .................55

mortFishTerrPredF9 .................55

mortFishTerrPredH1 ................55

mortFishTerrPredH9 ................55

mortFishTerrPredL1 .................55

mortFishTerrPredL9 .................55

mortFishTerrPredMin ............ 27,

29, 54, 55, 63

mortFishTerrPredT1 .................55

mortFishTerrPredT9 .................55

mortFishTerrPredV1.................55

mortFishTerrPredV9.................55

mortFishVelocityV1..................51

mortFishVelocityV9..................51

mortReddDewaterSurv............65

mortReddHiTT1 ........................69

mortReddHiTT9 ........................69

mortReddLoTT1 ........................68

mortReddLoTT9 ........................68

mortReddScourDepth ...... 66, 67

mortReddShearParamA...........67

mortReddShearParamB ...........67

R 

reddDevelParamA ............ 20, 21

reddDevelParamB............. 20, 21

reddDevelParamC ............ 20, 21

reddNewLengthMean...... 21, 22

reddNewLengthVar.......... 21, 22

reddSize ..................................... 70

S 

sppDomFactor .......................... 13

U 

UPPER_LOGISTIC_DEPENDENT

48

76 USDA Forest Service Gen. Tech. Rep. PSW-GTR-182. 2001. 
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