li rh Y .i 

## - .i 0 cd 

# Entrainment Impact 

# Estimate

- A!gG 21 11975 

# Using the 

# Equivalent Adult 

# A b *­

./- L 3 1The Biological Services Program was established 

### wi hin th U.S. 

### Fish and Wildlife Service to supply scientific informat 

### on and methodologies on key environmental issues which-impact fish and wi dlife resources and their supporting ecosystems. The 

### mission of the Program 

### is as follows: 1. 

### To strengthen the Fish and Wildlife Service in its role as a primary source of information on national fish and wildlife resources, particularly inrespect 

### to environmental impact assessment. 2. 

### To gather, analyze, and present information that will aid

. decision makers inthe identification and resolution of problems associated with 

### major land and water use changes. 3. 

### To provide better ecological information and evaluation 

### for Department of the Interior development programs, such as those relating 

### to energy development. Information developed by the Biological Services 

### Program is intended for use inthe planning and decision making process 

### to'prevent or minimize the impact of development on fish and wildlife. Biological Services research activities and technical assistance services are based on an analysis of the issues, the decision makers involved and their 

### information needs, and an evaluation of the stateof the 

### artto identify information gaps and determine priorities. This 

### is a strategy to assure that the products produced and disseminated will be timely and useful. Biological Services projects have been initiated in the following areas: Coal extraction and conversion Power plants Geothermal 

### ,mineral

### ,and oil shale development Water resource analysis

## , including stream a1terations and western water allocation Coastal ecosystems and Outer Continental Shelf development Systems and inventory, including National Wetlands Inventory, habitat classification and analysis, and information transferThe Program consists of the Office of Biological Services 

### inWash- j ington, D.C., which 

### is responsible for overall.planningand management; National Teams which provide the Prosram's central scientific and technical expertise and who arrange for contracting Biological Services 

### studies with States, universities, consulting firms, and others; Regiona 

# I staff who provide a link to problems atthe operating level; and staff atcertain Fish and Wildlife Service research facilities who conduct 

### in-~___ -. Bi

### ological Services Progan

__ FbiS/OGS-78/65 July 1978



### US

## fNG

## THE EQUIVALENT 

## ADULT 

# APPROACE

C. Phi11ip 

### Goodycar Mational Power Plant Team 1451 Green Road 

### Ann Arbor., Michigan 48105

Power Plant Project Office of Biological Services Fish and Wildlife Service U.S. Department of the Interior

. . . . . . . ... . .... . : t’ Fish and Wildlife Service 

### -~ 1J.S. Department of the Interior

## ---

-- 

### ENTRAINMENT IMPACT ESTIMATES ! 

### USING 

### THE EQUIVALENT ADULT APPROACH ! 

### Abstract One approach to analyzing the importance of entrainment of fish I 

### eggs and larvae by power plants has been to

### estimate the number of 

### adults which would have resulted from the entrained larvae. Certain limitations of 

### a commonly used model can lead to serious underestimates of 

### the actual impact. These limitations are discussed and an alternative formulation is presented which will reduce the bias. The approach is also expanded to

### provide estimates 

### of the reduction in numbers of fish captured by 

### fishermen. 

### INTROD

### UCT

### I0N 

### One approach to assessing the importance of entrainmentmortality of 

### eggs and larvae of fish and shellfish by power plants is to estimate the number of adult organisms which this loss represents. This concept was iptroducpd by Horst 

### I

### 1975) 

### as a "simplistic approach'' that could be used when it is not possible to employ more sophisticatedmethods because of the lack of available data. He formulated the model.$? follows: 

### Na = S, 

### Ne 

# ..................... .(1) where 

### Na = 

### number of 

### adults that would have resulted from the entrained 1

### arvae

### , S,? = 

### survivorship from larvae to adulthood, and

* 

### Ne = 

### number of larvae killed by entrainment. The paramater S, of

### equation 

### (1) can be defined for a population that is in equilibrium if 

### the average lifetime fecundity of adult females (Fa) and the survival probability from a newly spawned egg to 

### larvae are known. At population equilibrium each adult female produces a sufficient number of 

### eggs during her lifetime to replace herself; thus, the probability of an 

### egg surviving to produce an 

### average adult female 

### is equal to the reciprocal of the average lifetime fecundity. 

### If it is assumed, in addition, that one adult male is

### produced for each adult female, then the probability 

### (S) of 

### an egg surviving to

### become an adult is \---2

## ­
e 

### s=- 

# .................... .(2) I I 

### Fa 

### I
r

, ­ .. . j'

.I

.. . :

. -.. .....

# 9 --:..-:. ..i..r..

.......... .. I

......
. .,. ..........._.= .. ~ 

### . .:. _I .-- 

### 2 and the probability of

### a larva surviving 

### to become 

### an adult 

### is 

## s, = 

## s/s, = 2


# ............... . (3) 'eF, where Se = the survival probability 

### iron a newly spawned 

### egg to an entrained larvae. Thus the estimate of the nunber of adiiits lost using the'tiorst formulation 

### is dependent on the pararneters S 

### , F. 

### , and 

### N 

# . The value of the parameter N 

### must be determined froin fie?d sgmpling %ndmay be subject to cons7derable bias or error becai.!se of inappropriate sampling or data reduction procedures. However, it

### is assumed here that the '. number of larvae killed by entrainment can be accurately determined. 1

### n H0

### rSA&

### rmu1-a.t.is 

### a-t. 

### he-..e.s..t 

### Smate.._of_-slJr~-val...~l?__~~-_~~-.en-~-r~~ne 1a

### rvae,

# r)-,- he-cans.La.nL3ar-

### a11 en1;

### rai

### n_ed-laryag

### ,and 

### thi

### s d is.,-a.s

### s~me.$-.-to.­ is--a--po-fefitialsource of substantial errcr, 

### as noted by SaundeTC(-(1477)­ and-D-a7;ri-b~1~7~~~-The\/f-~-~~-actuaifunction of the 

### aye ly a of the affected larvae. This point 7s important because of the low survival rate typically associated with the younger larval stages. Most of the larvae that are entrained tend to be the younger ages, but most of the impact may be associated with the older, less abundant larvae. In this situation an estimate of the mean S which would be representative formost of the entrained larvae, 

### the young& ones, would underestimate 

### the impact. ALTERNAT

### IVE 

### E40DE

### L

iclNiSi]. 

# .............. (4) where 

### n = number of larval age classes that are subject to entrainment mortality, Ni = number of age class i larvae that are killed by enirainment, Si = survival probability from age class i to adulthood, 2 

### s. = 

### 'e,i Fa 

# ................* (5) Se,i = survival-probability front egg 

### to age class i, and


## - Fa = average lifetime fecundity of a female recruit.--- . -. -3

-
.......... The use of equation (4) requires est.irnates.ofthe number of larvae entrained 

### for each larval age class (Ni) and the rate of survival from the egg stage 

### toeach age cla.ss (S.)

## . If the duratioils of the selected age class intervals are sufficiently long 

### that the survival probabilities of older individuals of the age class are significantly higher than the younger ones, 

### than the nuinber of adults predicted using equation (4) may still underestiinate the true impact. This tendency can be 

### an important consideration because itis generally very difficult 

### todetermine the age of larvae precisely enough 

### to allow the age class interval 

### to be reduced sufficiently to eliminate this bias. ES'rII;ll.\TES OF EGG TO LARVA 

### SURVIVAL Because of the difficulty in aging larval fish itis often desirable 

### to describe mortality as 

### a function of length rather 

### than age (Swedberg and Walburg 1970). Data on abundaiice of larvae, grouped by body length categories, can be used 

### to estiinate a probability of survival from one length class 

### to the next during the period that larvae are vulnerable to entrainment. Using this atter approach, the nuinber of adults that would have resulted froin arvae killed by entrainment can be estimated by rewriting equation (4) 

### as follows: k Na=X NS 

## . 

## ................... .(6) R =1 P' K. where 

### k = nutnber of larval length classes 

### that are subject to entrainriletit nior-tality N, = tiutrtber of length class R larvae 

### that are killed by eiitraiillnetit S, = survival probability 

### froiri length class R to adulthood



### - 2


### - --___ 

## .................... .(7) si 'e,, 

### Fa >_ Se,%= survival probability froiri egg to length class 

## a. The estimate of survival fraction by length can be obtained 

### from cumulative catch data segregated into length classes. If the plot 

### 'of the log of the cuniulative catch against length is 

### a straight line (Figure 

### 1) then mortality 

### is 

### a constant function oflength and the instantaneous rate of mortality with increasitig leng-th is defined 

### as:

. . . . . . ,'. -_ --._

. . . . c4

- . 

### Cumulative Abundance 

### of Larvae

-I Y I-1 0 d 0 0 0 0 0

7 2. tn S -5 0

r 0 S tn rt 3 3 3 U

3... 5 where d = instantaneous total mortality during length class R, NL+l = cumulative catch 

### for length class R + 1 i N, = cumulative catch 

### for length class R and, Se,, = He-d(L,-h)



## ....................( 9) where 

### -H = 

### fraction of eggs that hatch, L, = length cflength class R, and

h = length 

### athatching. If the plot of the log of the cumulative catch against length is not 

### a straight line (Figure Z), then mortality 

### is not a constant function of length and equations (8) and (9) are.not applicable. In this case, the value of S can be estimated as follows: e,z 

## s =H-. 

### Nz


# .................... (10) e,, NO where H = fraction of eggs that hatch, i N, = number of larvae of length class R, and No = initial number of larvae. Equations (9) and (10) both assume 

### thatthe change in cumulative catch as a function of length reflects the true population change in abundance. This assumption requires the sampling to be non-selective by length and the sampling effort to be constant throughout the period that larvae 

### grow through the 

### various length classes (i.e., the probability of 

### an individual being captured at a given 

### length 

### must be the same for all 1ength classes). This method assumes that length increases ljnearly with time during the entrainment period. Violation of 

### this assumption will introduce some bias into the impact estimates. ESTIMATES OF 

### AVERAGE LIFETIME FECUNDITY 

### OF "ADULTS" In addition 

### to the estimate of Se the parameter 

### S, of equation (6) requires--an-<stimateof the averagg 1ifetime fecundity of adult females (F ). For-species which spawn more than'once'during their lifetime, the value of Fa is not likely to be the same as the average fecundity of the extant adults, but 

### is a'function of age of recruitment tothe spawning population, frequency of spawning, relative fecundity of

. ::%: - . . .... .. ..... .... ;I_ . . . .... . I . ._-. . ........ . . . . .. .. - . ... ... . -.
.... -.- . - 6.

. 

### Cumulative Abundance

. .­

0 --I " 0 0 4 0 0 0 0 u 0 a 0

P
cn
Q,

--I 0

-.) N

N N
N P N o\ N (*,
W' 0'

. 4. 

## = -

### -- 7 each age class, and total survival between age classes. Ttw average lifetime Fecundity equals the average fecuridity of adults in the population orily 

### when the age structure of the adult population conforms to the stable age distribution that \crould

### exist; atequilibriuiii. To determine average lifetime fecundity of an adult feiiiale it is necessEry to define the age atwhich the individual becorries an adult. Two alternative definitions are ponsidered here: (1) an adult 

### is 

### a recruit to the age class inwhich spawiling 

### is first obset*ved,or (2) an "adult" 

### is an itidividual in 

### the first aye class tliat isrecruited to a fisfrery. If \E zssurne 

### that feriiales spwn only once each year, then for either Jefiiiitiori, the average lifetiiiie fecuridity of a fmale recruit to 

### the "adul

### t" poptrlatiori isyiveri by:
C P.S-EJ 

## ....................(I'l) 

### j=z J ~ aye of recruitincnt of the "adult" population, 111 = tiuiiiber of age classes in the populatioti, P .

J = .fk-action 0.f females that are iiiatuve iti age class j, 

## sj

- survival probabi'lity froiii recruitilierrt to age class j 

### , and 

### E. = average fecundity 0-Finature feiriales of age class j .

J if rscruitirtent to ttie ''adult" population is cons-idevedto occur at the instant that spawning occurs then ttie value of S . J 

### is given by: Sj = e -Z(j-a) 

## ...................(12) where 

### Z isthe instantaneous rate of total niortality. E. in equation (llihisthe average riumber of eggs deposited by niatureJfeina1es OFttie j age class. Fecundity estiiriates based 011 counts of eggs it1 the ovaries 

### of females are generally soiiiewtiat higher thati the riuinber ofeggs that are actually spawned because soiiie of the ova reiiiain in the ovary after spawning. The unspawned eggs can be accounted for by t-educing 

### the fecundity estimates derived in this manher by ttie preportioii of eggs that reniain inspent feriiales. 

### PROJECTIONS Of IMPACT

-. -._

._I ... .Afterthe values 

### for S N,, arid Fa have been determined, the nuniber of potential adults 

### bt are el

- i m W -.b,y-enLr&mt can be estiiria-ted using equation (6):

..
. ­ -_ . . - . .... .: - ...­ .. . . ~. .... .. . . ..... ........ ...--. 8 k Na = C M, S, R'l

n The reduction innumbers of fish captured by the fishery (Nf) can be estimated 

### as: Nf 

### - - 

### - NaF


# . .

# . . . .

# . . . . . . 

# . . . . . . . . . . .(13) where 

### F isthe instantaneous rate of fishing mortality.
L

### I

### MITATIONS adu1

### ts 

### E_s

### tima

### tes of the

### ,J.~ss~e~Qfuslugitheaquiya-lent-adu-1t-appxoac h pr$-s_umethat

"-__. 

### --.- "___.-__ **..--..r----i--. -.-. mortality occurring between there 

### is no densia --.-

dependent C.__^_

~ ~ the tJme tKa.t..the1ar;va-iskilled by.ent.rainment and"Wt-iijiCX.-would have .been -recruited,

### to'the "adult'!...p. opul,atio,n_. However, if these estimates

C.____^__.__,.,.__. _. -. .. are assumed 

### to represent the long term impact of entrainment losses then density dependent effects are assumed 

### to operate between generations. This conclusion results from the fact 

### that a reduction in adults in one generation 

### is imp1ici tly-asSumed .to

### not reduce the number of adults recruited to 

### the following generations.. Otherwise there would be feedback between generations 

### thatwould cause the 

### impact of the power plant 

### to become rriore severe with time. There 

### is for some populations, of course, a possibility-of feedback between generations. 

### Thus, the equivalent adult methodology provides

-_­
. .. . 

### 1i

### t

### t1

### e i

### nsi9h

### t i&t

### o t

### h~~~.~.~~~~~~.i~~--~~-~.h~--a.�f~.c~~~.~~~l-ati-o.n s and should be._~us~~_,~nly~..t.o~~.~~~~~~.~s~~.a~~,~~x~..ma~.i~o~~ 

### of the severity omntial 1Oss.e~. In applications, special 

### consideraiio%-'sXGI?!-be

~

## _____ given to the accuracy of the estimates of the number of larvae killed by entrainment, and 

### tothe fraction of eggs that 

### survive to become larvae. EXAMP

### LE A hypothetical power plant withdraws its cooling water from a lake which supports a popular sport fishery. 

### An intensive sampling program in

### the lake and at the power station has provided the data needed to use the equivalent adult approach outlined herein. Fish are recruited 

### to the fisherywhen they become 3 years of age and are exposed to an annual instantaneous 'fishing mortality of 0.29 thereafter. Some aremature at age 4, all aremature by age 8, and they spawn once each year. The reduction innumbers of fish captured by 

### the fishery 

### is estimated as

- follows:

- -9 Step 1. The average lifetime fecunaitvf a 3 year-old-female recruit 

### is estimated by 

### use of equation (11) 

### to be 534,507 eggs (Table 119 Step 2. The instantaneous rate of larval mortality with increasing length was estimated to be 0.43 (Table 

### Z), Step 3. Estimates of survival 

### from egg to the midpoint 

### of each larval length class (Se,% ) were made using equation (9) (Table 3), Step 4. Estimates of survival 

### from the midpoint of each larval length class to 3 year-old recruit were made 

### using equation (7) (Table 3)3 Step 5. The estimate of the reduction in 3 year-old recruits as 

### a result of entrainment mortality was made 

### using equation (6) (Table 

### 4), and Step 6. The number of catchable fish lost to the fishery as a result of entrainment mortality 

### is determined as follows:

- (836500) (0.29) Nf

### - 0.5108 Nf = 470,000

..

.. . -

. .., ..

.. .... , ,: , .

.-.

.. .

. . . . . . ..

.. . ... . . . .. . 

# '4

... .. . . - ..-----



## -- ...... .: ;. . ,..,. - 7 . .- . 11

.. , . -. - .. I
.%?' .

.. Table 2.: Seasonal length 

### frequency distribution of larvae necdcd 

### to

. -

.1 estimate the instantaneous 

### rate of mortality on length (d). Length"c1ass Length (mm) 

### Number m1-iccted (

### 4
6.0 

## - 6.9 952 I 2.-

.I .7.0 

### - 7.9 61S 3 8.0 

### - 8.9 38'3 4 9.0 

### - 9.9 163 5 10.0 

## - 10.9 235

I
_ 6 ll.@

## - 11.9 216 

### 7 12.0 

### - 12.9 66 8 13.0 

### - 13.9 53 9 14.0 

## - 14.9 20 9 

### c 

### N, 

## * d.=

## - .In 

### a=2 9

618+389+168+235+216+66+59+20 = 

### .-In ( 952+618+389+168+235+216+66+59+20

.. i 5 

### d.= 

### 0..43

. ., 

## *

This equation was adapted from Section 2.7.4 of Ricker (1975).

a : . :. .;.

### . i. is

...

# 1

-

.... .. ...
... ..

-....... . -

.-_ .- .

.. .

... . ...... .... C '

.... - .. . : ..t 

### ­ 12

I. a VI rtWZ 33-5 0 OCDIDrt SLnW rD W os U Dm P w IV -rD n crt wnJ3 w-3 -1.W

-I d d -I -1 0 0 0 0 0 0 0 0 0 I I I I I 1 I I I -I P -I w --I Tu A -I -I 0 co Q cn P 0 N -I 0 ? 03 U cn

co W co co W co co co

IDv, cos a'5 < rt -I. -I d Iv W br 10 d Iu w o< 0 cn Dm u3 

# - w P N h-4 nJ co os co os -I co P Tu 

### 2 wJrD 3-a X x X X X X x X x 

# - ID m'5 -I --t A -I -I 4 -I -r 4 P rto 0 0 0 0 0 0 0 0 0 -3u w a I I I 1 I I 30- rD P .b P P P P w w w 

# c,z

. WSCfLn nJ­ rtLn 3-Ln Ln --I. -ID r+ Lnrt %+c 3 k m 3-nJD P -h 3m -rt rtc -5 Tot?- 

### 2 WrD 3 ID -0 rD

w N d ? N --I -I P W N N P P P 0 W 03 cn 0 cn rn 0 Lo X X X X x X X X x --1 --I --I Ad4 d 0

I 0 I 0 I 00 I I 0 I 0 I N N N W W w 0

;

~ ... . .. . , , . . .-. .. _.- .. . . .

. - .._ ­ -. .. .. . ._

...

..

. .

.13

ln a3 h P Lo 0 0 LCJ C< Lo d u3 0-l a3 m

0, m 0 0 0 0 co CD e N 7 N 

## * N )I N

Lo 0 03 h M h co CD L3 d m m cr) 0 0

0 0 0 In u3 In co h or G-l 0 0 0 0 0

-
Lo CD Ln In Lo

0 0 0 0 0 I- F I- 7 I-- x x x X x M m m cy) m

0 Lo -0 0 0 Lo In h -0 03 N I=-- N P P

. .

.. m ln 01 Q, 0 0, N 0-l m h co ? P I-- I I I I I I I 0 0 0 0 0 0 0 co h co 0-l 0 N c3 P 7 c

N m bv) h eo

.. ’.

. .~.

. .:

.... ... .. .......... .... * .­

.... liT._l.. ... .......Ir .... -.: .... ;.
.. . .-> ........

. .... , 1.: . - .