# ;:- -.,
The Biological Services Program was established within the U.S. Fish 

### and Wildlife Service 

### to supply scientific information and methodologies on key environmental issues which-impact fish and wild1ife 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 state of the 

### art 

### to 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 inthe following areas: Coal extraction and conversion Power plants Geothermal, mineral, and oil shale development Water resource analysis, including stream alterations and western water allocation Coastal ecosystems and Outer Continental Shelf development

= Systems and inventory, including National Wetlands Inventory, habitat classification and analysis, and information transfer The Program consists of the Office 

### of Biological Services 

### inWashington, D.C. 

### ,which 

### is responsible 

### for overall 

### planning and management; National Teams which provide the Program's central scientific and technical expertise and who arrange for contracting Biological Services studies with States, universities, consulting 

### firms, and others; Regional 

# ! staff who provide 

### a link 

### to problems 

### atthe operating level; and staff atcertain Fish and Wildlife Service research facilities who conduct in-

. . .;

... ._
.. ,-. 2: >>-. house research studies.

. . .-.. , .. ...-----


### Wildlife Biolgical 

### Services Prog-raiii

~ ~ -_ 

# I 

# ' I __- FbIS

### /0G5-

### 7816

### 5 July 1978



## EPIT'RAIFI~~1EPJT 

## IFPACT ESTIP!ATES US

## IrIG 

## THE EQU

## IVALEPIT 

## ADULT APPROACE

hy
C. Phi

### 11ip

### Guoclycar National Power 

### Plant Team 

### 1451 GwenRoad Ann Arbor., Nichigan 48105



### Power Plant Project Office of 

### Biological Services Fish 

### and Wildlife Service U.S. 

### Department of

### the Interior



# --__

t 

### Fish and -____ 

### Service U.S. 

### Department of 

### the Interior Fcr male by the Suprintendcnt of Document.. US. Oovwnmcnt 

### 'i Prlntrng Offtce.Washlngton,

### .. O.C. '"I"' 

### n-- 

### ENTRAINMENT IMPACT ESTIMATES USING THE 

### EQUIVALENT ADULT 

### APPROACH


### Abstr xt
One approach 

### to analyzing the importance 

### of entrainment of fish 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.
INTRODUCTION


### One approach to assessing the importance of entrainment mortality of 

### eggs and larvae of 

### fish and shellfish by 

### power plants is to estimate the number of adult organis

### ms which this loss repre= ts. This concept was iptroduced by 

### Hnrst [

### 1975) as 

### a "simplistic approach" that could 

### be used 

### when it is 

### not possible to employ more sophisticated methods because of the 

### lack of 

### available data. He formulated the model 

### &! follows: 

### Na = S, 

### Ne. 

# .................... .(l) where 

### Na = 

### number of adults that would have resulted from the entrained 1arvae, S, = 

### survivorship from larvae to adulthood, and

h 

### 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 'lifetimefecundity. 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 

### ­ 

### s=-



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

### Fa-- . . 2
and the probability of a larva surviving to become an adult 

### is 

## sR 

### =s/s =--. 2



## ............... (3) 

### e 'eF, where Se = the survival probability from 

### a newly spawried 

### egg to an entrained larvae. Thus the est.imate of the nuniSer of acfl~its lost 

### using the 

### Horst formulation is dependent on the parameters 5 

### , F., and 11 

## . The value of the parameter N must be determined 

### froin fieyd simpling 

### grid may be subject 

### to cons7deraSle bias or error becaiise of inappropriate sampling or data reduction procedures. However, it is assumcd here that the number of larvae killed by entrainment can be accurately determined. I

### n tiors_t_l

### sf o

### rmul-a.t.io

### n

.

### -t. he

...

### e.stima

### te

..

### g!--sl)IKi-va1fr?m--ea-- 

### t:o-.cnt.r>ai_ne d 1arvae 

## F).-i en_traineclll_arva~., and 

### this 5..ass-um,e,d. to, he..cDns~.an.~_f.o-r.-a.ll. is-apotefitial source of substantial errcr, 

### as noted by Saundem-m and-Da~-berg-~77r-.~~i~-s--~~-ac~ual ly a function of the 

### age of the affected larvae. This point 7s iciportant 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 youny&r.ones, woiJ1d underestimate the impact. ALTERFlATIVE F4ODEL

jclNiSi> 

# ..............(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 entrainment, Si = survival probability from age class i 

### to adulthood,



## - 2



### - F, 

## ................* (5) 'i 

## s~,~ Se,i = surviva.1 probability froiii egg 

### to age class i, and Fa = average lifetime fecundity of 

### a female recruit.--- 3 The use of equation (4) requires est.irnates of the nuiriber of larvae entrained for each larval age class (Ni) and the rate of survival froni the egg stage 

### toeach age class (8.). If the durations of the selected age class intervals are sufficiently long 

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

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

### an important consideration because it is generally very difficult 

### todetermine the age 

### of larvae precisely enough to allo\ittie age class interval to be reduced sufficiently 

### to eliiriinste this bias. E8TII;IATES OF EGG TO LARVA 

### SURVIVAL Because of the difficulty it) aging larval fish it is often desirable 

### to describe mortal ity 

### as a function of length rather than age (Swedberg and Walburg 1970). Data 011 abutidatice of larvae, grouped by body length categories, can be used 

### toestimate 

### a probability of survival from one length class to the next during the period that larvae are vulnerable to entrainment. Using this latter approach, the nuinber of adults that would have resulted from larvae killed by entrainment can be estimated by rewriting equation (4) 

### as follows: k 

### Na=c N SY. 

## .................... 

# - .(6) 9, R=1 where k = nuri:ber of larval letigth classes that are subject to eritrairiiiieiit mortal ity 

### N, = nuiriber of lencjtli class R larvae that are killed by en

### traiiiineti

### t 

### Sk = survival probabi ity froiri length class R to adulthood



## ................ .(7)

.. Se,%= survival probability froiri egg to length class R. The estimate of survival fraction by length can be obtained from cuinulative catch data segregated into length classes. If the plot of 

### the log of the cuniu'lative catch against length isa straight 

### line (Figure 1) then mortality is 

### a constant Function OF length and the instantaneous rate of mortality with increasing length 

### is defined 

### as: -___ 

### .

### Cumulative Abundance of Larvae

0 A 

# -
4 0 3 3 3 -.1 0 0 -.1 0 0 0

mo ?-r+C+

mob; 033 s-0 wo­ --hm

rto fu c a's -i< mow 0

N

P

0,

co

d 0

-I N

d P

d 0-l

A co N 0
N N

ro P N 0,
N 03 W 05
where d = instantaneous total mortality during length class R, NRtl = cumulative catch for length class R t 1 N, = cumulative catch for length class R and Se,, = He-d(L,- h) 

## ....................( 9)
where H = fraction ofeggs 

### that hatch, L, = length cf length class R, and

h = length at hatching. 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: eyn. S 

### =H-. 

# .................... (10)

e,, NO where H = fraction of 

### eggs that hatch, N, = number of larvae of length class R, and

= initial 

### number of larvae. NO I I Equations (9) and (10) both assume that the 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 length 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 11,

### the parameter S, of equation (6) requires an-estimate of the averag6 lifetime fecundity of adult females (F ). FoFspecies 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

_ -Cumulative Aburid;lncc

--I --. 0 .) -il 0 0 0 0 0 0 0

. 4.

J7
each age class, and total survival between age classes. Tile average -__ 1i.fetime fecundity equals the average fecuridity of adults iri the population only wlieri the age structure 

### of the adult population confotms 

### to the stable age distribution that would exist 

### atequilibriuiri. To dcterniine average lifetime fecutidity of 

### an adult feiiiale it is necess2r.y to define the age 

### atwhich the individual becurries an adult. Two a1ternative definitions are Gonsidered here: (1) an adult is a recruit to the aye 

### class inwhich spawriirlg isfirst observed, or (2) an "adult" is an iridividual iri the first aye class 

### tllat isrecruited to a fistier-y. If \E zsslirile that feriiales spwii only once each year, then for either deriiiitiott, the averaye lifetinie fecutitlity of a female recruit to ttie "adult" popiilatiori 

### is yiveri by:

c P.S.E j=z JJj

## ....................(-l'l)
age of recru'itinent of the "adult" populatiun,
Ill = tiuiiiber of age classes in the populatioil, P .

J = ft.actioii of feinales tliat are iriatut'e it1 age class j, 5. = svrvival prwbabi.1ity froiii recruitiiietit: 

### to age class j, and

J E.

3 = average fecundity of [nature feiiiales OF age class j. if recr~uitirient 

### to the "adult" population is considptved 

### to occur 

### at ttie itistatit 'that sparitling occurs then tlie value of S . J isgiver) by: S. = e -z(j-a)



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

J where Z 

### is the instantatieous rate of total mortality. E. in equation (Ilkhisthe average number of 

### eggs deposited by niatureJfetiiales of the j age class. Fecundity estiiiiates based OH counts of eggs in the ovaries 0.f females are generally soi:iewhat higher thaii the riuinber 

### of eggs 

### that are actually spawned because soure of the 

### ova remain it, the ovary after spawning. The unspawned eggs can be accounted for by reducing ttie fecundity estiiiiates derived in this manner by the prcportioii of eggs that remain in spent feiiiales.
PROJECTIONS OF IMPACT

.. -..- After. the

### .values for S Rs N,, and Fa have been determined, the number. of potential adult5 %Ratare e!dKinakr!.&.-.enh-aim 

### t cati be e-d usiny equation (6):

.d..... j . +-:--. &--

-- . 

# I.

-­ 8 

## i 

# I.

I 

### k I Na = c N, S, ! R=1
where 

### s,

# ' = 'e,, 2 

### Fa 

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

### as:Na Nf = - 

# z . . . . 

# . . 

# . . . . . . 

# . . . 

# . . . 

# . . . .(13) where F is the instantaneous rate of fishing mortality.

LIMITATIONS Es 

### tiRia

### te

### s 

### ~f-o~e-,ll.mses-cif adu1

### ts&jngltheaqu iva-1enLadu.1

### .t

. ~

### ap

### proach

~ ~ . _ -".~ -.-.

~ i s presume that there

--....no densiudependent mortality occurring between the time 

### that the 

### larva.iskilled by entrainment andTfFt-imiE-would

_.__.____.__C_ - have been recruited to the "adultl!..-Ropulation. However, if these estimates are assumed 

### to represent the long term irnpact 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 implicitly-assumed,to

### not reduce the number of adults recruited to the following generations. Otherwise there would be feedback between generations 

### that would cause the impact of the power plant 

### to become more severe with time. There is for some populations, of course, a possibility*of feedback between

# + generations. 

### Thus, the equivalent adult methodology provides
~.

~

__ 

### 1ittle 

### insi h t _e--- ati-ons into th~~~.Elrm_lLi.~~i..~-..Q~-~h~--~~f~c~~~,~~ul an?ou__be.-.used-onl~y-

### tnsh~n_~-~rst_.app.~ox~.mati~o~ of the severity

.... omntiallosses. In applications, special consideration--slioula'-'~e given to the accuracy of the estimates of the number of larvae killed by entrainment, and 

### tothe fraction of eggs that survive 

### tobecome larvae. 

### EXAMPLE 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 

### touse the equivalent adult approach outlined herein. Fish are recruited 

### to the fishery when they become 3 years of age and are exposed to an 

### annual instantaneous-Tishing mortality of 0.29 thereafter. Some are mature 

### at age 4, all are mature by age 8, and they spawn once each year. The reduction innumbers of fish captured by the fishery is estimated 

### as follows:

-i

.-...,

.9


### Step 

### 1. The average lifetime fecudityof a 3

### year-old-female recruit is estimated by use of 

### equation 

### (11) to be 534,507 eggs (Table 11, 

### Step 

### 2. The instantaneous rate of larval mortality with increasing length was estimated to

### be 0.43 

### (Table 2), 

### Step 3. 

### Estimates of 

### survival from egg to the midpoint of each larval length class (Se,L) were made using equation (9) 

### (Table 3), 

### I Step 

### 4. Estimates of 

### survival from the midpoint of each larval
w 

### length class to3 

### year-old recruit were made using equation 

### (7) (Table 

# I 3) Y 

# 1 Step 5. 

### The estimate of 

### the reduction in 3 

### year-old recruits as a 

# I I 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:

NaF 

### Nf = 

## - Z
N

### f =( 

### 836500) 

### (0.29) 0.5108 

### Nf = 

### 470,000-- J ASJ?3



### 4 !j 

### -6 7 3 9 10 11 .I2 13 14 15

­ 

# 5 0.00 0.10 0.25 0.50 0.75 1

## .oo 1.@O 1

### .oo 1

## .oo 1

### .oo 1

## .oo 1

## .oo 1

## .oo
15

C P.S.E j=3 JJJ - Ej
425,000 550,000 750,000 950,000 1,200,000 

### 1,4UO,OOO 1,70O,OOO 1,900,000 2

### ,100

### ,000 2,200,000 2,3OO, 000 2,400,000



### - 

## PjSjEj 0 25,500 49

### ,500 81,000 92,340 93,312 65,318 47

### ,589 31,913 21,163 13,303

8,344 5,224

534

### ,507

. I.

..

. .. .,

.. A

### ------- L . .. 11
Table 2. Seasonal length frequency distributron of larvae necdcd to



### . estimate the instantaneous rate of mortality on lenglh (d).
Length class Length 

### (mm) Nimber rnl1ected (11)

-----... ----_

> ­ 1 6.0 

### - 6.9 95? 2. 7.0
- 7.9 610 3 8.0 

### - 8.9 383 4 9.0 

### - 9.9 1F3 5 10.0 

### - 10.9 235 11.0 

## - 11.9 21i; 12.0 

### - 12.9 6G 13.0 

### - 13.9 59 14.0 

## - 14.9 20

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

# -' ( 952+618+389+168+235+216+66+59+20
d = 0.43 

## *

This equation was adapted from Section 2.1.4 of Ricker (1975).



## .__

I ' 

# IC/

- i12

Lc m cn P W N w

P -I d d 4 P ? 4 0 UJ Q, U t- 0 0 0 0 0 0 0 ID 3 I I I I I I I m rt --I -I -I --I W 0s v 3- w --I 0 n CD W W W W W W 3 3 v

--I 4 w cn W --I Iu o< 0 m G --I w P N QJ W Q 03 -I W P N ---_I X x X X X x X d d 

# - d -I 

# ­ 0

I 0 I 0 I 0 I 0 I 0 I 0 I P P P P P 0 0

0 3

-m mc 3 3 cn< W m r+ -I. 3c P 4 Lo 0 - D 0 N co d X X X
4 d d 0 0 0 -0­

w L3 w 0- ct -I0 - A. 

### --. wrt -cc rD D I I I PD

w-l -h -5 < W 

## 2 tDn

CD
? (v

Lo 0 a3 h u3 W m M M

0 0 0 Ln W h 0 0 0

m ln m

0 0 0 F 7 7 X x x M M (?

0 0 Ln u) 0 h N N c

m 0, 0, W h co

I I I 0 0 0 rn h co

F (u

... m a3 h cr, 0 0 Lo In rl- u3 m m

0 

# - m 0, 0 co u3 m 0

0 d N

0 co 0 cur-000

ooooLno oComw#-7 c

I 1 1 1 1 1

. --. ..REFEREFICES

### ci-rm Dahlbery, 11. D. 1977. Application of survival cuj’ves to assessmmt of fish larval enirainnient impact. Paper presented at Energy and Environmental Stress inAquatic Systems, the fifth in a series of ecological symposia, Augusta, Ga., 2-4 November 1377. 

### (Ahstr..) 

### Horst., T. (1. 1975. The assessment o-F impact. du~? 

### to entraiiin.ent of ictithyopiaiikton. Pages 107-118 in S. B. Saild, 

### eci. Fislieritjs and energy production: 

### a symposium. D. C. tleath, Lcxingtcin, Mass. Ricker, GI. E. 1975. Coriiptrtation and interpretation of I.iioloqical statistics of fish bopulatioris. Fish. f?es. Boiird Can., hill. 191. 382 pp. Saunders, bl. P., Jr. 1977. A discussion of the iisc of a s’imple niodt.1 for assessing the potential loss OF adult fish res111ting froili ichthyoplanktoii entiaiment. Paper presentcd atEnergy aid Eiivironinental Stress inAquatic Systems, the fifth in 

### a scries of ecological symjxsiz, Augusta, Ga., 2-4 November 1977. (Ahstr.) Swedberg, 

### D. V.

### , and C. II. Walbury. 1970. Spawning and early life histor-y of the freshmter di-um in Lewis and Clark l~ke, t-lissoirri River. Trans. Am. 

### Fish. SOC.90:560-570.