;:--., 

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 wild1 ife 

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 in respect to environmental impact 

assessment. 

2. To gather, analyze, and present information that will aid 

decision makers in the 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 in the 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 in the 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 in Washington, 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 at the operating level; and staff 

at certain Fish and Wildlife Service research facilities who conduct in- . . .; ... ._ ..,-. 2: >>-. house research studies. . ..-.., .. ... 
----- 

Wildlife 

Biolgical Services Prog-raiii ~ ~ -_ I ' I __-

FbIS/0G 5 -78165 

July 1978 

EPIT'RAIFI~~1EPJTIFPACT ESTIP!ATES 

US I rIG THE EQUIVALEPIT ADULT APPROACE 

hy 

C. Phi 11 ip Guoclycar

National Power Plant Team 

1451 Gwen Road 

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 Suprint endcnt of Document.. US. Oovwnmcnt 

'i Prlntrng Offtce. Washlngt on, ..

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 mortal ity 

of eggs and larvae of fish and shellfish by power plants is to estimate 

the number of adult organisms 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 '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 -_ 

s=--2 ­ .................... .(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~itslost 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 ti o rs_t_lsf o rmul-a.t.ion .-t.he...e.st ima te ..g!--sl)IKi-v a1 fr?m--ea-- t:o-.cnt.r>ai_ne d 

1arvae F).-i 5.. ass-um,e,d. to, he.. cDns~.an.~_f.o-r.-a.ll. en_traineclll_arva~., and this

is-a potefitial 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

for most of the entrained larvae, the youny&r. ones, woiJ1d underestimate 

the impact. 

ALT ERFl AT I V E 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 to each 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 to determine the 

age of larvae precisely enough to allo\i ttie 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 to estimate 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 S9, Y. .................... - .(6)

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 t rai iiineti t 

Sk = survival probabi ity froiri length class R to adulthood 

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

.. 

S

e,% = 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 is a 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 

0 
5 

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 

S 

e,, = He 

-d (L,- h ) ....................(9) 

where H = fraction of eggs 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 

to the spawning population, frequency of spawning, relative fecundity of 

_ -
Cumulative Aburid;lncc 

--I 

--. 0 

.) 

-il 0 0

0 0 0 0 0 

. 4. 

J 
7 

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 at equilibriuiri. 

To dcterniine average lifetime fecutidity of an adult feiiiale it is 

necess2r.y to define the age at which the individual becurries an adult. 

Two a1 ternative definitions are Gonsidered here: (1) an adult is a 

recruit to the aye class in which spawriirlg is first observed, or (2) an 

"adult" is an iridividual iri the first aye class tllat is recruited 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" populat iun, 

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 recrui tiiietit: to age class j, and

J 

E. 

3 = average fecundity of [nature feiiiales OF age class j. 

if recr~uitirientto the "adult" population is considptved to occur at 

ttie itistatit 'that sparitling occurs then tlie value of S .

J 

is giver) by: 

S. = e -z(j-a) .................. .(12) J 

where Z is the instantatieous rate of total mortality. 

E. in equation (Ilkhis the 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 %Rat are e !dKinakr!.&.-.enh-aim t ca ti be 

e-d usiny equation (6): 

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

-- 

.

I. -­

8 

iI. 

I k 

I Na = c N, S, ! R= 1 

where s,'= 

'e,, 

2 

Fa ' 

The reduction in numbers of fish captured by the fishery (Nf) can 

be estimated as: 

Na N 

f = - z . . . . . . . . . . . . . . . . . . . . . .(13) 

where F is the instantaneous rate of fishing mortality. 

LIMITATIONS 

Es t iRia tes ~f-o~e-,ll.mses-cif adu 1ts&jngltheaqu iv a-1 enLa du.1.t. ~ a p proa ch 

presume ~ that ~ there . _ -".~ -i s-....no densiudependent -.-. mortality ~ occurring between 

the time that the larva .is killed by entrainment andTfFt-imi E-would 

have _.__.____.__C_ been recruited - to the "adul tl!..-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 ~.__ ~

1 i ttl e insi h t_e--- into th~~~.Elrm_lLi.~~i..~-..Q~-~h~--~~f~c~~ati-ons

an?ou__be.-.used-onl~y-tnsh~n_~-~rst_.app.~ox~.mati~o~ of the severity 

omntial .... losses. In applications, special consideration--slioula'-'~e 

given to the accuracy of the estimates of the number of larvae killed by

entrainment, and to the fraction of eggs that survive to become 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 to use 

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 in numbers 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 to 3 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 

Nf =( 836500) (0.29)

0.5108 

Nf = 470,000 
-- 

J 

ASJ? 

3 

4 

!j 

-6 

7 

3 

9 

10 

11 

.I 2 

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 mortali ty on lenglh (d). 

Length class Length (mm) Nimber rnl1 ected 

( 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 21 i; 

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/ - i 
12 

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 

0 

d d - d -I ­ I 0 

I 0 

I 0 

I 0 

I 0 

I 0 

P P I 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 tD 
n 

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 in Aquatic 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 res111 ting froili 

ichthyoplanktoii entiaiment. Paper presentcd at Energy aid Eiivironinental Stress in Aquatic 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.