FISHERY BULLETIN: VOL. 81, NO. 3 



single cohort (e.g., year class) in the sense of Good- 

 year's (1978) equivalent adult mortality. The second 

 analysis estimates the long-term equilibrium impact 

 of combined removals, including entrainment and 

 impingement by one or more power plants, and all 

 other nonnatural removals, including fishery har- 

 vests. 



SHORT-TERM IMPACT 



In the natural state, where no spawning products 

 are removed by entrainment, the adult abundance of 

 a cohort, N' c (at a reference age T), is given by 



Nl = Pe 'I^ x)dx 



(1) 



where P is initial production of newly spawned eggs, x 

 is age, and /jl(x) is per capita natural mortality rate at 

 age x, i.e., —dN{x)/Ndx. 



A more convenient approximation of Equation (1) 

 is 



N [ = p e -™,<, a nd T = Z.L 



(2) 



where t l is the length of age interval i, and M, is a per 

 capita natural mortality rate, assumed to be constant 

 over interval i. 



In the presence of mortality due to entrainment, the 

 adult abundance of the impacted cohort, N c (again at 

 reference age T ) is given by 



jV = pg-nEi+M-Hi 



(3) 



where E, is the per capita rate of entrainment mortali- 

 ty during age interval i. 



The abundance of an impacted cohort relative to 

 an unimpacted cohort is denoted R c , and is given 

 by 



R c = N c /N' c 



(4) 



and after substituting Equations (2) and (3), this sim- 

 plifies to 



R=e 



-ZE:t, 



(5) 



which is related to the conditional mortality rate (m) 

 described by Ricker (1975: equation 1.9; here m = 1 

 — R c ) . Note that Tneed not be specified, since we now 

 need sum over only those age intervals in which E, is 

 nonzero. This is convenient since fish often cease be- 

 ing entrained at about the same time they cease being 

 available to plankton sampling gear. More important 

 is the fact that Equation (5) requires no knowledge of 



life history parameters. The main assumption here is 

 that there is no compensatory change in the per 

 capita rate of natural mortality during early life 

 stages which offsets the added effect of entrain- 

 ment mortality. 



Equation (5) is similar in concept and derivation to 

 recently published methods of calculating impact 

 rate (e.g., Boreman etal. 1981; Jensen and Hamilton 

 1982). Those methods explicitly include water 

 volumes and are especially appropriate to cases of 

 highly fluctuating water flows. For the purposes of 

 the assessment methods discussed in this paper, 

 either method of calculating impact rate is appli- 

 cable. 



The entrainment mortality rates, E„ are fairly easy 

 to estimate. Larval mortality may be assumed to con- 

 form to a "Type 2 fishery" in the sense of Ricker 

 (1975), wherein natural mortality occurs along with 

 entrainment, and each occurs at a constant per capita 

 rate during each age interval i. If power plant activity 

 is fairly constant over the spawning season, each E t is 

 constant, and it is unnecessary to distinguish be- 

 tween Ricker's two types of recruitment. According 

 to Ricker's (1975) equation 1.17, the quantity of lar- 

 vae at stage i removed during a unit time by entrain- 

 ment (L,) is related to the mean abundance of lar- 

 vae at stage i in the source water (L*) by the equa- 

 tion 



L, = E, L* 



(6) 



Therefore, E, may be estimated by the equation 



E, = L,/L* (7) 



where L, is a direct in-plant sample estimate of the 

 quantity of stage i larvae entrained p_er day (or other 

 convenient short time interval), and L? is an estimate 

 of the mean standing crop of stage i larvae over that 

 same time interval in the source water, which may be 

 estimated by quantitative plankton net tows. Note 

 that entrainment rate E, has units of inverse time 

 according to the time interval used. Care must be 

 taken to assure that time units are consistent 

 throughout the analysis. Also note that i now refers to 

 a stage, as it is generally most convenient to sort sam- 

 ples or planktonic larvae by size or stage categories. 

 The length of time spent in each size category must 

 also be determined. The most direct method may be 

 to examine larval otoliths for daily growth rings (see 

 Brothers et al. 1976) in order to ascertain the number 

 of days (or other time unit employed) spent in stage i. 

 Lacking this direct information on t„ it may be ne- 

 cessary to assume that the larvae grow at the same 



614 



