MacCALL ET AL.: POWER PLANT IMPACT ASSESSMENT 



rate as does some better known similar species in a 

 similar environment. 



Equivalent adult loss from a cohort (A c ) may be 

 defined as 



A c = N' e - N c . 



(8) 



However, a standing stock of adults often consists of 

 several cohorts. Under the common fishery assump- 

 tion that the age composition of the standing stock is 

 at equilibrium, overall equivalent adult losses (A e ) 

 from the stock are given by 



TV -N 



(9) 



where JV denotes unimpacted stock abundance, and 

 N denotes impacted stock abundance, given the 

 same initial production, of eggs. Although this equi- 

 librium assumption is often violated, it is nonetheless 

 the basis of management of many fish stocks. Since 

 the quantity R ( . describes the ratio for a cohort A^/A^, 

 under equilibrium it also describes the population 

 ratio N/N 1 , here denoted R. The latter may be sub- 

 stituted into Equation (9) to give 



or 



A e = N (I- R) 

 A t =N (i-1). 



(10) 

 (ID 



Thus equivalent adult losses can be calculated if 

 adult abundance has been estimated, and this does 

 not require the extensive knowledge of life history pa- 

 rameters demanded by Goodyear's (1978) approach. 

 Equations (10) and (11) raise a dilemma with re- 

 spect to short- and long-term impact. Estimation of 

 short-term impact has been based on the assumption 

 of a fixed initial production of eggs. However, when 

 real data are used, preimpact abundance (N') will 

 usually arise from a larger egg production than does 

 postimpact abundance (N ), for the very reason than 

 N ' is larger thaniV, and egg production is itself depen- 

 dent upon adult abundance. For this reason, Equa- 

 tion (10) is misleading, and will tend to overestimate 

 the amount of adult equivalent losses actually occur- 

 ring from an impacted stock at equilibrium. However, 

 in most cases, preimpact abundance is unknown, and 

 sampling programs produce estimates of N, which re- 

 quire application of Equation (11). Moreover, Good- 

 year's (1978) equivalent adult losses are calculated 

 for an impacted stock making Equation (11) appro- 

 priate. As will be seen below, our method of estimating 

 long-term equilibrium impact does not require ex- 

 plicit calculation of equivalent adult losses, and 

 avoids the above complications. 



LONG-TERM IMPACT 



Whereas short-term impact may be described in 

 simple terms of adult equivalent losses, long-term 

 impact is more difficult to quantify. Short-term loss 

 of adults implies loss of reproductive potential (egg 

 production), and this loss is compounded over 

 several generations. If compensatory mechanisms 

 were not present, the impacted population would 

 decline exponentially to extinction, given that it was 

 in equilibrium prior to the impact. Fortunately, there 

 are many types of compensatory mechanisms that 

 allow the population to augment its reproductive rate 

 so that it reaches a new equilibrium in the presence of 

 an increased mortality rate (see Goodyear 1980). For 

 example, lowered adult abundance may lead to in- 

 creased per capita fecundity, decreased age of first 

 reproduction, and/or increased survivorship at var- 

 ious life stages. Unfortunately, the actual mecha- 

 nisms are poorly known and can be seldom quantified 

 even for well-studied species. Detailed knowledge 

 cannot be expected in routine impact analyses. 

 Rather, we need simple approximations that will re- 

 quire a minimum of data. 



Fishery management has long been concerned with 

 the effect of removal (harvests) rates on fish abun- 

 dance. Most of the work has been concerned with 

 long-term equilibrium, and many fishery models are 

 directly applicable to impact analysis. In particular, 

 the "production model" (see Ricker 1975, Chapter 

 13), by means of simplifying assumptions, requires 

 minimal knowledge of life history parameters. One of 

 the simplest production models is the Graham- 

 Schaefer model, which is constructed on the assump- 

 tion of logistic population growth. The model 

 assumes that equilibrium stock abundance declines 

 linearly with an increasing rate of harvest (fraction of 

 stock removed per unit time). The maximum net pro- 

 ductivity in terms of total harvest by a fishery is 

 therefore assumed to be achieved at a stock size 

 which is exactly one-half the virgin level of abun- 

 dance or carrying capacity, K (Fig. 1). 



Normally, the production model is useful when a 

 long time series of catches and fishing efforts (rates of 

 removal) is available. In such cases, the production 

 curve can be estimated from the data by statistical 

 regression. On the other hand, there are many fish- 

 eries for which there is no history of exploitation, or 

 for which the required data were never collected. 

 Here, we may draw on the "potential yield" formula, 

 first proposed by Alverson and Pereyra (1969), pro- 

 mulgated by Gulland (1970, 1971), and critically re- 

 viewed by Francis (1974). This approximation 

 assumes that net productivity is maximal when abun- 



615 



