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Fishery Bulletin 90(3). 1992 



management of fish stocks has recently been chal- 

 lenged by Walters and Collie (1988) and Walters (1989). 

 In simulated management examples, Walters (1989) 

 finds that only extremely accurate forecasts of recruit- 

 ment can offer significant improvements over using the 

 long-term mean recruitment in stock assessment 

 models. Thus, while studies of the early stages of 

 marine fish may reveal insights into their ecology, it 

 is unclear whether sufficiently accurate forecasts of 

 recruitment wall ever be possible from these early 

 stages. 



In this paper I first pose the question, "How strong 

 are the correlations between abundances or mortality 

 rates of the early life stages and recruitment likely to 

 be?" I develop a simple analytical model based on key- 

 factor analysis (Varley and Gradwell 1960, Manly 

 1977). I use parameter estimates compiled from a 

 literature survey to calculate the expected correlations 

 between life stages for the prediction of fish recruit- 

 ment. I suggest that the assertion that year-class 

 strength is fixed in the early-larval stages is not gen- 

 eral, and, furthermore, under likely field conditions it 

 will be difficult to quantitatively test this hypothesis. 



The model 



I developed a simple model to simulate the variability 

 in population numbers and the strength of correlations 

 between life stages. In brief, the model generated an- 

 nual abundances and mortality rates over a specified 

 number of years from which correlations between 

 early-life-history stages and recruitment were calcu- 

 lated. This process was repeated in a Monte Carlo 

 fashion to estimate the sampling distribution of the 

 correlation coefficients. 



I divided the egg-recruit period into four intervals: 

 (1) egg-yolksac larvae, (2) early-feeding larvae, (3) late- 

 feeding larvae, and (4) juveniles from metamorphosis 

 to age 1, which I assumed to be the age of recruitment. 

 I assumed that populations would be sampled at five 

 distinct times that divide the egg-recruit period into 

 four intervals. Sampling points were: eggs spawned 

 (Ng), first-feeding larvae (Nf), young larvae (N|),meta- 

 morphs (N^), and recruits (Nr). First-feeding larvae 

 were operationally defined as larvae that have just 

 begun to feed, while young larvae were defined as 

 having an age of 10 days after the onset of feeding. 



In any year, the number of recruits is the product 

 of the number of eggs spawned and the survival rates 

 of the prerecruit stages: 



Recruitment = Eggs • Sys • Sei • Su • Sj , 



where the subscripts refer to the egg-yolksac, early- 



larval, late-larval, and juvenile periods outlined above. 

 Expressing survival rates as instantaneous mortalities, 

 M = - ln(S), and taking logs of the abundances give the 

 usual equation of key-factor analysis (Varley and Grad- 

 well 1960): 



N, = N, - M,, - M,, - Mn - M 



*ys 



^J' 



(1) 



where Nr and Ng are log abundances of recruits and 

 eggs of a particular cohort, and the M; values are 

 interval-specific instantaneous mortalities for four in- 

 tervals defined above. I assume, following Hennemuth 

 et al. (1980) and Peterman (1981), that log abundances 

 and instantaneous mortality rates are normally dis- 

 tributed with stage-specific variances described below. 

 This multiplicative process results in lognormally dis- 

 tributed recruitment, consistent with empirical results 

 (Hennemuth et al. 1980). All subsequent references to 

 abundance made in this paper are to log-transformed 

 values. 



Since I am interested in short-term forecasting, I 

 assumed that stock size and, therefore, mean egg pro- 

 duction are stationary in time and that variation in egg 

 production is independent of recruitment. Thus, in the 

 absence of density-dependent processes, recruitment 

 is linearly related to egg production. 



To introduce stochastic variation in the model, the 

 abundance of eggs, Ng, and the interval-specific mor- 

 tality rates were simulated as normal random variables. 

 As the time-series of egg production was stationary and 

 my interest is in correlations rather than abundances, 

 the abundance of eggs and the mortality rates all had 

 a mean of 0. 



To start the sequence of calculations in a given model 

 year, the initial abundance of eggs was randomly 

 chosen. In the simplest version of the model, which 

 assumes mortality in each interval is independent of 

 the others and is density-independent, the following 

 equation was then used to calculate the numbers of 

 each subsequent stage: 



Nk+i = Nk-mk, 



(1) 



where N^ is the abundance of stage k, and m is a nor- 

 mal random deviate that simulates random interannual 

 variability in mortality of interval k. 



The complete independence of mortality of one stage 

 with that of a subsequent stage is probably an un- 

 realistic assumption because, for example, years which 

 are good for yolksac larval survival may also be good 

 for the survival of older larvae. This can be modeled 

 by introducing covariances between the interval- 

 specific mortality rates (Gerrodette et al. 1984). Co- 

 variation between interval-specific mortality rates was 

 modeled by assuming that there was a positive corre- 



