Time series bias in the estimation of density-dependent mortality in stock-recruitment models

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Abstract
Large biases can occur in parameter estimates for stock–recruitment models because the stock sizes are not chosen independently, being correlated with variability in recruitment. We examine the importance of this "time series bias" by a comprehensive analysis of available stock–recruitment data and the use of simulations. For semelparous species, i.e., species that reproduce only once, time series bias is important for all populations for which we had data. For iteroparous species, i.e., species that reproduce more than once, large biases occur if the populations are exploited at close to the maximum that is biologically possible. Notably, when there is autocorrelation in natural mortality, for univoltine species, the direction of bias is reversed due to model misspecification. Given moderate sample sizes and moderate levels of exploitation, time series bias is small for species such as Atlantic cod (Gadus morhua), for which α, the slope of the relationship between recruitment and number of spawners as the number of spawners goes to zero, is large. Time series bias will usually be important in species such as hakes (Merluccius) for which α appears to be relatively small.