A simple length-structured model based on life history ratios and incorporating size-dependent selectivity: application to spawning potential ratios for data-poor stocks

Selectivity in fish is often size-dependent, which results in differential fishing mortality rates across fish of the same age, an effect known as Lee's Phenomenon. We extend previous work on using length composition to estimate the spawning potential ratio (SPR) for data-limited stocks by developing a computationally efficient length-structured per-recruit model that splits the population into a number of subcohorts, or growth-type-groups, to account for size-dependent fishing mortality rates. Two simple recursive equations, using the life history ratio of the natural mortality rate to the von Bertalanffy growth parameter (M/K), were developed to generate length composition data, reducing the complexity of the previous approach. Using simulated and empirical data, we demonstrate that ignoring Lee's Phenomenon results in overestimates of fishing mortality and negatively biased estimates of SPR. We also explored the behaviour of the model under various scenarios, including alternative life history strategies and the presence of size-dependent natural mortality. The model developed in this paper may be a useful tool to estimate the SPR for data-limited stock where it is not possible to apply more conventional methods.