A logistic function to track time-dependent fish population dynamics

Abstract

This paper uses a two-parameter logistic function to model the dynamics of length-at-maturation for the Barents Sea capelin over the past 47 years. We estimate the function parameters using a combination of length-age data from scientific surveys, and commercial catch statistics.

Using temporal variability in the function parameters, we demonstrate that the time series of stock biomass defines a three-state Markov process, that qualitatively represent high, moderate, and collapse states of the stock biomass. We make inference about transition times between the states by calculating the mean passage times for the Markov process.

Our analyses also show that maturation intensity is higher at low stock size (leading to shorter lengths at maturation), compared to when biomass levels are either high or moderately high. Our results are central to management of this stock, as uncertainty in estimating the proportion of maturing biomass affects harvest decisions and ultimately, the sustainability of the stock.