A logistic function to track time-dependent fish population dynamics

Mahmood Jokar,Sam Subbey,Harald Gjøsæter

doi:10.1016/j.fishres.2020.105840

Mahmood Jokar, Sam Subbey + Show 1 more

Open Access

https://doi.org/10.1016/j.fishres.2020.105840

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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.

Highlights

Maturation rates are key drivers of fish stock population dynamics, as they are intrinsically linked to the reproduction potential of the stock
We study the variation in length at maturation for the Capelin (Mallotus villosus) fish stock in the Barents Sea (BS)
The results show that the spikes are coincidental with years of rela tively low Capelin stock biomass, and p1 is inversely related to the capelin biomass

Summary

Introduction

Maturation rates are key drivers of fish stock population dynamics, as they are intrinsically linked to the reproduction potential of the stock (see e.g., Trippel, 1995). The maturation stage of individuals may be determined (for most species) by direct inspection of gonads during periods pre ceding the spawning period (Flores et al, 2015; Williams and Babcock, 2005; Smith and Walker, 2004; Berglund, 1992). This is not always feasible, especially for species where there is a large time-span between when scientific surveys are conducted, and the onset of matu ration. This challenge may be addressed by the use of mathematical/statistical growth models

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