Effects of stochasticity in early life history on steepness and population growth rate estimates: an illustration on Atlantic bluefin tuna.

Daniel Gaertner,Sylvain Bonhommeau,Jean-Marc Fromentin,Maximilien Simon,Jon Brodziak,Marie-Pierre Etienne

doi:10.1371/journal.pone.0048583

Abstract

The intrinsic population growth rate (r) of the surplus production function used in the biomass dynamic model and the steepness (h) of the stock-recruitment relationship used in age-structured population dynamics models are two key parameters in fish stock assessment. There is generally insufficient information in the data to estimate these parameters that thus have to be constrained. We developed methods to directly estimate the probability distributions of r and h for the Atlantic bluefin tuna (Thunnus thynnus, Scombridae), using all available biological and ecological information. We examined the existing literature to define appropriate probability distributions of key life history parameters associated with intrinsic growth rate and steepness, paying particular attention to the natural mortality for early life history stages. The estimated probability distribution of the population intrinsic growth rate was weakly informative, with an estimated mean r = 0.77 (±0.53) and an interquartile range of (0.34, 1.12). The estimated distribution of h was more informative, but also strongly asymmetric with an estimated mean h = 0.89 (±0.20) and a median of 0.99. We note that these two key demographic parameters strongly depend on the distribution of early life history mortality rate (M0), which is known to exhibit high year-to-year variations. This variability results in a widely spread distribution of M0 that affects the distribution of the intrinsic population growth rate and further makes the spawning stock biomass an inadequate proxy to predict recruitment levels.

Highlights

Bayesian state-space modeling is developing into a practical approach for stock assessment studies and appears adapted for fisheries management because it provides a statistically rigorous framework for deriving quantitative estimates for decision analyses [1,2]
The aim of the present study was the elicitation of prior distributions for the steepness parameter of the stock-recruitment relationship (SR) and for the intrinsic population growth rate of the biomass dynamic model for the Atlantic bluefin tuna (ABFT, Thunnus thynnus thynnus)
Mortality Rate from Recruitment to Terminal Age From age 1 to terminal age, we considered the age-specific natural mortality vector [mM(1)....mM(A)] given by the scientific committee of ICCAT which is based on tagging experiments conducted on southern bluefin tuna, Thunnus maccoyii (SBT) [69]

Summary

Introduction

Bayesian state-space modeling is developing into a practical approach for stock assessment studies and appears adapted for fisheries management because it provides a statistically rigorous framework for deriving quantitative estimates for decision analyses [1,2]. Bayesian models require specification of prior probability distribution functions (pdf) for model parameters; posterior probability distributions are derived from the combination of prior information and the sample likelihood information contained in the data. This sequential learning process allows for the incorporation of expert and biological knowledge into the prior pdf and the use of informative priors can improve inference by multiplying the available information sources [3]. The approach allows the use of additional and independent information from different sources that is usually ignored within traditional stock assessment models. The Bayesian framework has been applied to many different exploited fish stocks, such as salmon [2], tuna [6], rockfish [7], small pelagics [8] and sharks [9]

Objectives

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Conclusion