Population dynamics

The tuna population dynamics simulation sub-model in sepodym is a spatial multigear, multispecies model. It is age-structured to account for growth and gear selectivity. It includes a movement model based on a diffusion-advection equation in which the advective term is proportional to the gradient of the adult habitat index.

D diffusion coefficient (random movement of tuna),

I, habitat index

Xo, advective coefficient (the viscosity coefficient in Mc Call (1990) acceptation)

N, tuna population,

R, recruitment,

Z, total (natural and fishing) mortality

A description of the population dynamics can be found in Bertignac et al. (1998). The total level of recruitment is scaled to obtain a standing stock at equilibrium in agreement with independent estimations. Tuna stock-recruitment relationships are poorly known and recruitment is usually assumed to be independent of the adult population density, mainly because tuna have very high fecundity and spawn throughout the year over a large area. Therefore, the simulation does not assume any stock-recruitment relationship, but the spatial distribution of recruits is environmentally constrained by the processes occurring in the pre-recruitment period (see spawning habitat index). During a short period of development (4 months), larvae and juveniles are passively transported by the currents. Following this period, young tuna become autonomous and move according to the gradient of habitat index as the adults.

Single- or multi-species structured population models developed with rigorous statistical estimations relying on fishing and tagging data are useful for estimating the population parameters, such as biomass, mortality, growth, vulnerability to capture, and gear selectivity. Biological studies (growth, reproduction, and diet), physiological experiments, and acoustic tracking and archival tagging make it possible to better define various aspects of the biology of the species, including their habitat and behaviour. Individual-based models (IBMs) are a useful approach for integrating these different types of information and testing and formulating mathematically the behaviours, growth variability, and survival probabilities of individuals of specific species through time, as determined by environmental conditions.

The parameterization of SEPODYM benefits from the concurrent development of the statistical fish population model MULTIFAN-CL and its application to the main tuna stocks in the Pacific. In particular, the total level of recruitment is scaled to obtain a standing stock at equilibrium in agreement with MULTIFAN-CL estimates.

While MULTIFAN-CL produces recruitment and biomass estimates from robust statistical methods, SEPODYM recruitment and biomass are predicted from environmental constrains. Comparisons between these two independent estimates are useful to investigate hypotheses on the mechanisms of recruitment.