Estimating Consumption to Biomass Ratio in Non-Stationary Harvested Fish Populations.

The food consumption to biomass ratio (C) is one of the most important population parameters in ecosystem modelling because its quantifies the interactions between predator and prey. Existing models for estimating C in fish populations are per-recruit cohort models or empirical models, valid only for stationary populations. Moreover, empirical models lack theoretical support. Here we develop a theory and derive a general modelling framework to estimate C in fish populations, based on length frequency data and the generalised von Bertalanffy growth function, in which models for stationary populations with a stable-age distributions are special cases. Estimates using our method are compared with estimates from per-recruit cohort models for C using simulated harvested fish populations of different lifespans. The models proposed here are also applied to three fish populations that are targets of commercial fisheries in southern Chile. Uncertainty in the estimation of C was evaluated using a resampling approach. Simulations showed that stationary and non-stationary population models produce different estimates for C and those differences depend on the lifespan, fishing mortality and recruitment variations. Estimates of C using the new model exhibited smoother inter-annual variation in comparison with a per-recruit model estimates and they were also smaller than C predicted by the empirical equations in all population assessed.

Modelling production per unit of food consumed in fish populations.

The ratio of production-to-consumption (ρ) reflects how efficiently a population can transform ingested food into biomass. Usually this ratio is estimated by separately integrating cohort per-recruit production and consumption per unit of biomass. Estimates of ρ from cohort analysis differ from those that consider the whole population, because fish populations are usually composed of cohorts that differ in their relative abundance. Cohort models for ρ also assume a stable age-structure and a constant population size (stationary condition). This may preclude their application to harvested populations, in which variations in fishing mortality and recruitment will affect age-structure. In this paper, we propose a different framework for estimating (ρ) in which production and consumption are modelled simultaneously to produce a population estimator of ρ. Food consumption is inferred from the physiological concepts underpinning the generalised von Bertalanffy growth function (VBGF). This general framework allows the effects of different age-structures to be explored, with a stationary population as a special case. Three models with different complexities, depending mostly on what assumptions are made about age-structure, are explored. The full data model requires knowledge about food assimilation efficiency, parameters of the VBGF and the relative proportion of individuals at age a at time y (Py(a)). A simpler model, which requires less data, is based on the stationary assumption. Model results are compared with estimates from cohort models for ρ using simulated fish populations of different lifespans. The models proposed here were also applied to three fish populations that are targets of commercial fisheries in the south-east Pacific. Uncertainty in the estimation of ρ was evaluated using a resampling approach. Simulation showed that cohort and population models produce different estimates for ρ and those differences depend on lifespan, fishing mortality and recruitment variations. Results from the three case studies show that the population model gives similar estimates to those reported by empirical models in other fish species. This modelling framework allows ρ to be related directly to population length- or age-structure and thus has the potential to improve the biological realism of both population and ecosystem models.