title: Modelling production per unit of food consumed in fish populations.
abstract: 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.
authors.affiliation: Centre for Research into Ecological and Environmental Modelling, School of Mathematics and Statistics. University of St. Andrews, The Observatory, Buchanan Gardens, St. Andrews KY16 9LZ, Scotland, UK. Electronic address: rodrigo.wiff@gmail.com.
authors.forename: Rodrigo
authors.initials: R
authors.lastname: Wiff
authors.affiliation: Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile.
authors.forename: Mauricio A
authors.initials: MA
authors.lastname: Barrientos
authors.affiliation: Instituto Nacional de Investigación y Desarrollo Pesquero (INIDEP), Paseo Victoria Ocampo No. 1, 7600 Mar del Plata, Argentina; Comisión de Investigaciones Científicas de la Provincia de Bs.As (CIC). Calle 526, 1900, La Plata, Buenos Aires, Argentina.
authors.forename: Andrés C
authors.initials: AC
authors.lastname: Milessi
authors.affiliation: Institute for Marine and Antarctic Studies, University of Tasmania, Private Bag 49, Hobart, Tasmania 7001, Australia; División de Investigación Pesquera, Instituto de Fomento Pesquero (IFOP), Blanco 839, Valparaíso, Chile.
authors.forename: J C
authors.initials: JC
authors.lastname: Quiroz
authors.affiliation: Centre for Research into Ecological and Environmental Modelling, School of Mathematics and Statistics. University of St. Andrews, The Observatory, Buchanan Gardens, St. Andrews KY16 9LZ, Scotland, UK.
authors.forename: John
authors.initials: J
authors.lastname: Harwood
mesh_terms: D000818:Animals; D018533:Biomass; D005399:Fishes / Q000502:physiology*; D020387:Food Chain; D008954:Models, Biological; D010140:Pacific Ocean
keywords: Consumption; Population energetics; Von Bertalanffy growth function