title: Estimating Consumption to Biomass Ratio in Non-Stationary Harvested Fish Populations.
abstract: 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.
authors.affiliation: Center of Applied Ecology and Sustainability (CAPES), Pontificia Universidad Católica de Chile, Av. Alameda 340, Santiago, Chile.
authors.forename: Rodrigo
authors.initials: R
authors.lastname: Wiff
authors.affiliation: King Fahd University of Petroleum and Minerals, Center for Environment and Water, Dhahran 31261, Saudi Arabia.
authors.forename: Ruben H
authors.initials: RH
authors.lastname: Roa-Ureta
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, United Kingdom.
authors.forename: David L
authors.initials: DL
authors.lastname: Borchers
authors.affiliation: Comisión de Investigaciones Científicas de la Provincia de Bs.As (CIC). Calle 526, 1900, La Plata, Argentina; Instituto Nacional de Investigación y Desarrollo Pesquero (INIDEP), Paseo Victoria Ocampo No. 1, 7600 Mar del Plata, Argentina.
authors.forename: Andrés C
authors.initials: AC
authors.lastname: Milessi
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
mesh_terms: D000818:Animals; D018533:Biomass; D005398:Fisheries; D005399:Fishes; D008954:Models, Biological; D011157:Population Dynamics