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

RESEARCH ARTICLE Estimating Consumption to Biomass Ratio in Non-Stationary Harvested Fish Populations Rodrigo Wiff1*, Ruben H. Roa-Ureta2, David L. Borchers3, Andrés C. Milessi4,5, Mauricio A. Barrientos6 1 Center of Applied Ecology and Sustainability (CAPES), Pontificia Universidad Católica de Chile, Av. Alameda 340, Santiago, Chile, 2 King Fahd University of Petroleum and Minerals, Center for Environment and Water, Dhahran 31261, Saudi Arabia, 3 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, 4 Comisión de Investigaciones Científicas de la Provincia de Bs.As (CIC). Calle 526, 1900, La Plata, Argentina, 5 Instituto Nacional de Investigación y Desarrollo Pesquero (INIDEP), Paseo Victoria Ocampo No. 1, 7600 Mar del Plata, Argentina, 6 Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile * Abstract OPEN ACCESS Citation: Wiff R, Roa-Ureta RH, Borchers DL, Milessi AC, Barrientos MA (2015) Estimating Consumption to Biomass Ratio in Non-Stationary Harvested Fish Populations. PLoS ONE 10(11): e0141538. doi:10.1371/journal.pone.0141538 Editor: Andrea Belgrano, Swedish University of Agricultural Sciences, SWEDEN Received: June 12, 2015 Accepted: October 10, 2015 Published: November 3, 2015 Copyright: © 2015 Wiff et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 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. Data Availability Statement: All relevant data are within the paper and its Supporting Information file. Funding: Rodrigo Wiff was funded by CONICYT (Chile) scholarship for postgraduate studies abroad (“Beca Presidente de la Republica para Estudios de Postgrado en el Extranjero”), CONICYT/FONDECYT post-doctoral project number 3130425 and by CAPES Project Conicyt FB 0002 (2014). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Introduction Food consumption of a population is one of the most important quantities required to implement multiespecies models in aquatic ecosystems, because it directly quantifies the intensity of interactions between predator and prey. Regular stock assessment programs provide annual estimates of abundance of the most productive fish stocks of various marine ecosystems around the world. To connect these estimates in multispecies models we need estimates of food PLOS ONE | DOI:10.1371/journal.pone.0141538 November 3, 2015 1 / 13 Consumption to Biomass Ratio in Fish Populations Competing Interests: The authors have declared that no competing interests exist. consumption to biomass ratio (hereafter C) at the population level. This ratio can be seen as the number of times a population eats its own weight during a certain period of time (usually a year), a kind of standardised population consumption rate. Methods for estimating consumption rates of fish at the individual level have been well studied (see [1]). Conversely, estimating C at the population level is a laborious and difficult task that is usually done using methods that depend on strong assumptions. This is problematic for most fish species because the strong assumptions of existing methods imply serious limitations. Here, we develop and demonstrate the applicability of a new general method based on data on the population size structure. Conventional methods to estimate population consumption rates fall roughly into two categories: (i) methods, like those of Pauly [2] and Aydin [3], in which experimental and field data are combined to estimate C by integrating consumption and biomass over a cohort lifespan, thus providing per-recruit estimator for C. (ii) Methods that use an empirical relationship between C and some environmental and body size attributes [4]. Pauly’s model relies on the assumption of stable age-distribution and the parameters defining individual consumption have no clear biological meaning. Aydin [3] extended Pauly’s model to incorporate biological parameters which describe consumption but this model still relies on the assumption of stable age-distribution. The per-recruit analysis framework used in Pauly [2] and Aydin [3] has two main drawbacks for estimating C. First, the use of the specialised von Bertalanffy growth model implies the assumption of an anabolism parameter, d = 2/3, but this specific value is unusual for teleost fishes [5]. Second, the assumption of a stable age-distribution may be valid for stationary populations but it may not be useful for fished populations because fishing exploitation often produces inter-annual variations in age-dependent mortality and recruitment [6]. The application of empirical models on the other hand, is straightforward, but these models lack theoretical support, relying on assumptions of constant coefficients across species and environments, and they cannot account for shifts in population structure. These limitations suggest that alternative approaches are needed. The relationship between the growth rate of an individual fish and the amount of food it ingests has been noted by several authors (e.g. see [7–10]). The existence of this relationship implies that food consumption can be inferred from growth rate [11, 12]. In this reductionist approach, food (...truncated)