A logistic function to track time-dependent fish population dynamics

publishedVersio

The specification of the data model part in the SAM model matters

This paper considers a general state-space stock assessment modeling framework that integrates a population model for a fish stock and a data model. This way observed data are linked to unobserved quantities in the population model. Using this framework, we suggest two modifications to improve accuracy in results obtained from the stock assessment model SAM and similar models. The first suggestion is to interpret the “process error” in these models as stochastic variation in natural mortality, and therefore include it in the data model. The second suggestion is to consider the observed catch as unbiased estimates of the true catch and modify the observation error accordingly. We demonstrate the efficacy of these modifications using empirical data from 14 fish stocks. Our results indicate that the modifications lead to improved fits to data and prediction performance, as well as reduced prediction bias.publishedVersio

Caveats with estimating natural mortality rates in stock assessment models using age aggregated catch data and abundance indices

We consider the challenge in estimating the natural mortality, M, in a standard statistical fish stock assessment model based on time series of catch- and abundance-at-age data. Though anecdotal evidence and empirical experience lend support to the fact that this parameter may be difficult to estimate, the current literature lacks a theoretical justification. We first discuss the estimatability of a time-invariant M theoretically and present necessary conditions for a constant M to be identifiable. We then investigate the practical usefulness of this by estimating M from simulated data based on models fitted to 19 fish stocks. Using the same data sets, we next explore several model formulations of time varying M, with a pre-specified mean value. Cross validation is used to assess the prediction performance of the candidate models. Our results show that a time-invariant M can be estimated with reasonable precision for a few stocks with long time series and typically high values of the true M. For most stocks, however, the estimation uncertainty of M is very large. For time-varying M, we find that accounting for variability across age and time using a simple model significantly improves the performance compared to a time-invariant M. No significant improvement is obtained by using complex models, such as, those with time dependencies in variability around mean values of M.publishedVersio

Final report for the REDUS project - Reduced Uncertainty in Stock Assessment

The REDUS project (2016-2020) has been a strategic project at the Institute of Marine Research (IMR) aimed at quantifying and reducing the uncertainty in data-rich and age-structured stock assessments (e.g., cod, herring, haddock, capelin). Work was organized in four topical work-packages: Fisheries-dependent (catch) surveys and assessment modeling (WP1), Fishery-independent (scientific) surveys (WP2), Evaluating and testing of long-term management strategies (WP3), and Communication of uncertainty, dissemination of project results and capacity building (WP4). The Norwegian Computing Center (NR) was contracted in as a strategic partner in statistical modeling and analysis, contributing mainly to WP1 and WP2, but found the research of fundamental interest therefore also allocating internal (NR) funding to develop the statistical science base of several of the methods.publishedVersio

Non-deterministic modelling of food-web dynamics

A novel approach to model food-web dynamics, based on a combination of chance (randomness) and necessity (system constraints), was presented by Mullon et al. in 2009. Based on simulations for the Benguela ecosystem, they concluded that observed patterns of ecosystem variability may simply result from basic structural constraints within which the ecosystem functions. To date, and despite the importance of these conclusions, this work has received little attention. The objective of the present paper is to replicate this original model and evaluate the conclusions that were derived from its simulations. For this purpose, we revisit the equations and input parameters that form the structure of the original model and implement a comparable simulation model. We restate the model principles and provide a detailed account of the model structure, equations, and parameters. Our model can reproduce several ecosystem dynamic patterns: pseudo-cycles, variation and volatility, diet, stock-recruitment relationships, and correlations between species biomass series. The original conclusions are supported to a large extent by the current replication of the model. Model parameterisation and computational aspects remain difficult and these need to be investigated further. Hopefully, the present contribution will make this approach available to a larger research community and will promote the use of non-deterministic-network-dynamics models as ‘null models of food-webs’ as originally advocated

A logistic function to track time-dependent fish population dynamics

This paper uses a two-parameter logistic function to model the dynamics of length-at-maturation for the Barents Sea capelin over the past 47 years. We estimate the function parameters using a combination of length-age data from scientific surveys, and commercial catch statistics. Using temporal variability in the function parameters, we demonstrate that the time series of stock biomass defines a three-state Markov process, that qualitatively represent high, moderate, and collapse states of the stock biomass. We make inference about transition times between the states by calculating the mean passage times for the Markov process. Our analyses also show that maturation intensity is higher at low stock size (leading to shorter lengths at maturation), compared to when biomass levels are either high or moderately high. Our results are central to management of this stock, as uncertainty in estimating the proportion of maturing biomass affects harvest decisions and ultimately, the sustainability of the stock

Maturation in the Barents Sea capelin – Contrasting length- and gonad-based metrics

It is assumed that maturation in the Barents Sea capelin is length-dependent, and that fish of at least 14 cm will potentially spawn. Current assessment and management models for the stock are based on this assumption of constant maturity at length (MaL). Using data from scientific surveys, this paper examines the validity of the constant MaL assumption, and contrasts it with maturation based on examination of fish gonads. Our analyses, based on time series of 16 years, show that MaL-based estimates of the proportion of maturing stock usually exceed gonad-based estimates. The difference varies consistently with time, and stock-size. We discuss the consequence of our results in the context of uncertainty associated with the current harvest rule