Murdoch K. McAllister

Using demographic methods to construct Bayesian priors for the intrinsic rate of increase in the Schaefer model and implications for stock rebuilding

Even though Bayesian methods can provide statistically rigorous assessments of the biological status of fish eries resources, uninformative data (e.g., declining catch rate series with little variation in fishing effort) can produce highly imprecise parameter estimates. This can be counteracted with the use of informative Bayesian prior distributions (priors) for model parameters. We develop priors for the intrinsic rate of increase ( r) in the Schaefer surplus production model using demographic methods and illustrate the utility of this with an application to large coastal sharks in the Atlantic. In 1996, a U.S. stock assessment obtained a point estimate for r of 0.26. For such long-lived and low-fecund organisms, this could potentially be too high. Yet it was used to predict that within about 10 years, a 50% reduction in the 1995 catch level should result in >50% chance of increasing the population to the abundance required to produce maximum sustainable yield. In contrast, a Bayesian assessment that used demographic analysis to construct a prior for r with a median of 0.07 and coefficient of variation (CV) of 0.7 indicated that within 30 years, this policy would have only a very small chance of increasing the population to maximum sustainable yield. Résumé: Bien que les techniques bayésiennes puissent fournir des estimations statistiquement rigoureuses du statut biologique des ressources halieuthiques, des données pauvres en information (e.g., un série de taux de capture associée à un effort de pêche peu variable) peuvent produire des estimations de paramètres très imprécises. Ce problème peut être contrecarré par l’utilisation de distributions bayésiennes a priori (priors) pour les paramètres du modèle. Nous avons développé des distributions a priori pour le taux intrinsèque de croissance ( r) dans le modèle de production excédentaire de Schaefer à l’aide de méthodes démographiques et nous illustrons l’utilité de cette approche en l’appliquant aux grands requins côtiers de l’Atlantique. En 1996, une évaluation de stock faite aux États-Unis a donné une estimation ponctuelle de r de 0,26. Pour des organismes à grande longévité et à faible fécondité, cette valeur est potentiellement trop élevée. Néanmoins, elle a servi à prédire que, dans à peu près 10 ans, une réduction de 50% dans le taux de capture de 1995 aurait pour conséquence une probabilité de >50% de faire croître la population suffisam ment pour atteindre le niveau de rendement maximal soutenu. En revanche, une estimation de type bayésien qui a utilisé une analyse démographique pour établir une distribution a priori de r av c une médiane de 0,07 et un coefficient de variation de 0,7 indique qu’une telle politique de capture n’aurait, au bout de 30 ans, qu’une très faible probabilité de permettre à la population d’atteindre le rendement maximal soutenu. [Traduit par la Rédaction] Perspectives 1890

Atlantic Bluefin Tuna: A Novel Multistock Spatial Model for Assessing Population Biomass

Atlantic bluefin tuna (Thunnus thynnus) is considered to be overfished, but the status of its populations has been debated, partly because of uncertainties regarding the effects of mixing on fishing grounds. A better understanding of spatial structure and mixing may help fisheries managers to successfully rebuild populations to sustainable levels while maximizing catches. We formulate a new seasonally and spatially explicit fisheries model that is fitted to conventional and electronic tag data, historic catch-at-age reconstructions, and otolith microchemistry stock-composition data to improve the capacity to assess past, current, and future population sizes of Atlantic bluefin tuna. We apply the model to estimate spatial and temporal mixing of the eastern (Mediterranean) and western (Gulf of Mexico) populations, and to reconstruct abundances from 1950 to 2008. We show that western and eastern populations have been reduced to 17% and 33%, respectively, of 1950 spawning stock biomass levels. Overfishing to below the biomass that produces maximum sustainable yield occurred in the 1960s and the late 1990s for western and eastern populations, respectively. The model predicts that mixing depends on season, ontogeny, and location, and is highest in the western Atlantic. Assuming that future catches are zero, western and eastern populations are predicted to recover to levels at maximum sustainable yield by 2025 and 2015, respectively. However, the western population will not recover with catches of 1750 and 12,900 tonnes (the “rebuilding quotas”) in the western and eastern Atlantic, respectively, with or without closures in the Gulf of Mexico. If future catches are double the rebuilding quotas, then rebuilding of both populations will be compromised. If fishing were to continue in the eastern Atlantic at the unregulated levels of 2007, both stocks would continue to decline. Since populations mix on North Atlantic foraging grounds, successful rebuilding policies will benefit from trans-Atlantic cooperation.

Experimental Design in the Management of Fisheries: A Review

Abstract Despite the accumulating theoretical interest in experimental management, there are few practical applications of it. Because most fisheries management plans lack rigorous experimental design, managers often face controversy when results appear consistent with several alternative mechanisms or when results yield little information about causes of fish population dynamics. We provide a synthesis of the problems of experimental design in fisheries science and management, and we show how these problems can be solved to generate better information and better decisions, especially when combined with proper statistical practices and formal decision analysis. Reasons why experimental management is currently rare are (1) lack of unfamiliarity of management agencies with designing management actions to yield information, (2) logistical constraints placed on replication by fish migratory patterns, (3) resistance by fishermen who fear experimentation will lower incomes, or (4) risk of stock collapse, Howeve...

Species‐Area Curves, Diversity Indices, and Species Abundance Distributions: A Multifractal Analysis

Although fractals have been applied in ecology for some time, multifractals have, in contrast, received little attention. In this article, we apply multifractals to the species‐area relationship and species abundance distributions. We highlight two results: first, species abundance distributions collected at different spatial scales may collapse into a single curve after appropriate renormalization, and second, the power‐law form of the species‐area relationship and the Shannon, Simpson, and Berger‐Parker diversity indices belong to a family of equations relating the species number, species abundance, and area through the moments of the species abundance–probability density function. Explicit formulas for these diversity indices, as a function of area, are derived. Methods to obtain the multifractal spectra from a data set are discussed, and an example is shown with data on tree and shrub species collected in a 50‐ha plot on Barro Colorado Island, Panama. Finally, we discuss the implications of the multifractal formalism to the relationship between species range and abundance and the relation between the shape of the species abundance distribution and area.

Statistical Evaluation of a Large-Scale Fishing Experiment Designed to Test for a Genetic Effect of Size-Selective Fishing on British Columbia Pink Salmon (Oncorhynchus gorbuscha)

Past work suggested that size-selective harvesting of large fish combined with heritability of body size has caused the large (up to 34%) decrease in mean adult weight of British Columbia pink salmon (Oncorhynchus gorbuscha) since 1950. In a companion paper (Can. J. Fish. Aquat. Sei. 49: 1294–1304) we evaluated the statistical performance of a large-scale fishing experiment that could enable managers to test this hypothesis and at the same time increase catch biomass if that hypothesis were correct. In this paper we evaluate the economic performance of the proposed experiment using Monte Carlo simulation and decision analysis under a wide range of conditions that encompasses existing biological uncertainties. We accounted for uncertainties through prior probabilities placed on two key biological hypotheses. We computed the expected economic value of catch biomass for the experimental and current nonexperimental (status quo) management strategies using a 20-yr time horizon and a 10-yr experiment with four ...

A sequential Bayesian methodology to estimate movement and exploitation rates using electronic and conventional tag data: application to Atlantic bluefin tuna (Thunnus thynnus)

This paper presents a Bayesian methodology to estimate fishing mortality rates and transoceanic migration rates of highly migratory pelagic fishes that integrates multiple sources of tagging data and auxiliary information from prior knowledge. Exploitation rates and movement rates for Atlantic bluefin tuna (Thunnus thynnus) are estimated by fitting a spatially structured model to three types of data obtained from pop-up satellite, archival, and conventional tags for the period 1990–2006 in the western North Atlantic. A sequential Bayesian statistical approach is applied in which the key components of the model are separated and fitted sequentially to data sets pertinent to each component with the posterior probability density function (pdf) of parameters from one analysis serving as the prior pdf for the next. The approach sequentially updates the estimates of age-specific fishing mortality rates (F) and transoceanic movement rates (T). Estimates of recent F are higher than the estimated rate of natural m...

Erratum: Simulating spatial dynamics to evaluate methods of deriving abundance indices for tropical tunas

Relative abundance indices derived from nominal catch-per-unit-effort (CPUE) data are a principle source of information for the majority of stock assessments. A particular problem with formulating such abundance indices for pelagic species such as tuna is the interpretation of CPUE data from fleets that have changed distribution over time. In this research, spatial population dynamics are simulated to test the historical pattern of fishing effort as a basis for making inferences about relative abundance. A number of age-structured, spatially disaggregated population dynamics models are described for both Atlantic yellowfin tuna (Thunnus albacares) and bigeye tuna (Thunnus obesus) to account for uncertainty in spatial distribution and movement. These models are used to evaluate the reliability of standardization methods and a commonly applied model selection criterion, Akaike’s information criterion (AIC). The simulations demonstrate the pitfalls of aggregating CPUE data over spatial areas and highlight th...

Chapter 15 Operational management procedures: An introduction to the use of evaluation frameworks*

Publisher Summary A management procedure is a simulation-tested set of rules used to determine management actions, in which the data, assessment methods, and the harvest control rules for implementing management actions are prespecified. An operational management procedure (OMP) is defined as a management procedure that is currently being used to determine management actions or has been intensively tested by a competent management body to a level where it could be used in practice. An important benefit of management procedures is they can be designed to satisfy a variety of pre-agreed management objectives, including both biological and economic factors, making them more likely to be acceptable to a wide range of user groups. However, the modelling philosophy may be difficult to understand for non-experts, which means that extra effort is needed to explain them and how they are designed. This chapter describes various aspects of management procedures, including the philosophy behind them, how they are constructed based on available data and knowledge, their objectives, the methods used to evaluate them, and their differences and advantages over traditional stock assessment and management regimes. In addition, some examples of management procedures are also reviewed.

A new improved method to compute swept area estimates of biomass from commercial catch rate data: application to Namibian orange roughy (Hoplostethus atlanticus)

Abstract Swept area estimates of Namibian orange roughy ( Hoplostethus atlanticus ) biomass were recently obtained from commercial catch rate data and applied to temporally stationary strata. This methodology resulted in enormous biomass estimates, especially in the first few years. However, analysis of spatial and temporal patterns in commercial catch rates indicates that there is considerable spatial and temporal heterogeneity in fish biomass and sampling coverage. Keeping the strata temporally stationary results in the extrapolation of estimated extremely high densities in very well-sampled areas to large poorly sampled areas in some years (especially the first few years). It does not appear that such extrapolations are justified and could result in large over-estimates of biomass in early years. This paper outlines and applies an alternative swept area method that uses non-stationary strata for each of the four Namibian orange roughy stocks. Three types of strata are identified, as before: one with very high densities of aggregating orange roughy, one with intermediate densities and another with relatively low densities. Strata were constructed separately for each year on each of the four major fishing grounds. We demonstrate the utility of the approach by showing how its results can be used to evaluate the plausibility of alternative hypotheses for a large apparent drop in aggregating mature biomass seen in the two other orange roughy abundance series. Resulting biomass estimates on each ground are all lower than those obtained previously and no longer show this catastrophic drop in relative biomass that could not be easily explained by catch removal alone. However, on all fishing grounds, the biomass estimates in, and area of, high-density strata were the highest in 1997. Moreover, the proportion of fish in high density to low density strata is also highest in 1997 and then dropped dramatically in the next 2 years. These patterns are not entirely inconsistent with the hypothesis that fishing on aggregations has tended to disturb and disperse them and reduce the catchability of aggregating orange roughy. The large aggregations in 1997, compared to earlier years, could also suggest that the intensity of aggregation on the fishing grounds may be intermittent and independent of previous years of fishing effort.

Bayesian Decision‐Network Modeling of Multiple Stakeholders for Reef Ecosystem Restoration in the Coral Triangle

Proposals for marine conservation measures have proliferated in the last 2 decades due to increased reports of fishery declines and interest in conservation. Fishers and fisheries managers have often disagreed strongly when discussing controls on fisheries. In such situations, ecosystem-based models and fisheries-stock assessment models can help resolve disagreements by highlighting the trade-offs that would be made under alternative management scenarios. We extended the analytical framework for modeling such trade-offs by including additional stakeholders whose livelihoods and the value they place on conservation depend on the condition of the marine ecosystem. To do so, we used Bayesian decision-network models (BDNs) in a case study of an Indonesian coral reef fishery. Our model included interests of the fishers and fishery managers; individuals in the tourism industry; conservation interests of the state, nongovernmental organizations, and the local public; and uncertainties in ecosystem status, projections of fisheries revenues, tourism growth, and levels of interest in conservation. We calculated the total utility (i.e., value) of a range of restoration scenarios. Restricting net fisheries and live-fish fisheries appeared to be the best compromise solutions under several combinations of settings of modeled variables. Results of our case study highlight the implications of alternate formulations for coral reef stakeholder utility functions and discount rates for the calculation of the net benefits of alternative fisheries management options. This case study may also serve as a useful example for other decision analyses with multiple stakeholders.