6533b86dfe1ef96bd12c9252

RESEARCH PRODUCT

Species distribution modelling in fisheries science

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Latest fisheries directives propose adopting an ecosystem approach to manage fisheries \citep{FAO-EAFM}. Such an approach aims to protect important ecosystems based on the principle that healthy ecosystems produce more and thus enhance sustainability. Unfortunately, quantifying the importance of an ecosystem is a difficult task to do due the immense number of interactions involved in marine systems. This PhD dissertation relies on the fact that good fisheries distribution maps could play a very important role as they allow a visual and intuitive assessment of different marine areas. Unfortunately, the limited amount of data available and the inherent difficulties of modelling fishery data has resulted in relatively low quality maps in the near past (see \citep{atlas} and \url{http://www.ices.dk/marine-data/maps/Pages/ICES-FishMap.aspx)}. As a result, the spatial fisheries management framework requires competent statistical approaches to quantify the importance of different marine areas with an appropriate measure of uncertainty associated to the estimates. The aim of this PhD is to provide competent spatial and spatio-temporal modelling approaches that allow us characterise different fishery processes that are relevant for their sustainable management. More specifically, the objectives of this PhD are: 1- To propose a spatial modelling framework that properly assess the fishing-suitability of a fishing ground in terms of fishery discards. 2- To propose effective modelling frameworks to map the spatial or spatio-temporal distribution of economically important fisheries. In this regard, different modelling approaches are required to tackle different types of fishery data: 3- On-board or fishery dependent data is sampled preferentially, thus corrections are needed when modelling target species. An objective of this PhD has been, therefore, to test the use of Log-Gaussian Cox Process models to correct the model components of preferentially sampled fish abundance datasets. 4- Survey or fishery independent data provide information to assess changes in the macro-scale of fisheries distribution over the years. Another objective of this PhD has been to propose useful modelling structures to infer the spatio-temporal dynamism of different fishery processes, e.g. spawning and nursery grounds. 5- To propose an effective framework to fit appropriate model components in two-part or Hurdle models. 6- To assess the performance of point-referenced regression models in fishery transect data, including Euclidean distance-based geostatistical models. Our baseline statistical approach has been model based geostatistics. In particular we have developed structures upon it to adequate for different fishery processes and fishery data. Bayesian methods allow direct and intuitive quantification of the uncertainty through explicit probabilistic inference. Furthermore the Bayesian hierarchical model formulation allows defining complex statistical models, such as geostatistical models, in a rather easy and intuitive way. However, the computational cost of Bayesian methods can be a problem, specially in big and complex datasets. To tackle the computational burden of the proposed models, we have used the Integrated Nested Laplace Approximation (INLA) \citep{Rue-et-al09} method an the Stochastic Partial Differential Equations \citep{Lindgren-et-al11} (SPDE) approach. In Chapter (\ref{chap1}) we present the main problem in current fisheries management that motivated this PhD, the quantitative spatial assessment of our fisheries. Then we briefly present the main types of spatial data followed by a brief summary of the main species distribution modelling approaches, from linear regression to geostatistical models. Next, we introduce the benefits of Bayesian hierarchical models in spatial statistics and the different types of Bayesian computing approaches. In this chapter, we specially describe the INLA \citep{Rue-et-al09} method and the SPDE \citep{Lindgren-et-al11} approach to deal with complex geostatistical structures at assumable computational costs. Finally, we end up summarising the main model selection scores used along this PhD dissertation. The second Chapter (\ref{chap2}) is dedicated to fishery discards, which spatial distribution has most of the times been assessed using biomass based units, e.g. discards per unit effort (DPUE) \citep{feekings2012, feekings2013, viana2013disentangling, elias2014, Pennino2014}. The fishing suitability of a given area, however, should contrast the actual biomass benefit against biomass loss of a fishing operation. To do so, we propose using spatial beta regression to model discard proportions (discarded biomass divided by the total catch of a fishing operation). Along the chapter, we review the different approaches used in the past to model proportions and end up proposing a Bayesian hierarchical spatio-temporal beta regression model to identify fishing suitable areas. The third Chapter (\ref{chap3}) approaches the modelling of target species using fishery dependent data. The main property of fishery dependent data is that fishermen choose fishing locations based on their knowledge (best locations to catch more target species biomass) and therefore our sample is subject to the preferential sampling problem \citep{Diggle-et-al10}. As a consequence, the sampling process and the process being modelled are not stochastically independent, which violates a basic statistical modelling assumption. To correct for this bias, we make use of joint-modelling techniques between the marks (caught abundances) and the point pattern of the fishery (selected fishing locations). This way we are able to combine information derived from the spatial distribution of the samples (point pattern), as a proxy to the fishermen's knowledge about the underlying fish abundance distribution, and information coming from the fished abundances (marks). As a consequence, we manage to better inform our models, overcoming the preferential sampling problem, thus obtaining a better approximation of the underlying spatial field. Chapter (\ref{chap4}) deals with fishery survey data, which is the most widely used data for fisheries management. Fishery survey data, or fishery independent data, usually cover very wide areas and provide a macroscopic view of the fishery over the years. As most species distribution datasets, fishery data is also prone to zero observations at unfavourable conditions, resulting in spatio-temporal semi-continuous datasets. This chapter is devoted, on the one hand to improve the usual two-part modelling framework to deal with the semi-continuous nature of the data and on the other hand to infer the spatio-temporal behaviour of the fishery process under study. To do so, we compare different spatio-temporal structures and end up using joint-modelling techniques to fit better informed environmental effects in Hurdle models. In Chapter (\ref{chap5}) we investigate on the implications of point-referencing fishery data, which in reality represent a transect between the starting and ending points of the fishing operation (except purse seiners that fish almost static). This could be specially problematic when applying geostatistics, based in Euclidean distances, in small-scale study areas. In this chapter, we also propose an algorithm, that recognize the transect nature of the data, to approximate the underlying spatial field when enough data and enough cross-overs between fishing operations are present. Finally, Chapter (\ref{end}) presents some concluding remarks and future lines of research. Consequently the main contributions of this study to the knowledge in fisheries distribution modelling are: 1- The spatial analysis of discard proportions instead of total discard biomass units is a good alternative to assess the fishing-suitability of an area in terms of discards. 2- The use of LGCP models to correct the analysis of preferentially sampled data improves significantly the predictive capacity of the abundance models. This allows us use on-board fishery data to model the spatial distribution of targeted fisheries. The use of within-sample and similar model selection scores, e.g. WAIC, DIC, LCPO, etc., can be misleading as they fail to assess the out-of-sample predictive capacity. 3- The spatio-temporal distributional behaviour of fisheries can be effectively inferred by comparing a set of spatio-temporal structures. 4- Joint modelling techniques can improve fitted effects in two-part or Hurdle models. Visual validation of the models is important in the model selection process. 5- The point-referenced representation of fishery transects allows fairly good regression estimates fitting both; process-covariate relationships; and geostatistical fields even in small-scale study areas with respect to the size of the fishery transect. 6- The remarkable flexibility of R-INLA in extending common hierarchical models allows fitting complex structures that better resemble natural sciences. 7- The spatio-temporal representation of different fish species can effectively improve our understanding of fish ecology. Therefore, extending the hake and cod case studies of this thesis to other species could be very valuable to EAFM policy makers.