### Statistics and Fisheries

**Presenter:** James Thorson

**When:** Friday, July 15, 2016 **Time:** 11:00 AM - 12:30 PM

**Room:** Lecture Theatre (Level 1)

#### Session Synopsis:

###### Estimating dynamics, stability, and distribution shifts for fish communities using multispecies spatio-temporal models

Fisheries science and marine ecologists are increasingly interested in spatial dynamics and interactions among species in marine communities. For example, recent research suggests that spatial models are necessary to accurately estimate the magnitude of density dependence whenever interactions are based on nearby densities (i.e., if density dependence is local). Also, climate impacts are increasingly identified via spatial shifts in species distribution. However, spatio-temporal models have rarely been used for analyzing entire communities. In this talk, I discuss three examples of spatio-temporal models for analysing marine communities. First, I present model-based estimators for distribution shifts for West Coast fishes and the benefits of this approach over conventional sample-based estimators. Second, I introduce spatial dynamic factor analysis (SDFA), a method for jointly estimating spatio-temporal for multiple species. I specifically use SDFA to rapidly identify dominant patterns in dynamics for fishes and invertebrates in the Bering Sea. Third, I discuss ongoing efforts to estimate partial density dependence, where the community matrix (representing species interactions) may contain both compensatory and random-walk components. In each case, I discuss how rapid developments in spatial statistics and mixed-effects estimation is poised to revolutionize the analysis and management of marine communities.

### Statistics and Fisheries

**Presenter:** Pierre Gloaguen

**When:** Friday, July 15, 2016 **Time:** 11:00 AM - 12:30 PM

**Room:** Lecture Theatre (Level 1)

#### Session Synopsis:

###### Modelling movement using Stochastic Differential Equations in Fisheries Science

Individual's movement in fisheries science is of great interest, as it can provide information over: - Ressource spatial Distribution; - Adequacy of proposed management measures (MPAs, fishing closures); - Potential reaction of fishermen to management measures. Using GPS type tags, movement data are more and more available in Fisheries science. Mechanistic models can then be fitted to these data in order to answer some ecological questions. We propose here to describe the movement of individuals as a continuous stochastic process using Stochastic Differential Equations (SDEs) model. SDEs provide a large and flexible framework to model individuals movement as it can embed different type of drivers of the movement. However, inference over SDEs based model can be challenging, specially when dealing with GPS type data. In this work, we'll present a movement model based on a SDE whose drift is the gradient of a potential function. Parameters of the potential functions are estimated from data using a MCEM algorithm. The E step is approximated using exact conditionnal simulation of diffusion processes, which avoids the use of an Euler scheme, which induce bias in estimation. The algorithm, at the end, provides the Maximum Likelihood Estimator. Examples of application will be shown on fishing vessels movement data. Invited Session: Statistics for Fisheries

### Statistics and Fisheries

**Presenter:** Jean-Baptiste Lecomte

**When:** Friday, July 15, 2016 **Time:** 11:00 AM - 12:30 PM

**Room:** Lecture Theatre (Level 1)

#### Session Synopsis:

###### A spatio-temporal approach for abundance estimation with zero-inflated biomass data.

Abundance indices are an essential component of the management of marine species and can be critical for stock assessment of data-limited species. The lack of reliable, long-term abundance indices, where often the only long-term index comes from commercial fishing data or from very patchy survey observations, can increase the uncertainty and bias when providing management advice. Fishery-dependent catch-per-unit-effort (CPUE) indices are subject to biases arising from non-random fishing effort and from incorrect spatial assumptions that have the implicit assumption that average abundance in unobserved areas is the same as in observed areas. In addition, catch data often present a high proportion of zero observations, which require specific zero-inflated modelling approaches to avoid further bias. We propose a Bayesian hierarchical model for zero-inflated spatio-temporal biomass data to provide less biased abundance indices for marine species. Due to the excess of zero values, we use a Compound Poisson-Gamma model for the observation layer. The spatial structure is accounted for using a discrete convolution process (Higdon, 2012), that is the convolution (using exponential kernel) of a finite number of independent variables positioned on a spatial grid. This class of models offers a number of advantages over the standard classes of parametric variogram/covariance functions commonly used in geostatistics. The first advantage is the dimension reduction aspect. A second advantage is the flexibility of the modelling as the temporal dependency might be accounted for using a temporal autoregressive model for the random variables positioned on the grid, each of those AR processes involving independently. In addition, ecological factors such as temperature, depth and sediment type are included as predictors in the latent model. This approach is applied to different marine species to illustrate the capacity of the model. The spatio-temporal model developed is flexible and efficient and open a whole range of perspectives.Abundance indices are an essential component of the management of marine species and can be critical for stock assessment of data-limited species. The lack of reliable, long-term abundance indices, where often the only long-term index comes from commercial fishing data or from very patchy survey observations, can increase the uncertainty and bias when providing management advice. Fishery-dependent catch-per-unit-effort (CPUE) indices are subject to biases arising from non-random fishing effort and from incorrect spatial assumptions that have the implicit assumption that average abundance in unobserved areas is the same as in observed areas. In addition, catch data often present a high proportion of zero observations, which require specific zero-inflated modelling approaches to avoid further bias. We propose a Bayesian hierarchical model for zero-inflated spatio-temporal biomass data to provide less biased abundance indices for marine species. Due to the excess of zero values, we use a Compound Poisson-Gamma model for the observation layer. The spatial structure is accounted for using a discrete convolution process (Higdon, 2012), that is the convolution (using exponential kernel) of a finite number of independent variables positioned on a spatial grid. This class of models offers a number of advantages over the standard classes of parametric variogram/covariance functions commonly used in geostatistics. The first advantage is the dimension reduction aspect. A second advantage is the flexibility of the modelling as the temporal dependency might be accounted for using a temporal autoregressive model for the random variables positioned on the grid, each of those AR processes involving independently. In addition, ecological factors such as temperature, depth and sediment type are included as predictors in the latent model. This approach is applied to different marine species to illustrate the capacity of the model. The spatio-temporal model developed is flexible and efficient and open a whole range of perspectives.Abundance indices are an essential component of the management of marine species and can be critical for stock assessment of data-limited species. The lack of reliable, long-term abundance indices, where often the only long-term index comes from commercial fishing data or from very patchy survey observations, can increase the uncertainty and bias when providing management advice. Fishery-dependent catch-per-unit-effort (CPUE) indices are subject to biases arising from non-random fishing effort and from incorrect spatial assumptions that have the implicit assumption that average abundance in unobserved areas is the same as in observed areas. In addition, catch data often present a high proportion of zero observations, which require specific zero-inflated modelling approaches to avoid further bias. We propose a Bayesian hierarchical model for zero-inflated spatio-temporal biomass data to provide less biased abundance indices for marine species. Due to the excess of zero values, we use a Compound Poisson-Gamma model for the observation layer. The spatial structure is accounted for using a discrete convolution process (Higdon, 2012), that is the convolution (using exponential kernel) of a finite number of independent variables positioned on a spatial grid. This class of models offers a number of advantages over the standard classes of parametric variogram/covariance functions commonly used in geostatistics. The first advantage is the dimension reduction aspect. A second advantage is the flexibility of the modelling as the temporal dependency might be accounted for using a temporal autoregressive model for the random variables positioned on the grid, each of those AR processes involving independently. In addition, ecological factors such as temperature, depth and sediment type are included as predictors in the latent model. This approach is applied to different marine species to illustrate the capacity of the model. The spatio-temporal model developed is flexible and efficient and open a whole range of perspectives.Abundance indices are an essential component of the management of marine species and can be critical for stock assessment of data-limited species. The lack of reliable, long-term abundance indices, where often the only long-term index comes from commercial fishing data or from very patchy survey observations, can increase the uncertainty and bias when providing management advice. Fishery-dependent catch-per-unit-effort (CPUE) indices are subject to biases arising from non-random fishing effort and from incorrect spatial assumptions that have the implicit assumption that average abundance in unobserved areas is the same as in observed areas. In addition, catch data often present a high proportion of zero observations, which require specific zero-inflated modelling approaches to avoid further bias. We propose a Bayesian hierarchical model for zero-inflated spatio-temporal biomass data to provide less biased abundance indices for marine species. Due to the excess of zero values, we use a Compound Poisson-Gamma model for the observation layer. The spatial structure is accounted for using a discrete convolution process (Higdon, 2012), that is the convolution (using exponential kernel) of a finite number of independent variables positioned on a spatial grid. This class of models offers a number of advantages over the standard classes of parametric variogram/covariance functions commonly used in geostatistics. The first advantage is the dimension reduction aspect. A second advantage is the flexibility of the modelling as the temporal dependency might be accounted for using a temporal autoregressive model for the random variables positioned on the grid, each of those AR processes involving independently. In addition, ecological factors such as temperature, depth and sediment type are included as predictors in the latent model. This approach is applied to different marine species to illustrate the capacity of the model. The spatio-temporal model developed is flexible and efficient and open a whole range of perspectives.