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Abstract: This paper presents the parameter estimation and sensitivity analysis of the APECOSM-E model, which describes the basin scale 3D size-structured population dynamics of the skipjack tuna population in the Indian Ocean under the joint effect of environmental variability and fisheries exploitation. The model is presented in detail in the companion paper (Dueri et al., 2012). A common methodology based on the evaluation of a cost function that combines the negative log-likelihoods of commercial catches and size frequencies is used for both tasks. A Bayesian term representing the a priori probabilities about the model parameters is added to the cost function used for parameter estimation. The partial derivatives of the cost function with respect to the parameters are obtained by deriving the tangent linear code of the model by automatic differentiation of the direct code. A minimization algorithm is used to estimate the parameters related to fisheries and maximise the fitness of the model to the available observations. In a second step, we evaluate the local sensitivity of the non-estimated parameters and identify the model parameters that have an important effect on the output of the model and that would deserve better measurements in order to reduce the level of uncertainty in the model outputs. The comparison between the optimized simulation and the observations allows identifying the model''s strengths and limitations, in the perspective of using the model to test scenarios concerning the resilience of the population and the sustainability of its exploitation in the Indian Ocean. [Copyright &y& Elsevier]

Abstract: APECOSM-E (Apex-Predator-Ecosystem-Model-Estimation) is a deterministic model that represents the 3D distribution and population dynamics of tropical tuna under the joint effect of environmental conditions and exploitation by fisheries. It is a simplified version of the top predator component of the APECOSM framework, based on a single partial differential equation. The model is structured in 3D space and fish size and considers size dependent reproduction, growth, predation, natural mortality and fishing mortality. Processes are time, space and size-dependent and linked to the environment through mechanistic bioenergetic or behavioral parameterizations. Physiological rates such as growth, reproduction and ageing mortality are derived from the Dynamic Energy Budget (DEB) theory, while horizontal movements and vertical distribution obey a mechanistically derived advection–diffusion formulation driven by habitat gradients and oceanic currents. The effect of fishing is accounted for through the use of fleet-specific size and depth selectivity functions and time-dependent catchability coefficients which relate observed fishing effort to catches and size-frequencies. In this paper we present the mathematical formulations of the physiological and behavioral components of the model, and an application to the skipjack tuna population in the Indian Ocean. The model is run with a daily time step on a 1°×1° horizontal grid and considers 20 vertical layers, reaching a maximal depth of 500m. Results show the effects of spatial and temporal variability of environmental conditions on tuna physiology in terms of growth, reproduction and survival. Moreover, our results suggest that observed trends in reported catches are connected to environmental conditions by means of recruitment dynamics. In addition, the model allows representing the horizontal and vertical distribution of skipjack tuna and assessing the effect of accessibility of the resource to fisheries. The ability of the model to represent the distribution of biomass in accordance with the pattern given by the observed fishing activity was evaluated by comparing the spatial distribution of the simulated biomass with the observed distribution of commercial purse seiners and bait boats catches in the Indian Ocean. The likelihood based method used for estimating the model parameters as well as an analysis of its sensitivity to their values is provided in a companion paper (Dueri et al., 2012). [Copyright &y& Elsevier]