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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]