# Ecosystem models

Overview and introduction to Bioeconomic models

The marine social ecological system is described by a set of *n* marine stocks exploited by *m* distinct fleets. A state space formulation in discrete time is used to represent the evolution of the ecosystem. Thus the *n* stocks whose states at time *t* are denoted by *xi(t)* are governed by the following controlled and uncertain dynamic equations

*xi(t + 1)= fi(x(t), e(t), k(t), ω(t)) , (1)*

for initial time *t = t0* to temporal horizon *t = T* .

These states xi(t) can potentially be vectors of abundance or biomass at different ages or sizes or sex. The global state *x(t)* representing the community or ecosystem state is the vector of states *x(t) = (x1(t), . . . , xn(t))*. The controls of the system include the efforts (duration or number of vessels)* e(t) = (e1(t), . . . , em(t))* of the different fleets at time t along with environmental quality *k(t) = (k1(t), . . . , ki(t)) *of the ecosystem. Alternatively output controls through catches could be used through production functions as described below in equation (2). The variables *ω(t) = (ω1(t), . . . , ωp(t))* represent the uncertainties (stochasticities) affecting the dynamics of the system. The growth functions *fi* for each species (or groups of species) may account for inter-specific competition and/or trophic interactions.Environmental quality *k(t)* can depend on climate or marine habitae.The catches *hij (t)* of stocks *xi(t)* by fleet *j* depend on fishing effort *ej(t)* through the production function:

*hij (t) = hjxi(t), ej (t), ω(t) . (2)*

The harvest function *hj = (h1j , . . . , hij , . . . , hnj )* of every fleet *j* accounts for the technical interactions and bycatch which may occur and complexify the control of the ecosystem.