  We investigate the thermodynamics as well as the population dynamics of
ecosystems based on a stochastic approach in which the number of individuals of
the several species of the ecosystem are treated as stochastic variables. The
several species are connected by feeding relationships that are understood as
unidirectional processes in which a certain amount of biomass is exchanged
between species. We show that the equations for the averages in the numbers of
individuals are that given by the deterministic approach. We determine the
fluxes of mass, energy, and entropy as well as the rate of the entropy
production. This last quantity, which has a central role in the present
stochastic approach, is obtained by a formula appropriate for unidirectional
transitions. The flux of energy across the ecosystem is shown to be
proportional to the flux of entropy to the environment.
