  Spatial structure is one of the simplest and most studied ecological factors
that affect the evolution of cooperation. It has been shown that spatial
reciprocity promotes cooperation due to the formation of cooperative clusters,
which provide mutual support against defectors. The usual assumption is that of
constant population size, where no density-related effect is possible. Here, we
extend the investigation of density-related effects on the evolution of
cooperation. We integrate evolutionary game theory to the Lattice
Lotka-Volterra Model. In our model, the birth rate depends on the local density
and on the payoff accumulated in the interactions. We characterize the
evolution of cooperation in terms of the coexistence and the extinction of the
types. The main result is that cooperation is most favoured at moderate levels
of the death rate. Interestingly, defectors are extinct at values of the death
rate that are lower than that at which cooperators are extinct. When death
knocks the door, defectors are the first to perish, whereas cooperators stand
longer due to mutual support.
