  In this communication we propose a most general equation to study pattern
formation for one-species population and their limit domains in systems of
length L. To accomplish this we include non-locality in the growth and
competition terms where the integral kernels are now depend on characteristic
length parameters alpha and beta. Therefore, we derived a parameter space
(alpha,beta) where it is possible to analyze a coexistence curve
alpha*=alpha*(\beta) which delimits domains for the existence (or not) of
pattern formation in population dynamics systems. We show that this curve has
an analogy with coexistence curve in classical thermodynamics and critical
phenomena physics. We have successfully compared this model with experimental
data for diffusion of Escherichia coli populations.
