The equation ${\mathrm{p}}^2+2\mathrm{pq}+{\mathrm{q}}^2$ describes the genotype frequencies of 

The equation ${\mathrm{p}}^2+2\mathrm{pq}+{\mathrm{q}}^2$ describes the genotype frequencies of a population in Hardy-Weinberg equilibrium (i.e., not evolving). It applies to populations but not to communities.