Mathematical conditions identifying the singular strategies and their properties of evolutionary stability and convergence.

Strategy properties of the different models as a function of the convexity of the per worker intrinsic growth rate , the competitive kernel , and the colony’s size at carrying capacity . In both examples, mathematical conditions have been simplified assuming and depend on competition intensity , competition asymmetry , and parameter . a/conditions for x to be a singular strategy; b/condition for x to be an evolutionary stable strategy; c/conditions for x to be a convergent stable strategy.