The impact of different density stresses on the dynamics of two competitive populations

We compare the asymptotic dynamics of two competitive populations described by a system of two differential equations under different density stresses in order to clarify whether some parameters of the system or a function of them can be interpreted as a fitness criteria which a population should optimise to win the competition. Four types of stress are considered. First, it is an age-independent thinning of individuals that prevents that the common density of two competing populations would be greater than some limit value K. The second type of stress is a thinning of youngs and the third one is a thinning of adults. These three stresses come into play just when the limit is reached. The forth stress, like the first one, does not depend on age but, unlike it, begins to take action gradually and increases gradually as density approaches K. We show that in the first case the population with a greater Malthusian coefficient r will ultimately supplant the other one. In contrast, in the second and third cases, the greater value of r does not ensure winning but instead that population whose lifetime reproductive success, R0, is higher will supplant the other. And, at last, in the fourth case neither greater r nor R0 guarantee the win. Instead, that population whose environmental carrying capacity is greater than the capacity of the other population will supplant the other one.