Coexistence resulting from an alternation of density dependent and density independent growth

When two species compete with each other, one is likely to displace or exclude the other. Several circumstances under which they may coexist indefinitely have been presented in the literature; the present contribution presents examples of one more. Under circumstances where both populations are repeatedly decreased (for example because of annual environmental changes) then subsequent to each decrease both species grow unrestrictedly and then interact with each other in a competitive fashion. If the species that grows more rapidly under unrestricted conditions is at a disadvantage during competitive phases of growth, this effect prolongs coexistence but may not prevent eventual extinction of one or the other species. However, it is shown that there are certain broad ranges of conditions for population growth that lead to permanent cyclical stability. The stability described here is such that the ecosystem will return to the same dynamic balance even when severely perturbed. It is also shown that this kind of stability can be either favored or prevented in certain cases by random fluctuations in the environment affecting season length, kill factor, etc.