Competitive Coexistence in a Seasonally Fluctuating Environment II. Multiple Stable States and Invasion Success

Effects of seasonal environmental variation on coexistence of two competing species are investigated using the Lotka-Volterra competition system with periodically varying coefficients. In a symmetric case, there may appear triple stable periodic solutions and either coexistence or competitive exclusion can result depending on the initial abundances. It is also revealed that the timing of an invasion influences the outcome. In an asymmetric case in which the intrinsic growth rates and the competition coefficients of the two species are out of phase, a pair of stable coexistent periodic solutions are found. In each of four qualitatively different cases in the classical Lotka-Volterra system, an alternative possibility appears in a seasonal environment. Therefore, invasibility or stability of a boundary solution is insufficient to forecast the outcome of competition, and coexistence may be possible even when an invasion by a small number of individuals ends in failure.