The concepts of elasticity, invulnerability and invadability

Users of mathematical models in ecological research have emphasized mathematical elegance in elucidating the dynamics of ecosystem models with fixed collections of state variables instead of addressing the equally important question of what effects a changing ecosystem structure has on the system's dynamics. Our work addresses the effect of invasion on the species composition of communities. In the context of a linear model, we found that as communities were made more complex (in terms of the number of species they contained and the number of interactions among these species) the probability of their being stable decreased, but the probability of their being invulnerable to invasion by other species increased. These results are consistent with the hypothesis that, through time, communities approach an intermediate complexity at which the influences of environmental stochasticity (which tends to destabilize complex communities) and invasion pressure (which tends to add species to simple communities) counterbalance one another. At this intermediate complexity the average rate of change of species composition is low.