Invasion analysis is central to coexistence theory. Absent Allee effects, we expect that two species coexist stably if each has a positive geometric mean population growth rate as a rare species invading the other; similar (but more involved) criteria involving invasion growth rates hold in multi-species communities. Much of coexistence theory is grounded in the invasion analysis perspective.
Recently Pande et al. (Ecology Letters (2020) 23: 274) identified limits to invasion growth rates as a quantitative measure of persistence, finding that in some cases persistence times may decrease even as invasion growth rates increase in finite population models. They conclude that “one cannot quantify the contribution of a certain mechanism to persistence by comparing the value of [invasion growth rate] in the presence and in the absence of this mechanism”, which is the basis for both theoretical and empirical analyses of coexistence mechanisms in current coexistence theory.
We use recent mathematical theory for stochastic population models, combined with numerical simulations and extinction time calculations, to examine when invasion analysis needs to be complemented by other persistence measures. Computational methods are proposed that can be used in those situations to quantify the contributions of different mechanisms to persistence.
Results/Conclusions
Even in situations where invasion analysis should be complemented by other metrics, the “stochastic boundedness” persistence property guaranteed by invasion analysis is still crucial for long-term persistence because extinction times are generally much shorter when it fails (except when considering small spatial scales on which localized extinctions are inevitably frequent). Through case-studies of both simple theoretical models and more complex empirically-parameterized models of real communities, we demonstrate how functional Analysis of Variance can be used to extend to other persistence metrics the “decompose and compare” approach that quantifies the contributions of different coexistence mechanisms. We identify several important areas for future research, including challenges in generalizing the canonical fluctuation-dependent mechanisms from invasion analysis to analysis of extinction times.