Identifying the factors which facilitate the coexistence of species in an ecosystem is an important research area, and one of the most widespread general frameworks employed therein over the last few decades has been that of the modern coexistence theory (MCT). Its guiding principle is that the ability of a species to survive long-term in an ecosystem is well measured by its mean growth rate when rare E[r], under the effect of all the resident species. The higher the value of E[r] for a species, the better should be its persistence as measured by properties such as invasibility and the mean time to extinction (MTE).
In this work, through numerical and analytical means, we investigate this assumed correspondence between E[r] and persistence properties. With the supposition that E[r] does not capture the effect of temporal random abundance variations, we focus particularly on models where it is these variations which stabilise the system, such as the lottery model and the forest dynamics model. Using numerical simulations of these models we compare the behaviour of E[r] with actual measured values of invasibility and MTE as the abundance variations change.
Results/Conclusions
We varied the correlation time (δ) and the amplitude (σ) of the environmental fluctuations in simulations of the two-species lottery model with and without demographic stochasticity, and also in the forest dynamics model. Neither the invasibility nor the mean time to extinction were found to be single-valued functions of E[r]: different combinations of δ and σ that correspond to the same E[r] yielded different values of these persistence properties. More significantly, we found that these persistence properties were not even always monotonically increasing functions of E[r], meaning that a species could become more liable to extinction, despite an increase in E[r], when the system parameters such as δ and σ changed.
Consideration of the analytical models in the limit when the abundance variations are small helps explain these results and shows that a population may get trapped in regions of small abundance even when E[r] is large, thus rendering the magnitude of E[r] irrelevant.
Our results indicate clearly that E[r] does not, in general, have a one-to-one relationship with persistence properties, and its use to compare the persistence of different geographical communities, or to quantify the contributions of different mechanisms to coexistence, as often done in the literature, is dubious.