Theoretical Measures of Species Persistence

How persistent is a species in a particular ecosystem? This is a vital question in ecology, conservation and allied fields. To quantify this property various metrics are used, such as the mean time to extinction and the chance of invasion. One metric employed widely in the literature is the “invasion growth rate”, which measures how quickly a species grows on average when its abundance is low and all the other species in the system are at their equilibrium densities.

I begin my talk by laying out the advantages and disadvantages of using the invasion growth rate as a metric of persistence. In particular, I demonstrate how employing it as a quantitative indicator of properties like the mean time to extinction and the chance of invasion, as is frequently done in the literature, leads to incorrect conclusions when the environment fluctuates.

I then present our analytical formulae for the chance of invasion of a species for small as well as large fluctuation amplitudes, and small or large fitness differences between species. These formulae, which supersede previous diffusion-approximation-based approaches, are model-independent and only require parameters that may be easily ascertained from a time series of the focal species population when it has a small size. Finally, I present our analytical results for the mean time to extinction of species in fluctuating environments.