Electronic supplementary materials from Antagonistic effects of long- and short-term environmental variation on species coexistence

Assessing the impact of environmental fluctuations on species coexistence is critical for understanding biodiversity loss and the ecological impacts of climate change. Yet, determining how properties like the intensity, frequency or duration of environmental fluctuations influence species coexistence remains challenging, presumably because previous studies have focused on indefinite coexistence. Here, we model the impact of environmental fluctuations at different temporal scales on species coexistence over a finite time period by employing the concepts of time windowed averaging and performance curves to incorporate temporal niche differences within a stochastic Lotka–Volterra model. We discover that short- and long-term environmental variability has contrasting effects on transient species coexistence, such that short-term variation favours species coexistence, whereas long-term variation promotes competitive exclusion. This dichotomy occurs because small samples (e.g. environmental changes over long time periods) are more likely to show large deviations from the expected mean and are more difficult to predict than large samples (e.g. environmental changes over short time periods), as described in the central limit theorem. Consequently, we show the complex set of relationships among environmental fluctuations and species coexistence found in previous studies can all be synthesized within a general framework by explicitly considering both long- and short-term environmental variation.