Discussion
We have shown that the mean and variability of environmental fluctuation can have complex yet predictable effects on patterns of species coexistence. Notably, environmental variation can either promote or hinder species coexistence depending on the temporal scale of variation. This is because short-term environmental variation generally favors species coexistence, whereas long-term environmental variation promotes exclusion of competing species. Thus, if environments fluctuate simultaneously on different temporal scales (e.g. daily, seasonal, and annual patterns of temperature fluctuation), which commonly occur in nature, diverse relationships between environmental variability and species coexistence are expected. The mean environmental condition also plays a critical role in shaping the effects of environmental variation on species coexistence, depending on whether the mean condition approaches the optimal condition of one of the species or whether it occurs between the optimal conditions of the competing species.
Many seemingly contradictory results of species coexistence and environmental fluctuation from previous studies can be viewed as special cases of a more general result described here (Fig. 5). For example, Hutchinson (1953; 1961) discussed the impact of temporal scales of environmental variation on species coexistence in a nonequilibrium setting (i.e. species could go extinct by chance due to environmental fluctuation). He argued that both overly fast and overly slow fluctuations promote competitive exclusion between competing species because whichever species competes best on average will exclude the other. Thus, only environmental fluctuation occurring at an intermediate temporal scale will favor species coexistence. Our model partially agrees with Hutchinson’s hypothesis such that intermediate- and long-term environmental fluctuation favor species coexistence and exclusion, respectively. Nevertheless, our model demonstrates that short-term fluctuation is also predicted to facilitate species coexistence rather than exclusion. The key difference between long- and short-term environmental fluctuation is that fast-changing environments allow each competing species to experience their optimal and adverse environmental conditions prior to extinction, which prevents competitive exclusion, whereas slow-changing environments last longer and, thus, can favor one of the competing species to exclude the other. However, May and colleagues (May & MacArthur 1972; May 1973, 1974) proposed that niche differences need to be larger in fluctuating environments than in stable environments for species to coexist. Consequently, competitive exclusion is predicted to occur more easily in fluctuating environments than in stable environments. However, our model shows that May and colleagues’ prediction is a special case such that it is only valid for long-term environmental variation in a nonequilibrium, stochastic model setting.
Our model may also help resolve the longstanding debate over the intermediate disturbance hypothesis (Grime 1973; Connell 1978; Fox 2013; Huston 2014), which states that species richness of competing species will be “maximized at intermediate frequencies and/or intensities of disturbance or environmental change” (Fox 2013). Our model shows that there can be diverse patterns of species coexistence in relation to environmental variability. Therefore, with the right combination of long- and short-term environmental variation, intermediate disturbancecan generate higher species richness relative to higher or lower disturbance scenarios (e.g., Fig. 5b, left arrow). However, it is also true that intermediate disturbance does not always lead to the highest species richness because species coexistence depends at least partially on the temporal scale of environmental variation. The main differences between our model and previous models are that (1) environments in our model fluctuate stochastically and, therefore, species can go extinct by chance if they happen to experience unfavorable environments for an extended period of time (Adler & Drake 2008; Adler et al. 2010; Gravel et al. 2011), and (2) we explicitly consider the temporal scale of environmental variation, while simultaneously considering the effect of the mean environmental condition (i.e. environmental mean, variance, and their interaction are included in our model). Accordingly, we urge future studies testing the intermediate disturbance hypothesis to carefully distinguish between different properties of environmental disturbance (e.g. intensity and frequency) on the richness of competing species (Dillon et al.2016; Vázquez et al. 2017).
In conclusion, we show that contrasting results from previously published studies linking environmental variation to species interactions (Hutchinson 1961; May & MacArthur 1972; Chesson 2000) can be viewed as special cases of a more general framework that we develop here (Fig. 5). By explicitly taking into account different temporal scales of environmental variation, simultaneously considering the mean environmental condition, and modeling different types of stochastic environments, we develop a framework that can be used to explore rich patterns of species coexistence. This framework will be useful for developing testable predictions at a time when environmental fluctuation is increasing globally.
AcknowledgmentsS.-F.S. was supported by Academia Sinica (Career Development Award and Investigator Award, AS-IA-106-L01) and Minister of Science and Technology of Taiwan (S.-F.S., 100-2621-B-001-004-MY3, and 104-2311-B-001 -028 -MY3). D.R.R. was supported by the US National Science Foundation (IOS-1439985 and IOS-1656098).