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).