Figure legends and Tables
Figure 1 A demonstration of the species and environmental
variation properties in our model. (a) Following the concept of
biological performance curves, the difference between the two species
can be depicted by the per capita growth rates across all environments
(i.e. temperatures). We assume that there is a high temperature-adapted
species (orange line) and a low temperature-adapted species (blue line)
competing against one another (see methods for more details about the
thermal performance curves). The solid black line describes the time
series of temperature variation, whereas the dashed black line indicates
the average temperature. (b) To more easily visualize environmental
fluctuation at different temporal scales, the temperature time series
can be decomposed into waves of different frequencies through fast
Fourier transformation. (c) For each wave, the amplitude and frequency
are plotted as points on a continuous spectrum that characterizes the
temperature time series. (d) If the short-term temperature variation
increases, the spectrum, (e) would have a larger amplitude in the high
frequency regions than in the original spectrum (c, and the grey line ine ). (f) Conversely, increasing long-term variation causes the
spectrum, g , to have a larger amplitude in the low frequency
regions than in the original spectrum.
Figure 2 Short- and long-term temperature variation have
contrasting impacts on species coexistence. (a-d) Proportion of
simulations producing species coexistence dynamics, where brighter
colors indicate greater proportions of coexisting species. Each panel
has constant long-term variation (\(\sigma_{\text{long}}\), labeled
above each panel) but variable mean temperature (\(T_{\text{mean}}\),
x-axis) and short-term variation (\(\sigma_{\text{short}}\), y-axis).
Species coexistence occurs if both species sustain through 20,000
short-term variations and 286 long-term variations (4-million
calculations of population change). Each combination of mean and
variability is repeated for 100 times. (e-h) Proportion of coexistence
with the same definition, but each panel has constant short-term
variation (\(\sigma_{\text{short}}\), labeled above each panel) and
variable long-term variation (\(\sigma_{\text{long}}\), y-axis).
Figure 3 Examples of the complex patterns of variability and
mean temperature on species coexistence. (a-c) In the first case, we set
the mean and short-term variation as constant and only change the
magnitude of long-term variation. We find that coexistence occurs most
commonly under intermediate magnitudes of long-term variation (b). (d-f)
In the second case, we fix the size of the mean and long-term variation.
By changing short-term variation alone, we see that coexistence is
greatest when short-term variation is high (f). (g-i) In the third case,
we set the mean at another value (compared to the first case) and only
alter the magnitude of the long-term variation. We find that species
coexistence is more likely to occur when long-term variation is low (g).
Figure 4 Patterns of species coexistence changes with different
mean temperatures. (a-c) At a high mean temperature
(Tmean=31), increasing both short- and long-term
variation results in greater species coexistence. (d-f) When the mean
temperature is lower (Tmean=27), higher short- and
long-term temperature variation may still promote coexistence. (g-i)
However, if the mean temperature decreases further
(Tmean=23), coexistence occurs at both low levels (g) or
high levels (i) of short- and long-term variation.
Figure 5 Different combinations of short-term temperature
variation, long-term temperature variation, and mean temperature can
generate diverse patterns of species coexistence. (a) Coexistence can be
promoted by greater temperature variability. (b) Coexistence may also be
supported when temperature variability is intermediate (Hutchinson 1961;
Connell 1978) (solid line arrow), or (3) hindered by temperature
variability (May & MacArthur 1972) (dashed line arrow). (c) Finally, it
is also possible that coexistence is promoted when temperature
variability is either high or low. The size of short- and long-term
temperature variation are labeled above each panel.