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SUPPLEMENTARY MATERIAL
Here we consider the interaction between environmental amplitude (w) and colour (autocorrelation,
κ) in affecting community diversity in three different scenarios of environmental correlation. When
there is no migration in the system, species evenness monotonically decreases with increasing w,
independently of environmental colour or species environmental correlation (FIG. S1a-c). In the
presence of migration, communities with independent species environmental responses (IR) are associated with an intermediate maximum in species evenness with increasing w under blue noise
(FIG. S1d). Under red noise evenness decreases monotonically with increasing w. In contrast,
communities with positively correlated species environmental responses (CR) have decreasing
evenness with increasing w, independently of noise colour (FIG. S1e). Finally, communities with
hierarchically correlated species environmental responses (HR) have an intermediate minimum in
evenness with increasing w, independently of noise colour (FIG. S1f).
FIGURE S1. Environmental colour (autocorrelation, κ) and fluctuation amplitude (w) simultaneously affect
species evenness in closed (a-c, no migration) and open (d-e, migration) communities. The interaction between κ and w depends on whether species environmental responses are independent (IR, ρ = 0), positively
correlated (CR, ρ = 0.9), or hierarchically correlated (HR, , ρij = f(dij)). Results based on 100 replicates for
each parameter combination. Parameters: S = 30, r = 1, p = 0.1 (immigration), δ = 0.1 (emigration).
These patterns in species evenness can be understood by considering variation in species richness,
in the absence of migration (FIG. S2a-c). In contrast, species richness is not sufficient to explain
patterns in species evenness when migration is present (FIG. S2d-f). In this case information variation in species relative abundances are is needed to fully understand the observed patterns in evenness.
FIGURE S2. Environmental colour (κ) and fluctuation amplitude (w) simultaneously affect species richness in
closed (no migration) and open (migration) communities. The interaction between κ and w depends on
whether species environmental responses are independent (IR, ρ = 0), positively correlated (CR, ρ = 0.9), or
hierarchically correlated (HR, , ρij = f(dij)). Results based on 100 replicates for each parameter combination.
Parameters: S = 30, r = 1, p = 0.1 (migration), δ = 0.1 (migration).
Next we will consider how the results of species diversity in open communities is affected by variation in other model parameters. Increasing population growth rates (r) decreases species richness
(FIG. S3). Species richness (and evenness) is also equalised between the three scenarios for environmentyal correlation. Increasing r speciess evenness only between under- (r < 1) and overcompensatory (r > 1) population dynamics. The intermediate minimum in species evenness, observed in
HR communities with increasing w, is preserved over all r values considered. However, increasing r
switches the minimum evenness in HR communities to occur at lower levels of w. Variation in
community size (S) has no qualitative influence on species richness or evenness (FIG. S4). While
migration probability (p) and emigration rate (δ) can have some influence on the relative ranking
(with respect to species richness and evenness) of IR and CR communities (FIG. S5), they do not
qualitatively affect the relationship between environmental amplitude and species diversity reported
in the main manuscript. Increasing p increases species richness and evenness in all three scenarios
of environmental correlation (FIG. S5), while increasing δ tend to decrease these community metrics (FIG. S5), except that evenness in HRcommunities is largely unaffected by variation in δ. As
with r, increasing δ has an equalising effect on different scenarios of environmental correlation in
case of species richness. The results presented in FIGURES S1-S5 demonstrate that our conclusions
presented in the main manuscript hold under a wide range of model parameters.
In their recent paper Gonzalez & De Feo (2007) reported decreasing community evenness in association with environmental reddening. They analysed a similar system to ours (with the exception
that consumer species were competing for an explicit resource), where consumer species had a
Gaussian tolerance along a temperature gradient, specifying the consumer attack rate in given conditions. Each consumer species had an environmental optimum along the temperature gradient,
ranging between –1 and 1, with a tolerance (standard deviation of the Gaussian kernel) of w = 0.2.
In our model, where species niche optima were distributed between 0 and 1, the breadth of the resource distribution (σ = 0.3) close corresponds to the environmental tolerance (w) in the model of
Gonzalez & De Feo. Contrary to their results (Gonzalez & De Feo 2007) we reported increased
species evenness with environmental reddening (Fig. 3 in the main MS). It is tempting to attribute
this discrepancy to the linear versus non-linear species interactions in our model and their model,
respectively. However, an investigation of the parameter space in our model revealed that variation
in resource breadth can have a qualitative impact on the relationship between species evenness and
environmental reddening (FIG. S6); the value for environmental tolerance considered by Gonzalez
& De Feo (a comparable environmental tolerance for a gradient of unit length is w = 0.1) results in
decreasing evenness with environmental reddening, while our value for resource breadth (σ = 0.3)
leads to an increase in evenness with environmental reddening.
FIGURE S3. Sensitivity of model results to variation in the intrinsic population growth rate (r). Results are
based on communities in a white noise environment. Three different scenarios for species environmental
correlation (ρ) is considered: independent (IR, ρ = 0; dashed lines), positively correlated (CR, ρ = 0.9; solid
lines), or hierarchically correlated (HR, ρij = f(dij); dash-dotted lines) species responses to environmental
variation. Results based on 100 replicates for each parameter combination. Constant parameter values: S =
50 (community size), p = 0.1 (migration probability), δ = 0.1 (emigration rate).
FIGURE S4. Sensitivity of model results to variation in (maximal) community size (S). Results are based on
communities in a white noise environment. Three different scenarios for species environmental correlation
(ρ) is considered: independent (IR, ρ = 0; dashed lines), positively correlated (CR, ρ = 0.9; solid lines), or
hierarchically correlated (HR, ρij = f(dij); dash-dotted lines) species responses to environmental variation.
Results based on 100 replicates for each parameter combination. Constant parameter values: r = 1 (population growth rate), p = 0.1 (migration probability), δ = 0.1 (emigration rate).
FIGURE S5. Sensitivity of model results to variation in migration probability (p) and emigration rate (δ). Results are based on communities in a white noise environment. Three different scenarios for species environmental correlation (ρ) is considered: independent (IR, ρ = 0; dashed lines), positively correlated (CR, ρ = 0.9;
solid lines), or hierarchically correlated (HR, ρij = f(dij); dash-dotted lines) species responses to environmental variation. Results based on 100 replicates for each parameter combination. Constant parameter values: r = 1 (population growth rate), S = 50 (community size), p = 0.1 (migration probability), δ = 0.1 (emigration rate).
FIGURE S6. There is an interaction between resource breadth (σ) and environmental autocorrelation (κ) in
affecting species evenness, in the case of hierarchical species environmental responses (HR). The results
are based on a 3-species community, where species niche op-time (xi) are evenly distributed between [1 – (S
– 1)/S, (S – 1)/S] where S is the community size. Constant parameter values s = σ (species niche width), r =
1 (population growth rate), p = 1 (migration probability), δ = 0.1 (emigration rate). Results based on 100 replicates for each parameter combination.
SUPPLEMENTARY REFERENCES
Gonzales A, De Feo O (2007) Environmental variability modulates the insurance effects of diversity in non-equilibrium communities. In: Vasseur DA, McCann KS (eds) The impact of environmental variability on ecological systems. Springer, pp 159–177