Figure legends:
Figure 1. Various complementary visualizations of how diversity
could influence the position of tipping points in systems with
alternative stable states. (a, b) Illustrations of the possible
dependence of ecosystem state on an environmental driver (a)with no diversity and (b) with diversity. The ecosystem
illustrated can exist in either an anoxic state with high density of
sulfate-reducing bacteria or an oxic state with low density of
sulfate-reducing bacteria (other functional groups are omitted for
clarity). In the region of bistability (green) the state of the system
depends on its history. At tipping points, the ecosystem shifts abruptly
(grey arrows) to the alternative state. (b) illustrates
replacement of less tolerant by more tolerant strains as the
environmental driver increases (strain dynamics caused by a decreasing
environmental driver are omitted for clarity.) (c, d) Two
complementary visualizations of the effect of trait variation on
resilience. (c) The position of the two tipping points at
different levels of trait variation. (d) The effect size of
trait variation on resilience, i.e. on the position of the tipping
points. Effect size is the difference in oxygen diffusivity between a
tipping point without trait variation and with a given level of trait
variation. A positive effect size indicates increased resilience. The
depicted example shows a scenario where increasing trait variation
increases the resilience of both the oxic and the anoxic state. A
non-linear effect and linear effect are shown only to aid understanding.
Please see Box 1 for further explanation of terms.
Figure 2. The model ecosystem. We simulated interactions among
three functional groups of bacteria. Cyanobacteria inhibit phototrophic
sulfur bacteria and sulfate-reducing bacteria by producing oxygen, while
sulfate-reducing bacteria inhibit cyanobacteria by producing reduced
sulfur. All three groups consume phosphorus. In addition, the two sulfur
bacteria groups interact by producing the substrate that the other group
consumes: sulfate-reducing bacteria reduce oxidized sulfur to reduced
sulfur, while phototrophic sulfur bacteria oxidize reduced sulfur to
oxidized sulfur. Reduced sulfur is also oxidized abiotically. Finally,
all four chemical substrates diffuse into or out of the system depending
on their concentrations. Modified version of Figure 1 of Bush et al
(2017).
Figure 3. Effect of trait variation on resilience. As in Figure
1c-d, we here display the effects of trait variation on resilience with
two types of visualization which together provide two complementary
views of the same data and patterns. The left column of panels shows the
position of the tipping points at different levels of trait variation
(red: oxic-anoxic tipping point; blue: anoxic-oxic tipping point). Data
is missing in panels e, and i, when patterns of coexistence were
atypical of the classical pattern shown in Figure 1a (e.g. when
cyanobacteria coexisted with sulfur bacteria at low oxygen
diffusivities). The amount of trait variation was standardized to range
from 0 to 1 by dividing each value of trait variation by the maximum
amount of trait variation of the respective functional group. The green
area depicts the extent of the region of bistability, the thick grey
vertical bars indicate the bounds of oxygen diffusivity analyzed in our
simulations. The right column of panels shows the effect size of trait
variation on resilience. Effect size is displayed only when the tipping
point was within the investigated range of oxygen diffusivity. Figure
labels indicate which functional group(s) varied in traits (CB:
cyanobacteria, SB: sulfate-reducing bacteria, PB: phototrophic sulfur
bacteria). See Figure 1c-d and Box 1 for further explanation of terms.
Figure 4. Relationship of ecosystem state variables and oxygen
diffusivity when there is functional diversity among nine strains within
each functional group. The range of trait values is given in Table 1.
The different strains are shaded differently, so that in each functional
group (a-c) the darkest strain is the most tolerant, the lightest the
least tolerant. The left column of panels shows the trajectory of
decreasing oxygen diffusivity, the right column of panels shows the
trajectory of increasing oxygen diffusivity. Points (which often are so
close as to appear as thick lines) show the stable state at the end of
each period of constant oxygen diffusivity. Thin lines are for
visualization only and join the points. Grey arrows show the oxygen
diffusivity at which the system shifts, and the direction of the shift.
The length of the grey arrows is without meaning.