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.