Fig. 3.

Steady-state diversity is governed by a simple condition: Diversity crashes if there is an “oligotroph” whose strategy satisfies $R_{\sigma }<p$. (A) Probability of effective number of species $M$ at steady state. For each nutrient supply, we simulated 2,000 sets of 20 strategies. Strategies were chosen uniformly at random, except the case shown in red ($\overrightarrow{s}=\left(0.2,0.8\right)$), where oligotrophs were excluded. ${\tau }_D=10$ here and below. (B) For $\overrightarrow{s}=\left(0.4,0.6\right)$ (orange in A), we plot all strategies that appear in the most diverse 10% of simulations (90th percentile and above of $M$). No strategies appear in the oligotroph region, demarcated by the blue dashed lines. (C) Same as A but for 3 nutrients. (D) Strategies that appear in the most diverse 10% of simulations for $\overrightarrow{s}=\left(0.2,0.4,0.4\right)$ (teal in C). The oligotroph region is nearly empty.