Fig. 2: Distribution of fitness effects of first-step mutations as a function of community complexity.

a As in Fig. 1, a community is assembled from \({{{\mathcal{S}}}}\) initial species, leaving \({{{{\mathcal{S}}}}} {*}\) alive at equilibrium. The surviving species produce mutations, whose invasion fitness s_inv is equal to their initial relative growth rate. b Number of surviving species \({{{{\mathcal{S}}}}} {*}\) as a function of the sampling depth \({{{\mathcal{S}}}}\) and the standard deviation of the total uptake budget among sampled species, Std(X_μ). Curves show theory predictions from Supplementary Note 3.1, while points show means and standard deviations over 10³ simulation runs with \({{{\mathcal{R}}}}=200\), \({{{{\mathcal{R}}}}}_{0}=40\), and uniform resource supply. c Distribution of fitness effects of knock-out (and knock-in) mutations with ΔX = 0 in communities with two different levels of niche saturation (\({{{{\mathcal{S}}}}} {*}/{{{\mathcal{R}}}}\)). Black curve shows the theoretical predictions from Eq. (5), while dots represent a histogram over all possible strategy mutations in 10³ simulation runs using the same parameters as panel (b), with \({{{{\mathcal{S}}}}} {*}/{{{\mathcal{S}}}}=0.1\). d The width σ_inv of the distribution of fitness effects in panel C as a function of niche saturation, for various values of sampling permissivity \({{{{\mathcal{S}}}}} {*}/{{{\mathcal{S}}}}\) and per-species resource usage \({{{{\mathcal{R}}}}}_{0}\). Curves show the theoretical predictions from Eq. (5), while the dots show the average over 10³ simulation runs. e Pearson correlation between the fitness effect of a mutation in the community and its fitness effect in monoculture, for different values of niche saturation and scaled variation in resource supply rates, \({{{{\rm{Var}}}}}_{{{{\rm{env}}}}}/{{{{\rm{Var}}}}}_{{{{\rm{comm}}}}}\equiv \left[{{{\rm{Var}}}}(K)/{\overline{K}}^{2}\right]\cdot {{{{\mathcal{R}}}}}_{0}/(1-{{{{\mathcal{R}}}}}_{0}/{{{\mathcal{R}}}})\). Curves show the theoretical predictions from Supplementary Note 4.1, while points show the average over all mutations in 10³ simulated communities with parameters the same as panel (c).