FIG. 3. Co-existence and diversity.

Here we use the same parameters as in the previous plot, apart from allowing σ_m to vary, and show the cavity prediction of the fraction of surviving species ϕ_N as a function of p and the standard deviation over mean σ_m/m of the maintenance costs m_i of species. In this regime increasing p leads to more similar species by increasing the niche overlap ρ as defined in (8) from ρ ≈ 77 to ρ ≈ 99 in the range shown above. As predicted by niche theories, increasing ρ leads to increased competition and a smaller ϕ_N while decreasing σ_m/m_i leads to larger fraction of species surviving at a fixed p.