Fig. 3.

The nature of the transition between the niche and neutral phases. Note that the order parameters for the two models are different: The order parameter for the PA model is zero in the niche phase and greater than zero in neutral phase, whereas the order parameter for the LV model is greater than zero in the niche phase and zero in the neutral phase. The average entropy 〈H[P_PA]/S〉, which is a measure of fluctuations in the community composition, is positive in the neutral phase and zero in the niche phase, illustrating the freezing transition in the PA model. (Inset) In LV simulations the distance from neutrality 〈KL(P_LV∥P_N)〉 is essentially zero in the neutral phase and rises to large values in the niche phase. Parameters: $\tilde{\mu }=1.0$, $\tilde{\sigma }\approx 0.4$, $\tilde{\omega }\ln \tilde{\lambda }=3\tilde{K}/2$, μ = 1.0, σ ∼ 0.4, λ = 0.01.