Noise Promotes Species Diversity in Nature

Species diversity in nature is accomplished by coexistence. In a spatial environment, inferior but rapidly moving species can coexist with superior but relatively stationary species. Recent work showed that chaotic dynamics can provide the spatiotemporal variation in the fitness required for coexistence, via the dynamical mechanism of synchronization and intermittency. Utilizing a realistic model that consists of two interacting species in a two-patch environment, we discovered a stochastic-resonance phenomenon where noise can significantly enhance the coexistence and thereby promote species diversity.

Figure 1

For $r=3.0$, (a) time evolution of the frequency $p_1(t)$ of the inferior species in the absence of noise ($ϵ=0$), and (b) on-off intermittency in $Q(t)$. (c), (d) $p_1(t)$ and $Q(t)$, respectively, for $ϵ=4.0$.

Figure 2

For $r=2.6$, (a) for $ϵ=0$ the frequency of the inferior species $p_1(t)$ asymptotically approaches zero, and (b) restoration of the population by noise for $ϵ=4.0$. In both cases, an initial transient of 1000 iterations is disregarded.

Figure 3

For $r=3.0$, (a) distributions $P(\tau )$ for four noise levels and (b) average synchronization time $⟨\tau ⟩$ vs the noise amplitude $ϵ$.

Figure 4

For the Holt-McPeek model for $r=3.0$, stochastic resonance in coexistence as characterized by $R_C(ϵ)$, the degree of coexistence as a function of noise amplitude.