Speciation-rate dependence in species-area relationships

Abstract

The general tendency for species number (S) to increase with sampled area (A) constitutes one of the most robust empirical laws of ecology, quantified by species-area relationships (SAR). In many ecosystems, SAR curves display a power-law dependence, $S\propto A^z$. The exponent $z$ is always less than one but shows significant variation in different ecosystems. We study the multitype voter model as one of the simplest models able to reproduce SAR similar to those observed in real ecosystems in terms of basic ecological processes such as birth, dispersal and speciation. Within the model, the species-area exponent $z$ depends on the dimensionless speciation rate $ν$, even though the detailed dependence is still matter of controversy. We present extensive numerical simulations in a broad range of speciation rates from $ν=10^{-3}$ down to $ν= 10^{-11}$, where the model reproduces values of the exponent observed in nature. In particular, we show that the inverse of the species-area exponent linearly depends on the logarithm of $ν$. Further, we compare the model outcomes with field data collected from previous studies, for which we separate the effect of the speciation rate from that of the different species lifespans. We find a good linear relationship between inverse exponents and logarithm of species lifespans. However, the slope sets bounds on the speciation rates that can hardly be justified on evolutionary basis, suggesting that additional effects should be taken into account to consistently interpret the observed exponents.