Neutral models in ecology make the parsimonious assumption that all species are demographically equivalent, and so their abundances only differ due to demographic stochasticity. Despite neutral models being stochastic models, previous studies have focused mainly on their mean behaviour owing to the lack of formulae for specifying the full probability distributions for biodiversity indicators of interest. In a new paper by Tak, Sonali (former Chisholm lab intern) and Ryan, we use classic results from birth–death processes to derive formulae specifying the probability distributions of extinction times (e.g., see figure below), species richness, and immigration and extinction rates in the classic spatially implicit neutral ecological model.

We demonstrate the utility of our formulae in providing greater ecological insight in a few ways:

1. Firstly, we parameterised a neutral metacommunity model for trees in the Amazon, and used it to show that the age of a common tree species in the Amazon, which by time-symmetry of a neutral model is equivalent to the extinction time of the species, is greater than the oldest estimated age of angiosperms with very high probability. Thus, neutral models produce slow species-abundance dynamics that severely overestimate species age.

2. Secondly, we show how our formula for the probability distribution of species richness can be used to fit a neutral local community model to observed species richness at Barro Colorado Island in Panama, given an independent estimate of the immigration rate. This is more parsimonious than the standard approach of fitting to the full species abundance distribution.

3. Thirdly, we show that the curves of immigration and extinction rates versus species richness in the local community component of the neutral model are for the most part approximately linear, reflecting low variation of species richness around the mean value.

Probability distributions of extinction time for a species population with initial abundance 1 or 2 and per-capita birth and death rates equal to 1/yr, in a neutral metacommunity model with 500 individuals and a per-capita speciation probability of 0.05. The distributions were calculated using the new formula that we derived.

Fung, T., S. Verma, and R. A. Chisholm (2020). Probability distributions of extinction times, species richness, and immigration and extinction rates in neutral ecological models. Journal of Theoretical Biology, 485: 110051. [link: https://www.sciencedirect.com/science/article/pii/S0022519319304205]