New paper studying the mathematics of coloured environmental noise in the Journal of Mathematical Biology

Natural communities are exposed to a multitude of environmental events, such as fires, droughts and floods. These events cause random changes in environmental variables such as temperature and rainfall, which in turn shape the dynamics of species abundances and hence patterns of biodiversity. A common feature of time-series of environmental variables is that they are positively correlated over time. As a result, variables change more slowly than they would under zero correlation, and fluctuations of lower frequency have greater influence. In technical terms, this corresponds to “reddened” environmental noise, analogous to red light waves having relatively low frequencies, whereas the uncorrelated case corresponds to white noise. Previous ecological modelling studies have focussed mostly only on white noise rather than reddened noise.

In a new study recently published in the Journal of Mathematical Biology, we address this knowledge gap by constructing a new stochastic community model with reddened environmental noise, and then mathematically analysing the model to show how this type of noise changes the distribution of individuals among species. We find that redder noise (with greater correlation in time) helps to increase the expected number of species with higher abundances, by prolonging periods where the environment has a positive effect on species’ growth rates. This results in a flatter distribution of species across abundance classes compared with the white noise case. Overall, our findings highlight the importance of incorporating coloured noise when using models to predict patterns of biodiversity.

Fung, T., J. P. O’Dwyer, & R. A. Chisholm. Species-abundance distributions under colored environmental noise. Journal of Mathematical Biology (in press)


Species-abundance distributions from the new model under different colored environmental noise regimes