Understanding spatial patterns in ecosystems quantitatively can lead to insights regarding the relative importance of underlying physical processes, and allows us to better predict what will happen to ecosystems under natural and anthropogenic disturbances. The Maximum Entropy Theory of Ecology (METE) is a theory that can simultaneously predict many patterns and distributions, including spatial patterns. However, the predictions from METE do not seem to be as accurate in disturbed ecosystems.
To compare spatial data to theory, we can bisect a plot and consider the probability that there are n individuals on one side given N total individuals. METE predicts that this probability distribution will be uniform, which is equivalent to using the Laplace rule of succession as a colonization rule. Ecologically, this leads to strong spatial aggregation. Another common theoretical approach is the random placement model, which predicts a binomial distribution. For many ecosystems METE overpredicts the amount of spatial aggregation, but there is more than predicted by random placement, which has none.
We add a density dependent death rule to modify the prediction of METE, where individuals die with probability proportional to n to some exponent ɑ and are replaced with the METE colonization rule.
Results/Conclusions
We derive the bisection probability distribution that results from using the Laplace rule of succession as a colonization rule with a density dependent death rule. The predictions show that we can vary the amount of spatial aggregation by varying the density dependence ɑ. With ɑ = 1, the distribution is unchanged from the original predictions of METE, and with ɑ = 2, the distribution approaches the binomial distribution for large N. In the intermediate regime 1 < ɑ < 2, we show that this model predicts less spatial aggregation than METE, but more than random placement. We also show that this model fits the data well and relate it to systems where we suspect density dependence does and does not matter. In the future, we will extend this theory to finer spatial scales beyond the first bisection.