Evidence for power-law scaling in species aggregation

Perhaps the best-established observation in spatial ecology is that individuals of a species tend to be aggregated in space. One common means of quantifying this aggregation is the quadrat count distribution (QCD), which gives the probability that a particular species will have precisely n individuals in a plot of some area A (Diggle 2013). The QCD is often modeled as a negative binomial distribution (Green and Plotkin 2007) with two parameters, the distribution mean mu A and a parameter k A that is interpreted as an index of aggregation at some scale A. Here I present both model-based and empirical evidence that this aggregation parameter is likely to scale very generally as the power law k A. A0.5, particularly at large spatial scales. This finding contrasts with the spatial predictions of the Maximum Entropy Theory of Ecology and has important implications for the construction of sampled species-area relationships (Kitzes and Harte 2014), which are used to predict extinction rates and large scale diversity.