Dispersal distance determines the exponent of the spatial Taylor's power law

Abstract

The equation describing a power-law relationship between the mean and variance of population abundance in space or time is known as Taylor's power law (TPL), initially observed in samples of insects. Factors determining the TPL exponent are of particular concern to ecologists because the observations of the exponent usually range 1-2. Recent studies have suggested that TPL is caused solely by statistical artifacts rather than biological processes, with the corresponding statistical models lacking linkages to explicit population demography. In this study, we used two special forms of the Neyman-Scott cluster point process to study the effect of offspring dispersal distance from the parents on the TPL exponent. Results showed that dispersal distance could largely affect the TPL exponent. The response curve of TPL exponent to dispersal distance is similar to the shape of the left-skewed gamma distribution function multiplied by a constant which can permit its maximum value to exceed 1. That means, short-distance dispersals could produce large TPL exponents relative to the whole response curve. However, the TPL exponent will decline in the case that the dispersal is extremely short or long. To better understand the function of the exponent of TPL on fitness, we attempted to link plant seed dispersal ability to the TPL exponent, and we discussed the trade-off between investing in propagation energy and in performance energy of plants. Dispersal overlap of offspring each other to an extent can cause a large TPL exponent, providing maximum fitness in a population. A novel theoretical frame was proposed to explain the role of spatial TPL relationships in affecting the fitness of plants.