Tree clusters in savannas result from islands of soil moisture

Abstract

Patterns of tree clusters in savannas display well-established characteristics that are explained by exogenous dynamics related to hot spots of soil moisture. These characteristics are related to the probability distribution of the cluster sizes and the fractal dimension of the cluster perimeters, both of which have a narrow range of variation regardless of specific climates. Such characteristics match very well those of the hot spots of high soil moisture when accounting for the impact of fire and herbivores.Tree clusters in savannas are commonly found in sizes that follow power laws with well-established exponents. We show that their size distributions could result from the space–time probabilistic structure of soil moisture, estimated over the range of rainfall observed in semiarid savannas; patterns of soil moisture display islands whose size, for moisture thresholds above the mean, follows power laws. These islands are the regions where trees are expected to exist and they have a fractal structure whose perimeter–area relationship is the same as observed in field data for the clustering of trees. When the impact of fire and herbivores is accounted for, as acting through the perimeter of the tree clusters, the power law of the soil moisture islands is transformed into a power law with the same exponents observed in the tree cluster data.