Statistical patterns in tropical tree cover explained by the different water demand of individual trees and grasses

Abstract

Abstract. Tree cover varies enormously across tropical ecosystems-from arid savannas to closed rain forests-and yet a general predictive theory of tropical tree cover remains elusive. Here we use the maximum-entropy method to predict the most likely sample frequency distribution of ecosystems with different tree and grass fractional cover if balance between water supply and demand were the dominant constraint on community assembly. Assuming a hierarchy of individual plant water demand in which trees require more water than grasses, we reproduce observed trends in the means and the upper and lower limits of tropical tree and grass cover across the entire spectrum of tropical ecosystem water supply. Finer details not captured by our predictions indicate the influence of additional factors, such as disturbance. Our results challenge the view that tropical tree-grass coexistence is largely sustained by disturbances in moist environments (''unstable'' coexistence) with water supply playing a dominant role only in arid conditions (''stable'' coexistence). More generally, they suggest that macroecological patterns can be understood and predicted as the most likely outcome of a large number of stochastic processes being played out within a relatively small number of ecological constraints.

Climate seasonality, fire and global patterns of tree cover

“…On the other hand, the partitioning approach of regression trees is apt to capture the abrupt transitions where alternative stable states occur. We advocate for broad-scale analyses using a composite of independent approaches -mechanistic, experimental and correlative (examples in Bertram and Dewar 2013, De Michele and Accatino 2014, Ratajczak et al 2014, Laris et al 2016, Staal et al 2016) -to determine the source of bimodal tree cover patterns and the degree to which moisture and seasonality, jointly with fire, set thresholds for the emergence of binary states.…”

Maximum entropy models of ecosystem functioning

“…a mixture of tree and grass vegetation). In the model [9], a savanna site consists of fixed area (say 1 km 2 ) characterised by a given mean annual water supply, and populated by a large number of individual tree and grass patches. Each patch represents a typical tree or grass individual respectively.…”

“…Observed and predicted cover fractions versus mean annual water availability (E) for (from top to bottom) tree, grass and bare ground cover (adapted from ref. [9]). Points: sample frequency histogram of satellite-based fractional cover estimates.…”

“…In principle the MaxEnt tree/grass p.d. could reproduce this trough by including higher-order moment constraints; these might represent tree-tree interactions (density effects) or tree-grass interactions, possibly including fire disturbance [9]. Further research is required to determine the biophysical interpretation of these higher-order constraints in terms of disturbance, for example.…”

“…Recognising this insight, more recently ecologists have sought an alternative method for constructing statistical mechanical models, one not tied to physical concepts [3,4,5,6,7,8,9]. Jaynes' broader interpretation of statistical mechanics [10], which hinges on the entropy maximisation algorithm (MaxEnt), is of central importance here.…”