Abstract
The Maximum Entropy Theory of Ecology (METE) predicts the shapes of macroecological metrics in relatively static ecosystems, across spatial scales, taxonomic categories and habitats, using constraints imposed by static state variables. In disturbed ecosystems, however, with time‐varying state variables, its predictions often fail. We extend macroecological theory from static to dynamic by combining the MaxEnt inference procedure with explicit mechanisms governing disturbance. In the static limit, the resulting theory, DynaMETE, reduces to METE but also predicts a new scaling relationship among static state variables. Under disturbances, expressed as shifts in demographic, ontogenic growth or migration rates, DynaMETE predicts the time trajectories of the state variables as well as the time‐varying shapes of macroecological metrics such as the species abundance distribution and the distribution of metabolic rates over individuals. An iterative procedure for solving the dynamic theory is presented. Characteristic signatures of the deviation from static predictions of macroecological patterns are shown to result from different kinds of disturbance. By combining MaxEnt inference with explicit dynamical mechanisms of disturbance, DynaMETE is a candidate theory of macroecology for ecosystems responding to anthropogenic or natural disturbances.
Highlights
Ecology seeks insight into the shape and origin of patterns in the abundance, energetics and spatial distributions of taxa, across spatial scales and within different habitats
The study of dynamic ecosystems is a rising area in ecology (Hill & Hamer1998; Dornelas 2010; Turner 2010; Newman 2019), macroecological theory has largely focused on patterns in quasi-steady-state ecosystems, ignoring trending patterns in systems undergoing rapid succession, diversification or collapse (Fisher et al 2010)
Because the dynamics depends on the time-dependent state variables, we propose an iterative procedure for updating both constraints and macroecological distributions
Summary
Ecology seeks insight into the shape and origin of patterns in the abundance, energetics and spatial distributions of taxa, across spatial scales and within different habitats. Empirical evidence is accumulating that macroecological patterns differ between dynamic and static ecosystems We formulate and initially explore a theory, DynaMETE, to predict macroecological patterns in dynamic systems. Our starting point is a static theory based on the maximum entropy (MaxEnt) framework (Harte 2011; Harte & Newman 2014). MaxEnt selects the flattest, and least informative, probability distributions compatible with constraints imposed by prior knowledge. The maximum entropy form of a probability distribution, p(n), is obtained by maximising its Shannon information entropy (Shannon 1948), À∑npðnÞlogðpðnÞÞ, under imposed constraints
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