Abstract
Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We then separately include resource competition based on shared capture area. By varying rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the context of asymmetric competition, such as canopy shading or large colony dominance, whose effects primarily weaken the smaller of two competitors. When such competition couples slow timescales of growth to fast competitive death, it generates population shocks and demographic oscillations similar to those observed in forest data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth, which in turn, are the result of long-term evolutionary dynamics.
Highlights
Population-level scaling in ecological systems arises from individual growth and death with competitive constraints
We propose a minimal dynamical model that integrates timescales of individual growth and mortality with competitive attrition on a background of fluctuating resources
Since most ecological systems are out of equilibrium, we extend our model to consider transient phenomena and predict population shock waves from competitive interactions when there is metabolic growth
Summary
The fractal structure of a forest exists both at the level of the physical branching of individual trees and at the level of self-similar packing of differently sized individuals. When metabolic growth is determined by a power law, the simple size-class model fixes the forms of scaling in mortality and population as a combination of both the exponent driving growth and the relative timescales at which mortality and growth act [32] From this minimal model of tree growth under the scaling assumptions of individual tree allometry, we obtain a wide range of possible steady states encompassing both predictions consistent with metabolic scaling theory as well as virtually any other population number scaling. This reflects the fact that space filling in forests, when α = 2, does not depend separately on typical growth and mortality rates but is determined by the ratio of the scaling coefficients, which may be fixed by energetic constraints. Since these features only determine the exponent, deviations from space filling at steady state (such as for size distributions observed in large trees [figure 1 in ref. 34]) could arise from processes such as competitive interactions, which are not included in a model only accounting for metabolic scaling
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