Abstract
Humans are the ultimate ecosystem engineers who have profoundly transformed the world’s landscapes in order to enhance their survival. Somewhat paradoxically, however, sometimes the unforeseen effect of this ecosystem engineering is the very collapse of the population it intended to protect. Here we use a spatial version of a standard population dynamics model of ecosystem engineers to study the colonization of unexplored virgin territories by a small settlement of engineers. We find that during the expansion phase the population density reaches values much higher than those the environment can support in the equilibrium situation. When the colonization front reaches the boundary of the available space, the population density plunges sharply and attains its equilibrium value. The collapse takes place without warning and happens just after the population reaches its peak number. We conclude that overpopulation and the consequent collapse of an expanding population of ecosystem engineers is a natural consequence of the nonlinear feedback between the population and environment variables.
Highlights
There is hardly a landscape on Earth that has not been modified by past living beings as a result of the natural feedback between organisms and environment, whose study was initiated by Darwin in his last scientific book [1]
The collapse takes place just after the population reaches its peak number. This surprising outcome, which results from the nonlinear feedback between engineers and environment, could hardly be predicted without mathematics, lending credence to the tenets of the discipline Cliodynamics that advocates the mathematical modeling of historical processes [13,14]
The initial increase of the mean density het i reflects the expansion phase of the engineers, which is accompanied by the monotone decreasing of the unexplored patches, as expected
Summary
There is hardly a landscape on Earth that has not been modified by past living beings as a result of the natural feedback between organisms and environment, whose study was initiated by Darwin in his last scientific book [1]. This feedback results in a density-dependent carrying capacity This feature is the core of the continuous-time, space-independent mathematical model that Gurney and Lawton proposed to describe the population dynamics of ecosystem engineers [8]. The Gurney and Lawton model becomes more effective (and instructive) to simulate the human-environment interaction if we use its recently proposed spatial formulation, where an initial small settlement of engineers is surrounded by vast areas (patches) of virgin habitats, and a fraction of the engineers are allowed to move between neighboring patches [12]. The collapse takes place just after the population reaches its peak number This surprising outcome, which results from the nonlinear feedback between engineers and environment, could hardly be predicted without mathematics, lending credence to the tenets of the discipline Cliodynamics that advocates the mathematical modeling of historical processes [13,14].
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