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Overpopulation and environmental degradation due to inadequate resource-useare outcomes of human's ecosystem engineering that has profoundly modified theworld's landscape. Despite the age-old concern that unchecked population andeconomic growth may be unsustainable, the prospect of societal collapse remainscontentious today. Contrasting with the usual approach to modeling human-natureinteractions, which are based on the Lotka-Volterra predator-prey model withhumans as the predators and nature as the prey, here we address this issueusing a discrete-time population dynamics model of ecosystem engineers. Thegrowth of the population of engineers is modeled by the Beverton-Holt equationwith a density-dependent carrying capacity that is proportional to the numberof usable habitats. These habitats (e.g., farms) are the products of the workof the individuals on the virgin habitats (e.g., native forests), hence thedenomination engineers of ecosystems to those agents. The human-made habitatsdecay into degraded habitats, which eventually regenerate into virgin habitats.For slow regeneration resources, we find that the dynamics is dominated bycycles of prosperity and collapse, in which the population reaches vanishingsmall densities. However, increase of the efficiency of the engineers toexplore the resources eliminates the dangerous cyclical patterns of feast andfamine and leads to a stable equilibrium that balances population growth andresource availability. This finding supports the viewpoint of growth optimiststhat technological progress may avoid collapse.

Influence of technological progress and renewability on the sustainability of ecosystem engineers populations