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

Guilherme M Lopes; José F Fontanari; Guilherme M Lopes; José F Fontanari

doi:10.3934/mbe.2019173

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3450-3464. doi: 10.3934/mbe.2019173

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

Guilherme M Lopes ,
José F Fontanari ^,

Instituto de Fíısica de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil

Received: 27 December 2018 Accepted: 09 April 2019 Published: 18 April 2019

Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human's ecosystem engineering that has profoundly modified the world's landscape. Despite the age-old concern that unchecked population and economic growth may be unsustainable, the prospect of societal collapse remains contentious today. Contrasting with the usual approach to modeling human-nature interactions, which are based on the Lotka-Volterra predator-prey model with humans as the predators and nature as the prey, here we address this issue using a discrete-time population dynamics model of ecosystem engineers. The growth of the population of engineers is modeled by the Beverton-Holt equation with a density-dependent carrying capacity that is proportional to the number of usable habitats. These habitats (e.g., farms) are the products of the work of the individuals on the virgin habitats (e.g., native forests), hence the denomination engineers of ecosystems to those agents. The human-made habitats decay into degraded habitats, which eventually regenerate into virgin habitats. For slow regeneration resources, we find that the dynamics is dominated by rounds of prosperity and collapse, in which the population reaches vanishing small densities. However, increase of the efficiency of the engineers to explore the resources eliminates the dangerous oscillatory patterns of feast and famine and leads to a stable equilibrium that balances population growth and resource availability. This finding supports the viewpoint of growth optimists that technological progress may avoid collapse.
- discrete dynamical systems,
- human-nature dynamics,
- Beverton-Holt model,
- ecosystem engineers,
- population collapse
Citation: Guilherme M Lopes, José F Fontanari. Influence of technological progress and renewability on the sustainability ofecosystem engineers populations[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3450-3464. doi: 10.3934/mbe.2019173

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Abstract

Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human's ecosystem engineering that has profoundly modified the world's landscape. Despite the age-old concern that unchecked population and economic growth may be unsustainable, the prospect of societal collapse remains contentious today. Contrasting with the usual approach to modeling human-nature interactions, which are based on the Lotka-Volterra predator-prey model with humans as the predators and nature as the prey, here we address this issue using a discrete-time population dynamics model of ecosystem engineers. The growth of the population of engineers is modeled by the Beverton-Holt equation with a density-dependent carrying capacity that is proportional to the number of usable habitats. These habitats (e.g., farms) are the products of the work of the individuals on the virgin habitats (e.g., native forests), hence the denomination engineers of ecosystems to those agents. The human-made habitats decay into degraded habitats, which eventually regenerate into virgin habitats. For slow regeneration resources, we find that the dynamics is dominated by rounds of prosperity and collapse, in which the population reaches vanishing small densities. However, increase of the efficiency of the engineers to explore the resources eliminates the dangerous oscillatory patterns of feast and famine and leads to a stable equilibrium that balances population growth and resource availability. This finding supports the viewpoint of growth optimists that technological progress may avoid collapse.

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