ABSTRACT
Chapter 15 reviews the 100+ year effort to find mathematical models that accurately predict population growth, a prominent and divisive subject in ecology. At stake was the question of whether a balance of nature exists, proposed in the form of the equilibrium theory of ecology. It was hoped that like natural selection, the equilibrium theory could explain how nature regulated itself. Our current understanding is that population growth in the pattern of the logistic (S-shaped curve) is rare except in microbes even though researchers commonly find evidence of density dependence. For non-microbes, variability (boom and bust patterns) tends to prevail. Explanations include abiotic circumstances, the Allee effect, stunting, compensatory mortality, and the law of diminishing returns. Chaos as an explanation is reviewed. For predicting growth, the logistic equation is used, but with added algebraic features that include time lags, stage and age structure, matrix projection models, and stochasticity. Metapopulations, r and K life histories, and the Grime model provide further understanding. Components of the extinction vortex are reviewed, and occupancy models are described. In the end it appears that species composition is partly a result of chance, randomness, and patchiness. These combine with factors familiar to us – symbiosis, competition, predation, weather, soil quality, and other biotic and abiotic factors.
