# Selection-regulated population dynamics

When population dynamic feed-back selection is integrated with population dynamics, we obtain selection-regulated dynamics as a more general version of density-regulated growth.

Selection-regulated dynamics explain the population cycles that have fascinated ecologists for decades. It implies hyperexponential instead of exponential growth at low densities, it generates evolutionary rescue, and provides new insights into the limitation and exploitation of natural populations.

Applying AIC model selection to 1200 population dynamic trajectories for birds and mammals, about 90% of the selected models were regulated by selection. For the best data (coming from the North American Breeding Bird Survey), selection-regulated dynamics was found to be 25,000 times more probable than density-regulated growth. Selection was essential in 94% of the best models explaining 82% of the population dynamics variance across the North American continent.

This section describes the range of dynamics covering theory and evidence, and the modelling page of mrLife.org provides live selection-regulated simulations for birds and mammals, including the best models for the above mentioned data.

## Hyperexponential growth

The Malthusian law of exponential increase describes unchecked dynamics at the limit of zero population density. It assumes that evolutionary changes occur much slower than population dynamics, but evidence have found that this is often not the case.

Natural selection at zero density follows Fisher’s fundamental theorem, predicting a linearly increasing exponential growth rate, and a hyperexponentially increasing population.

Hyperexponential dynamics is more common among birds and mammals than exponential growth, and it accelerated the unchecked spread of Covid-19.

## Selection-accelerated growth

Ecologists have become used to describing populations by positive or negative growth, referring to growing or declining populations. This tradition follows from traditional population thinking, where a population under given environmental conditions is assumed to have a constant growth rate.

This assumption however is flawed because natural selection is typically either accelerating or decelerating the growth rate; even in a constant environment. Hyperexponential growth is a special case of the hyperexponential model, which is naturally divided into selection-accelerated growth and selection-decelerated growth.

Selection-accelerated growth includes cases with a constant selection increase in the growth rate over time. These populations may decline, or increase, or first decline and then increase in numbers.

## Selection-decelerated growth

Selection-decelerated growth includes cases with a constant selection decline in the growth rate over time. These populations may increase, or decline, or first increase and then decline in numbers.

## Evolutionary rescue

Evolutionary rescue is a special case of selection-regulated dynamics, where a declining population that would have gone extinct in the absence of evolution, is rescued by a natural selection acceleration of the growth rate.

## Selection-regulated dynamics

More generally, population dynamics is selection-regulated by a density-frequency-dependent selection of the exponential growth rate. This regulation is based on population dynamic feed-back selection that accelerates growth in populations that are below the population dynamic equilibrium and decelerates growth above. The result is a single-species mechanism for the population cycles that have fascinated ecologists for decades. Selection-regulation implies that it is the acceleration of the growth rate (and not the growth rate itself) that is a function of the density dependent environment.

## Population abundance

The abundancies of natural populations are not---as proposed by Malthus in 1798 and elaborated by density-regulation theory---determined by famine from intense competition for depleted resources. The population dynamic equilibrium of selection-regulated dynamics is instead a competitive interaction fix-point of population dynamic feed-back selection.

This implies that population densities are naturally selected to generate the intra-specific bias in resource access that is prespecified by the selection attractors of the competitive interaction fix-points. The result is a green and balanced world, where overexploitation is rare as species evolve balanced and intermediate population densities. This selects, among others, for an allometric solution, where Damuth's 3/4 power decline in abundance with mass follows as an essential prediction.

## Sustainable exploitation

Theory on sustainable use is traditionally based on density regulated growth, where the growth rate is a function of the environment and the sustainable yield has a maximum across the range of potential population densities. For selection-regulated dynamics it is not possible to determine the growth rate, but only the acceleration of the growth rate, as a function of the density dependent environment. This implies that there is no maximal sustainable yield at an optimal abundance of harvest, but a range of possible replacement yields for any given abundance.

For harvest situations where populations are allowed sufficient time to equilibrate at the evolutionary equilibrium, the abundance of the exploited population will be relatively independent of the harvest, but the intrinsic growth rate will increase, and the average body mass decline, with increased harvest.