“Stochastic evolutionary demography under a fluctuating optimum phenotype”

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Luis-Miguel Chevin, Olivier Cotto, and Jaime Ashander

Theoretical analysis of population dynamics and extinction risk caused by random fluctuations of an optimum phenotype

Extinction risk caused by fluctuating selection in a randomly changing environment

Most environments in nature fluctuate in a largely random way, beyond directional trends such as global warming. How do these random environmental fluctuations affect the ecology and evolution of populations, and their joint influence on extinction risk? This is the question that Luis-Miguel Chevin, Olivier Cotto (CNRS researchers at the CEFE in Montpellier), and Jaime Ashander (from UCLA), here address.

On the ecological side, stochastic (i.e., random) environments cause fluctuations in population size, which can be large since all individuals in the population are affected by the environment. Importantly, even for fluctuation patterns that allow population to persist on average, a sequence of bad years can lead a particular population to extinction. This is more likely to occur if a bad year is most often followed by another bad year, that is, under large temporal autocorrelation of the environment.

On the evolutionary side, a population is more likely to track a moving optimum phenotype by adaptive evolution if the movements of this optimum, despite being random, are still somewhat predictable. This occurs when the environment has high temporal autocorrelation.

To combine these ecological and evolutionary effects within a common framework, the authors model the situation where fluctuations in population growth rates depend on the mismatch between the population mean phenotype for a trait and the optimum value for this trait, set by the environment. They use this model to find the distribution of population size, that is, the probability that a population is below or above any given number. They show that this distribution can differ markedly from previous theoretical predictions, most notably by an excess of low population sizes, and thus elevated extinction risk. All parameters of this distribution of population size (its mean, variance among replicate populations, etc…) can be related to basic and measurable parameters of the model, such as the temporal variance and autocorrelation of the optimum, or the genetic variance of the trait. This work thus represents a large step forward in our ability to predict demography and extinction risk of an evolving population in a randomly changing environment. Read the Article