Effects of demographic stochasticity and life-history strategies on times and probabilities to fixation

Abstract

How life-history strategies influence the evolution of populations is not well understood. Most existing models stem from the Wright-Fisher model which considers discrete generations and a fixed population size, thus not taking into account any potential consequences of overlapping generations and demographic stochasticity on allelic frequencies. We introduce an individual-based model in which both population size and genotypic frequencies at a single bi-allelic locus are emergent properties of the model. Demographic parameters can be defined so as to represent a large range of r and K life-history strategies in a stable environment, and appropriate fixed effective population sizes are calculated so as to compare our model to the Wright-Fisher diffusion. Our results indicate that models with fixed population size that stem from the Wright-Fisher diffusion cannot fully capture the consequences of demographic stochasticity on allele fixation in long-lived species with low reproductive rates. This discrepancy is accentuated in the presence of demo-genetic feedback. Furthermore, we predict that populations with K life-histories should maintain lower genetic diversity than those with r life-histories.

Turnover shapes evolution of birth and death rates

“…Even though the field of population genetics is well-known for taking the effects of stochasticity seriously, the fact that new mutants may differ not only in terms of their expected growth rate, but also in terms of their turnover, has been largely ignored. While numerous studies have investigated and identified demographic stochasticity [25, 29] and life-history strategies [27] as important factors and explored their evolutionary consequences, the concept of turnover has remained fuzzy and the standard theory of population genetics and the models used in practice say very little about the role of turnover in evolution generally. Given the surprisingly simple yet fundamental equation (12) that governs the evolution of the mean turnover, defined as the sum of birth and death rates, we indeed believe that this concept is central to evolution, as evidenced also by the fixation and establishment results exemplified in Figs.…”

“…There exists a large body of literature covering the subject of fixation of beneficial mutations under various assumptions [22–25], which also includes life-history [26–29] and birth-death-like models [30–32]. However, most of the previous work has been done under the limiting assumptions that mutations change either only the birth rate (fecundity-mutants) or the death rate (generation-time mutants) while the other trait remains constant [24].…”

Eco-evolutionary dynamics for finite populations and the noise-induced reversal of selection

“…Lastly, noise-induced selection is particular to fluctuating populations and does not occur in models with fixed population sizes such as the Wright-Fisher or Moran models. Taken alongside other theoretical (Lambert, 2010; Parsons et al, 2010; Abu Awad and Coron, 2018; Kuosmanen et al, 2022; Mazzolini and Grilli, 2023) and empirical (Papkou et al, 2016; Chavhan et al, 2019) studies on evolution in fluctuating populations, this last point suggests that models which assume fixed total population size, such as Wright-Fisher and Moran, may miss out on important evolutionary phenomena that are only seen in finite, populations of non-constant size .…”

“…Here, probabilistic rules for birth and death are specified at the individual level. Such models allow us to capture a stochastically varying population size, and thus enable us to relax assumptions of constant population size as seen in models such as the Wright-Fisher or Moran process (Lambert, 2010;Abu Awad and Coron, 2018).…”

Analysis of diversity-dependent species evolution using concepts in population genetics

“…In this case, the type with the higher birth rate shows an increase in numbers during the growth phase at densities below the carrying capacity, whereas near the carrying capacity, the type with lower birth rate is favored, due to smaller fluctuations in population density – a phenomenon termed as ‘ r vs K selection’ (see e.g., Pianka ( 1970 )). Abu Awad and Coron ( 2018 ) use a scaling approach similar to ours to study effective population mass, absorption and extinction times, etc., for a population controlled by a carrying capacity. Chevin ( 2016 ) utilized diffusion approximation methods to analyze the evolution of binary discrete and continuous traits, and interpreted diversification models in terms of population genetics concepts of species selection and random drift.…”