Turnover shapes evolution of birth and death rates

Abstract

Population turnover, a key trait shaped by the organism's life history strategy, plays an important role in eco-evolutionary dynamics by fixing the timescale for individual birth and death events as well as in determining the level of demographic stochasticity related to growth. Yet, the standard theory of population genetics, and the models heavily used in the related data analysis, have largely ignored the role of turnover. Here we propose a reformulation of population genetics starting from the first principles of birth and death and show that the role of turnover is evolutionarily important. We derive a general stochastic differential equation for the frequency dynamics of competing birth-death processes and determine the appropriate turnover corrections for the essential results regarding fixation, establishment, and substitution of mutants. Our results reveal how both the absolute and relative turnover rates influence evolution. We further describe a deterministic turnover selection, the turnover flux, which operates in small populations. Finally, we analyse the evolution of mean turnover and show how it explains the key eco-evolutionary mechanisms underlying demographic transitions. In conclusion, our results explicitly show how competing life-history strategies, demographic stochasticity, ecological feedback, and evolution are inseparably intertwined, thus calling for a unified theory development starting from the underlying mechanisms of birth and death.

Promoting extinction or minimizing growth? The impact of treatment on trait trajectories in evolving populations

“…This implies that evolutionary rescue is less likely in populations of fast-turnover cells, which we indeed find when comparing the fractions of surviving replicates for different initial parental trait combinations of equal birth and death rates. Interestingly, Kuosmanen et al (2022) come to similar conclusions in a slightly different model. Importantly, this pattern can be affected by the assumptions on the mutational effect sizes.…”

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 .…”

“…A recent preprint (Kuosmanen et al, 2022) has also independently arrived at the equivalent of some of our equations using an alternative approximation scheme. Using certain discrete time stochastic processes and their approximation via techniques reminiscent of numerical stochastic integration, Kuosmanen et al, 2022 have arrived at our equation for type frequencies (Eq. 10) and the change of mean fitness and turnover in the population (Eq.…”

“…10 recovers the replicator-mutator equation in the infinite population ( K → ∞) limit when Q i models mutation and λ is a mutation rate (see section S7 in the supplementary). However, finite populations experience a directional force dependent on τ i ( x ), the per-capita turnover rate of type i , that cannot be captured in infinite population models (Week et al, 2021; Kuosmanen et al, 2022). This term shows that the effect of turnover rates is structurally identical to that of the differential fitness, but it acts in the opposite direction - a higher relative τ i leads to a decrease in frequency (Notice the minus sign before the second term in Eq.…”

“…28 with f = τ in Eq. 26 yields a dynamical equation for the evolution of mean turnover rates and reads This equation has been derived by Kuosmanen et al, 2022 using an alternative mathematical approximation scheme. The effect of classical natural selection on the evolution of mean turnover depends on whether birth rates or death rates have greater variation in the population, as captured by the first term — if birth rates have greater variance than death rates, then mean turnover increases due to natural selection, whereas if birth rates have lesser variance than death rates, mean turnover decreases due to natural selection.…”