Evolution of class-structured populations in periodic environments

Abstract

What is the influence of periodic environmental fluctuations on life-history evolution? We present a general theoretical framework to understand and predict the long-term evolution of life-history traits under a broad range of ecological scenarios. Indeed, this analysis yields time-varying selection gradients that help dissect the influence of the fluctuations of the environment on the competitive ability of a specific life-history mutation. We use this framework to analyse the evolution of key life-history traits of pathogens, such as transmission and virulence. These examples reveal how periodic fluctuations of the environment can affect the evolution of pathogens, and illustrate the usefulness and broad applicability of this new approach.

Regulation of prophage induction and lysogenization by phage communication systems

“…We thus have to determine the growth rate of a mutant after its appearance in a viral population dominated by a wild-type genotype. Since the virus may appear in two distinct states, a prophage in lysogenic bacteria (L) or a virion outside the cell (V), we can use the following matrix to describe the dynamics of the mutant 12…”

Multi-morph eco-evolutionary dynamics in structured populations

“…At a conceptual level, our approach is very relevant to the current revival of interest on the time scales of ecological and evolutionary processes, as it can be used to examine the role of 'fast evolution' when this is fueled by a large standing variation at the population level. In addition there is the potential to examine non-equilibrium outcomes such as those that arise during repeated epidemics driven by antigenic escape (Sasaki et al, 2021) or seasonality (Lion & Gandon, 2021).…”

“…Note that v i and u i are co-normalised such that . This co-normalisation condition means that the average quality of a morph- i individual is 1 at all times (Lion & Gandon, 2021).…”

“…We then show how, by assuming that each morph distribution is clustered around the morph mean, we can derive equations for the dynamics of class-specific morph frequencies, morph means, and morph variances using Taylor approximations of the vital rates describing between-classes transitions. We also apply recent theory on reproductive value (Lion, 2018a,b; Lion & Gandon, 2021) to simplify the morph dynamics at the population level. In particular, we show that the dynamics of morph means take the form of a frequency-dependent extension of Lande’s theorem (Lande, 1976, 1979, 1982; Barfield et al, 2011), where the marginal fitness effect on the vital rate from class j to class k is weighted by the morph’s reproductive value in class k (a measure of class quality) and by the fraction of morph- i individuals that are in class j (a measure of class quantity).…”

Targeted vaccination and the speed of SARS-CoV-2 adaptation

“…where R w is the transition matrix for the wild-type strain and λ(t) is the per-capita growth rate of the resident population at time t (see [6,11] for a more detailed description). For small ε, the mutant frequency p m changes slowly compared to the ecological variables f and v, and we can use a quasi-equilibrium approximations obtained by setting the right-hand-sides of equations (A.2) and (A.3) to zero.…”