The impact of dormancy on evolutionary branching.

In this paper, we investigate the consequences of dormancy in the 'rare mutation' and 'large population' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second 'small mutations' limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the 'speed of adaptation' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.

The role of connectivity on COVID-19 preventive approaches.

Preventive and modeling approaches to address the COVID-19 pandemic have been primarily based on the age or occupation, and often disregard the importance of heterogeneity in population contact structure and individual connectivity. To address this gap, we developed models based on Erdos-Rényi and a power law degree distribution that first incorporate the role of heterogeneity and connectivity and then can be expanded to make assumptions about demographic characteristics. Results demonstrate that variations in the number of connections of individuals within a population modify the impact of public health interventions such as lockdown or vaccination approaches. We conclude that the most effective strategy will vary depending on the underlying contact structure of individuals within a population and on timing of the interventions.

The interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes.

In this paper we investigate the interplay between two fundamental mechanisms of microbial population dynamics and evolution, namely dormancy and horizontal gene transfer. The corresponding traits come in many guises and are ubiquitous in microbial communities, affecting their dynamics in important ways. Recently, they have each moved (separately) into the focus of stochastic individual-based modelling (Billiard et al. 2016, 2018; Champagnat, Méléard and Tran, 2021; Blath and Tóbiás 2020). Here, we investigate their combined effects in a unified model. Indeed, we consider the (idealized) scenario of two sub-populations, respectively carrying 'trait 1' and 'trait 2', where trait 1 individuals are able to switch (under competitive pressure) into a dormant state, and trait 2 individuals are able to execute horizontal gene transfer, which in our case means that they can turn trait 1 individuals into trait 2 ones, at a rate depending on the density of individuals. In the large-population limit, we examine the fate of (i) a single trait 2 individual (called 'mutant') arriving in a trait 1 resident population living in equilibrium, and (ii) a trait 1 individual ('mutant') arriving in a trait 2 resident population. We analyse the invasion dynamics in all cases where the resident population is individually fit and the behaviour of the mutant population is initially non-critical. This leads to the identification of parameter regimes for the invasion and fixation of the new trait, stable coexistence of the two traits, and 'founder control' (where the initial resident always dominates, irrespective of its trait). One of our key findings is that horizontal transfer can lead to stable coexistence even if trait 2 is unfit on its own. In the case of founder control, the limiting dynamical system also exhibits a coexistence equilibrium, which, however, is unstable, and with overwhelming probability none of the mutant sub-populations is able to invade. In all cases, we observe the classical (up to three) phases of invasion dynamics à la Champagnat (2006).