Organisms often need to adapt more efficiently and devise new strategies for surviving difficult ecological circumstances. Mammals indeed spend the winter in hibernation to conserve energy, food,... Show moreOrganisms often need to adapt more efficiently and devise new strategies for surviving difficult ecological circumstances. Mammals indeed spend the winter in hibernation to conserve energy, food, etc., for future purposes. Microbial populations also possess similar characteristics, where organisms enter into a state of low metabolic activity in response to adverse environmental conditions. In plant populations, the analogous strategy is the suspension of seed germination for an extended period of time. Several studies suggest that this bet-hedging strategy has important evolutionary consequences and plays a crucial role in maintaining genetic diversities in a population. In this thesis, we draw motivations from biological populations featuring this trait and investigate its effect in a probabilistic framework. In particular, we introduce a mathematical notion of dormancy in several well-known stochastic interacting systems and study how it changes the qualitative and quantitative properties of the systems by characterizing their behaviors in the long run. The construction of our model is built upon a well-known stochastic process in mathematical population genetics called the Moran model. The Moran model describes the genetic evolution of a single, reproductively active, finite population without seed-bank. We modify the model to include dormancy and extend it to the context of spatially structured populations with varying sizes. Show less
In populations with a seed-bank, individuals can temporarily become dormant and refrain from reproduction until they can become active again. The repository of all dormant individuals in the... Show moreIn populations with a seed-bank, individuals can temporarily become dormant and refrain from reproduction until they can become active again. The repository of all dormant individuals in the population is called the seed-bank. Seed-banks are observed in many taxa, including plants, bacteria and other micro-organisms. Typically, they arise as a response to unfavourable environmental conditions. In this thesis we study the effect of a seed-bank on the genetic diversity in a population. The individuals in the population carry one of two gene types, live in colonies and can be either active or dormant. Active individuals can migrate between the colonies, resample and become dormant. Dormant individuals can only become active: they do not migrate and they do not reproduce themselves. The model is described by a system of interacting Fisher-Wright diffusions. Analysing this system of interacting diffusions, we show that the seed-bank enhances the genetic diversity in a population. If the individuals can become dormant for long enough times, the seed-bank can even prevent that a gene type becomes extinct. Show less
