Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Markov chain model of evolution in asexually reproducing populations: insight and analytical tractability in the evolutionary process
128
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The evolutionary process has been modelled in many ways using both stochastic and deterministic models. We develop an algebraic model of evolution in a population of asexually reproducing organisms in which we represent a stochastic walk in phenotype space, constrained to the edges of an underlying graph representing the genotype, with a time-homogeneous Markov Chain. We show its equivalence to a more standard, explicit stochastic model and show the algebraic models superiority in computational efficiency. Because of this increase in efficiency, we offer the ability to simulate the evolution of much larger populations in more realistic genotype spaces. Further, we show how the algebraic properties of the Markov Chain model can give insight into the evolutionary process and allow for analysis using familiar linear algebraic methods.
rate research
Read More
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a mutant type. We consider a two-state Moran model, where selection intensity at equilibrium may differ (in amplitude and in sign) from selection during periods of sharp growth and sharp decline. Using Kimuras diffusion approximation we present simple formulae for effective population size and effective selection, and use it to calculate the chance of ultimate fixation, the time to fixation and the time to absorption (either fixation or loss). Our analysis shows perfect agreement with numerical solutions for neutral, beneficial and deleterious mutant. The contributions of different processes to the mean and the variance of abundance variations are additive and commutative. As a result, when selection intensity $s$ is weak such that ${cal O}(s^2)$ terms are negligible, periodic or stochastic environmental variations yield identical results.
We revisit the spatial ${lambda}$-Fleming-Viot process introduced in [1]. Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the case where the process acts on the entire two-dimensional plane, and on a finite rectangle. Utilizing a differential equation linking $T_0$ with the physical distance between the lineages, we arrive at simple and reasonably accurate approximation schemes for both cases. Furthermore, our analysis enables us to address the question of whether the genealogical process of the model comes down from infinity, which has been partly answered before in [2].
In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or driver, mutations from passenger mutations that have no selective effect. Toward this end, we prove results concerning the frequency of neutural mutations in exponentially growing multitype branching processes that have been widely used in cancer modeling. Our results yield a simple new population genetics result for the site frequency spectrum of a sample from an exponentially growing population.
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in ecology, which is used to explain how species may survive when faced with the evolutionary risks associated with temporally varying environments. In order to support a deeper understanding of the adaptive role of spontaneous phenotypic variations in fluctuating environments, we consider a system of non-local partial differential equations modelling the evolutionary dynamics of two competing phenotype-structured populations in the presence of periodically oscillating nutrient levels. The two populations undergo spontaneous phenotypic variations at different rates. The phenotypic state of each individual is represented by a continuous variable, and the phenotypic landscape of the populations evolves in time due to variations in the nutrient level. Exploiting the analytical tractability of our model, we study the long-time behaviour of the solutions to obtain a detailed mathematical depiction of evolutionary dynamics. The results suggest that when nutrient levels undergo small and slow oscillations, it is evolutionarily more convenient to rarely undergo spontaneous phenotypic variations. Conversely, under relatively large and fast periodic oscillations in the nutrient levels, which bring about alternating cycles of starvation and nutrient abundance, higher rates of spontaneous phenotypic variations confer a competitive advantage. We discuss the implications of our results in the context of cancer metabolism.
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects have, however, proved to be sensitive to the details of the underlying topology and dynamics. Here we introduce a minimal population structure that is described by two distinct hierarchical levels of interaction. We believe this model is able to identify effects of spatial structure that do not depend on the details of the topology. We derive the dynamics governing the evolution of a system starting from fundamental individual level stochastic processes through two successive meanfield approximations. In our model of population structure the topology of interactions is described by only two parameters: the effective population size at the local scale and the relative strength of local dynamics to global mixing. We demonstrate, for example, the existence of a continuous transition leading to the dominance of cooperation in populations with hierarchical levels of unstructured mixing as the benefit to cost ratio becomes smaller then the local population size. Applying our model of spatial structure to the repeated prisoners dilemma we uncover a novel and counterintuitive mechanism by which the constant influx of defectors sustains cooperation. Further exploring the phase space of the repeated prisoners dilemma and also of the rock-paper-scissor game we find indications of rich structure and are able to reproduce several effects observed in other models with explicit spatial embedding, such as the maintenance of biodiversity and the emergence of global oscillations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
