Sharif Digital Repository

Environmental heterogeneity, or environmental interactions in evolutionary graphs can drastically change the population dynamics compared to the uniform environment. Such heterogeneity can be imposed in different ways. In this study we choose periodic pattern for the environmental heterogeneity with different values for amplitude and period. Imposing periodic heterogeneity on cyclic graphs, we studied the fixation probability and time. We use birth-death Moran model as the update rule. We observe that with such heterogeneity, an advantageous type in the uniform environment can turn into deleterious in the presence of heterogeneity. Also, the opposite way can happen. The results show that... 

Natural selection in structured populations is considered a crucial subject in evolutionary and population genetics. There is no explicit relationship between discrete-time stochastic models such as the Moran process and continuous-time models such as the Fisher-Kolmogorov equation. However, under specific conditions and within the limits of natural selection and weak selection, a connection can be found between these two models. To gain a better understanding of the specific relationship between these two models, we obtain partial differential equations for the spatiotemporal dynamics of natural selection by extending the birthdeath and death-birth processes of the Moran process to a...