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12 M.Sc. Public Lecture
**M.Sc. Public Lecture**
Speaker: Zahra Shafiei (Western) "Impact of fluctuating selection on genetic variation when new mutations are expected to be deleterious" Time: 12:30 Room: WSC 248 Current research continues to debate the influence of fluctuating selection on genetic diversity within populations. In most previous models of fluctuating selection for studying genetic diversity, the distribution of selection coefficients is assumed to be symmetrical, meaning that the chances of having positive and negative selection coefficients are identical over time. These models predict that selective fluctuations reduce genetic diversity similar to the stochastic influence of genetic drift. Using stochastic simulations and analytical approaches based on diffusion approximations, we analyze the impact of fluctuating selection on genetic diversity when the distribution of selection coefficients over time is not symmetric, but is instead shifted to negative values. This captures the fact that new mutations are more likely to be deleterious. We show that, unlike the symmetric case, selective fluctuations can greatly increase genetic variation when new mutations are deleterious on average. We show that this phenomenon occurs because deleterious mutations that would be kept at low frequency in constant environment are able to transiently attain high frequencies in a changing environment. Our findings suggest that fluctuating selection could be an important force for generating genetic diversity even if it does not lead to long-term coexistence of alternate alleles. Ph.D. Public Lecture
**Ph.D. Public Lecture**
Speaker: Udit Mavinkurve (Western) "Fundamental group(oid) in discrete homotopy theory" Time: 13:00 Room: MC 107 Discrete homotopy theory is a homotopy theory designed for studying graphs and for detecting combinatorial, rather than topological, holes.'' Central to this theory are the discrete homotopy groups, defined using maps out of grids of suitable dimensions. Of these, the discrete fundamental group in particular has found applications in various areas of mathematics, including matroid theory, subspace arrangements, and topological data analysis. In this talk, we introduce the discrete fundamental groupoid, a multi-object generalization of the discrete fundamental group, and use it as a starting point to develop some robust computational techniques. A new notion of covering graphs allows us to extend the existing theory of universal covers to all graphs, and to prove a classification theorem for coverings. We also prove a discrete version of the Seifert--van Kampen theorem, generalizing a previous result of H. Barcelo et al. We then use it to solve the realization problem for the discrete fundamental group through a purely combinatorial construction. One of the biggest open problems in the subject currently is determining whether the cubical nerve functor provides an equivalence between the discrete homotopy theory of graphs and the classical homotopy theory of spaces. We propose a new line of attack towards this open problem, by breaking it into more tractable problems comparing the homotopy theories of the respective $n$-types, for each nonnegative integer n. We also solve this problem for the first nontrivial case, $n=1$. |
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16 Ph.D. Public Lecture
**Ph.D. Public Lecture**
Speaker: Alan Flatres (Western) "Group living features can challenge predictions for the evolution of altruistic behaviors" Time: 12:30 Room: TBA Altruistic behaviors occur when an individual decreases its personal fitness to help another individual. Such behaviors occur across a range of species and environments, and they take different forms. The diversity of altruistic behaviors is also characterized by various group living features, including group structure and social interactions. In this thesis, I develop models to study how the specificities of group living can influence the evolution of altruistic behaviors. I use inclusive fitness models to understand how the social environment the group creates, the ecological factors, and the benefits of altruistic behaviors impact the evolution of social behaviors. In the first model, I study the evolution of delayed dispersal with group size benefits. Dispersal tends to be delayed when breeding opportunities are scarce, i.e., when the habitat is saturated. I find that habitat saturation is not always associated with a high level of dispersal. This finding challenges previous results and highlights the need to model environmental feedback explicitly. In a second model, I measure how redirected help can emerge when individuals disperse near their relatives. Redirected help happens when an individual whose entire brood fails reallocates the effort it would have expended on parental care to help a related neighbor. The adaptive significance of this strategy may look straightforward, but if the population is viscous, the helper also competes with its relatives. This population viscosity creates additional costs and benefits that can restrain the evolution of altruism. To investigate the evolution of redirected help in a viscous population, I use an infinite-island model where redirected help can provide survival or fecundity benefits to the recipients. I find that the survival benefits associated with redirected help sometimes promote the emergence of help better than fecundity benefits, which contradicts previous findings. In a third model, I delve more deeply into the evolution of redirected help by explicitly accounting for spatial structuring within the population. I find that switching to a spatially explicit model has repercussions for the evolution of redirected help. For instance, the influence of offspring dispersal on the evolution of redirected help is reversed between the two models. My findings highlight the impact of spatial structure on the evolution of social behaviors. Overall, my thesis shows that different group living features can challenge predictions on the evolution of social behaviors. |
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