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 - 13:30

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

Speaker: Udit Mavinkurve (Western)

"Fundamental group(oid) in discrete homotopy theory"

Time: 13:00 - 14:00

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, $n=1$.

M.Sc. Public Lecture

Speaker: Siyi Zhang (Western)

"Impact of Energy Allocation on Fish's Maturation Age and Weight at Maturation by Mathematical Models"

Time: 13:00 - 14:00

Room: MC 204

The age and size at maturation are crucial traits in an organism’s life cycle, influencing its growth, survival, and reproduction. While energy allocation models have been used to study growth and reproduction, they have not been directly applied to age and size at maturation. To investigate how energy allocation strategies affect age and weight at maturation, we propose a biphasic energy allocation model, focusing on pre-maturity and post-maturity, to understand the mechanisms of maturation and estimate the age and weight at maturation. This model is parameterized for female lake whitefish (Coregonus clupeaformis), and we perform parameter estimation, model selection, and sensitivity analysis. Our results indicate that lake whitefish allocate an almost consistent fraction of energy to growth throughout their lifetime and shift energy allocation from storage to reproduction at maturation. We find that (i) the weight at maturation is positively related to the fraction of energy allocated to growth; (ii) the age at maturation is highly sensitive to the coefficient and exponent in the energy assimilation rate; (iii) higher energy conversion efficiency to weight leads to earlier maturation at larger sizes. These findings suggest that energy allocation strategies cause variations in age and weight at maturation across populations. Additionally, our new insights into the ratio between asymptotic weight and mature weight across populations potentially resolve the discrepancies between the ratio's theoretical predictions and its empirical observations highlighted in previous studies.

M.Sc. Public Lecture

Speaker: Sepideh Bahrami (Western)

"Osculating Curves"

Time: 15:00 - 16:00

Room: MC 107

A curve is said to osculate a second curve if the two touch only at a point. A straight line tangent to a curve is a familiar example. The straight line osculates the curve at the point where it touches the curve. A second example will be familiar to some calculus students: an osculating circle. In this case, the circle not only touches a given curve, but also matches the curvature of the curve at the point of touching.

Osculating curves approximate the curve they are touching in the neighbourhood of the contact point. For this reason, they are used a lot in Computer Aided Design (CAD) to speed up calculations and to ensure that curves and surfaces remain smooth at places where they join.

The thesis develops a new way of calculating osculating curves, without being restricted to straight lines or circles. This allows formulae of greater generality than before to be computed.

M.Sc. Public Lecture

Speaker: Bita Ghodsi (Western)

"Host-Pathogen Coevolution with Vertical Transmission of Infections and Density-dependent Dynamics"

Time: 13:00 - 14:00

Room: MC 204

Pathogens can be transmitted both vertically (from the parent to the offspring) and horizontally. Here, I model the co-evolution of pathogens and their hosts allowing for vertical and horizontal transmission and density-dependent host population growth. My analysis uses evolutionary game theory. I use computational methods to find that increasing vertical transmission does not always result in more benign disease outcomes. Instead, it can lead to higher pathogen-induced mortality. Furthermore, more benign outcomes evolve more readily when horizontal transmission is more profitable for the pathogen, and overall virulence increases as horizontal transmission becomes more profitable. The results also indicate that vertical transmission, when associated with high virulence, can drive selection-driven extinction of the pathogen, which highlights the importance of considering both transmission modes in evolutionary studies.

Ph.D. Public Lecture

Speaker: Nick Eekhof (Western)

"Competition Effects in an Intraguild Predation Model"

Time: 13:00 - 14:00

Room: MC 204

In the biological world, many interactions exist between various species. These interactions generally, consist of predator-prey relationships, competition between species and beneficial relationships. One observed phenomenon, termed the fear effect, occurs when one species reacts to an increased risk of predation by another species. The fear response causes the affected species to reproduce and forage for food less. In some cases, the fear response can be beneficial, while in other times it can be harmful. In this thesis, we consider a four compartment food-chain model in which there exists a top-level predator, a mesopredator and two types of prey who directly compete with one another. The model accounts for each lesser species’ fear response to the next highest one. We aim to examine how competition and the fear effect can work together to adjust the structure of the food chain. We used some standard techniques of dynamical systems to glean some results about the long-term dynamics of the system. We found that the fear response and competition effects can play an important part in the long-term dynamics of the system and cause a restructuring in the food chain itself.