Integrodifference models for neutral genetic patterns and trade-offs in ecology

  • Author / Creator
    Marculis, Nathan
  • Integrodifference equations are a common tool used in ecology to model the spread of populations. In this thesis, I explore the neutral genetic patterns formed by range expansions and how dispersal-reproduction trade-offs impact the spread of populations. In Chapter 2, we investigate the inside dynamics of integrodifference equations to understand the genetic consequences of a population with nonoverlapping generations undergoing range expansion. We consider thin-tailed dispersal kernels and a variety of per capita growth rate functions to classify the traveling wave solutions as either pushed or pulled fronts. We find that pulled fronts are synonymous with the founder effect in population genetics. Adding overcompensation to the dynamics of these fronts has no impact on genetic diversity in the expanding population. However, growth functions with a strong Allee effect cause the traveling wave solution to be a pushed front preserving the genetic variation in the population. In Chapter 3, a stage-structured model of integrodifference equations is used to study the asymptotic neutral genetic structure of populations undergoing range expansion. We show that, under some mild assumptions on the dispersal kernels and population projection matrix, the spread is dominated by individuals at the leading edge of the expansion. This result is consistent with the founder effect. In the case where there are multiple neutral fractions at the leading edge, we are able to explicitly calculate the asymptotic proportion of these fractions found in the long-term population spread that depends
    only on the right and left eigenvectors of the population projection matrix evaluated at zero and the initial proportion of each neutral fraction at the leading edge. In the absence of a strong Allee effect, multiple neutral fractions can drive the long-term population spread, a situation not possible with the scalar model. In Chapter 4, we develop a neutral genetic mutation model by extending the previously established scalar inside dynamics model. We show that the spread of neutral genetic fractions is dependent on individuals at the leading edge of population as well as the structure of the mutation matrix. Specifically, we find that the neutral fractions that contribute to the spread of the population are those that belong to the same mutation class as the neutral fraction found at the leading edge of the population. We prove that the asymptotic proportion of individuals at the leading edge of the population spread is determined by the dominant right eigenvector of the associated mutation matrix, independent from growth and dispersal parameters. In Chapter 5, we construct a model that incorporates a dispersal-reproduction trade-off effect that allows for a variety of different shaped trade-off curves. We show there is a unique reproductive-dispersal allocation that gives the largest value for the spreading speed and calculate the sensitivities of the reproduction, dispersal, and trade-off shape parameters. Uncertainty in the model parameters affects the expected spread of the population and we calculate the optimal allocation of resources to dispersal that maximizes the expected spreading speed. Higher allocation to dispersal arises from uncertainty in the reproduction parameter or the shape of the reproduction trade-off curve. Lower allocation to dispersal arises form uncertainty in the shape of the dispersal trade-off curve, but does not come from uncertainty in the dispersal parameter. Our findings give insight into how parameter sensitivity and uncertainty influence the spreading speed of a population with a dispersal-reproduction trade-off.

  • Subjects / Keywords
  • Graduation date
    Fall 2019
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
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