Date of Award

Spring 2022

Project Type

Thesis

Program or Major

Mathematics

First Advisor

James Pringle

Second Advisor

Mark Lyons

Third Advisor

Easton White

Abstract

ABSTRACT

Estimation and Consequences of Asymmetric Dispersal on the Genetics of Coastal Marine Organisms in 1-D Habitats

Many natural populations have a dispersal that is biased in one direction (asymmetric dispersal), due to physical factors in the environment such as currents in the ocean that transport larvae or winds that carry seeds. These physical factors create a preferred direction for offspring to be carried (the “downstream” direction). When there is asymmetric dispersal there are two parameters that define the dispersal distance, the mean downstream distance, and the standard deviation of dispersal distances. This present research analyzes the effects of the mean downstream dispersal distance and standard deviation of dispersal on the genetic diversity and gene flow of a population as well as generating new statistical techniques to quantify dispersal from genetic distances. In chapter 2, the effects of asymmetric dispersal on a population are analyzed by deriving equations for the time and location of the most recent common ancestor. These equations are dependent on the mean downstream distance and the standard deviation. The equations are verified using a numeric simulation of a population with asymmetric dispersal. These equations show that the average location of the most recent common ancestor is in the upstream edge of the habitat and the average time to the most recent common ancestor is decreased when there is asymmetric dispersal. In chapter 3, existing genetic techniques that use isolation by distance to estimate dispersal distance are analyzed and shown to fail at estimating both parameters of dispersal when the dispersal is asymmetric. In chapter 4 a new statistical technique is developed that relies on sampling the alleles of a population both spatially and temporally. Equations for the mean and standard deviation of genetic distances in time are derived and used in an approximate Bayesian computation rejection algorithm to estimate the mean downstream distance and the standard deviation. The robustness of the estimation is verified for increasing population sizes and the number of loci used as well as when sampling in time and space. Overall, when there is asymmetric dispersal between offspring and parents the genetic diversity of the population becomes dependent on the mean downstream dispersal and the standard deviation of dispersal distances. Existing estimates of dispersal that use isolation by distance fail to estimate both dispersal parameters well. By using both spatial and temporal data, estimates of the mean downstream dispersal distance and standard deviation of dispersal distances can be made.

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