This thesis is composed of two parts. Part one develops a theory that allows demographic parameters to be estimated from a population with geographic structure, but without subdivision into discrete demes. The analysis focuses on the case of a finite, one-dimensional habitat in which gene flow is limited. That is, there is a correlation between the locations of parents and offspring, which generates a correlation between geographic proximity and genetic similarity. An analytic solution is derived for the joint probability distribution of the times and locations of the most recent common ancestor of a pair of homologous DNA sequences evolving neutrally in such a one-dimensional habitat. Demographic parameters are estimated using composite likelihood maximization. Consideration is given to how the method could be extended to permit demographic inference from populations with more complex geographic structures.; Part two includes three theoretical analyses of genomic imprinting, the phenomenon whereby an allele's pattern of expression depends on its parental origin. The kinship theory explains imprinting as the outcome of a conflict arising when the effects of increasing expression at a locus have different effects on matrilineal and patrilineal inclusive fitness. The best-studied imprinted genes are expressed in fetal tissues of placental mammals and affect fetal growth via the distribution of maternal resources among offspring. The first of the three analyses models the coevolution of two oppositely imprinted loci with antagonistic effects on fetal growth. This analysis makes specific predictions both about the patterns of imprinting allowable under the kinship theory and about the historical progression of evolutionary events at the two loci. The second analysis presents a model for understanding the evolution of imprinting at loci that are expressed in the brains of adult mice and affect the quality of maternal care provided to their offspring. The third analysis proposes and explanation of an observed asymmetry in the mechanisms of silencing at maternally silenced and paternally silenced loci. The model also suggests a novel explanation for the loss of imprinting at particular loci, and makes specific predictions that will permit this hypothesis to be tested.
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