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Diffusion limit for the phenomenon of random genetic drift

100%

Marciniak A.

tom 27

nr 1

81-101

The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as the telegraph equations). Applying the modified Chapman-Enskog procedure we show the transition from this system to a macroscopic model which is a diffusion type equation. Finally, the error of approximation is estimated.

DNA polymorphism in population that has undergone size changes in its history

86%

Łobos E.

1999

tom Vol. 19, no. 4

91-98

In this paper we consider mutations which occur in genealogy of an n-individual sample taken from population which has undergone size changes in the course of its evolution. For any n = 2,3, ... we derive recurrent formulae for the probability generating function of the number of segregating sit es in the sample. If population size is constant the formulae reduce to known Watterson formulae [1]. From these formulae we obtain probabilities for numbers of segregating sites in triplets and we use it in exemplary numerical calculations. Computations are performed for four population models - two theoretical and two based on research concerning human population (from [2] and [3]). Then we compare our computations with the experimental data.

Praca dotyczy rozkładu liczby mutacji, które pojawiły się w genealogii n-elementowej próbki pochodzącej z populacji, o której zakładamy, że jej rozmiar jest funkcją czasu. Podano wzory rekurencyjne na funkcje tworzące liczby miejsc segregujących w takich próbkach. Wzory te są uogólnieniem znanych wzorów G.A. Wattersona dla populacji, których rozmiar nie zmienia się w czasie. Obliczenia przeprowadzono w przypadku n = 3 dla czterech modeli rozwoju populacji -- dwóch teoretycznych i dwóch opartych na badaniach dotyczących populacji ludzi. Następnie porównano je z wynikami symulacji oraz danymi eksperymentalnymi.

Conservation genetics of managed ungulate populations

58%

Scribner K. T.

tom 38

nr 2

Natural populations of many species are increasingly impacted by human activities. Perturbations are particularly pronunced for large ungulates due in part to sport and commercial harvest, to reductions and fragmentation of native habitat, and as the result of reintroductions. These perturbations affect population size, sex and age composition, and population breeding structure, and as a consequence affect the levels and partitioning of genetic variation. Three case histories highlighting long-term ecological genetic research on mule deer Odocoileus hemionus (Rafinesque, 1817), white-tailed deer O. virginianus (Zimmermann, 1780), and Alpine ibex Capra i. ibex Linnaeus, 1758 are presented. Joint examinations of population ecological and genetic data from several populations of each species reveal: (1) that populations are not in genetic equilibrium, but that allele frequencies and heterozygosity change dramatically over time and among cohorts produced in successive years, (2) populations are genetically structured over short and large geographic distances reflecting local breeding structure and patterns of gene flow, respectively; however, this structure is quite dynamic over time, due in part to population exploitation, and (3) restocking programs are often undertaken with small numbers of founding individuals resulting in dramatic declines in levels of genetic variability and increasing levels of genetic differentiation among populations due to genetic drift. Genetic characteristics have and will continue to provide valuable indirect sources of information relating enviromental and human perturbations to changes in population processes.