The probability of fixation in populations of changing size.

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

[1]  W J Ewens,et al.  The probability of survival of a new mutant in a fluctuating environment , 1967, Heredity.

[2]  A. Robertson,et al.  The Effect of Inbreeding on the Variation Due to Recessive Genes. , 1952, Genetics.

[3]  T. Ohta,et al.  Probability of gene fixation in an expanding finite population. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Motoo Kimura,et al.  A NOTE ON THE SPEED OF GENE FREQUENCY CHANGES IN REVERSE DIRECTIONS IN A FINITE POPULATION , 1974, Evolution; international journal of organic evolution.

[5]  Robert C. Elston,et al.  Mathematical population genetics, Biomathematics. , 1981 .

[6]  C. Krebs,et al.  Population Cycles in Small Mammals , 1974 .

[7]  M. Slatkin.  In Defense of Founder-Flush Theories of Speciation , 1996, The American Naturalist.

[8]  Y. Svirezhev,et al.  Diffusion Models of Population Genetics , 1990 .

[9]  Motoo Kimura,et al.  Some Problems of Stochastic Processes in Genetics , 1957 .

[10]  R. A. Fisher,et al.  On the dominance ratio , 1990 .

[11]  H. Carson.  The Genetics of Speciation at the Diploid Level , 1975, The American Naturalist.

[12]  C. Krebs,et al.  Impact of Food and Predation on the Snowshoe Hare Cycle , 1995, Science.

[13]  Rory A. Fisher,et al.  XVII—The distribution of gene ratios for rare mutations , 1931 .

[14]  G. O. Batzli.  Dynamics of Small Mammal Populations: A Review , 1992 .

[15]  Mandy J. Haldane,et al.  A Mathematical Theory of Natural and Artificial Selection, Part V: Selection and Mutation , 1927, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  H. A. Orr,et al.  The Genetics of Adaptation: A Reassessment , 1992, The American Naturalist.

[17]  Jeremy T. Kerr,et al.  Effects of Human Activity on Global Extinction Risk , 1995 .

[18]  M. Kimura,et al.  Stochastic Processes in Population Genetics, with Special Reference to Distribution of Gene Frequencies and Probability of Gene Fixation , 1970 .

[19]  J. Myers,et al.  Can a General Hypothesis Explain Population Cycles of Forest Lepidoptera , 1988 .

[20]  N. Barton.  Linkage and the limits to natural selection. , 1995, Genetics.

[21]  G. O. Batzli,et al.  Population cycles revisited. , 1996, Trends in ecology & evolution.

[22]  C. Krebs.  Ecology: The Experimental Analysis of Distribution and Abundance , 1973 .

[23]  M. Lynch,et al.  MUTATION LOAD AND THE SURVIVAL OF SMALL POPULATIONS , 1990, Evolution; international journal of organic evolution.

[24]  M. Kimura,et al.  On the probability of fixation of mutant genes in a population. , 1962, Genetics.

[25]  S. Wright,et al.  Evolution in Mendelian Populations. , 1931, Genetics.