Abstract
A mathematical theory of the population genetics of the self-incompatibility polymorphism is developed for the case where self-incompatibility is controlled by a single, multiallelic gene, S, expressed gametophytically in the pollen. The theory is based on the probability of a particular allele occurring in a new plant and an approximate equation for this is compared, using computer simulation, with the true value, which depends upon the frequencies of the genotypes of the parental generation. This probability is used to express the frequency of a single established allele, from a population with both overlapping generations and variation in plant size, as a time series. The frequency is shown to follow closely the normal distribution which leads to a simple equation for the variance of the distribution. This variance is approximately equal to the average variance of the frequencies of the different alleles in a single generation and the values closely match the computer simulation results of Brooks et al. (1996). The theory allows alternative scenarios to be investigated easily and the effects of varying the parameter values are discussed. The time to steady state can also be calculated.
Similar content being viewed by others
Article PDF
References
Arthur, A E, Gale, J S, and Lawrence, M J. 1973. Variation in wild populations of Papaver dubium. VII. Germination time. Heredity, 30, 189–197.
Brooks, R J, Tobias, A M, and Lawrence, M J. 1996. The population genetics of the self-incompatibility polymorphism in Papaver Rhoeas. XI. The effects of limited pollen and seed dispersal, overlapping generations and variation in plant size on the variance of 5-allele frequencies in populations at equilibrium. Heredity, 76, 367–376.
Brooks, R J, Tobias, A M, and Lawrence, M J. 1997. A time series analysis of the population genetics of the self-incompatibility polymorphism. 2. Frequency equivalent population and the number of alleles that can be maintained in a population. Heredity, 79, 361–364.
Crosby, J L. 1966. Self-incompatibility alleles in the population of Oenothera organensis. Evolution, 20, 567–579.
Emerson, S. 1939. A preliminary survey of the Oenothera organensis population. Genetics, 24, 524–537.
Emerson, S. 1940. Growth of incompatible pollen tubes in Oenothera organensis. Bot Gaz, 101, 890–911.
Ewens, W J. 1964. On the problem of self-sterility alleles. Genetics, 50, 1433–1438.
Ewens, W J, and Ewens, P M. 1966. The maintenance of alleles by mutation - Monte Carlo results for normal and self-sterility populations. Heredity, 21, 371–378.
Fisher, R A. 1958. The Genetical Theory of Natural Selection, 2nd edn. Dover Publications, New York.
Kimura, M, and Maruyama, T. 1966. Personal communication. Mayo, H. 1966.
Levin, D A, Ritter, K, and Ellstrand, N C. 1979. Protein polymorphism in the narrow endemic Oenothera organensis. Evolution, 33, 534–542.
Mayo, O. 1966. On the problem of self-incompatibility alleles. Biometrics, 22, 111–120.
Moran, P A P. 1962. The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.
Wright, S. 1939. The distribution of self-sterility alleles in populations. Genetics, 24, 538–552.
Wright, S. 1960. On the number of self-incompatibility alleles maintained in equilibrium by a given mutation rate in a population of a given size: a reexamination. Biometrics, 16, 61–85.
Wright, S. 1964. The distribution of self-incompatibility alleles in populations. Evolution, 18, 609–619.
Yokoyama, S, and Hetherington, L E. 1982. The expected number of self-incompatibility alleles in finite plant populations. Heredity, 48, 299–303.
Yokoyama, S, and Nei, M. 1979. Population dynamics of sex-determining alleles in honey bees and self-incompatibility alleles in plants. Genetics, 91, 609–626.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brooks, R., Tobias, A. & Lawrence, M. A time series analysis of the population genetics of the self-incompatibility polymorphism. 1. Allele frequency distribution of a population with overlapping generations and variation in plant size. Heredity 79, 350–360 (1997). https://doi.org/10.1038/hdy.1997.167
Received:
Issue date:
DOI: https://doi.org/10.1038/hdy.1997.167
Keywords
This article is cited by
-
Inferences on the number and frequency of S-pollen gene (SFB) specificities in the polyploid Prunus spinosa
Heredity (2008)
-
A time series analysis of the population genetics of the self-incompatibility polymorphism. 2. Frequency-equivalent population and the number of alleles that can be maintained in a population
Heredity (1997)
