On the persistence of random genetic drift

1978 ◽  
Vol 15 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Peter L. Antonelli ◽  
Kenneth Morgan
Keyword(s):  
Tangent Plane ◽  
Balance Theory ◽  
Standard Brownian Motion ◽  
Random Genetic Drift ◽  
Effective Population ◽  
Frequency Space ◽  
Theory Of Evolution ◽  
Shifting Balance Theory ◽  
Shifting Balance ◽  
Fisher Process

It is demonstrated that standard Brownian motion in the tangent plane at the centroid of frequency space does not well approximate the discrete Wright—Fisher process for more than 2N generations where N is the effective population size. This result is obtained using Wright's concept of negligible mutation rate for the study of systematic evolutionary effects together with Ludwig's notion of the persistence of a dynamical system. This work may be viewed as a mathematical elaboration of a portion of Wright's shifting balance theory of evolution.

On the persistence of random genetic drift

1978 ◽  
Vol 15 (01) ◽  
pp. 179-183 ◽  
Author(s):  
Peter L. Antonelli ◽  
Kenneth Morgan
Keyword(s):  
Tangent Plane ◽  
Balance Theory ◽  
Standard Brownian Motion ◽  
Random Genetic Drift ◽  
Effective Population ◽  
Frequency Space ◽  
Theory Of Evolution ◽  
Shifting Balance Theory ◽  
Shifting Balance ◽  
Fisher Process

It is demonstrated that standard Brownian motion in the tangent plane at the centroid of frequency space does not well approximate the discrete Wright—Fisher process for more than 2N generations where N is the effective population size. This result is obtained using Wright's concept of negligible mutation rate for the study of systematic evolutionary effects together with Ludwig's notion of the persistence of a dynamical system. This work may be viewed as a mathematical elaboration of a portion of Wright's shifting balance theory of evolution.

scholarly journals PERSPECTIVE: A CRITIQUE OF SEWALL WRIGHT'S SHIFTING BALANCE THEORY OF EVOLUTION

Evolution ◽  
1997 ◽  
Vol 51 (3) ◽  
pp. 643-671 ◽  
Author(s):  
Jerry A. Coyne ◽  
Nicholas H. Barton ◽  
Michael Turelli
Keyword(s):  
Balance Theory ◽  
Theory Of Evolution ◽  
Shifting Balance Theory ◽  
Shifting Balance

scholarly journals Sewall Wright, 21 December 1889 - 3 March 1988

1990 ◽  
Vol 36 ◽  
pp. 567-579 ◽  
Keyword(s):  
Population Genetics ◽  
Evolutionary Biology ◽  
Natural Populations ◽  
Coat Colour ◽  
Balance Theory ◽  
Theory Of Evolution ◽  
Shifting Balance Theory ◽  
Sewall Wright ◽  
Shifting Balance ◽  
Active Research

Sewall Wright's active life spanned the development of genetics from a new discipline when the principles of inheritance were still being elucidated to the technology of recombinant gene construction and insertion. He was one of the major pioneers of population genetics, which gave a quantitative basis to the studies of evolution, of variation in natural populations and of animal and plant breeding. He contributed most significantly to methods and ideas over a long period, indeed his four volume treatise was written long after he formally ‘retired’ and his last paper (211) was published a few days before his death at the age of 98. In the field of population genetics Wright developed the method of path coefficients, which he used to analyse quantitative genetic variation and relationship, but which has been applied to subjects as diverse as economics, the ideas of inbreeding coefficient and F -statistics which form the basis of analysis of population structure, the theory of variation in gene frequency among populations, and the shifting balance theory of evolution, which remains a topic of active research and controversy. Wright contributed to physiological genetics, notably analysis of the inheritance of coat colour in the guinea pig, and in particular the epistatic relationships among the genes involved. There was a critical interplay between his population and physiological work, in that the analysis of finite populations on the one hand and of epistatic interactions on the other are the bases of Wright’s development of the shifting balance theory. A full and enlightening biography of Sewall Wright which traces his influence on evolutionary biology and his interactions with other important workers was published recently (Provine 1986) and shorter appreciations have appeared since his death, notably by Crow (1988), Wright’s long-time colleague. This biography relies heavily on Provine’s volume, and does no more than summarize Wright’s extensive contributions. Many of his important papers have been reprinted recently (1986).

Factor interaction and linkage in evolution

1965 ◽  
Vol 162 (986) ◽  
pp. 80-104 ◽  
Keyword(s):  
Random Processes ◽  
Phase Shifting ◽  
Balance Theory ◽  
Secondary Importance ◽  
Theory Of Evolution ◽  
Shifting Balance Theory ◽  
Three Phase ◽  
Shifting Balance ◽  
The Mean ◽  
Factor Interaction

Reasons are presented for the view that linkage disequilibrium is of only secondary importance in the general theory of evolution although of primary importance in the theory for particular organisms. It is pointed out that the pattern of factor interaction that is significant in evolution is that which pertains to the mean selective value of populations. The three-phase shifting balance theory of evolution, proposed by the author in 1931, is reviewed briefly as a basis for deciding which sort of interaction system is most pertinent. Some of the misinterpretations of this theory are discussed. It is concluded that the overwhelmingly most important pattern of factor interaction is that in which selection is directed toward an optimum that is never far from the middle of the range of variability. This pattern is characterized by a great many selective peaks. The number rises rapidly with the number of interacting loci and the number of alleles. The effects of linkage in simple two and three factor cases of thisoptimum model are treated mathematically. The effect is to make the saddles shallower without obliterating them, unless a certain amount of overdominance with respect to selective value is superimposed. The roles of the three phases (random processes within demes as a trigger for intrademic selection toward a new peak, the latter as a trigger for interdemic selection) are illustrated in a hypothetical case with six selective peaks. This indicates a possible interpretation of the ‘area effects’ of Cain & Currey.

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