Mathematical Topics in Population Genetics

✍ Scribed by S. Wright (auth.), Ken-ichi Kojima (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1970
• Tongue: English
• Leaves: 407
• Series: Biomathematics 1
• Edition: 1
• Category: Library

✦ Synopsis

A basic method of analyzing particulate gene systems is the proba­ bilistic and statistical analyses. Mendel himself could not escape from an application of elementary probability analysis although he might have been unaware of this fact. Even Galtonian geneticists in the late 1800's and the early 1900's pursued problems of heredity by means of mathe­ matics and mathematical statistics. They failed to find the principles of heredity, but succeeded to establish an interdisciplinary area between mathematics and biology, which we call now Biometrics, Biometry, or Applied Statistics. A monumental work in the field of popUlation genetics was published by the late R. A. Fisher, who analyzed "the correlation among relatives" based on Mendelian gene theory (1918). This theoretical analysis over­ came "so-called blending inheritance" theory, and the orientation of Galtonian explanations for correlations among relatives for quantitative traits rapidly changed. We must not forget the experimental works of Johanson (1909) and Nilsson-Ehle (1909) which supported Mendelian gene theory. However, a large scale experiment for a test of segregation and linkage of Mendelian genes affecting quantitative traits was, prob­ ably for the first time, conducted by K. Mather and his associates and Panse in the 1940's.

✦ Table of Contents

Front Matter....Pages I-IX
Random Drift and the Shifting Balance Theory of Evolution....Pages 1-31
Changes in Mean Fitness under Natural Selection....Pages 32-78
Models and Analyses of Dispersal Patterns....Pages 79-103
Avoidance and Rate of Inbreeding....Pages 104-127
Genetic Loads and the Cost of Natural Selection....Pages 128-177
Stochastic Processes in Population Genetics, with Special Reference to Distribution of Gene Frequencies and Probability of Gene Fixation....Pages 178-209
Theory of Limits to Selection with Line Crossing....Pages 210-245
A Theory of Limits in Artificial Selection with Many Linked Loci....Pages 246-288
The Evolution of Dominance....Pages 289-316
Survival of Mutant Genes as a Branching Process....Pages 317-336
The Incomplete Binomial Distribution....Pages 337-366
Evolutionary Significance of Linkage and Epistasis....Pages 367-388
Fitness and Optimization....Pages 389-400

✦ Subjects

Mathematics, general