Text

Mathematical Topics in Population Geneticcs

---

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.

By 1930 or thereabout, R. A. Fisher and J. B. S. Haldane in England, and Sewall Wright in the United States of America were identified as the founders of population genetics. A series of papers was published by Haldane on mathematical analyses of selection, mutation, etc., in popula- tions of Mendelian genes, and the most of these analyses were assembled in his The Causes of Evolution (1932). Fisher's book called The Genetical Theory of Natural Selection was published in 1930. The inspiration one gets from reading these books is unmeasurable.

Sewall Wright has been contributing extensively to the development of population genetics ever since the publication dealing with the in- heritance of coat color characteristics in guinea pigs (1916). In 1921, he published five papers in a row concerning "Systems of Mating". Then came a historical paper by Wright Evolution in Mendelian Populations in 1931. In this paper he introduced the concept of "Effective Population Size", and "Genetic Random Drift" in finite size populations. Undoubt edly, a three-volume series by Sewall Wright, of which the first volume appeared in 1968, will make another cornerstone in population genetics

I am extremely grateful to have Professor Sewall Wright as one of the contributors in this volume.

There are dozens of very capable investigators whose backgrounds vary. Just mentioning several, Samuel Karlin and his group at Stanford University with bona fide mathematics backgrounds. There is Walter Bodmer, also at Stanford University, who is a brilliant investigator in both theoretical and experimental genetics. There are Oscar Kempthorne, Howard Levene, R. E. Comstock, Everett Dempster and many others with statistical backgrounds. However, there is a limit for this kind of undertaking, assembling authors, topics and matching them. Conse- quently, I had to reluctantly drop several investigators from a list of potential contributors, letting a higher priority go to those with biological

backgrounds. My original aim of this book was to document major issues and ideas that appeared during the development of population genetics in the past half century. However, some papers in this book are the results of original researches, and others are reviews of some aspects of popula- tion genetics.

While I have been editing this book, I have begun to feel a new trend and "revival" (according to I. M. Lerner) in population genetics. The new generation of population geneticists recognizes various factors such as population density, non-constant fitness values of a given genotype including frequency-dependent selection, biochemical aspects of popula- tion genetics, and ecological conditions for a population, and so forth. Thus, I am convinced that the studies of genetic populations have entered into a new phase, and this is a good reason to document various mathe-

matical studies made up-to-date by geneticists in one volume. Several authors in this book dedicated their papers to Professor Th. Dobzhansky for his seventieth birthday.

I am personally grateful for the encouragement and leniency for the time schedule for publication of this book given by Dr. Klaus Peters of Springer-Verlag, and the National Institutes of Health of the United States for their summer supports through the project program grant GM 15769. My personal thanks go to Mrs. JoBeth Porterfield who typed up almost all of the manuscripts in the final form and assisted with editorial work. I also acknowledge Dr. Yoshiko Tobari and Mrs. Myrtle Wing who supervised my laboratory work while I was heavily involved in editorial work.

---

Availability

7895

575.1:578.087 KOJ m

Perpustakaan PPKS Medan Lt. 1 (575.1:578.087)

Available

Detail Information

Series Title

-

Call Number

575.1:578.087 KOJ m

Publisher

Germany : Springer-Verlag., 1970

Collation

vii, 400 hal.: ill; 23,5 cm

Language

English

ISBN/ISSN

-

Classification

575.1:578.087

Content Type

-

Media Type

-

Carrier Type

-

Edition

-

Subject(s)

Matematika Statistik

Specific Detail Info

-

Statement of Responsibility

-

Other version/related

File Attachment

Comments

---

You must be logged in to post a comment