Algebras in Genetics. by Angelika Wörz-BusekrosReview by: I. M. H. EtheringtonBiometrics, Vol. 37, No. 3 (Sep., 1981), p. 627Published by: International Biometric SocietyStable URL: http://www.jstor.org/stable/2530586 .

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Book Reviews Book Reviews Book Reviews Book Reviews 627 627 627 627

wall'. The relationship of this volume to others in the series is unclear; many of the articles could easily have appeared elsewhere. Yet the book is stimulating and interesting and gives a fair impression of much of 'contemporary quantitative ecology', let alone 'related ecometrics'.

DAVID BROWN Agricultural Research Council Statistics Group,

Department of Applied Biology, University of Cambridge,

Cambridge, England.

WORZ-BUSEKROS, ANGELIKA. Algebras in Genetics. Lecture Notes in Biomathematics, No. 36. Springer-\lerlag, Berlin, 1980, 236 pp. £7-75.

I initiated the study of genetic algebras in several papers between 1939 and 1951 (e.g. Proceedings of the Royal Society of Edinburgh 59, 242-258). I was in- trigued by the unusual properties of these algebras, which were quite unlike anything in the literature. I also thought that, from the point of view of geneticists, the subject had a future. My belief was fortified by kindly letters from J. B. S. Haldane and Lancelot Hogben, and still more by the appearance of R. D. Schafer's seminal paper in 1962 in Mathematica Scan- dinavica; also by Olav Reiers0l's paper in 1949 in the American Joumal of Mathematics. Over the years, from 1966 onwards, many papers about genetic alge- bras have appeared and are still appearing. Frankly, I am unable to keep up with them, so that I am no longer the expert on the subject. The experts now are Philip Holgate (Professor of Statistics, Birkbeck Col- lege, London), Ivar Heuch (Professor at the University of Oslo, but a citizen of the world, and a pupil of O. Reierssbl), and especially the present author, Angelika Worz-Busekros (Professor of Biomathematics, Uni- versity of Tubingen), who knows ERIERYTHING about genetic algebras.

The book under review lists in its bibliography all that has been published on genetic algebras, including several papers yet to appear. In all there are some 50 contributions by 16 authors and an editor. It can be read at various levels. If you are already knowledge- able on the subject, it is safe to say that you are sure to find things here that you did not know about it. If you have written papers on genetic algebras, see what she says about your papers: you will find them ex- pounded, discussed and placed in a wider context, and your theorems will probably be generalized. If you are a geneticist, mathematically literate, but do not know what an algebra is, here you will find all lucidly explained: without going into details you can read sample theorems and safely take the proofs on trust.

The author is very careful and painstakingly thorough. There is a sprinkling of misprints and mis- spellings which will cause no troubles (e.g. Monique Bertrand, author of a booklet on genetic algebras, is referred to more than once as Bertran).

I. M. H. ETHERINGTON Tigh-an-Duin, Easdale, Via Oban,

Argyll, Scotland.

wall'. The relationship of this volume to others in the series is unclear; many of the articles could easily have appeared elsewhere. Yet the book is stimulating and interesting and gives a fair impression of much of 'contemporary quantitative ecology', let alone 'related ecometrics'.

DAVID BROWN Agricultural Research Council Statistics Group,

Department of Applied Biology, University of Cambridge,

Cambridge, England.

WORZ-BUSEKROS, ANGELIKA. Algebras in Genetics. Lecture Notes in Biomathematics, No. 36. Springer-\lerlag, Berlin, 1980, 236 pp. £7-75.

I initiated the study of genetic algebras in several papers between 1939 and 1951 (e.g. Proceedings of the Royal Society of Edinburgh 59, 242-258). I was in- trigued by the unusual properties of these algebras, which were quite unlike anything in the literature. I also thought that, from the point of view of geneticists, the subject had a future. My belief was fortified by kindly letters from J. B. S. Haldane and Lancelot Hogben, and still more by the appearance of R. D. Schafer's seminal paper in 1962 in Mathematica Scan- dinavica; also by Olav Reiers0l's paper in 1949 in the American Joumal of Mathematics. Over the years, from 1966 onwards, many papers about genetic alge- bras have appeared and are still appearing. Frankly, I am unable to keep up with them, so that I am no longer the expert on the subject. The experts now are Philip Holgate (Professor of Statistics, Birkbeck Col- lege, London), Ivar Heuch (Professor at the University of Oslo, but a citizen of the world, and a pupil of O. Reierssbl), and especially the present author, Angelika Worz-Busekros (Professor of Biomathematics, Uni- versity of Tubingen), who knows ERIERYTHING about genetic algebras.

The book under review lists in its bibliography all that has been published on genetic algebras, including several papers yet to appear. In all there are some 50 contributions by 16 authors and an editor. It can be read at various levels. If you are already knowledge- able on the subject, it is safe to say that you are sure to find things here that you did not know about it. If you have written papers on genetic algebras, see what she says about your papers: you will find them ex- pounded, discussed and placed in a wider context, and your theorems will probably be generalized. If you are a geneticist, mathematically literate, but do not know what an algebra is, here you will find all lucidly explained: without going into details you can read sample theorems and safely take the proofs on trust.

The author is very careful and painstakingly thorough. There is a sprinkling of misprints and mis- spellings which will cause no troubles (e.g. Monique Bertrand, author of a booklet on genetic algebras, is referred to more than once as Bertran).

I. M. H. ETHERINGTON Tigh-an-Duin, Easdale, Via Oban,

Argyll, Scotland.

wall'. The relationship of this volume to others in the series is unclear; many of the articles could easily have appeared elsewhere. Yet the book is stimulating and interesting and gives a fair impression of much of 'contemporary quantitative ecology', let alone 'related ecometrics'.

DAVID BROWN Agricultural Research Council Statistics Group,

Department of Applied Biology, University of Cambridge,

Cambridge, England.

WORZ-BUSEKROS, ANGELIKA. Algebras in Genetics. Lecture Notes in Biomathematics, No. 36. Springer-\lerlag, Berlin, 1980, 236 pp. £7-75.

I initiated the study of genetic algebras in several papers between 1939 and 1951 (e.g. Proceedings of the Royal Society of Edinburgh 59, 242-258). I was in- trigued by the unusual properties of these algebras, which were quite unlike anything in the literature. I also thought that, from the point of view of geneticists, the subject had a future. My belief was fortified by kindly letters from J. B. S. Haldane and Lancelot Hogben, and still more by the appearance of R. D. Schafer's seminal paper in 1962 in Mathematica Scan- dinavica; also by Olav Reiers0l's paper in 1949 in the American Joumal of Mathematics. Over the years, from 1966 onwards, many papers about genetic alge- bras have appeared and are still appearing. Frankly, I am unable to keep up with them, so that I am no longer the expert on the subject. The experts now are Philip Holgate (Professor of Statistics, Birkbeck Col- lege, London), Ivar Heuch (Professor at the University of Oslo, but a citizen of the world, and a pupil of O. Reierssbl), and especially the present author, Angelika Worz-Busekros (Professor of Biomathematics, Uni- versity of Tubingen), who knows ERIERYTHING about genetic algebras.

The book under review lists in its bibliography all that has been published on genetic algebras, including several papers yet to appear. In all there are some 50 contributions by 16 authors and an editor. It can be read at various levels. If you are already knowledge- able on the subject, it is safe to say that you are sure to find things here that you did not know about it. If you have written papers on genetic algebras, see what she says about your papers: you will find them ex- pounded, discussed and placed in a wider context, and your theorems will probably be generalized. If you are a geneticist, mathematically literate, but do not know what an algebra is, here you will find all lucidly explained: without going into details you can read sample theorems and safely take the proofs on trust.

The author is very careful and painstakingly thorough. There is a sprinkling of misprints and mis- spellings which will cause no troubles (e.g. Monique Bertrand, author of a booklet on genetic algebras, is referred to more than once as Bertran).

I. M. H. ETHERINGTON Tigh-an-Duin, Easdale, Via Oban,

Argyll, Scotland.

wall'. The relationship of this volume to others in the series is unclear; many of the articles could easily have appeared elsewhere. Yet the book is stimulating and interesting and gives a fair impression of much of 'contemporary quantitative ecology', let alone 'related ecometrics'.

DAVID BROWN Agricultural Research Council Statistics Group,

Department of Applied Biology, University of Cambridge,

Cambridge, England.

WORZ-BUSEKROS, ANGELIKA. Algebras in Genetics. Lecture Notes in Biomathematics, No. 36. Springer-\lerlag, Berlin, 1980, 236 pp. £7-75.

I initiated the study of genetic algebras in several papers between 1939 and 1951 (e.g. Proceedings of the Royal Society of Edinburgh 59, 242-258). I was in- trigued by the unusual properties of these algebras, which were quite unlike anything in the literature. I also thought that, from the point of view of geneticists, the subject had a future. My belief was fortified by kindly letters from J. B. S. Haldane and Lancelot Hogben, and still more by the appearance of R. D. Schafer's seminal paper in 1962 in Mathematica Scan- dinavica; also by Olav Reiers0l's paper in 1949 in the American Joumal of Mathematics. Over the years, from 1966 onwards, many papers about genetic alge- bras have appeared and are still appearing. Frankly, I am unable to keep up with them, so that I am no longer the expert on the subject. The experts now are Philip Holgate (Professor of Statistics, Birkbeck Col- lege, London), Ivar Heuch (Professor at the University of Oslo, but a citizen of the world, and a pupil of O. Reierssbl), and especially the present author, Angelika Worz-Busekros (Professor of Biomathematics, Uni- versity of Tubingen), who knows ERIERYTHING about genetic algebras.

The book under review lists in its bibliography all that has been published on genetic algebras, including several papers yet to appear. In all there are some 50 contributions by 16 authors and an editor. It can be read at various levels. If you are already knowledge- able on the subject, it is safe to say that you are sure to find things here that you did not know about it. If you have written papers on genetic algebras, see what she says about your papers: you will find them ex- pounded, discussed and placed in a wider context, and your theorems will probably be generalized. If you are a geneticist, mathematically literate, but do not know what an algebra is, here you will find all lucidly explained: without going into details you can read sample theorems and safely take the proofs on trust.

The author is very careful and painstakingly thorough. There is a sprinkling of misprints and mis- spellings which will cause no troubles (e.g. Monique Bertrand, author of a booklet on genetic algebras, is referred to more than once as Bertran).

I. M. H. ETHERINGTON Tigh-an-Duin, Easdale, Via Oban,

Argyll, Scotland.

OHTA, T. Evolution and Variation of Multigene Families. Springer-\lerlag, Berlin, 1980, 131 pp. $9.80.

One of the most interesting discoveries of molecular genetics is that an appreciable part of the genetic material in higher organisms consists of multiple, re- peated copies of the same gene lined up close together on the same chromosome. Such a system is called a multigene family. The evolutionary behavior of such a family of genes differs in important ways from that of a conventional single-copy gene and presents an inter- esting challenge to population geneticists, which was taken up by Tomoko Ohta in 1975 after reading a book review (which shows that book reviews can be useful). The present book describes her work on this subject since then.

A remarkable feature of multigene families is the phenomenon of coincidental evolution, whereby the same mutation spreads to all the genes in the family to become a species characteristic. Several hypotheses have been put forward to explain this phenomenon, the most likely of which is the model of unequal crossing-over. If two homologous chromosomes pair up at meiosis slightly out of alignment, crossing-over will lead to duplication of some gene copies and deletion of others (as well as to a change in the total number of genes in the family). By continuation of this process, a mutant gene may by chance spread on the chromosome to become the dominant gene of the fam- ily; the process will lead to homogeneity of the genes in the family in the same way as genetic drift at a single locus in a small population leads to homozygos- ity, though variability will from time to time be rein- troduced by mutation.

The book presents a detailed mathematical investig- ation of the consequences of this model of unequal crossing-over. The author also presents an interesting statistical analysis of sequence variability of immunog- lobulins (the antibody multigene family) in the light of her theoretical results. Much of the work reported has already appeared in various journals, but it is useful to have it brought together under one cover. It must be said, however, that the book is not easy reading. It seems a pity that the author did not take the oppor- tunity to make her interesting work accessible to a wider audience by explaining the biological back- ground more fully and omitting some of the algebraic details.

MICHAEL BULMER Department of Biomathematics,

University of Oxford, Oxford, England.

SIMPSON, GEORGE GAYLORD. VVhy and How; Some Problems and Methods in Historical Biology. Pergamon International Library, Foundations and Philosophy of Science and Technology Series, 1980, 263 pp. £18*00 hardback, £9 00 flexicover.

This book contains 35 of Simpson's papers, selected and annotated by him from his life's work which also includes several books. Most of the papers have been shortened to advantage. In a recent review of another work, Macbeth places Simpson primus inter pares of

OHTA, T. Evolution and Variation of Multigene Families. Springer-\lerlag, Berlin, 1980, 131 pp. $9.80.

One of the most interesting discoveries of molecular genetics is that an appreciable part of the genetic material in higher organisms consists of multiple, re- peated copies of the same gene lined up close together on the same chromosome. Such a system is called a multigene family. The evolutionary behavior of such a family of genes differs in important ways from that of a conventional single-copy gene and presents an inter- esting challenge to population geneticists, which was taken up by Tomoko Ohta in 1975 after reading a book review (which shows that book reviews can be useful). The present book describes her work on this subject since then.

A remarkable feature of multigene families is the phenomenon of coincidental evolution, whereby the same mutation spreads to all the genes in the family to become a species characteristic. Several hypotheses have been put forward to explain this phenomenon, the most likely of which is the model of unequal crossing-over. If two homologous chromosomes pair up at meiosis slightly out of alignment, crossing-over will lead to duplication of some gene copies and deletion of others (as well as to a change in the total number of genes in the family). By continuation of this process, a mutant gene may by chance spread on the chromosome to become the dominant gene of the fam- ily; the process will lead to homogeneity of the genes in the family in the same way as genetic drift at a single locus in a small population leads to homozygos- ity, though variability will from time to time be rein- troduced by mutation.

The book presents a detailed mathematical investig- ation of the consequences of this model of unequal crossing-over. The author also presents an interesting statistical analysis of sequence variability of immunog- lobulins (the antibody multigene family) in the light of her theoretical results. Much of the work reported has already appeared in various journals, but it is useful to have it brought together under one cover. It must be said, however, that the book is not easy reading. It seems a pity that the author did not take the oppor- tunity to make her interesting work accessible to a wider audience by explaining the biological back- ground more fully and omitting some of the algebraic details.

MICHAEL BULMER Department of Biomathematics,

University of Oxford, Oxford, England.

SIMPSON, GEORGE GAYLORD. VVhy and How; Some Problems and Methods in Historical Biology. Pergamon International Library, Foundations and Philosophy of Science and Technology Series, 1980, 263 pp. £18*00 hardback, £9 00 flexicover.

This book contains 35 of Simpson's papers, selected and annotated by him from his life's work which also includes several books. Most of the papers have been shortened to advantage. In a recent review of another work, Macbeth places Simpson primus inter pares of

OHTA, T. Evolution and Variation of Multigene Families. Springer-\lerlag, Berlin, 1980, 131 pp. $9.80.

One of the most interesting discoveries of molecular genetics is that an appreciable part of the genetic material in higher organisms consists of multiple, re- peated copies of the same gene lined up close together on the same chromosome. Such a system is called a multigene family. The evolutionary behavior of such a family of genes differs in important ways from that of a conventional single-copy gene and presents an inter- esting challenge to population geneticists, which was taken up by Tomoko Ohta in 1975 after reading a book review (which shows that book reviews can be useful). The present book describes her work on this subject since then.

A remarkable feature of multigene families is the phenomenon of coincidental evolution, whereby the same mutation spreads to all the genes in the family to become a species characteristic. Several hypotheses have been put forward to explain this phenomenon, the most likely of which is the model of unequal crossing-over. If two homologous chromosomes pair up at meiosis slightly out of alignment, crossing-over will lead to duplication of some gene copies and deletion of others (as well as to a change in the total number of genes in the family). By continuation of this process, a mutant gene may by chance spread on the chromosome to become the dominant gene of the fam- ily; the process will lead to homogeneity of the genes in the family in the same way as genetic drift at a single locus in a small population leads to homozygos- ity, though variability will from time to time be rein- troduced by mutation.

The book presents a detailed mathematical investig- ation of the consequences of this model of unequal crossing-over. The author also presents an interesting statistical analysis of sequence variability of immunog- lobulins (the antibody multigene family) in the light of her theoretical results. Much of the work reported has already appeared in various journals, but it is useful to have it brought together under one cover. It must be said, however, that the book is not easy reading. It seems a pity that the author did not take the oppor- tunity to make her interesting work accessible to a wider audience by explaining the biological back- ground more fully and omitting some of the algebraic details.

MICHAEL BULMER Department of Biomathematics,

University of Oxford, Oxford, England.

SIMPSON, GEORGE GAYLORD. VVhy and How; Some Problems and Methods in Historical Biology. Pergamon International Library, Foundations and Philosophy of Science and Technology Series, 1980, 263 pp. £18*00 hardback, £9 00 flexicover.

This book contains 35 of Simpson's papers, selected and annotated by him from his life's work which also includes several books. Most of the papers have been shortened to advantage. In a recent review of another work, Macbeth places Simpson primus inter pares of

OHTA, T. Evolution and Variation of Multigene Families. Springer-\lerlag, Berlin, 1980, 131 pp. $9.80.

One of the most interesting discoveries of molecular genetics is that an appreciable part of the genetic material in higher organisms consists of multiple, re- peated copies of the same gene lined up close together on the same chromosome. Such a system is called a multigene family. The evolutionary behavior of such a family of genes differs in important ways from that of a conventional single-copy gene and presents an inter- esting challenge to population geneticists, which was taken up by Tomoko Ohta in 1975 after reading a book review (which shows that book reviews can be useful). The present book describes her work on this subject since then.

A remarkable feature of multigene families is the phenomenon of coincidental evolution, whereby the same mutation spreads to all the genes in the family to become a species characteristic. Several hypotheses have been put forward to explain this phenomenon, the most likely of which is the model of unequal crossing-over. If two homologous chromosomes pair up at meiosis slightly out of alignment, crossing-over will lead to duplication of some gene copies and deletion of others (as well as to a change in the total number of genes in the family). By continuation of this process, a mutant gene may by chance spread on the chromosome to become the dominant gene of the fam- ily; the process will lead to homogeneity of the genes in the family in the same way as genetic drift at a single locus in a small population leads to homozygos- ity, though variability will from time to time be rein- troduced by mutation.

The book presents a detailed mathematical investig- ation of the consequences of this model of unequal crossing-over. The author also presents an interesting statistical analysis of sequence variability of immunog- lobulins (the antibody multigene family) in the light of her theoretical results. Much of the work reported has already appeared in various journals, but it is useful to have it brought together under one cover. It must be said, however, that the book is not easy reading. It seems a pity that the author did not take the oppor- tunity to make her interesting work accessible to a wider audience by explaining the biological back- ground more fully and omitting some of the algebraic details.

MICHAEL BULMER Department of Biomathematics,

University of Oxford, Oxford, England.

SIMPSON, GEORGE GAYLORD. VVhy and How; Some Problems and Methods in Historical Biology. Pergamon International Library, Foundations and Philosophy of Science and Technology Series, 1980, 263 pp. £18*00 hardback, £9 00 flexicover.

This book contains 35 of Simpson's papers, selected and annotated by him from his life's work which also includes several books. Most of the papers have been shortened to advantage. In a recent review of another work, Macbeth places Simpson primus inter pares of

This content downloaded from 62.122.78.43 on Wed, 25 Jun 2014 07:49:05 AMAll use subject to JSTOR Terms and Conditions