Mathematical and Statistical Developments of Evolutionary Theory

370 Pages·1990·9.11 MB·English

by  Ethan Akin (auth.)

Mathematical and Statistical
Developments of Evolutionary Theory
NATO ASI Series
Advanced Science Institutes Series
A Series presenting the results of activities sponsored by the NA TO Science Committee,
which aims at the dissemination of advanced scientific and technological knowledge,
with a view to strengthening links between scientific communities.
The Series is published by an international board of publishers in conjunction with the
NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation
B Physics London and New York
C Mathematical Kluwer Academic Publishers
and Physical Sciences Dordrecht, Boston and London
o
Behavioural and Social Sciences
E Applied Sciences
F Computer and Systems Sciences Springer-Verlag
G Ecological Sciences Berlin, Heidelberg, New York, London,
H Cell Biology Paris and Tokyo
Series C: Mathematical and Physical Sciences· Vol. 299
Mathematical and
Statistical Developments of
Evolutionary Theory
edited by
Sabin Lessard
Departement de mathematiques et de statistique,
Universite de Montreal,
Montreal, Canada
Proceedings of the NATO Advanced Study Institute and
Seminaire de Mathematiques Superieures on
Mathematical and Statistical Developments of Evolutionary Theory
Montreal, Canada
August 3-21, 1987
Kluwer Academic Publishers
Dordrecht / Boston / London
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Inst~ute and
Seminaire de Mathematiques Superieures on
Mathematical and Statistical Developments of Evolutionary Theory
Montreal, Canada
August 3-21, 1987
Library of Congress Cataloging In Publication Data
NATO Advanced Study InstitutefSeminaire de Matnematiques Sup6rieures
on MatheMat1cal and Statist1cal Developments of Evolutionary Theory
(1987 Montreal. Quebec)
Mathematical and statistical developMents of evolutionary theory
proceedings of the NATO Advanced Study Inst1tute/Selinaire de
Mathematiques Superieures on MatheMatical and Statistical
Developments of Evolutionary Theory. Montreal, Canada, August 3-21,
1987 ! edited by Sabin Lessard.
p. CI. -- (NATO ASI series. Series C, Mathematical and
pnysical sciences; v. 299)
"Published in cooperation with NATO Scientific Affairs Division."
ISBN·13: 978·94·0 10 ·6717·1 e·ISBN·13: 978·94·009·0513·9
DOl: 10.10071978·94·009·0513·9
I. Evolution--Statistical methods--Congresses. 2. Evolution-
-Mathenatics--Congresses. I. Lessard, Sabin. 1951- II. North
Atlant1c Treaty Organi2ation. Scie~t1f1c A-fa1rs D1vis1on.
III. T1tle. IV. Series.
QH323.5N37 1987
575.0l'Ol51--dc20 89-26702
ISBN-13: 978·94-0 10 ·6717·1
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Kluwer Academic Publishers incorporates the publishing programmes of
D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.
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Printed on acid-free paper
All Rights Reserved
© 1990 by Kluwer Academic Publishers
Softcover reprint of the hardcover 1st edition 1990
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utilized in any form or by any means, electronic or mechanical, including photo
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permission from the copyright owner.
TABLE OF CONTENTS
PREFACE vii
LIST OF P ARTICIP M'TS ix
LIST OF CONTRIBUTORS xiii
E. AKIN
The Differential Geometry of Population Genetics and Evolutionary Games 1
C. CANNINGS
Topics in the Theory of ESS's 95
F.B. CHRISTIANSEN
Selection in Natural Populations 121
W.J. EWENS
Population Genetics Theory - The Past and the Future 177
W.G.S. HINES with D. ANFOSSI
A Discussion of Evolutionarily Stable Strategies 229
S. LESSARD
Evolution du rapport num~rique des sexes et modeles dynamiques connexes 269
S. LEVIN and C. . CASTILLO-CHAVEZ
Topics in Evolutionary Ecology 327
Ir-.'DEX 359
PREFACE
Mathematical and statistical approaches to evolutionary theory are numerous. The
NATO Advanced Study Institute (ASI) held at the Universite de Montreal, Montreal,
August 3-21, 1987, was an opportunity to review most of the classical approaches and to
study the more recent developments. The participation of theoretical biologists and
geneticists as well as applied mathematicians and statisticians made possible exchanges of
ideas between students and scholars having different views on the subject.
These Proceedings contain the lecture notes of seven (7) of the eleven (11) series of
lectures that were given.
ESS (Evolutionarily Stable Stragety) theory is considered from many perspectives,
from a game-theoretic approach to understanding behavior and evolution (W.G.S. Hines),
and a systematic classification of properties and patterns of ESS's (C. Cannings) to
particular applications of the differential geometry of the Shahshahani metric (E. Akin).
Extensions of ESS theory to sexual populations and finite populations, not to mention
games between relatives, are presented (W.G.S. Hines). Special attention is given to the
classical game called the War of Attrition but with n players and random rewards (C.
Cannings). The Shahshahani metric is also used to show the occurrence of cycling in the
two-locus, two-allele model (E. Akin).
Various inference problems in population genetics are adressed. Procedures to detect
and measure selection components and polymorphism (in particular, the Wahlund effect) at
one or several loci from mother-offspring combinations in natural populations are
discussed at length (F.B. Christiansen).
The sampling theory of neutral alleles and the new retrospective theory in population
genetics (as opposed to the classical prospective theory) are presented: the Ewens
sampling formula and tests for neutrality, Kingman coalescent processes and procedures to
determine the age of alleles in a sample or in the entire population (W. Ewens).
Topics in evolutionary ecology include coevolution of virulence and resistance in host
parasite and plant-herbivore systems and the effects of varying environments on dispersal
and dormancy strategies. There is also a discussion of evolution as an optimization
process (S. Levin and C. Castillo-Chavez).
Finally, evolution in sex-differentiated selection models is studied with regard to the
population sex ratio. The validity of a product maximization principle in Mendelian
populations with two sexes is discussed (S. Lessard).
The four series of lectures not reported in the Proceedings dealt with other major
aspects of the subject: quantitative genetics and multifactorial inheritance, including
mutation-selection balance (S. Karlin), molecular biology and DNA sequences, in
particular the evolution of multigene families (T. Ohta-Harada), kin selection theory and
vii
viii PREFACE
the evolution of social behaviors (C. Matessi), and phylogenic trees and the differentiation
of species (D. Sanlcoff).
Nine special lectures on related topics were also given by R. Chakrabarty, P. Donelly,
J. Haigh, K. Holsinger, C. Lefevre, D. Pierre-Loti-Viaud, Z. Taib, E. Thompson, M.
Uyenoyama.
My sincere thanks to all lecturers and all participants for their contribution. I also wish
to thank the members of the Organizing Commitee, especially Aubert Daigneault, director
of the ASI, Ghislaine David, secretary of the ASI, Gert Sabidussi, technical editor of the
Proceedings, and Lise PerreaUlt, who typed the manuscript. The credit for the success of
the ASI must be given to all.
The ASI was made possible by financial support from NATO, the Natural Sciences
and Engineering Research Council of Canada, the Ministere de l'education du Quebec and
the Universite de Montreal. Special thanks for their efforts on behalf of the ASI are due to
the NATO Scientific Affairs Division, in particular to Dr. Craig Sinclair, then Director of
the ASI program.
Sabin Lessard
Scientific Director
LIST OF PARTICIPANTS
Frederick ADLER David BROWN
Center for Applied Mathematics Department of Zoology
Cornell University Umversity of Toronto
312 Sage Hall 25 Harbord St.
Ithaca, NY 14853 Toronto, Ont. MSS 1A1
USA Canada
Ethan AKIN Robert BRUNET
Department of Mathematics Departement de matMmatiques
The City College of CUNY et de statistique
New York, NY 10031 Universite de Montreal
USA C.P. 6128, Succ. A
Montreal, Que. H3C 317
Dominique ANFOSSI Canada
Department of Mathematics
and Statistics Chris CANNINGS
University of Guelph Department of Probability and Statistics
Guelph, Ont. NlG 2WI Umversity of Sheffield
Canada Sheffield S 10 2TN
United Kingdom
Adel ANTIPP A
Departement de physique Carlos CASTILLO-CHAVEZ
Uruversite du Quebec a Trois-Rivieres Section of Ecology and Systematics
C.P. 500 Cornell University
Trois-Rivieres, Que. G9A 5H7 Corson Hall
Canada Ithaca, NY 14853-2701, USA
Chris BASTEN Ranajit CHAKRABORTY
Department of Mathematics Genetics Center
Washington State University University of Texas
Pullman, WA 99164-2930 Health Science Center
USA P.O. Box 20334
Houston, TX 77225, USA
Marc BOURDEAU
Department de matMmatiques Freddy B. CHRISTIANSEN
appliquees Institute of Ecology and Genetics
Ecole l'ofytechnique University of Aarhus
C.P. 6079, Montreal, Que. H3C 3A7 Ny Munkegade, Bldg. 550
Canada DK-8000 Aarhus C
Denmark
Lisa BROOKS
Biomed Department Mariana CONSTANTINESCU
Box G Departement de matMmatiques
Brown University et de physique
Providence, RI 02912 Universite de Moncton
USA Moncton, New Brunswick E1A 3E9
Canada
ix
x LIST OF PARTICIPANTS
Ross CRESSMAN John HAIGH
Department of Mathematics Mathematics Division
Wilfrid Laurier University University of Sussex
Waterloo, Ont. N2L 3C5 Mathematics & Physics Bldg.
Canada Falmer, Brighton BNl 90H
United Kingdom
Kalyan DAS
Departement de mathematiques David HALL
et de statistique Department of Zoology
Universite de Montreal Duke University
C.P. 6128, Succ. A Durham, NC 27706, USA
Montreal, Que. H3C 317
Canada Andre HARDY
Departement de Mathematique
Peter DONNELLY Fac. Universitaires de Namur
Department of Statistical Science Remj>art de la Vierge, 8
Umversity College B-5000 Namur, Belgium
Gower Street
London WClE 6BT Ruben HERNANDEZ
United Kingdom Dpto de Estadistica
Univ. Nac. Aut6noma de Mexico
Simplice DOSSOU-GBETE Apdo. Postal 70-429
Departement de mathematiques ClUdad Universitaria
Umversite de Pau 04510 Coyoacan D.F.
Avenue de l'Universite Mexico
64000 Pau
France Gordon HINES
Department of Mathematics
Guillemette DUCHATEAU and Statistics
4, rue Casimir Perier University of Guelph
75007 Paris Guelph, Onto NIG 2WI
France Canada
Yves ESCOUFIER Howard HINES
Departement d'informatique Department of Mathematics
Uruversite des Sciences et Uruversity of the West Indies
Techniques du Languedoc Mona, Kmgston 7
99, ave d'Occitanie Jamaica W.I.
34075 Montpellier Ctdex
France Kenneth J. HOCHBERG
Department of Mathematics
Warren J. EWENS and Computer Sicence
Department of Mathematics Bar-Han University
Monash University 52100 Ramat Gan, Israel
Clayton, Victoria 3168
Australia Kent E. HOLSINGER
Department of Ecology and
Vincent FERRETTI Evolutionary Biology
6826, rue Boyer Box U-43, Room TLS314
Montreal, Que. H2S 2V7 University of Connecticut
Canada Storrs, CT 06268, USA
Carmela GUGLIELMINO Fred M. HOPPE
Istituto di Genetica, Biochimica Department of Mathematics
ed Evoluzionistica, CNR and Statistics
Universittl di Pavia McMaster University
Via Abbiategrasso, 207 1280 Main Street West
27100 Pavia Hamilton, ant. L8S 4Kl
Italy Canada
LIST OF PARTICIPANTS xi
H~l~ne JOLY Sabin LESSARD
Division des Sciences Biologiques D~partement de mathematiques
Pi~ce 3121 et de statistigue
Conseil National de Recherche Universire de Montr~al
100, Promenade Sussex C.P. 6128, Succ. A
Ottawa, Ont. KIA OR6 Montr~al, Que. H3C 317
Canada Canada
Paul JOYCE Simon A. LEVIN
Department of Mathematics Section of Ecology and Systematics
UnIversity of Utah Cornell University
233 Widtsoe BI~ Corson Hall
Salt Lake City, 84112 Ithaca, NY 14853-2701, USA
USA
Carlo MATESSI
Miiriivvet KARA Istituto di Genetica, Biochimica
~rations Research Unit ed Evoluzionistica, CNR
armara Scientific and Universita di Pavia
Industrial Research Institute Via Abbiategrasso, 207
P.O. Box 21 27100 Pavia
Gebze-Kocaeli Italy
Turkey
Francine MAYER
Samuel KARLIN Centre de recherches caraibes
Department of Mathematics Universit~ de Montr~al
Stanford UniversiR C.P. 6128, Succ. A
Stanford, CA 943 5 Montr~al, Que. H3C 317
USA Canada
Eric KINDAHL Marcel MONGEAU
Section of Genetics and Departement de mathematiques
Development et de statistique
Cornell University Universite de Montreal
Emerson Hall C.P. 6128, Succ. A
Ithaca, NY 14853-1902 Montreal, Que. H3C 317
USA Canada
Mokhtar KIRANE Michael MOODY
4, rue des Sorbiers Department of Mathematics
92000 Nanterre Washington State University
France Pullman, WA 99164-2930
USA
Michel KRIEBER
D;ftartment of Biology, LSB Annie MORIN
D housie University 42, rue Vasselot
Halifax, Nova Scotia B3H 3J5 35100 Rennes
Canada France
Yolande LAVOIE Tim MOUSSEAU
Departement de demo~raphie Department of Biology
Uruversite de Montrea McGill University
C.P. 6128, Succ. A 1205, Ave Docteur Penfield
Montreal, Que. H3C 317 Montreal, Que. H3A 18 1
Canada Canada
Claude LEFEVRE One NERMAN
Avenue van Becelaere 24B Department of Mathematics
Boile 12 Chalmers University of Technology
B-1170 Bruxelles S-4l2 96 Gtiteborg
Belgium Sweden