Mathematical and Statistical Developments of Evolutionary Theory PDF
Preview Mathematical and Statistical Developments of Evolutionary Theory
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. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322,3300 AH Dordrecht, The Netherlands. Printed on acid-free paper All Rights Reserved © 1990 by Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 1990 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photo copying, recording or by any information storage and retrieval system, without written 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
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