Stochastic Spatial Processes Mathematical Theories and Biological Ap

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1212 Stochastic Spatial Processes Mathematical Theories and Biological Applications Proceedings of a Conference held in Heidelberg, September 10-14, 1984

Edited by P. Tautu

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

Editor

Petre Tautu Abtlg. Mathematische Modelle Institut fur Dokumentation, Information und Statistik Deutsches Krebsforschungszentrum, 1m Neuenheimer Feld 280 6900 Heidelberg 1, West Germany

Mathematics Subject Classification (1980): 60-06, 60G 60, 60K35, 92-06, 92A 15 ISBN 3-540-16803-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-16803-6 Springer-Verlag New York Berlin Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich,

© Springer-Verlag Berlin Heidelberg 1986 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210

STOCHASTIC SPATIAL PROCESSES MATHEMATICAL THEORIES AND BIOLOGICAL APPLICATIONS

TABLE OF CONTENTS Foreword List of contributors I.INTRODUCTORY EDITORIAL Stochastic spatial processes in biology: A concise historical survey P.TAUTU II.WORKSHOP CONTRIBUTIONS Tests for space-time clustering A.D.BARBOUR and G.K.EAGLESON Age distributions in birth and death processes A.BOSE Critical clustering in the two dimensional voter model J.T.COX and D.GRIFFEATH Measure-valued processes. Construction,qualitative behavior and stochastic geometry D.DAWSON Dual processes in population genetics P.DONNELLY Some peculiar properties of a particle system with sexual reproduction R.DURRETT Computer simulation of developmental processes in biology: Models for the developing limb D.A.EDE Asymptotics and spatial growth of branching random fields L. G. GO R0STI ZA Generation dependent branching processes with immigration: Convergence of distributions T.GUTZ On a class of infinite particle systems evolving in a random environment A. GREVEN Percolation processes and dimensionality G.GRIMMETT Birth and death processes with killing and applications to parasitic infections K.P.HADELER

42 52

59

69 94

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112

124 136

145 165 175

TABLE OF CONTENTS

Limit theorems for multi type branching random walks G.IVANOFF On the reproduction rate of the spatial general epidemic K.KUULASMAA Nearest particle systems; Results and open problems T.M.LIGGETT Neutral models of geographical variation T.NAGYLAKI Stochastic measure diffusions as models of growth and spread G.ROSENKRANZ L2 convergence of certain random walks on Zd and related diffusions W.G.SULLIVAN Random fields; Applications in cell biology P.TAUTU Correlated percolation and repulsive particle systems D.J.A.WELSH

187 195

200 216

238 249

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FOREWORD

The present volume -brings together 20 papers presented at