Author

# Robert M. May

Other affiliations: Royal Society, California Institute of Technology, Princeton University ...read more

Bio: Robert M. May is an academic researcher from University of Oxford. The author has contributed to research in topics: Population & Ecology (disciplines). The author has an hindex of 148, co-authored 471 publications receiving 107001 citations. Previous affiliations of Robert M. May include Royal Society & California Institute of Technology.

##### Papers published on a yearly basis

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11 Jul 1991

TL;DR: This book discusses the biology of host-microparasite associations, dynamics of acquired immunity heterogeneity within the human community indirectly transmitted helminths, and the ecology and genetics of hosts and parasites.

Abstract: Part 1 Microparasites: biology of host-microparasite associations the basic model - statics static aspects of eradication and control the basic model - dynamics dynamic aspects of eradication and control beyond the basic model - empirical evidence of inhomogeneous mixing age-related transmission rates genetic heterogeneity social heterogeneity and sexually transmitted diseases spatial and other kinds of heterogeneity endemic infections in developing countries indirectly transmitted microparasites. Part 2 Macroparasites: biology of host-macroparasite associations the basic model - statics the basic model - dynamics acquired immunity heterogeneity within the human community indirectly transmitted helminths experimental epidemiology parasites, genetic variability, and drug resistance the ecology and genetics of host-parasite associations.

7,675 citations

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TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.

Abstract: First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

6,118 citations

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21 Aug 1973

TL;DR: Preface vii Preface to the Second Edition Biology Edition 1.

Abstract: Preface vii Preface to the Second Edition Biology Edition 1. Intoduction 3 2. Mathematical Models and Stability 13 3. Stability versus Complexity in Multispecies Models 4. Models with Few Species: Limit Cycles and Time Delays 79 5. Randomly Fluctuating Environments 109 6. Niche Overlap and Limiting Similarity 139 7. Speculations 172 Appendices 187 Afterthoughts for the Second Edition 211 Bibliography to Afterthoghts 234 Bibliography 241 Author Index 259 Subject Index 263

5,083 citations

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TL;DR: In this article, the authors explore the consequences of placing players in a two-dimensional spatial array: in each round, every individual 'plays the game' with the immediate neighbours; after this, each site is occupied either by its original owner or by one of the neighbours, depending on who scores the highest total in that round; and so to the next round of the game.

Abstract: MUCH attention has been given to the Prisoners' Dilemma as a metaphor for the problems surrounding the evolution of coopera-tive behaviour1–6. This work has dealt with the relative merits of various strategies (such as tit-for-tat) when players who recognize each other meet repeatedly, and more recently with ensembles of strategies and with the effects of occasional errors. Here we neglect all strategical niceties or memories of past encounters, considering only two simple kinds of players: those who always cooperate and those who always defect. We explore the consequences of placing these players in a two-dimensional spatial array: in each round, every individual 'plays the game' with the immediate neighbours; after this, each site is occupied either by its original owner or by one of the neighbours, depending on who scores the highest total in that round; and so to the next round of the game. This simple, and purely deterministic, spatial version of the Prisoners' Dilemma, with no memories among players and no strategical elaboration, can generate chaotically changing spatial patterns, in which cooperators and defectors both persist indefinitely (in fluctuating proportions about predictable long-term averages). If the starting configurations are sufficiently symmetrical, these ever-changing sequences of spatial patterns—dynamic fractals—can be extraordinarily beautiful, and have interesting mathematical properties. There are potential implications for the dynamics of a wide variety of spatially extended systems in physics and biology.

3,822 citations

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TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.

Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

39,297 citations

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TL;DR: A ‘silver bullet’ strategy on the part of conservation planners, focusing on ‘biodiversity hotspots’ where exceptional concentrations of endemic species are undergoing exceptional loss of habitat, is proposed.

Abstract: Conservationists are far from able to assist all species under threat, if only for lack of funding. This places a premium on priorities: how can we support the most species at the least cost? One way is to identify 'biodiversity hotspots' where exceptional concentrations of endemic species are undergoing exceptional loss of habitat. As many as 44% of all species of vascular plants and 35% of all species in four vertebrate groups are confined to 25 hotspots comprising only 1.4% of the land surface of the Earth. This opens the way for a 'silver bullet' strategy on the part of conservation planners, focusing on these hotspots in proportion to their share of the world's species at risk.

24,867 citations

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TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

17,647 citations

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TL;DR: Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols used xiii 1.

Abstract: Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

14,171 citations

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TL;DR: The traditional view of natural systems, therefore, might well be less a meaningful reality than a perceptual convenience.

Abstract: Individuals die, populations disappear, and species become extinct. That is one view of the world. But another view of the world concentrates not so much on presence or absence as upon the numbers of organisms and the degree of constancy of their numbers. These are two very different ways of viewing the behavior of systems and the usefulness of the view depends very much on the properties of the system concerned. If we are examining a particular device designed by the engineer to perform specific tasks under a rather narrow range of predictable external conditions, we are likely to be more concerned with consistent nonvariable performance in which slight departures from the performance goal are immediately counteracted. A quantitative view of the behavior of the system is, therefore, essential. With attention focused upon achieving constancy, the critical events seem to be the amplitude and frequency of oscillations. But if we are dealing with a system profoundly affected by changes external to it, and continually confronted by the unexpected, the constancy of its behavior becomes less important than the persistence of the relationships. Attention shifts, therefore, to the qualitative and to questions of existence or not. Our traditions of analysis in theoretical and empirical ecology have been largely inherited from developments in classical physics and its applied variants. Inevitably, there has been a tendency to emphasize the quantitative rather than the qualitative, for it is important in this tradition to know not just that a quantity is larger than another quantity, but precisely how much larger. It is similarly important, if a quantity fluctuates, to know its amplitude and period of fluctuation. But this orientation may simply reflect an analytic approach developed in one area because it was useful and then transferred to another where it may not be. Our traditional view of natural systems, therefore, might well be less a meaningful reality than a perceptual convenience. There can in some years be more owls and fewer mice and in others, the reverse. Fish populations wax and wane as a natural condition, and insect populations can range over extremes that only logarithmic

13,447 citations