Ecology Robert H. MacArthur
by
Henry S. Horn
  • LAST REVIEWED: 26 August 2013
  • LAST MODIFIED: 26 August 2013
  • DOI: 10.1093/obo/9780199830060-0065

Introduction

In his short life (b. 1930–d. 1972), Robert MacArthur was a highly influential architect of modern ecology. He was, as much as anyone, responsible for bringing theoretical population biology into mainstream ecology at a time when many empirical ecologists were openly hostile to theory. He inquired broadly, read widely, and wrote clearly and concisely. He was an enthusiastic naturalist and an analytical thinker; but more importantly, he mixed these roles, applying his mathematical insights in the field and being inspired by observation in his theoretical work. His PhD thesis became the renowned 1958 Ecology paper on the coexistence of five species of warblers in northeastern coniferous forests. His Warbler Paper is still prominent as a motivating example in introductory ecology texts. MacArthur used graphical analyses to generalize theorems about ecology and genetic evolution. He derived fundamental relations between ecosystem structure and function. He developed a conceptual framework for competition between species, and he applied and tested that framework with field studies of birds. With Edward O. Wilson, he developed the view that an island flora or fauna could be viewed as a potential equilibrium between the arrival of new species and the extirpation of residents. MacArthur’s current citations, copious as they are, vastly underestimate his enduring contribution to contemporary ecology. This is partly because fully one quarter of his publications were books or book chapters, rather than articles in peer-reviewed journals. But it is largely because he encouraged such independence and inspired such confidence in his students, colleagues, and followers that they adopted much of his perspective as their own. They advanced his ideas, and then cited themselves and each other as often as they cited him. Nevertheless, it is still worthwhile to return to his original papers for historical perspective and for prescient ideas that may have been forgotten, as well as for reminders to include evolutionary analysis in ecological theory and for exemplars of the primacy of patterns of natural history in setting and addressing ecological questions. Accordingly, this bibliography will favor references to MacArthur’s own work over his legacy in contemporary literature. After reviewing Mentors, Robert MacArthur’s Life and Work, and MacArthur’s Way of Doing Science, this bibliography will cite and comment on Topical Publications and Commentary. Finally, his first and last books offer Contemplative Bookends to the body of his work, including insights that are still fresh today.

Mentors

MacArthur’s most direct mentor was his doctoral supervisor, G. Evelyn Hutchinson (for more information on Hutchinson, see Oxford Bibliographies in Ecology article G. Evelyn Hutchinson by David Skelly). Accordingly, knowing about Hutchinson enriches one’s knowledge of MacArthur. Slack 2010 provides a detailed biography of Hutchinson that also gives novel insights into MacArthur. Hutchinson 1951, Hutchinson 1957, and Hutchinson 1959 announce specific ideas that MacArthur developed later. Slobodkin 1962 represents a crystallization of theory in population biology that was developing during MacArthur’s graduate student days, in part due to Slobodkin’s own talents for innovation and exposition. There is little public record of MacArthur’s postdoctoral year with David Lack, but Lack 1954 had recently been published, codifying a view of population regulation that MacArthur often expressed. Finally, throughout his career MacArthur cited the genetical theory of Fisher 1930 and the natural history of Grinnell 1943 so often and so admiringly that these biologists may be considered to be his indirect mentors.

  • Fisher, Sir Ronald A. 1930. The genetical theory of natural selection. Edited (1999) with introduction and notes by J. Henry Bennett. Oxford: Oxford Univ. Press.

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    A landmark in population genetics, definitively applying it to questions raised by Darwin. MacArthur was impressed by anyone who also appreciated, let alone understood, Fisher’s work. He generalized several of Fisher’s ideas: the logical structure of Darwin’s theory of evolution by natural selection, Fisher’s fundamental theorem of natural selection, and the evolution of optimal sex ratios.

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  • Grinnell, Joseph. 1943. Joseph Grinnell’s philosophy of nature: Selected writings of a western naturalist. Berkeley: Univ. of California Press.

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    Collected excerpts from his major papers, exemplifying patterns that he had planned to gather into a book during retirement. Grinnell was MacArthur’s ideal of a naturalist. The outline of Grinnell’s planned book, Geography and Evolution, lists many topics later elaborated in MacArthur 1972, cited under Geographical Ecology (1972), and MacArthur explicitly cites Grinnell’s early expression of modern ideas.

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  • Hutchinson, G. Evelyn. 1951. Copepodology for the ornithologist. Ecology 32.3: 571–577.

    DOI: 10.2307/1931745Save Citation »Export Citation » Share Citation »

    A collection of facts about copepods, viewed through contemporary ornithological concepts. Many topics in this paper became recurring themes for MacArthur: selective versus non-selective feeding, size differences among coexisting species, clutch size variation, and fugitive species. The paper ends with a section “Concluding Remarks,” which has become a trope for Hutchinson and his followers.

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  • Hutchinson, G. Evelyn. 1957. Concluding remarks. Cold Spring Harbor Symposia on Quantitative Biology 22:415–427.

    DOI: 10.1101/SQB.1957.022.01.039Save Citation »Export Citation » Share Citation »

    Formalization of the ecological “niche” and the competitive-exclusion principle, followed by a wealth of examples from natural history. This paper resulted from discussions in A Seminar in Advanced Ecology, made up largely of Hutchinson’s students. The term “fundamental niche” is credited to MacArthur in a footnote (p. 416).

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  • Hutchinson, G. Evelyn. 1959. Homage to Santa Rosalia or why are there so many kinds of animals? American Naturalist 93:145–159.

    DOI: 10.1086/282070Save Citation »Export Citation » Share Citation »

    Hutchinson’s paper firmly sets food chains (now called “food webs”) and their interactions as the context for questions about the origin and maintenance of biological diversity and about the effects of spatial variations in the environment. This is the context for much of MacArthur’s later work, and Hutchinson generously cites MacArthur, along with others of his students.

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  • Lack, David. 1954. The natural regulation of animal numbers. London: Oxford Univ. Press.

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    Lack argues that fluctuations in natural populations are limited by mechanisms that require feedback from population size itself and that are subject to natural selection. He cites copious examples from natural history, especially birds. His ideas heavily influenced the next generation of ecologists.

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  • Slack, Nancy G. 2010. G. Evelyn Hutchinson and the invention of modern ecology. New Haven, CT: Yale Univ. Press.

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    This is a fascinating account of Hutchinson’s personal and intellectual life, tracing the history of his brilliant idiosyncrasies and their effects on his students and on the field of ecology. In addition, Hutchinson’s correspondence provides important vignettes of his beloved former students, notably material that is not available elsewhere on Robert MacArthur from his student days to his death.

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  • Slobodkin, Lawrence B. 1962. Growth and regulation of animal populations. New York: Holt, Rinhardt and Winston.

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    This definitive introduction to the mathematics of populations and their interactions is a concise and transparent summary of much of what was discussed in MacArthur’s student days and early career. Slobodkin made an easy transition from the biology of populations to the energetics of ecosystems and lured later students into the original literature of both arenas.

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Robert MacArthur’s Life and Work

All of the papers in this section give some impression of MacArthur as a person, but particularly moving are Brown 1999, Fretwell 1975, and Pianka and Horn 2005. Essentially complete bibliographies of MacArthur are found in Cody and Diamond 1975 and Wilson and Hutchinson 1989. These bibliographies provide appropriate material for an excellent advanced seminar, perhaps organizing the topics as in Fretwell 1975 and posing the questions raised by Pianka and Horn 2005 (p. 216). Fretwell reviews most of MacArthur’s publications in an excellent outline that has helped to organize the present bibliography, and that could profitably organize future reviews of MacArthur’s intellectual legacy. Fretwell’s outline begins by codifying seven central concepts in modern ecology, and discussing MacArthur’s role in putting them into their modern form (as of 1975). Fretwell continues with ten areas of novelty in ecology (again as of 1975) that MacArthur developed or even originated. More comprehensive reviews have uncovered, and will uncover, parallel developments by others, but Fretwell’s list is still superb for organizing discussion of MacArthur’s work. (For his associates, “Professor MacArthur” quickly became “Robert,” and so he is called “Robert” in personal references in this section.) Among the common themes of his biographies are: love of science and of family, treating young colleagues as family; analytical intellect and bewilderment at arguments that lacked rigor, but impatience with manifestly sloppy or ill-informed opinion; and love of natural history and walking, observing, and discussing it outdoors. He also showed full respect for the individuality of students and colleagues. Accordingly, each of the accounts in this section is written from a very different perspective, often telling as much about the writer as about Robert. But even the latter portray characteristics of the writers that were strengthened through their interactions with Robert.

  • Brown, James H. 1999. The legacy of Robert MacArthur: From geographical ecology to macroecology. Journal of Mammalogy 80.2: 333–344.

    DOI: 10.2307/1383283Save Citation »Export Citation » Share Citation »

    Brown gives a moving and balanced personal account of Robert’s many strengths and few weaknesses, with vignettes showing a loving father, literally to his children and figuratively to his younger colleagues. Brown then reviews patterns within geographical ecology to which MacArthur made innovative contributions.

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  • Cody, Martin L., and Jared M. Diamond, eds. 1975. Ecology and evolution of communities. Cambridge, MA: Harvard Univ. Press.

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    A memorial volume based on a symposium held in November 1973, a year after Robert MacArthur’s death. Cody and Diamond introduce MacArthur’s background of natural history and analytic inquiry and his accomplishments in theoretical and empirical ecology. The eighteen chapters by twenty-one authors are still worth perusing for the astounding range and quality of research that MacArthur directly inspired.

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  • Fretwell, Stephen D. 1975. The impact of Robert MacArthur on ecology. Annual Review of Ecology and Systematics 6:1–13.

    DOI: 10.1146/annurev.es.06.110175.000245Save Citation »Export Citation » Share Citation »

    An early, topically organized review of MacArthur’s intellectual legacy. Fretwell begins with a charming account of the almost spiritual way in which Robert affected his own intellectual development, followed by an informal analysis of what he saw as Robert’s philosophy of science, scholarship, and publication.

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  • Pianka, Eric R., and Henry S. Horn. 2005. Ecology’s legacy from Robert MacArthur. In Ecological paradigms lost: Routes to theory change. Edited by Kim Cuddington and Beatrix E. Beisner, 213–232. Amsterdam: Elsevier Academic Press.

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    A recent and idiosyncratic review of MacArthur’s intellectual legacy. Pianka and Horn list MacArthur’s major accomplishments and cite relevant publications organized essentially into the topics of the present bibliography. They offer reflections on their scientific and personal interactions with Robert, adding valuable detail about how he mentored with gentle strength. They also cite equally caring accounts by others.

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  • Wilson, Edward O., and G. Evelyn Hutchinson. 1989. Robert Helmer MacArthur 1930–1972. In Biographical memoirs. Vol. 58. Washington, DC: National Academy of Sciences.

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    Formal biography of MacArthur as a deceased member of the National Academy of Sciences. It concisely and forcefully reviews MacArthur’s early work on the theory of ecosystem structure, his exploration of relative patterns of species’ abundances, his conceptually driven empirical study of warblers, and his later work on community structure, accompanied by illuminating accounts of his personality and perspective.

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MacArthur’s Way of Doing Science

For the most part, MacArthur simply practiced science instead of talking about it. The closest he came to a statement about his philosophy of science is probably MacArthur 1972: “Anyone familiar with the history of science knows that it is done in the most astonishing ways by the most improbable people and that its only real rules are honesty and validity of logic, and that even these are open to public scrutiny and correction” (p. 259). Kingsland 1995 makes a cogent case for MacArthur’s mathematization of ecological ideas, especially about competition, being a major force in “the eclipse of history” as a factor in ecological explanations: but she also (in the afterword of her 1995 edition) cites passages in MacArthur’s work that presage a later resurrection of “the new natural history.” MacArthur’s interactions with students and colleagues always balanced mathematized generalizations with the details of natural history, and later views of his attitude toward historical explanations were likely polarized by the general adversarial tone that prevailed in ecological discourse around the time of his death. Ishida 2007, May 1986, Paine 1984, and MacArthur 1969 himself argue that his inspiration was always the facts of natural history, which in turn defined the range of applicability of his theoretical ideas, and that the tests of his ideas were analyses of data gathered in the field. The pluralism of MacArthur’s thought was recognized explicitly by McIntosh 1987. MacArthur’s influence has been acknowledged by several of the early winners of the Ecological Society of America’s biennial MacArthur Award for meritorious contributions by mid-career ecologists, notably Levin 1992, May 1986, and Paine 1984.

  • Ishida, Yoichi. 2007. Patterns, models, and predictions: Robert MacArthur’s approach to ecology. Philosophy of Science 74:642–653.

    DOI: 10.1086/525610Save Citation »Export Citation » Share Citation »

    Ishida argues against the notion that MacArthur’s approach was “ahistorical.” MacArthur started with the facts of natural history and abstracted and interpreted those common features that represented a general pattern. Such interpretation does not diminish the potential importance of departures from the general pattern, and his interest in equilibria should not detract from the importance of transient dynamics.

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  • Kingsland, Sharon E. 1995. Modeling nature: Episodes in the history of population ecology. 2d ed. Chicago: Univ. of Chicago Press.

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    A history of population and community ecology in which MacArthur plays a pivotal role. Kingsland’s analysis of the interactions between the ideas of MacArthur and his mentor Hutchinson are particularly detailed and insightful (pp. 176–205, 213–225, and “MacArthur” in Index). Originally published in 1985.

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  • Levin, Simon A. 1992. The problem of pattern and scale in ecology. Ecology 73.6: 1943–1967.

    DOI: 10.2307/1941447Save Citation »Export Citation » Share Citation »

    Introducing a synthesis of work on pattern and scale over the twenty years after Robert MacArthur’s death, Levin pays explicit homage to MacArthur for his influence in transforming ecology to embrace a role for theory in exploring and explaining patterns of natural history, and in applying dynamic evolutionary insights to resource management and conservation.

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  • MacArthur, Robert H. 1969. The ecologist’s telescope. Ecology 50:353.

    DOI: 10.2307/1933882Save Citation »Export Citation » Share Citation »

    Using an analogy of the astronomer’s need to balance academic city life and telescopic observations in pristine skies with the ecologist’s need for both academic discussion and fieldwork, MacArthur argues for a network of ecological field stations to parallel and interact with colleges and universities.

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  • MacArthur, Robert H. 1972. Coexistence of species. In Challenging biological problems. Edited by John A. Behnke, 253–259. Oxford: Oxford Univ. Press.

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    Reflection on a major theme of MacArthur 1972, cited under Geographical Ecology (1972). This chapter stands, together with the preface and introduction to the book, as MacArthur’s definitive statement of how he did science. It is more balanced and powerful, and yet more gentle than most of what has been written by his disciples, detractors, and analysts.

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  • May, Robert M. 1986. The search for patterns in the balance of nature: Advances and retreats. Ecology 67.5: 1115–1126.

    DOI: 10.2307/1938668Save Citation »Export Citation » Share Citation »

    May quotes MacArthur as the inspiration for his own work, emphasizing an essential difference between “laws” sought by physicists, and “contingent generalizations” sought by ecologists. Ecologists today would endorse May’s encomium, “This lecture is dedicated to Robert MacArthur not so much because he gave us the right answers, but because he continually reminded us of the right questions” (p. 1116).

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  • McIntosh, Robert P. 1987. Pluralism in ecology. Annual Review of Ecology and Systematics 18:321–341.

    DOI: 10.1146/annurev.es.18.110187.001541Save Citation »Export Citation » Share Citation »

    A comprehensive, thoughtful, and eloquent review of the variety of approaches to ecological information and explanation. This was written as ecology was emerging from a series of ill-advised conflicts among philosophical approaches, which pitted theory against fieldwork and even dynamic theory against equilibrial theory. McIntosh recognizes MacArthur’s importance in developing equilibrial theory but also lauds his pluralism.

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  • Paine, Robert T. 1984. Ecological determinism in the competition for space. Ecology 65.5: 1339–1348.

    DOI: 10.2307/1939114Save Citation »Export Citation » Share Citation »

    Paine is unusually explicit among MacArthur awardees in describing his heartfelt debt to Robert MacArthur. He reminds us especially that “MacArthur continually urged ecologists to draw their inspiration from naturally occurring patterns and to use their naturalist’s intuition” (p. 1339).

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Topical Publications and Commentary

This section consists of papers that can be discussed under a common heading. The classification is somewhat artificial and should not preclude reading a paper from one heading in the context of another. The section Warbler Paper is first for the topic’s enduring impact and for the range of other work that it presages. Evolution and Genetics features papers that make an explicitly genetic argument, though evolution is implicit in most of the rest of MacArthur’s work: where almost every equilibrial result is subjected to an analysis of what happens when a species with variant properties invades. Ecosystem Structure and Function reviews work on systems with trophic structure, instead of (or in addition to) competition. Relative Abundances and “Broken Stick” Models represents one of the few topics that MacArthur contributed to heavily early on, yet repudiated later. Competition, Coexistence, and Species’ Packing is perhaps the topic for which MacArthur developed the most original theory. Bird Species’ Diversity is the topic for which he gathered, compiled, and interpreted the most empirical evidence, with special emphasis on contrasts between tropical and temperate communities. The data that he gathered often involved novel modifications of Field Techniques and Data Analysis. A Note on Spatial Patterns presents the paradox that MacArthur’s productive analyses of patchy environments were not explicitly spatial. Finally, Island Biogeography is but a précis of what should be expanded into a separate bibliography.

The Warbler Paper

MacArthur 1958, his most widely known contribution to ecology and behavior, is his study of what allows five species of very similar warblers to coexist in a seemingly simple habitat. His best-known finding is that coexisting warbler species may avoid each other, and hence may ameliorate competition, by specialized foraging in different parts of conifer trees. Students often playfully total the recorded number of seconds of critical observation and ask, “Can I do a Ph.D. thesis too in 4 hours, 22 minutes, and 54 seconds of fieldwork?” The answer is obvious to any naturalist who has tried to watch the behavior of small birds in dense vegetation. But the warbler paper also shows a huge range of innovative observations, analyses, and interpretations that foreshadow major themes of MacArthur’s later contributions: graphical analysis that generalizes theoretical results beyond the details of particular analytic equations; direct demonstration of density-dependent regulation of populations, including the role of territoriality; behavior that adapts foraging to environmental structure; choice of habitat; adaptive responses of breeding to changing resources; temporal partitioning of the environment; the importance of tropical biology; and the effect of habitat structure on resident bird biodiversity. Indeed, the only themes of later work that are missing in MacArthur’s warbler paper are genetic evolution, ecosystem energetics, and large-scale geographic patterns. In addition to being cited for its primary results, the paper has been widely cited by later ecologists as a primary influence in attracting them into their profession, with its exemplary combination of conceptual analysis, inventive empiricism, and detailed natural history. Kaspari 2008 provides a superb example of its enduring attraction, and should be required reading to accompany MacArthur’s work.

  • Kaspari, Michael (with illustration by Debbie Kaspari). 2008. Knowing your warblers: Thoughts on the 50th anniversary of MacArthur (1958). Bulletin of the Ecological Society of America 89.4: 448–458.

    DOI: 10.1890/0012-9623(2008)89[448:KYWTOT]2.0.CO;2Save Citation »Export Citation » Share Citation »

    The history, legacy, and continuing importance of MacArthur’s warbler paper. Michael Kaspari relates the paper to a wisely selected bibliography, including signposts to more recent work on warblers; he also adds important facts about MacArthur gleaned from personal discussions. Debbie Kaspari charmingly depicts all five warbler species inhabiting a realistic branch of the Blackburnian Warbler’s “data-tree.”

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  • MacArthur, Robert H. 1958. Population ecology of some warblers of northeastern coniferous forests. Ecology 39:599–619.

    DOI: 10.2307/1931600Save Citation »Export Citation » Share Citation »

    The published version of MacArthur’s PhD thesis. Initially the warblers posed a counterexample to the principle of competitive exclusion among similar species. The subtlety of the differences between the warblers set the stage for rephrasing the problem as “What is the minimum difference that allows coexistence?” This question ultimately underlies most of MacArthur’s later publications.

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Evolution and Genetics

Most of MacArthur’s work on competition and ecology has a strong evolutionary component: having derived characteristics that allow a population to persist, he asks whether variants can invade and flourish, i.e., whether the population is likely to evolve. In this section are several papers explicitly about evolutionary population genetics. MacArthur 1961 explores the tension between individual fitness and the good of the species. The paper is under-cited, given its novelty within population genetics at the time, and even under-cited by MacArthur himself, given that it presents the genetic mechanisms underlying much of his later ecological work. Traditional population genetic theory had been developed through the 1950s under the assumptions of a fixed degree of inbreeding and adaptive values of genotypes that were independent of population density. Fisher had proved that reproductive fitness always increases at a rate depending on heritable variance in fitness, and Haldane had shown that the number of genetic deaths as an advantageous novel gene sweeps through a population is independent of the advantage of the new homozygote over the old (see Oxford Bibliographies in Ecology article Population Genetics by Rob Kulathinal). MacArthur 1962 assumes a population with a fixed, though evolvable carrying capacity and no particular inbreeding structure. In a dense but highly rewarding argument, he develops analogs of Haldane’s and Fisher’s theorems in which carrying capacity replaces reproductive rate as the responding variable (see also MacArthur 1971, cited under Bird Species’ Diversity). The quantitative results of the analogs correspond to Haldane’s result, and to the rate of evolution in Fisher’s. However, the direction in which the carrying capacity evolves depends on dynamic interaction of the competitors with their shared resources, not just on the direct interactions between the competitors themselves. MacArthur 1965 and MacArthur 1968a later solved that problem explicitly. Indeed, he offers a progressive extension of the mechanisms of population genetics: to competing populations in a dynamic consumer-resources system in MacArthur 1965 and MacArthur 1968b, to patchy environments and gradients in Levins and MacArthur 1966, and to temporally varying environments in MacArthur 1968a. MacArthur 1970 summarizes the results of his previous papers. A curious feature of several papers in this section is that some arguments are sufficiently elliptical that they do not stand firmly on their own. They are developed elsewhere by MacArthur and colleagues, but the appropriate citations are incomplete or missing. Accordingly, it is worthwhile to juxtapose close readings of all these papers.

  • Levins, Richard, and Robert H. MacArthur. 1966. The maintenance of genetic polymorphism in a spatially heterogeneous environment: Variations on a theme by Howard Levene. American Naturalist 180:585–589.

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    Levene had specified sufficient conditions for maintaining heterozygosity without heterozygote superiority, with random mating and random dispersal in a heterogeneous environment. Levins and MacArthur add variation in mate choice and in habitat choice among dispersers, and derive results of special importance to the early stages of speciation.

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  • MacArthur, Robert H. 1961. Population effects of natural selection. American Naturalist 95:195–199.

    DOI: 10.1086/282175Save Citation »Export Citation » Share Citation »

    Rigorous qualitative arguments specifying when natural selection favors the good of the species versus that of individuals. Special cases of optimization include sex ratio of offspring, avian clutch size, choices of habitat and food, and correlation between local species diversity and exploitative opportunities in the habitat.

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  • MacArthur, Robert H. 1962. Some generalized theorems of natural selection. Proceedings of the National Academy of Sciences of the United States of America 48:1893–1897.

    DOI: 10.1073/pnas.48.11.1893Save Citation »Export Citation » Share Citation »

    Population genetic theory extended to species near their carrying capacities. The criterion of selection, i.e., fitness, is shown to be carrying capacity rather than reproductive rate. This is the founding analysis of “r and K selection” as christened by MacArthur and Wilson 1967, cited and discussed under Island Biogeography.

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  • MacArthur, Robert H. 1965. Ecological consequences of natural selection. In Theoretical and mathematical biology. Edited by T. H. Waterman and H. J. Morowitz, 388–397. New York: Blaisdell.

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    MacArthur shows that in a dynamic consumer-resource system, the criterion of selection may be the ability of the consumer to persist at a lower level of resource. He also uses an essentially game-theoretic analysis to generalize Fisher’s optimization of sex ratio as equal total parental expenditure on both sexes of offspring.

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  • MacArthur, Robert H. 1968a. Selection for life tables in periodic environments. American Naturalist 102:381–383.

    DOI: 10.1086/282550Save Citation »Export Citation » Share Citation »

    A traditional demographic argument is generalized in graphical form to prove that variable environments select for variation in reproductive output, even at the potential expense of lowered reproductive output in a stationary environment of the same mean quality.

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  • MacArthur, Robert H. 1968b. The theory of the niche. In Population biology and evolution. Edited by R. C. Lewontin, 159–176. Syracuse, NY: Syracuse Univ. Press.

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    MacArthur 1968b proves the previous speculation of MacArthur 1965 that in a dynamic consumer-resource system, the criterion of selection is the ability of the consumer to persist at lower amounts of resource. Other than that new result, this paper reviews joint theoretical work with Levins, casting the results in falsifiable form and drawing empirical examples from MacArthur’s other published work.

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  • MacArthur, Robert H. 1970. Graphical analysis of ecological systems. In Some mathematical questions in biology. Foreword by Murray Gerstenhaber, 61–72. Providence, RI: American Mathematical Society.

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    MacArthur begins: “My aim is very simply stated: I want to learn as much as possible by graphical means about the solutions of the ‘ecological equations.’” He does just that, including the new result that particular combinations of competitors are favored by particular ratios and renewal rates of resources.

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Ecosystem Structure and Function

MacArthur was more interested in competition than in predator-prey and ecosystem dynamics, though he made three contributions to the latter. He argued that, under plausible assumptions, biotic assemblages would tend toward a steady-state composition of their components, variously: for age distributions within a population in MacArthur 1958, for species within a trophic level or a community in MacArthur 1958 and MacArthur 1960a, and for species or functional units within an ecosystem in MacArthur 1955. MacArthur 1955 was an important initiator of the discussion about the relation between diversity and stability; the paper has often been misconstrued as proving that diversity conveys stability, but it is cited admiringly and treated correctly by Rooney and McCann 2012. MacArthur 1960b suggests the use of reproductive value in studies of predator-prey relations, though the context of the suggestion seems more theoretical than practical. Rosenzweig and MacArthur 1963 develops a powerful qualitative graphical analysis of predator-prey dynamics, including a speculative extension to three trophic levels: plant, herbivore, and carnivore. The promise of this work has been dramatically realized by McCann 2012.

  • MacArthur, Robert H. 1955. Fluctuations of animal populations, and a measure of community stability. Ecology 36:533–536.

    DOI: 10.2307/1929601Save Citation »Export Citation » Share Citation »

    If energy flow is linear and time-invariant, an ecosystem tends toward constant energy in each component, independent of starting conditions. This insight from the theory of ergodic Markov chains was new to ecology. MacArthur proposed the diversity of energy flow among links as a measure of stability against disruptions.

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  • MacArthur, Robert H. 1958. A note on stationary age distributions in single-species populations and stationary species populations in a community. Ecology 39:146–147.

    DOI: 10.2307/1929977Save Citation »Export Citation » Share Citation »

    The Brouwer fixed point theorem of combinatorial topology is applied to show that if a population is regulated between two limits there is a stationary age composition, and analogously, in a similarly regulated community, a stationary species composition. Stability is not analyzed but is implicitly assumed by the marginal conditions implied by “regulated.”

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  • MacArthur, Robert H. 1960a. Community. In The encyclopedia of the biological sciences. Edited by Peter Gray, 262–264. New York: Reinhold.

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    Among several conventional statements of ecological principle, MacArthur suggests that successional convergence of a community on a “climax” condition, if it exists, is a simple property of the community dynamics as an ergodic Markov chain. His bibliography is eclectic but idiosyncratic.

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  • MacArthur, Robert H. 1960b. On the relation between reproductive value and optimal predation. Proceedings of the National Academy of Sciences of the United States of America 46:144–145.

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    Maximum sustainable yield is achieved when a predator removes prey that have a maximum ratio of value to predator divided by reproductive value (sensu Fisher 1930, cited under Mentors) of the prey eaten. Although this criterion is theoretically interesting, it is hard to imagine a predator with the information and opportunity to realize it, and appropriate behavior by humans is often impractical.

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  • McCann, Kevin S. 2012. Food webs. Princeton, NJ: Princeton Univ. Press.

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    A far-ranging theory and account of food webs that follows the aspiration, spirit, and technique of Rosenzweig and MacArthur 1963. Of particular value for students is chapter 2 (pp. 20–46), “A primer for dynamical systems,” which introduces phase-plane analysis and shows its power and flexibility.

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  • Rooney, Neil, and Kevin S. McCann. 2012. Integrating food web diversity, structure and stability. Trends in Ecology and Evolution 27:40–46.

    DOI: 10.1016/j.tree.2011.09.001Save Citation »Export Citation » Share Citation »

    A modern analysis inspired by MacArthur 1955. Rooney and McCann make a clear distinction between what MacArthur proved and what he asserted as plausible and useful. They then discuss the kinds and strengths of interactions that can stabilize or destabilize food webs, showing that even after a half century, a close reading of MacArthur’s paper can generate novel insight.

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  • Rosenzweig, Michael, and Robert H. MacArthur. 1963. Graphical representation of stability conditions of predator-prey interactions. American Naturalist 97:209–223.

    DOI: 10.1086/282272Save Citation »Export Citation » Share Citation »

    Applies to predator-prey dynamics the same kind of analyses that MacArthur applied to the dynamics of competitors (see, e.g., Competition, Coexistence, and Species’ Packing). Phase-plane diagrams allow strong inferences from natural history boundary conditions, independent of details of underlying analytic math, indeed without specifying it.

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Relative Abundances and “Broken Stick” Models

MacArthur 1957 initiated the metaphor of a “broken stick” for the ways in which environmental resources could be divided exclusively among competing species: but he also proposed two other models, one sharing the resources, and the other assigning them as random particles. Accordingly, this was an important paper for setting multiple hypotheses speculatively representing different biological assumptions and testing to see which came closest to expressing a pattern of relative abundances in nature. MacArthur 1960 soon extended the arguments to the relative abundances of species whose populations were not constrained by current resources. Vandermeer and MacArthur 1966 discovers and corrects errors in one of the initial models, and when Pielou 1966 discovered a further error in the correction, MacArthur 1966 concluded, “Let us hope these comments do not draw attention to what is now an obsolete approach to community ecology, which should be allowed to die a natural death.” That MacArthur did no further work on patterns of relative abundance is triply ironic. First, the ultimate correction strengthened the initial conclusion of MacArthur 1957 that birds seem to divide resources rather than sharing them or taking them at random. Second, the study of patterns of relative abundances soon became a flourishing enterprise, for example when May 1986 cited, among other examples, the pattern of abundances of species of different sizes, the very example that first interested Hutchinson and MacArthur 1959. Third, the original models were “neutral theory” and the differences among them were “niche-based.” See Oxford Bibliographies in Ecology article Niche Versus Neutral Models of Community Organization by Lindsay Turnbull for evidence of a contemporary need for interaction between the neutral and the niche-based approaches.

  • Hutchinson, G. Evelyn, and Robert H. MacArthur. 1959. A theoretical ecological model of size distributions among species of animals. American Naturalist 93:117–125.

    DOI: 10.1086/282063Save Citation »Export Citation » Share Citation »

    Hutchinson and MacArthur assume that the area an individual can explore is correlated with its size, and derive a log-normal distribution of animal sizes. They test this distribution against selected data from odonates and mammals. This paper is now of more interest for setting the problem than for the way it was addressed.

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  • MacArthur, Robert H. 1957. On the relative abundance of bird species. Proceedings of the National Academy of Sciences of the United States of America 43:293–295.

    DOI: 10.1073/pnas.43.3.293Save Citation »Export Citation » Share Citation »

    In this classic paper, MacArthur proposes three alternative statistical models, analogous to three ways in which species could exploit “niche space” or resources: non-overlapping niches, continuous overlapping niches, and discrete independent niches. The model with non-overlapping, continuous niches fits local relative abundances of birds better than do the other models.

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  • MacArthur, Robert H. 1960. On the relative abundance of species. American Naturalist 94:25–36.

    DOI: 10.1086/282106Save Citation »Export Citation » Share Citation »

    “Opportunistic species,” whose populations were determined by their most recent history of reproduction, are likely to display a log-normal distribution of abundances. Conversely “equilibrium species,” whose numbers are constrained by available resources, may have varied distributions depending on their overlaps in resource use. Several groups of species are reviewed for equilibrial dynamics, with inconclusive results.

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  • MacArthur, Robert H. 1966. Note on Mrs. Pielou’s comments. Ecology 47:1074.

    DOI: 10.2307/1935661Save Citation »Export Citation » Share Citation »

    A politely petulant response to Pielou and Arnasson’s correction of Vandermeer and MacArthur’s correction of MacArthur’s original formulation of the “broken stick” model for overlapping niches.

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  • May, Robert M. 1986. The search for patterns in the balance of nature: Advances and retreats. Ecology 67.5: 1115–1126.

    DOI: 10.2307/1938668Save Citation »Export Citation » Share Citation »

    A synthesis, critique, and prospectus for the study of pattern in nature, with realistic consideration of spatial and statistical heterogeneity, temporal variation, and dynamic interactions that adapt on different time scales. May also reviews a productive resurgence in interest in patterns of relative abundance in communities, ultimately inspired by MacArthur.

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  • Pielou, E. C. 1966. Comment on a report by J. H. Vandermeer and R. H. MacArthur concerning the broken stick model of species abundance. Ecology 47:1073–1074.

    DOI: 10.2307/1935660Save Citation »Export Citation » Share Citation »

    An error in Vandermeer and MacArthur’s correction is itself corrected.

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  • Vandermeer, John, and Robert H. MacArthur. 1966. A reformulation of alternative b of the broken stick model of species abundance. Ecology 47:139–140.

    DOI: 10.2307/1935751Save Citation »Export Citation » Share Citation »

    Vandermeer and MacArthur derive a corrected version of expected abundance versus rank curves for species that divide niche space with arbitrary overlap. They predict more even abundances than are usually found in nature.

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Competition, Coexistence, and Species’ Packing

The papers in this section all address the question: “How many potentially competitive species can be packed into a given environment?” The papers form an orderly sequence in complexity, subtlety, and power: from increasing competitive effects that disfavor coexistence in Hutchinson and MacArthur 1959, to dividing discrete renewable resources by exploiting particular ratios of those resources in MacArthur and Levins 1964, to the same with continuous and non-renewable resources in MacArthur and Levins 1967, to adding an explicit evolutionary component in MacArthur 1969, to an extension to other forms of competition in MacArthur 1970, and MacArthur 1972. A curious tendency in this sequence is for each paper to concentrate so much on new points that some issues resolved in early papers are referred to only vaguely. Temporal variation in resources plays a crucial role in setting the optimal range of utilized resources, and hence setting the limit to species’ packing on a gradient, but this is not fully recognized and proved until May and MacArthur 1972. MacArthur and Levins’s classic work in this area was extended and explicitly applied to plant competition for resources by Tilman 1982, leading to a resurgence in its interest and application, as reviewed by Lindsay Turnbull in the Oxford Bibliographies in Ecology article Niche Versus Neutral Models of Community Organization.

  • Hutchinson, G. Evelyn, and Robert H. MacArthur. 1959. On the theoretical significance of aggressive neglect in interspecific competition. American Naturalist 93:133–134.

    DOI: 10.1086/282065Save Citation »Export Citation » Share Citation »

    Hutchinson and MacArthur point out that the fitness cost of aggressive behavior toward another species can be viewed as a simple addition to the competitive effect of that second species. They then discuss the consequences of enlarged competition coefficients.

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  • MacArthur, Robert H. 1969. Species packing and what interspecific competition minimizes. Proceedings of the National Academy of Sciences of the United States of America 64:1369–1371.

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    Dynamic equations for populations competing for resources that are governed by complementary equations with carrying capacities for each resource. A new competitor can invade if there is any unexploited resource; i.e., surpluses are minimized. There is no formal limit to the number of competitors that can coexist, but it is likely constrained by the number of resources and their seasonality.

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  • MacArthur, Robert H. 1970. Species packing and competitive equilibrium for many species. Theoretical Population Biology 1:1–11.

    DOI: 10.1016/0040-5809(70)90039-0Save Citation »Export Citation » Share Citation »

    Reviews and strengthens the argument in MacArthur 1969 and extends it to direct interference and competition to withstand varied predators. If competitive effects are symmetrically spread throughout the community (an assumption often violated in nature), then adding a new species usually decreases dynamic stability. A decrease in unexploited surplus resources is an evolutionary criterion, analogous to fitness, for communities.

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  • MacArthur, Robert H. 1972. Strong, or weak, interactions. Transactions of the Connecticut Academy of Arts and Sciences 44:177–188.

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    The result of this paper is that competitive species should invade communities until the overlap between them is just sufficient for the rate of competitive extinction to balance the rate of new arrivals.

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  • MacArthur, Robert H., and Richard Levins. 1964. Competition habitat selection and character displacement in a patchy environment. Proceedings of the National Academy of Sciences of the United States of America 51:1207–1210.

    DOI: 10.1073/pnas.51.6.1207Save Citation »Export Citation » Share Citation »

    An analysis of competition between species that are adapted to patchily distributed discrete and renewable resources of two types, and to proportionate mixtures of those types. The main result is that specialized species will prevail in the environment to which they are most adapted, including adaptations to particular ratios of resources, as long as those ratios remain temporally constant.

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  • MacArthur, Robert H., and Richard Levins. 1967. The limiting similarity, convergence and divergence of coexisting species. American Naturalist 101:377–385.

    DOI: 10.1086/282505Save Citation »Export Citation » Share Citation »

    Extension of the 1964 paper to continuous and non-renewable resources. A new result is that if two species are sufficiently far apart (modulo their niche breadths) on a single resource gradient, a new intermediate species can invade between them, but otherwise a new invader will either be excluded or converge toward, and compete with, one of the extant species.

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  • May, Robert M., and Robert H. MacArthur. 1972. Niche overlap as a function of environmental variability. Proceedings of the National Academy of Sciences of the United States of America 69:1109–1113.

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    Analysis of how species can be packed along a single niche gradient when the resources along that gradient are subject to temporal variation. The main result, robust over a surprisingly wide range of variation, is that species can be packed about as far apart as the standard deviation of each species’ use of resources along that gradient.

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  • Tilman, David. 1982. Resource competition and community structure. Princeton, NJ: Princeton Univ. Press.

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    An extension, application, and christening of “resource ratio theory” to resources of plants that are variably: essential, partially substitutable, or wholly substitutable. This work is now a classic for a vibrant field of current research.

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Bird Species’ Diversity

Four patterns of bird species diversity were of special interest to MacArthur: the larger number of tropical species compared to temperate, the role that taxonomic adaptation might play in that difference, the environmental determinants of local diversity, and the special circumstances of birds on islands, discussed under Island Biogeography. MacArthur 1959 reports his postdoctoral work with David Lack, interpreting differences between neo-tropical migrants and year-round residents in North America. Klopfer and MacArthur 1960 and Klopfer and MacArthur 1961 initially gathered indirect evidence that tropical niches were narrower than temperate, but MacArthur 1964 later suggested that this was due more to specialized habitat choice than to extreme specialization within a habitat, and MacArthur 1969 added that perhaps the tropics had had more time for recently evolved species to accumulate. MacArthur and MacArthur 1961 found that an important environmental determinant was the vertical distribution of foliage, and MacArthur, et al. 1966 argued that the division was finer in the tropics and coarser on islands. MacArthur 1971 reviews these and other patterns, somewhat elliptically, starting with Warbler Paper.

  • Klopfer, Peter H., and Robert H. MacArthur. 1960. Niche size and faunal diversity. American Naturalist 94:293–300.

    DOI: 10.1086/282130Save Citation »Export Citation » Share Citation »

    Compiled bird censuses from North America and Mexico are consistent with the traditional view that passerine behavior is more flexible than non-passerine, allowing the former to occupy the broader and more variable niches available in the temperate zone, while the specialized non-passerines are more at home in the smaller stable niches of the tropics.

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  • Klopfer, Peter H., and Robert H. MacArthur. 1961. On the causes of tropical species diversity: Niche overlap. American Naturalist 95:223–226.

    DOI: 10.1086/282179Save Citation »Export Citation » Share Citation »

    The bill-length ratios for species pairs that differ mainly in size in four genera of tropical birds are 1.1 or less, substantially smaller than the 1.3 that Hutchinson recorded for temperate birds. Klopfer and MacArthur suggest that this is evidence that tropical birds’ niches overlap more than those of temperate birds.

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  • MacArthur, Robert H. 1959. On the breeding distribution pattern of North American migrant-birds. Auk 76:318–325.

    DOI: 10.2307/4081809Save Citation »Export Citation » Share Citation »

    North American neotropical migrants are the largest proportion of all individual birds in Eastern deciduous forests: there is a somewhat smaller proportion in spruce-fir forests, followed by pine, the smallest proportion being in grassland and desert. Northern migrants are individually more common than residents; in the south the pattern is reversed. These patterns correlate with seasonal changes in vegetation and hence in food supply.

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  • MacArthur, Robert H. 1964. Environmental factors affecting bird species diversity. American Naturalist 98:387–397.

    DOI: 10.1086/282334Save Citation »Export Citation » Share Citation »

    Makes novel use of diversity metrics to characterize species abundances, foliage height distribution, additions of species with area sampled, and seasonal distributions. Bird species diversity is locally correlated with the distribution of foliage density among three layers: canopy trees, understory shrubs, and ground cover. Diversity increases with area sampled, augmented by spatial heterogeneity in habitat.

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  • MacArthur, Robert H. 1969. Patterns of communities in the tropics. Biological Journal of the Linnean Society 1:19–30.

    DOI: 10.1111/j.1095-8312.1969.tb01809.xSave Citation »Export Citation » Share Citation »

    Heterogeneous data are presented to argue the now-obvious point that species interact in determining their patterns of abundance and diversity. MacArthur offers a speculative model that shows how an increased rate of speciation could account for higher species diversity in tropical, compared to temperate, regions.

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  • MacArthur, Robert H. 1971. Patterns of terrestrial bird communities. In Vol. 1, Avian biology. Edited by Donald S. Farner and James R. King, 189–221. New York: Academic Press.

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    This idiosyncratic review of bird community ecology illustrates MacArthur’s theoretical insights with empirical patterns discovered or compiled by himself and close colleagues. He also notes that “Natural selection is presumably the cause of all patterns,” followed by an elegant and eloquent synopsis of two major tenets of population genetics, Fisher’s “fundamental theorem” and Wright’s “adaptive peaks” (pp. 190–193).

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  • MacArthur, Robert H., and John W. MacArthur. 1961. On bird species diversity. Ecology 42:594–598.

    DOI: 10.2307/1932254Save Citation »Export Citation » Share Citation »

    Bird species diversity is correlated linearly with foliage height diversity (evenness of foliage distribution among canopy, understory, and ground cover), with no predictive value added by plant species diversity. The raw data are tabulated for bird censuses and can be reconstructed from graphs for foliage density.

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  • MacArthur, Robert H., Harry Recher, and Martin Cody. 1966. On the relation between habitat selection and species diversity. American Naturalist 100:319–332.

    DOI: 10.1086/282425Save Citation »Export Citation » Share Citation »

    Plotting bird species diversity against vertical distribution of foliage, the authors find that using two foliage layers in Puerto Rico, and four in Central America, reduces variance and brings all data close to the same line. Bird species change per layer between habitats is steepest for tropical mainland, and lowest for Puerto Rico, suggesting both vertical and horizontal habitat selection.

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Field Techniques and Data Analysis

MacArthur was inventive in gathering and analyzing field data. Warbler Paper is always worth re-reading with this in mind. His ways of measuring vegetation density are quick and surprisingly reliable; they are described in MacArthur and MacArthur 1961; MacArthur, et al. 1962; and MacArthur and Horn 1969. They all involve projections of leaves onto a plane, and so they are usually underestimates of true leaf area per unit of ground area; but when MacArthur was in the field, he chose among the methods in such a way that the biases were uniform, and so his relative distributions of leaf area index among foliage layers and among species were accurate. MacArthur, et al. 1962 suggested a novel way of representing foliage percentages in canopy, understory, and ground cover as a point plotted within an equilateral triangle, and they proposed to use this technique to enlighten the causes of increased tropical bird species diversity. They never did, perhaps because the addition of a fourth foliage layer prohibits the simple graphical representation in a two-dimensional figure, and the analogous multivariate cluster analysis has less rhetorical appeal. MacArthur 1965 reviews measures of species diversity with applications to bird communities. Dethier and MacArthur 1964 is an early instance of MacArthur’s involvement with a manipulative experiment, augmenting the reproduction of a butterfly species in a field near Dethier’s summer home. MacArthur and MacArthur 1972 is a later experiment, notable for correctly measuring birds’ foraging preferences by testing their behavior relative to the foods of lesser preference. MacArthur’s distinction between “preference” and mere inclusion in the diet could strengthen the design of many contemporary studies of choice of habitat and diet. Finally, MacArthur and MacArthur 1974 develops a simple analysis to use captures and recaptures in mist nets to estimate populations of both resident birds and drifters.

  • Dethier, Vincent G., and Robert H. MacArthur. 1964. A field’s capacity to support a butterfly population. Nature 21:728–729.

    DOI: 10.1038/201728a0Save Citation »Export Citation » Share Citation »

    Populations of a checkerspot, Melitaea harrisii, and its food plant were monitored for eight years in patchy fields near Bluehill, Maine. One autumn the population was augmented with twenty-five times the contemporary number of local larvae; they survived well, but many emigrated to field edges, and the number of adults was not comparably increased.

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  • MacArthur, Robert H. 1965. Patterns of species diversity. Biological Reviews 40:510–533.

    DOI: 10.1111/j.1469-185X.1965.tb00815.xSave Citation »Export Citation » Share Citation »

    MacArthur reviews various metrics of species diversity, favoring the information measure H = -∑ipi log pi, where pi is the proportion of the sample composed of the ith species, because it can be modified to express differences between communities. He presents patterns of species diversity studied by himself and close colleagues, including rudiments of the theory of Island Biogeography.

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  • MacArthur, Robert H., and Henry S. Horn. 1969. Foliage profile by vertical measurements. Ecology 50:802–804.

    DOI: 10.2307/1933693Save Citation »Export Citation » Share Citation »

    An accurate but exceedingly tedious way to measure the vertical distribution of horizontal projection of leaf area, by focusing a vertically aimed single-lens-reflex camera with a gridded viewfinder and calibrated telephoto lens. The equations developed here were later used in early studies measuring foliage-height-distribution with aerial LIDAR.

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  • MacArthur, Robert H., and John W. MacArthur. 1961. On bird species diversity. Ecology 42:594–598.

    DOI: 10.2307/1932254Save Citation »Export Citation » Share Citation »

    In addition to its interpretive results, this paper describes several simple, rapid, and reliable ways to measure foliage density (leaf area index) in canopy, understory, and ground cover.

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  • MacArthur, Robert H., and Duncan MacArthur. 1972. Efficiency and preference at a bird feeder. Journal of the Arizona Academy of Science 7:3–5.

    DOI: 10.2307/40024356Save Citation »Export Citation » Share Citation »

    A cafeteria of four foods was offered to sixteen species of birds during the winter of 1969–1970 in Tucson, Arizona. Preferences and rates of ingestion were measured for each of nine species, both in the cafeteria and in separate offerings of food of lesser preference. Birds tended to prefer the foods that they ingested most rapidly.

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  • MacArthur, Robert H., and Alan T. MacArthur. 1974. On the use of mist nets for population studies of birds. Proceedings of the National Academy of Sciences of the United States of America 71:3230–3233.

    DOI: 10.1073/pnas.71.8.3230Save Citation »Export Citation » Share Citation »

    Simple equations are developed to estimate the numbers of residents and drifters. An example is given from ten 12 m × 2.6 m mist nets, run for ten days in late June and early July of 1971 and 1972 in a forest in Marlboro, Vermont. A detailed discussion describes how the natural history of individual species affects the reliability of the technique.

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  • MacArthur, Robert H., John W. MacArthur, and James Preer. 1962. On bird species diversity II: Prediction of bird censuses from habitat measurements. American Naturalist 96:167–174.

    DOI: 10.1086/282219Save Citation »Export Citation » Share Citation »

    To characterize habitat, measured proportions of vegetation in canopy, understory, and near-ground are plotted as an interior point in an equilateral triangle. Clusters of points characterize habitat choice for a species or for an individual bird. The size of the cluster represents variability of habitat structure, or the generality of habitat choice.

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A Note on Spatial Patterns

MacArthur had a knack for making rigorous analytic arguments by graphical means; he had a rhetorical flair for representing data in graphical form; and he cited, at least in his books and lectures, maps of the distribution of species and individuals at many spatial scales. Yet his conceptual contributions to the study of spatial pattern were never explicitly spatial but were rather a consideration of the equilibrial distribution of different organisms among different patches of environment. This paradox is most apparent in his work with Garfinkel, et al. 1964. Viewed from the 21st century, this paper is a quaint vignette. It sets explicitly spatial examples of a territorial bird and a tree with its immediate sphere of influence, and suggests representing the dynamics of their populations as differential equations portraying Monte Carlo statistics or Markov chain transitions. The spatial aspect is left unexploited, perhaps because of the rudimentary graphic capabilities of the accessible computers of the time. Furthermore, statistical sampling and discrete events of life history are expressed in a differential format, which is then approximated by discrete numerical calculations, masking the dynamic richness of nature. MacArthur and Pianka 1966, Levins and MacArthur 1969 (see also citations under Evolution and Genetics and Competition, Coexistence, and Species’ Packing, and discussion under Geographical Ecology [1972]), and Horn and MacArthur 1972 were all about ecology and behavior in patchy environments, and could all have profited from an explicit spatial context. Together they also show that similar analyses can inform studies at different scales of environmental heterogeneity, from ecological choice of habitat to behavioral choice of diet. Issues of scale were soon framed in explicit spatial models, particularly by Levin 1992, who credits the strong influence of MacArthur.

  • Garfinkel, David, Robert H. MacArthur, and Richard Sack. 1964. Computer simulation and analysis of simple ecological systems. Annals of the New York Academy of Sciences 115:943–951.

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    A call for numerical simulation of the dynamics of complex systems not easily addressed by analytical solutions of linear differential equations. An instructive example is developed for a two-level predator/prey system, with grass, rabbits, and fox.

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  • Horn, Henry S., and Robert H. MacArthur. 1972. Competition among fugitive species in a harlequin environment. Ecology 53:749–752.

    DOI: 10.2307/1934797Save Citation »Export Citation » Share Citation »

    Explores the dynamics of a system of two species of competitors and two kinds of patches, and conjectures equilibrial theories for the number of patches occupied by insular species, fugitive plants and invertebrates, and infesting parasites. The results are consequences of a graphical phase-plane analysis, and so are independent of details of the dynamic equations.

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  • Levin, Simon A. 1992. The problem of pattern and scale in ecology. Ecology 73.6: 1943–1967.

    DOI: 10.2307/1941447Save Citation »Export Citation » Share Citation »

    Levin’s lecture to the Ecological Society of America on receiving their MacArthur Award for his work on explicitly spatial dynamics. He shows that theoretical, empirical, and practical ecologies pose conceptual problems of representation and analysis of patterns at changing temporal and spatial scales, and he highlights some important and understudied mechanisms at one scale that produce results at another scale.

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  • Levins, Richard, and Robert H. MacArthur. 1969. An hypothesis to explain the incidence of monophagy. Ecology 50:910–911.

    DOI: 10.2307/1933709Save Citation »Export Citation » Share Citation »

    Levins and MacArthur extend Levins’s criteria for optimal habitat selection to optimal selectivity of diet. Monophagy is only favored when there is no alternative (i.e., when other foods provide no benefit) or when the best food is sufficiently better and more abundant than alternatives.

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  • MacArthur, Robert H., and Eric R. Pianka. 1966. On optimal use of a patchy environment. American Naturalist 100:603–609.

    DOI: 10.1086/282454Save Citation »Export Citation » Share Citation »

    Predators that must spend a lot of time (and energy) pursuing individual prey should specialize on only the most profitable prey, and those that spend much time searching for easily pursued prey should eat most of what they find. An analogous argument is made for habitat choice in a patchy environment.

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Island Biogeography

The landmark paper MacArthur and Wilson 1963, and its later expansion and extension in a 1967 book, explored and explained a variety of patterns of species diversity on islands and archipelagos, and inaugurated a whole field of novel theoretical, empirical, and practical research. MacArthur and Wilson 1967 stated at the outset, “We do not seriously believe that the particular formulations advanced . . . will fit for very long the exacting results of future empirical investigation. We hope instead that they will contribute to the stimulation of new forms of empirical studies, which will in turn lead to a stronger general theory” (p. v). An indication that their hope was realized is the range of work presented and reviewed by Losos and Ricklefs 2010, though the result so far is several stronger particular theories rather than a single general theory. Of special interest is the “neutral” theory of Hubbell 2001, which starts with explicit homage to MacArthur’s work, and, without reference to “niches,” develops an impressive range of quantitative patterns that fit empirical data on geographical scales from local communities to comparisons among continents. The work of Hubbell and his colleagues has generated a flourishing field of innovation and controversy, reviewed in the Oxford Bibliographies in Ecology article Niche Versus Neutral Models of Community Organization by Lindsay Turnbull. MacArthur and Wilson 1963 is also the most cited source for the contrast of “r and K selection” (p. 149). This distinction, between species whose population dynamics are dominated by episodes of reproduction and dispersal, and those whose dynamics are dominated by competitive interactions with local neighbors, is now considered simplistic, but it has a long history of enlightening application (see Oxford Bibliographies in Ecology article Reproductive Allocation in Animals by James Gilbert). Geographical Ecology (1972); MacArthur, et al. 1972; and MacArthur, et al. 1973 returned to a co-emphasis on natural history as well as statistics of colonization and persistence in their interpretations of island avifaunas. In doing so, MacArthur converged on a view long held by his postdoctoral mentor, Lack 1976. Finally, Powledge 2003 argues that even MacArthur and Wilson’s initial ideas about island biogeography, and the metaphors that they engendered, are important to policymakers and the general public. The literature of island biogeography, especially of its application to conservation and critiques thereof, is so voluminous that a separate bibliography is needed to do it justice.

  • Hubbell, Stephen P. 2001. The unified neutral theory of biodiversity and biogeography. Princeton, NJ: Princeton Univ. Press.

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    The definitive development of a theory of relative abundances, species’ diversities, and their geographical patterns that is largely independent of the natural histories of the component species.

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  • Lack, David. 1976. Island biology, illustrated by the land birds of Jamaica. Berkeley: Univ. of California Press.

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    With encyclopedic descriptions and tabulations of natural history, Lack argues that remote islands may have fewer resources and so may be packed with fewer species, rather than having fewer species because there are fewer colonists, as the theory of MacArthur and Wilson 1967, cited under Island Biogeography, implies. In a poignant preface (pp. x–xii), Lack, who was also facing terminal cancer, regrets that neither he nor MacArthur had the time to discuss the convergence in their views, embodied in MacArthur 1972.

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  • Losos, Jonathan B., and Robert E. Ricklefs, eds. 2010. The theory of island biogeography revisited. Princeton, NJ: Princeton Univ. Press.

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    This twenty-six-authored volume is the most extensive sample yet of the bulk, variety, and high-quality research that has been inspired by, developed from, and even proposed to replace MacArthur and Wilson’s theory of island biogeography.

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  • MacArthur, Robert H., Jared M. Diamond, and James R. Karr. 1972. Density compensation in island faunas. Ecology 53:330–342.

    DOI: 10.2307/1934090Save Citation »Export Citation » Share Citation »

    An analysis of mist-net captures of birds on islands of the Pearl Archipelago in the Gulf of Panama. The total population of each species is estimated as the X-intercept of a linear plot of rate of capture against the number of birds caught so far. Island species have higher densities than in comparable mainland habitats, and presumably occupy broader niches.

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  • MacArthur, Robert H., John MacArthur, Duncan MacArthur, and Alan MacArthur. 1973. The effect of island area on population densities. Ecology 54:657–658.

    DOI: 10.2307/1935357Save Citation »Export Citation » Share Citation »

    The plots described in MacArthur, et al. 1972 are similar for two islands within the Pearl Archipelago of Panama that differ in area by a factor of seven (Isla de Cañas at 500 hectares and Isla de Puercos at 70).

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  • MacArthur, Robert H., and Edward O. Wilson. 1963. An equilibrium theory of insular zoogeography. Evolution 17:373–387.

    DOI: 10.2307/2407089Save Citation »Export Citation » Share Citation »

    Developing a theory that the number of species on an island should reach an equilibrium at which immigrations of new species just balance extinctions of old, the authors explain how species number increases with island area. They derive formulas for curves of immigration and extinction versus number of resident species. Using the theory, they draw insights from exemplary island avifaunas.

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  • MacArthur, Robert H., and Edward O. Wilson. 1967. The theory of island biogeography. Princeton, NJ: Princeton Univ. Press.

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    Review and extension of topics in the 1963 paper. Probabilities of colonization and establishment are derived from demographic parameters. Persistence of competitors is related to evolving use of resources. Effects of dispersal and “stepping stones” on archipelagos are developed for random and directed dispersal. Plant and animal examples juxtapose theory, natural history, and secular histories of different island systems.

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  • Powledge, Fred. 2003. Island biogeography’s lasting impact. BioScience 53.11: 1032–1038.

    DOI: 10.1641/0006-3568(2003)053[1032:IBLI]2.0.CO;2Save Citation »Export Citation » Share Citation »

    A brief, engaging, and convincing account of MacArthur and Wilson’s original theory of island biogeography, its transformations, and its continuing impact.

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Contemplative Bookends

MacArthur wrote two books for a general student audience, one in mid-career with Joseph Connell, Biology of Populations (1966 with Joseph Connell), and the other after he had been diagnosed with terminal cancer, Geographical Ecology (1972). The book with Connell helped to define the field of population ecology as a suitable course of study for undergraduate and graduate students, and the 1972 book was both a retrospective on MacArthur’s career and a hopeful prospectus for much of population ecology. It is particularly instructive to compare the two books, to see both the changes in his perspective, and the degree to which he fulfilled his own hopes. Both books have a greater balance of outright natural history than the format of his published papers allowed, and the 1972 book explicitly expounds his philosophy of the crucial role of natural history in the science of ecology. Furthermore, both books develop ideas in a broader context than do MacArthur’s papers. Accordingly the books are full of insights that are still fresh today.

The Biology of Populations (1966 with Joseph Connell)

MacArthur and Connell 1966 was the third in a series of books (following the Biology of Cells and the Biology of Organisms) instigated and published by John Wiley, and intended as texts for a college biology course for students who already had solid high school backgrounds in biology, mathematics, and the physical sciences. MacArthur and Connell adopted a highly conceptual outline, emphasizing broad patterns; but outright facts of natural history are as prominent as graphs and equations. Much of the material can also be found in contemporary intermediate college textbooks of ecology and evolution, but several topics are developed in a way that was unusual for the time. In particular, the global distribution of major biomes and their biological properties are developed as a predictive scheme (pp. 14–38), starting with the physics of climatology as the basis of bioclimatic diagrams of vegetation distribution, and discussing how that distribution is modified by biotic feedbacks. This account could be read with profit by contemporary ecologists who are developing “novel predictive rather than phenomenological models” of biome distribution to anticipate effects of unprecedented anthropogenic climate change. Another example that is still worth contemporary attention is the extraordinarily clear and compact précis of classical population genetics (pp. 80–94). Finally, the presentation of the theory of predator-prey and competitive interactions (pp. 152–163) is a very clear and elementary development of an advanced technique that still generates new ideas in contemporary ecology, namely qualitative inference from generalized graphs of population-growth-isoclines in population-size-phase-space (see also McCann 2012, cited under Ecosystem Structure and Function).

  • MacArthur, Robert H., and Joseph W. Connell. 1966. The biology of populations. New York: Wiley.

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    An early defining textbook for the field of “population biology,” with passages that still provide fresh insights, especially: the climatological interpretation of biomes (pp. 14–38), classical population genetics (pp. 80–94), and graphical insights into predator-prey and competitive interactions (pp. 152–163).

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Geographical Ecology (1972)

In his preface, MacArthur 1972 says, “In this book I have written about my favorite part of ecology, the part that combines the adventure of field work in varied places with the discipline of making non-trivial theory” (p. xi). The book summarizes and often extends most of the major themes of his research. Particular extensions include a very compact logical development of global climatology from physical first principles (pp. 3–19; see MacArthur and Connell 1966, cited under Biology of Populations (1966 with Joseph Connell)), and a more generalized and realistic development of the theory of optimal foraging, superseding not only MacArthur’s initial work with Levins and with Pianka but also much of the subsequent literature that seems unaware of this account (pp. 59–69, especially p. 62; see, for example, Oxford Bibliographies in Ecology article Optimal Foraging by David Stephens). His calculation of extinction probability (pp. 121–126; see also MacArthur and Wilson 1967, cited under Island Biogeography) also deserves wider citation than it gets. Throughout the book, natural history and secular history come to the fore, especially in the chapters on island patterns (pp. 79–120) and the role of history (pp. 239–251). The book’s enduring impact is shown by its frequent citation as “foundational” in many of the other Oxford Bibliographies in Ecology articles.

  • MacArthur, Robert H. 1972. Geographical ecology: Patterns in the distribution of species. New York: Harper and Row.

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    A summary of much of MacArthur’s conceptual work, with frequent reference to the natural history that inspired it, and still-enlightening discussions of: geographical patterns of climate (pp. 3–19), optimal foraging theory (pp. 59–69), and extinction probability estimated from vital statistics (pp. 121–126).

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