• MArk V. Lomolino

    1. Department of Environmental and Forest Biology, SUNY College of Environmental Science and Forestry, Syracuse, New York, USA E-mail:
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      Mark V. Lomolino's research and teaching focus on biogeography and conservation of biological diversity. He received the American Society of Mammalogist Award, and serves on the editorial advisory board for Biological Conservation, is an Editor of Global Ecology and Biogeography: A Journal of Macroecology, and is coauthor with James H. Brown of Biogeography (published by Sinauer Associates).

`…there are areas too small, and areas too large, to show clear diversity patterns…' R. H. MacArthur (1972: 191)

Comment on M. Williamson, K.J. Gaston, and W.M. Lonsdale (2001) The species–area relationship does not have an asymptote. Journal of Biogeography, 28, 827–830.

Inertia is a fundamental property of nature and, in a very real sense, an important force in the development of science. Even during periods of conceptual stasis, inertial resistance to paradigmatic shifts temper the development of a discipline, resisting careless adoption of just any new and novel theory that challenges the champion. Eventually, however, our understanding of the complexity of nature stretches far beyond the elastic limits of the long-standing paradigm. At such times, inertial resistance to alternative and unconventional views may impede the advance of scientific disciplines, sometimes for decades. The case of such delayed scientific development that I am most familiar with is that of the equilibrium theory of island biogeography. Eugene Gordon Munroe's early articulation of the equilibrium theory in 1948 was ignored by his colleagues, yet it was conceptually equivalent to that proposed and finally accepted as the paradigm of the field of island biogeography in the late 1960s (see Munroe, 1948, 1953; MacArthur & Wilson, 1963, 1967; Brown & Lomolino, 1989). Central to the acceptance of the equilibrium theory of island biogeography was the paradigmatic shift from the view of island biotas as static assemblages of species, to one where insular communities are viewed as dynamic in time—varying in their species composition due to recurrent immigrations and extinctions. It was likely more than just coincidence that it was also in the late 1960s that scientists finally accepted the theory of continental drift and plate tectonics, which holds that the earth itself is dynamic. The theory was first formerly proposed by Alfred Wegener and F. B. Taylor in the early 1900s (Taylor, 1910; Wegener, 1912), but was resisted and often ridiculed by most `respectable' scientists until the accumulated burden of information on the dynamics of earth and its biotas finally snapped the long-standing doctrine of geological stasis; but not until some five decades after Taylor and Wegener published their challenges to the static theory, and centuries after Abraham Ortelius (1596) first commented on the fit of the continents.

These lessons in delayed development of scientific theories characterizes the dynamic tension between accepted, theoretical constructs and our ever-expanding appreciation for the complexity of nature. The topic of Williamson et al.'s (2001) critique of my article (Lomolino, 2000a) on the `protean' and possible sigmoidal nature of the species–area relationship may not be as monumental as the paradigm shifts discussed above, but some of the same lessons may apply. In the 1920s, Arrhenius (1921) and Gleason (1922) proposed alternative mathematical formulae to describe and analyse the species–area relationship—both depicting curves with positive, albeit attenuating slopes. In 1962, Preston canonized Arrhenius' log–log, or `power' model and its exponent `z' as the formula of choice for most biogeographers. Yet, in his long and rich double-manuscript on the species–area relationship (Preston, 1962a,b), he discussed an alternative form of the species–area relationship—the sigmoidal curve (1962a: 187, 214–215). Later, in their seminal monograph on island biogeography, MacArthur & Wilson (1967: 32) referred to the peculiarities of biotas on small islands such as the plants of Kapingamarangi Atoll, Polynesia (Niering, 1963) and ants of Micronesia (Wilson & Taylor, 1967). For such small islands, species-richness seemed to vary independently of island area—a pattern inconsistent with the conventional mathematical models (power or semi-log) of the species–area relationship. These conventional models also do not allow for the possible contribution of in situ (within island) speciation to insular biotas which, as Munroe suggested in 1953, should contribute to a secondary increase in the slope of the species–area relationship on very large islands. As Robert MacArthur concluded in his final monograph, Geographical Ecology (1972: 191), `The general conclusion of this section [on environmental scale] is that there are areas too small, and areas too large, to show clear diversity patterns, but that for the proper intermediate census area, the patterns are clear.' Thus, my suggestion that the species–area relationship may be sigmoidal (Lomolino & Weiser, 2001; fig. 1), and therefore fundamentally different from the models most of us have been using for decades, may still appear heretical, but not as original as it may have first seemed. Again quoting Preston (1962: 215), `the possibility that such [sigmoidal] curves may exist can hardly be disputed on theoretical grounds; how often they occur in practice is a matter for observation.' Recently, Losos & Schluter (2000), and Crawley & Harral (2001) have provided some very relevant `observations' on the potential sigmoidal nature of the species–area relationship—adding their voices to the epistemological rumblings (see also Meadows, 2001). Michael Weiser and I have followed up my challenges to the existing paradigm (Lomolino, 2000a, b, c; Lomolino, 2001) with a review and analysis of the form of the species–area relationship in just over 100 insular biotas. Sigmoidal species–area relationships appear to be relatively common, and it seems that alternative analytical models can be used to investigate fundamentally different components of the species–area relationship (see Lomolino & Weiser, 2001).

Williamson et al. (2001) raise some interesting questions, but their view appears to be based largely on visual inspection of three graphs and their assertions that (i) the species–area relationship does not have an asymptotic or limited richness, and (ii) that there is no small island effect. First, once the species pool is defined, the maximum number of species can not exceed this value, whether we call it an asymptote or boundary. Perhaps this is just a semantic difference, and one that appears much more subtle than my challenge to assess the importance of the small island effect, the potential sigmoidal nature of the species–area relationship, and a possible secondary increase in the species–area curve where in situ speciation may become relevant (Lomolino & Weiser, 2001: fig. 1; see also Heaney, 2000). That is, it appears that the key distinction between conventional models and the newer alternatives (Lomolino, 2000a, b, c; Losos & Schluter, 2000; Crawley & Harral, 2001; Lomolino, 2001) is that the latter include scale-dependent phase shifts. Along gradients of increasing area, as different structuring forces come into play and take prominence, the nature of the species–area curve changes. The `thresholds', or island sizes at which these phase shifts occur, have biological and practical relevance and therefore should receive increasing attention from ecologists and biogeographers.

These and other responses to my calls for alternative models to investigate this very fundamental pattern, and criticisms of related views presented in the above-mentioned papers, are to be expected and embraced because they form the fabric of the filters that control and direct the development of our science. In this particular case, however, I believe it is time to modify the traditional, paradigmatic models – the power and semi-log models – in favour of a model which includes a means to test for potential, sigmoidal patterns and phase shifts. As discussed in recent papers (Lomolino, 2000a, b, c; Lomolino & Weiser, 2001), the primary advantage of these alternative models is that they provide an objective means to study the scale-dependent forces structuring insular communities—what MacArthur (1972: 186) termed the `hierarchical structure' of the `real environment.' These scale-dependent forces include hurricanes and other disturbances that may strongly influence community structure especially on the smaller islands, to more deterministic, ecological factors and processes associated with habitat diversity, carrying capacity and immigration/extinction dynamics on islands of intermediate size, and finally to speciation on islands large enough to provide the geographical isolation (within islands) necessary for evolutionary divergence.

As we have shown (Lomolino & Weiser, 2001), `alternative' models for the species–area relationship can include these thresholds while retaining basic elements of the conventional models (semi-log and power models). Thus, in addition to studying z-values and other parameters of the traditional models, the modified models can shed light on some important questions. How should the first threshold (i.e. the range of the small island effect) and the second threshold (marking islands where speciation becomes a prominent structuring force) vary among biotas or among types of archipelagoes? What proportion of islands fall within the range of the small island effect, where area is a poor predictor of diversity, and how much does richness vary within this range? For all its early heuristic value and long-standing tenure as the reigning, paradigmatic model, the power model provides no means to examine such questions. To the extent to which we believe these are important questions, we should continue to search for alternative approaches for studying one of ecology's most fundamental patterns (see also Brown & Lomolino, 2000; Heaney, 2000; Whittaker, 2000). If these and other challenges to the existing paradigm prove fruitless, so be it, but continued adherence to a traditional paradigm should be based on repeated challenges and re-evaluation, and not on inertia and acceptance by default.


Michael D. Weiser provided useful comments on an earlier version of this manuscript. I thank the members of the Foundations of Biogeography Working Group, National Center for Ecological Analysis and Synthesis (USA) for their stimulating and provocative discussion of some of the ideas presented here.


  1. BIOSKETCHMark V. Lomolino's research and teaching focus on biogeography and conservation of biological diversity. He received the American Society of Mammalogist Award, and serves on the editorial advisory board for Biological Conservation, is an Editor of Global Ecology and Biogeography: A Journal of Macroecology, and is coauthor with James H. Brown of Biogeography (published by Sinauer Associates).