The Ecological and Evolutionary Dynamics of Species' Borders

Robert D. Holt
Department of Systematics and Ecology
Museum of Natural History
University of Kansas
Lawrence, KS 66045


All species are distributed in space -- but within limits. Understanding the factors determining range limits is a central concern in both ecology (Lawton et al. 1994, e.g., the study of invasions, Lodge 1993) and evolutionary biology (e.g., faunal responses to environmental fluctuations, Graham et al. 1996). There is rapidly growing interest in the ecology and evolution of species' borders (e.g., Stevens and Fox 1991, Hoffmann and Blows 1994, Gaston 1996, Kirkpatrick and Barton, in press, Holt and Gomulkiewicz, in press). This working group will focus on theoretical studies of species' borders, the integration of models with analyses of empirical patterns, and the blending of ecological and evolutionary perspectives.

Problem Statement

Range limits arise from the interplay of three basic features of the world: i) species experience spatial variability in the demographic parameters of birth and death, such that in some environments populations cannot deterministically persist,ii) environments are spatially correlated, for instance varying systematically along major gradients, and iii) organisms disperse to varying degrees. The factors causing (i) may be abiotic or biotic (say, spatial variation in predator abundance, e.g. Lawton and Woodroffe 1991). A full understanding of species' borders requires placing population dynamics in a broad community perspective. Moreover, if spatial variation in the environment implies spatial variation in natural selection, genetic variation and evolution (e.g., gene flow into marginal populations) can influence the dynamics of species' borders.

There are many significant unanswered questions regarding species borders. Here are some fruitful directions for the proposed working group.

Pattern description: With the recent explosion in geographical information systems, computerization of systematic databases, and maturation of national biotic surveys, there is an increasing need for quantitative tools to characterize species' distributions and integrate such data with ecological theory. At times (e.g., the tropics) available data will be merely presence/absence; or one may have estimates of local abundance across ranges through time. Optimal descriptors of range limits may be constrained by the datasets available. For instance, Maurer (1994) has argued that macroscopic, statistical descriptors of ranges are needed, given the scant information usually available about underlying processes. He has shown using data for North American birds that geographical range boundaries are discontinuous at multiple scales, and that fractal dimension provides interpretable descriptors of perimeters shapes. Is the fractal dimension of a range insensitive to data type, i.e., presence/absence vs. abundance? What are characteristic "shapes" of species borders, and do they vary among species in interpretable ways (e.g., by trophic level; dispersal mode; recent invaders vs. stable residents vs. species in decline)? Are sharp borders associated with obvious environmental thresholds or strong gradients (e.g., transitions between soil types, presence of competitors)? What is the temporal stability of species borders for non-invasive species? Several members of the working group have access to datasets permitting such questions to be addressed consistently across systems.

Brown (1984, Enquist et al. 1995, Brown et al. 1995) hypothesizes several patterns: local abundances are variable near range centers, but predictably low near range edges; some species fit roughly normal distributions, whereas others are strongly leptokurtic, with a long 'tail' of low-density populations. The generalities of these patterns is unknown (Caughley et al. 1988, Gaston 1990). Carter and Prince (1987) present examples where species become more restricted in the number of sites occupied near range edges, with no effect on within-site abundance. One aim of the working group will be to assess the robustness of these patterns across taxa and biomes.

Population dynamics of species borders: Because divergent patterns in the distribution-abundance relation can reflect different ecological processes, techniques are needed for describing spatial patterns in abundance near range limits which are both statistically robust and linked to dynamical models. How do species borders arise from local and regional dynamical processes? Are there useful spatial 'signatures' of dynamical processes? For instance, a species' border arising from colonization-extinction dynamics in a patchwork might be more fractal than one resulting from smooth gradient-like variation. The working group will utilize two broad classes of population dynamic models: reaction-diffusion models (appropriate to continuous spatial variation), and metapopulation and discrete-habitat models (appropriate to mosaic landscapes).

Consider a simple model for local dynamics of species i along a smooth gradient, x: dNi(x)/dt = [ri(x) - di(x)Ni(x) -mi(x,t)]Ni(x), where r= intrinsic growth rate (at x), d= the strength of density-dependence, and m= a time-varying factor of density-independent mortality (e.g., disturbances). Conditional on persistence, the long-term average abundance for species i at x is = [ri(x) - ]/di. A species may be rare because: i) it is near the edge of its fundamental niche (low r), ii) experiences strong density-dependence (large d), or iii) suffers frequent, severe disturbance (high ). The working group will examine how these disparate reasons for rarity might result in different time-series patterns in marginal populations.

To first-order, parametric variation with x in such models determines the shape of the species distribution. More detailed models (e.g., with Allee effects, or competitors and predators) provide mechanisms for specific patterns, e.g. sharp species borders. Dispersal can modify the border shape. Incorporating dispersal leads to the framework of reaction-diffusion and integrodifferential models. There is a large literature on such models, but to my knowledge there has not been a systematic attempt to relate such models to empirical patterns in species' borders (except transient borders during invasions, e.g., Veit and Lewis, in press). Moreover, this modelling framework may be inappropriate for mosaic landscapes. If suitable habitats are patches in an unsuitable matrix, and local patches experience extinctions and colonizations, range limits may arise if habitat patches are sparse. Let p(x) be the fraction of patches occupied at x along a gradient, c(x) and e(x) local colonization and extinction rates, and h(x) the fraction of the local landscape suitable for the species. The standard metapopulation model (e.g., Hanski 1996) is dp(x)/dt = c(x)p(x)(h(x)-p(x)) - e(x)p(x). The species is absent along the gradient whereever h(x) < e(x)/c(x). A species border may arise because of variation in landscape structure (measured by h), even without spatial variation in within-patch properties (encapsulated by e and c). Making dispersal spatially explicit leads to the framework of discrete-habitat landscape models (e.g., source-sink models, Pulliam 1996, Holt 1993). As with reaction-diffusion theory, there is a large body of theory, which to date has only tangentially addressed the species' border issue.

This working group will synthesize existing theory, develop new theory, and apply these theoretical structures to observed patterns. It will examine the implications of models of both single-species and interacting species for patterns at species' borders.

Evolutionary dynamics of species borders: There are compelling reasons to integrate ecological and evolutionary perspectives on species borders. Species are not genetically uniform; some species respond evolutionarily to environmental change over ecological time-scales (e.g., the evolution of resistance to pesticides, Alstad and Andow 1995). Population dynamics provides the templet for evolutionary dynamics occurs, whereas evolutionary dynamics sculpts the parameters driving the population dynamics; ignoring this interplay is likely to lead to misleading results at species borders (e.g., see Holt 1983). A species' border arising because of smooth changes along a continuous environmental gradient likely experiences different selective dynamics than one arising from metapopulation processes (Pease et al 1989, Harrison and Hastings 1996).

Dispersal may be a two-edged sword in defining edge limits. Over ecological time scales, dispersal permits species to colonize empty habitats and smooths spatial variability in abundance. Over evolutionary time scales, however, dispersal from central into marginal populations may hamper local adaptation, preventing range expansion (Antonovics 1976, Kirkpatrick and Barton in press, Holt and Gomulkiewicz in press). In a changing environment, dispersal permits species to track environments to which it is already well-adapted, without marked evolution.. Species' range sizes are conservative within at least some large phylogenetic clades (Ricklefs 1989). Some mechanisms generating species' borders may be particularly prone to such conservatism. One fruit of the working group will be a better understanding of circumstances leading to evolutionary stability (vs. lability) of species borders, and the time-scale of evolutionary changes in borders.

Rationale for NCEAS Support

The working group includes empiricists with large cross-species datasets; statisticians developing methods to estimate range limits and spatial relations; experimentalists focusing on particular species' limits; mathematical ecologists expert in reaction-diffusion and patch dynamic models; and evolutionary biologists concerned with evolution along gradients and in marginal populations. Identification of empirical, cross-species patterns in distributional limits is a valuable synthetic activity in its own right. Such synthesis can also highlight profitable directions for theory development. Conversely, theoretical studies can assess proposed metrics for describing species borders. Thus, the activities of the working group address the broad focus of NCEAS on analysis and synthesis. One of the stated areas of emphasis is spatiotemporal dynamics. This working group will focus on spatiotemporal dynamics of species' borders.

Proposed Activities and Timetable

I have assembled a tentative participant list (Table 1). Eleven persons have already been contacted; each has expressed a keen interest in participating. I would like to invite several other participants, up to say 15, and provide a list of possible candidates. There are doubtless individuals whom I have not thought of, who would be valuable participants. I will complete the roster after receiving feedback from the NCEAS Science Advisory Board, and input from individuals already invited.

I request support for one postdoctoral fellow. Mathematical modelling of species range limits, extending existing theory in collaboration with workshop participants, could easily occupy a competent mathematical biologist for two years. Moreover, having a resident post-doc should facilitate cross-linkages with other Center activites. Were this proposal funded, I would like to work with the SAB and Director during the search.

I propose that this working group assemble first during January-March 1997, for roughly 5 days. The first two days will be a symposium where for each area outlined above (pattern analysis, population dynamics, evolutionary dynamics), speakers will provide a critical overview of the current state of understanding of species borders. This will highlight lacunae in theoretical and empirical studies. We will then divide into sub-groups (with overlapping membership), to articulate profitable directions for collaboration. The final day, we will meet as a "committee of the whole" to lay out the agenda for the following two years. During this period, subgroups will meet at Santa Barbara to execute the research agenda. I expect about half the initial participants would spend considerable time at the Center, scattered over this period. Finally, toward the end of year 2 the entire working group will meet.

Anticipated Results and Beneficiaries

Some expected results are sketched in the paragraphs above defining the problem. It should be stressed that a deeper understanding of the dynamics of species borders is key to many applied ecological problems. For instance, in attempting to predict the biotic effects of global climate change, a standard protocol is to correlate a species' distribution with environmental factors, then to use these correlations to map out likely distributional shifts driven by changing climate (e.g., Davis and Zabinski 1992). Although this is a sensible first step, the robustness of this protocol rests on implicit assumptions about the forces producing the borders in the first place, and the assumed absence of evolutionary responses. One aim of the working group may be to arrive at a clearer understanding of when it is safe to ignore evolutionary responses when modelling distributional shifts.

With respect to specific products, I hope to organize a symposium at the 1998 ESA meetings, with the proceedings as a Special Feature in the journal Ecology. I believe that enough exciting new results will emerge to warrant an edited volume, too. An intangible but important intellectual product which I hope this working group will achieve is a greater integration of ecological and evolutionary perspectives in addressing spatiotemporal dynamics.

Required Resources

Item Year 1 Year 2
Travel (no. of travellers)U.S. 20 20
Foreign 4 4
Expenses (no. of researcher- days) 140 140
Sabbatical support 0 0
Post-doc requested Yes Yes

Literature Cited

Alstad, D.N. and D.A. Andow. 1995. Managing the evolution of insect resistance to transgenic plants. Science 268:1894-1896.

Antonovics, J. 1976. The nature of limits to natural selection. Annals of the Missouri Botanical Gardens 63:224-247.

Brown, J.H. 1984. On the relationship between abundance and distribution of species. Am. Nat. 124:255-279.

Brown, J. H., D.W. Mehlman and G.C. Stevens. 1995. Spatial variation in abundance. Ecology 76:2028-2043.

Carter, R.N. and S.D. Prince. 1987. Distribution limits from a demographic viewpoint. Symposia of the British Ecological Society 28:165-184.

Caughley, G. D. Grice, R. Barker and B. Brown. 1988. The edge of the range. J. of Anim. Ecol. 57:771-785.

Davis, M.G. and C. Zabinski. 1992. Changes in geographical range resulting from greenhouse warming: effects on biodiversity in forests. pp. 297-208 in R.L. Peters and T.E. Lovejoy, eds. Global Warming and Biological Diversity. Yale University Press.

Enquist, B.J., M.A. Jordan and J.H. Brown. 1995. Connections between ecology, biogeography, and paleobiology: relationship between local abundance and geographic distribution in fossil and recent molluscs. Evolutionary Ecology 9:586-604.

Gaston, K.J. 1990. Patterns in the geographical ranges of species. Biol. Rev. 65:105-129.

Gaston, K.J. 1996. Species-range-size distributions: patterns, mechanisms and implications. TREE 11:197-200.

Graham, R.W. and 19 co-authors. 1996. Spatial response of mammals to late quaternary environmental fluctuations. Science 272:1601-1606.

Hanski, I. 1996. Metapopulation ecology. pp. 13-44 in O.E. Rhodes, R.K. Chesser and M.H. Smith, eds. Population Dynamics in Ecological Space and Time. University of Chicago Press.

Harrison, S. and A. Hastings. 1996. Genetic and evolutionary consequences of metapopulation structure. TREE 11:180-183.

Hoffmann, A.A. and M.W. Blows. 1994. Species borders: ecological and evolutionary perspectives. TREE 9:223-227.

Holt, R.D. 1983. Models for peripheral populations: the role of immigration. pp. 25-32 in H.I. Freedman and C. Strobeck, eds. Population Biology. Springer-Verlag, Berlin.

Holt, R.D. 1993. Ecology at the mesoscale: the influence of regional processes on local communities. pp. 77-88 in R.E. Ricklefs and D. Schluter, eds. Species Diversity in Ecological Communities. University of Chicago Press.

Holt, R.D. and R. Gomulkiewicz. in press. How does immigration influence local adaptation? A re-examination of a familiar paradigm. Am. Nat.

Holt, R.D., J. Lawton, T. Blackburn and K. Gaston. in press. On the relation between distribution and abundance: Back to basics. Oikos.

Huntley, B. and T. Webb, III. 1989. Migration: species' response to climatic variations caused by changes in the earth's orbit. J. of Biogeography 16:5-19.

Kirkpatrick, M. and N. Barton. in press. Evolution of a species' range. Am. Nat.

Lawton, J.H. and G.L. Woodroffe. 1991. Habitat and distribution of water volew: why are there gaps in a species' range? J. of Anim. Ecol. 60:79-91.

Lawton, J.H., S. Nee, A.J. Letcher and P.H. Harvey. 1994. Animal distributions: patterns and processes. pp. 41-58 in P.J. Edwards, R.M. May and N.R. Webb, eds., Large-scale Ecology and Conservation Biology. Blackwell, London.

Lewis, M.A. and P. Kareiva. 1991. Allee dynamics and the spread of invading organisms. Theor. Pop. Biol. 43:141-158.

Lodge, D.M. 1993. Species invasions and deletions: community effects and responses to climate and habitat change. pp. 367-387 in P.M. Kareiva, J.G. Kingsolver, and R.B. Huey, eds. Biotic Interactions and Global Change. Sinauer, Sunderland, MA.

Lynch, M. and R. Lande. 1993. Evolution and extinction in response to environmental change. pp. 234-250 in P.M. Kareiva, J.G. Kingsolver, and R.B. Huey, eds. Biotic Interactions and Global Change. Sinauer, Sunderland, MA.

Maurer, B.A. 1994. Geographical Population Analysis: Tools for the Analysis of Biodiversity. Blackwell, London.

Parmesan, C. in press. Climate effects on species' range. Nature.

Pease, C.M., R. Lande and J.J. Bull. 1989. A model of population growth, dispersal and evolutoin in a changing environment. Ecology 70:1657-1664.

Pulliam, R. 1996. Source and sinks: empirical evidence and population consequences, pp. 45-70 in O.E. Rhodes, R.K. Chesser and M.H. Smith, eds. Population Dynamics in Ecological Space and Time. University of Chicago Press.

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Veit, R.R. and M.A. Lewis. in press. Dispersal, population growth, and the Allee effect; dynamics of the House Finch invasion of eastern North America. Am. Nat.

Table 1. Working group participants
(the following have been contacted and have expressed a strong interest in participation)
Tim Blackburn (Centre for Population Biology, UK) Distributional ecology, particularly birds (access to databases for many taxa).
Ted Case (UC, Davis) Community assembly, interspecific competition, island-mainland comparisions
Steve Gaines (UC, Santa Barbara) Marine invertebrate range limits; statistical ecology
Richard Gomulkiewicz (Washington State University) Quantitative genetics, evolutionary implications of population dynamics
Robert Holt (University of Kansas) Community ecology, patch dynamics, predation, niche conservatism, source-sink dynamics
Mark Kirkpatrick (University of Texas, Austin) quantitative genetics, range evolution, reaction-diffusion models
Russell Lande (University of Oregon) Evolutionary genetics, evolution and extinction in changing environments, diffusion models
John Lawton (Centre for Population Biology, UK) Community ecology, distributional patterns, insect population dynamics, conservation
Mark Lewis (University of Utah) Mathematical ecology, spatial pattern formation, reaction-diffusion models
Brian Maurer (Brigham Young University) Distributional ecology, avian ecology, statistical descriptors of range, macroecology
Mark McPeek (Dartmouth College) Experimental community ecology; evolution of habitat specialization; aquatic insect biogeography
Camille Parmesan (NCEAS Fellow) Distributional ecology of butterflies, evolution of host specialization

Other potential participants (not specifically contacted; however, past conversations, correspondence, and publications suggest a strong interest in the working group topic)
Michael Austin (CSIRO, Australia) statistical models for species distributions; sampling methods in range studies
Nick Barton (Edinburgh University, Scotland) Evolutionary genetics, hybrid zones, clinal variation
James Brown (University of New Mexico) Community ecology, macroecology
Paula Dias (CNRS, Montpelier, France) Empirical studies of source-sink dynamics, gene flow- selection balance
Marie Josee Fortin (Canada) Spatial statistics, gradient analyses
Ilkka Hanski (University of Helsinki, Finland) Metapopulation dynamics, interspecific interactions
Ary Hoffmann (La Trobe, University) Genetics and adaptation in marginal vs. central populations of Drosophila
Tad Kawecki (University of Maryland) Adaptive evolution in source-sink environments
Richard Lenski (Michigan State University) Experimental studies of niche evolution; microbial ecology
Maureen Stanton (UC, Davis) Empirical studies of source-sink dynamics in plants
George Stevens (University of New Mexico) Causes of treeline; geographical patterns in species range sizes
Michael Whitlock (University of British Columbia) metapopulation genetics Last updated 05/13/96.