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Journalof Animal Ecology1997, 66, 579-601 Interspecificabundance-rangesize relationships:an appraisalof mechanisms KEVIN J. GASTON*t, TIM M. BLACKBURN: and JOHN H. LAWTON: tDepartmentof AnimalandPlantSciences,Universityof Sheffield,SheffieldSIO2TN, UK;andtNERC Centre for PopulationBiology,ImperialCollege,SilwoodPark,Ascot,BerkshireSL5 7PY, UK Summary 1. Positive relationships between the local abundance and the range size of the species in a taxonomic assemblage are very general. 2. Explanations for these relationships typically focus on two mechanisms, based on differencesin the niche breadths of species, or metapopulation dynamics. Others have, however, also been suggested. 3. Here we identify and clarify all the principal mechanisms proposed to explain positive interspecific abundance-range size relationships. We critically assess the assumptions and predictions that they make, and the evidence in support of them. 4. A number of predictions are common to all of the biological (as opposed to artefactual) mechanisms, but the combination of predictions and assumptions made by each is unique, suggesting that, in principle, conclusive tests of all of the mechanisms are possible. 5. On present evidence, no single mechanism has unequivocal support. We discuss reasons why this might be the case. Key-words:abundance, distribution, metapopulation, niche breadth, range size. Journal of Animal Ecology (1997) 66, 579-601 'Who can explain why one species ranges widely and is very numerous, and why another allied species has a narrow range and is rare?' C. Darwin (1859) Introduction Arguably,in the absenceof strictempiricallaws the foundationsof much of populationand community ecologywill have to be laid on broadstatisticalgen& McCoy 1993).One eralizations(Shrader-Frechette such generalizationis that locally abundantspecies tend to be widespreadand locallyrarespeciestendto be narrowlydistributed.Thatis, fora giventaxonomic assemblage,there is a positive interspecificabundance-rangesize relationship(Fig. 1). Such relationshipshavebeenwidelydocumented(Gaston1996collates publ. studies;for additionssee Taylor,Winston & Matthews1993;Solonen 1994;Waltho & Kolasa 1994; Durrer & Schmid-Hempel1995). They have been reportedfor a diversityof taxa, from a variety of habitatsand geographicalregions,and at a spectrum of spatial scales (for reviewssee Brown 1984; ? 1997British EcologicalSociety author. *Correspondence -0.2 .. -0.4 O -0.6 o 0.8 -0-8 00 * 0S *0 0 -1 2 -1.2 ~ ** 0 0. 1-1.8u=-1.6 0 'o0 0?* .1600 *' *0 0 0 3?00f 0 0 00 0~~~~~ 0 00 0 0 0 ~~ ~~~0 *0 30 ?no 00. 0. * .0* a 0 0 fP :0 0 0 -I-2 -2.2 1 0.4 0.6 0.8 Geographicrangesize Fig.1. Therelationshipbetweenlocaldensity(log0iterritories ha-') and the proportionof sites occupiedfor bird species on farmlandCommonBirdCensusplots in Britainin 1975. For furtherdetailssee Blackburnet al. (unpublished) 0 0.2 579 This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 580 Abundance-range size relationships Gaston & Lawton 1990a; Lawton 1993; Gaston 1994a, 1996, 1997). In addition to contemporary assemblages they have also been reported for palaeontological ones (Buzas et al. 1982; McKinney 1997). Indeed, positive interspecific abundance-range size relationships have come to be described as 'almost without exception' (Hanski, Kouki & Halkka 1993). Although there is considerable unexplained variance about positive interspecific abundance-range size relationships, the existence of the pattern has motivated a search for a general explanation that transcends the idiosyncrasies of particular assemblages. A number of mechanisms have been proposed, embracing sampling artefacts, species attributes and population dynamics. A few explicit tests of their validity have been performed (e.g. Burgman 1989; Hanski et al. 1993), but with no clear resolution as to whether any one explanation is appropriate in all cases; whether more than one mechanism is operating; and, if so, the circumstances in which different mechanisms might apply or predominate. In this paper we do four things: we identify and clarify the principal mechanisms postulated to determine positive interspecific abundance-range size relationships (summarized in Table 1); we assess the evidence for their assumptions; we identify the predictions which the different mechanisms make; and, where it is available, we assess the evidence in support of these predictions. Throughout, we concentrate on assemblages of closely related, ecologically similar species. It is for these that abundance-range size relationships tend to be strongest (Brown 1984; Gaston 1994a). We concentrate on studies in which both the local abundances and distributions of species are assessed across the same study area, rather than the circumstance in which local abundances are assessed across study sites in a very confined area relative to that over which distributions are determined. We also deal, briefly, with the few exceptions to the general positive relationship. For convenience, following Gaston & Blackburn (1996a), we distinguish between two kinds of analyses. First, there are those performed over areas that embrace all, or a very large proportion, of the extents of the geographical ranges of the species concerned (e.g. most studies performed at continental or oceanic scales). Second, there are those performed over areas that embrace the entire geographical ranges of none, or only a small proportion, of the species concerned (e.g. most studies performed at national, provincial and smaller scales). We term these 'comprehensive' and 'partial' analyses, respectively, (Gaston & Blackburn 1996a). Most studies of abundancerange size relationships have been partial. At the outset, it is desirable to clarify some terminology. By 'local abundance' we mean the number of individuals of a species at a site, and where averaged across space we assume that (unless otherwise specified) only those sites are included at which individuals of the species are present (this avoids artefactual positive abundance-range size relationships resulting from mean abundances being a direct function of the number of sites at which species did not occur; Lacy & Bock 1986). We use 'range size' in a generic sense to refer to the distributional extent of a species in a study area; we do not restrict its application to the entire geographical ranges of species. Eight principal mechanisms have been proposed to, or might conceivably, generate positive relationships between the local abundance and regional distribution of species. The first two mechanisms we regard as essentially artefactual and the other six as essentially biological. We consider the form, assumptions and predictions of each of these in turn. Predictions that are common to all of the biological mechanisms, albeit for different reasons, are addressed in a later section. 1. Sampling artefact The first question to ask of the positive interspecific abundance-range size relationship is whether or not it is real. Of most concern is that the pattern may simply represent a sampling artefact. If levels of sam- sizerelationships Table1. Summaryof the principalmechanismsproposedto explainpositiveinterspecific abundance-range Mechanism Relationshipresultsfrom: 1. Samplingartefact of the rangesizesof specieswithlowerlocal Systematicunderestimation abundances of speciesas datapointsfor statisticalanalysis Non-independence Speciescloserto the edgesof theirgeographicalrangeshavelowerabundancesin, and occupya smallerproportionof, studyarea Attainmentof higherlocal abundancesandwiderdistributionsby specieswith greaterresourcebreadths Attainmentof higherlocal abundancesandwiderdistributionsby specieswith greaterresourceavailability habitatselection Density-dependent Metapopulationstructures intrinsicgrowthratesacrosssitesfor Similarspatialpatternsof density-dependent deathratesableto differentspecies,but specieswith lowerdensity-independent attain higherabundancesand occupymoresites 2. Phylogeneticnon-independence 3. Rangeposition 4. Resourcebreadth 5. Resourceavailability ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 6. Habitatselection 7. Metapopulationdynamics 8. Vitalrates This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 581 K.J. Gaston, T.M. Blackburn& J.H. Lawton pling effort are insufficient, then species that occur at low densities will tend to be recorded from fewer localities than species that occur at high densities, even if they are actually equally widely distributed. Indeed, it is not unknown for locally rare species, originally thought to have very restricted ranges, to be found to be considerably more widely distributed after greater sampling effort. A spurious, but potentially strong, positive interspecific abundance-range size relationship may result from sampling artefacts. This possibility was apparently first explicitly noted by Brown (1984), and has subsequently been discussed by a number of other authors (Gaston & Lawton 1990a;Wright 1991; Hanski et al. 1993; Gaston 1994a; see also McArdle 1990; Reed 1996). EVALUATION Determining empirically the effect of sampling on observed abundance-range size relationships is not straightforward. Only Hanski et al. (1993) have explicitly attempted to do so. They assume a distribution of local abundances that is negative binomial, and thence that the fraction of unoccupied sites (p0) would be approximately related to average density (x) across all sites (occupied and unoccupied) by the expression: ln(-lnpo) ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 ln(lnx)-2 n CV eqnl where CV is the coefficient of spatial variation of abundances (also calculated across all sites). The distribution of a species decreases with decreasing density and increasing spatial variation in densities. A significant positive relationship between CV and po was observed when controlling for the effect of density, using data sets for several assemblages. Hanski et al. (1993) argue that this suggests that sampling contributes substantially to many observed interspecific abundance-range size relationships. The difficulty with this approach is that it remains unclear whether this result is a product of sampling per se, or whether it simply reflects genuine underlying changes in the spatial distribution of individuals of species of differing regional distribution and density. Without perfect knowledge of the real detailed distribution of local abundances it is not possible to distinguish between the effects of sampling and real changes in the patterns of abundance of individual species. Brown (1984) has argued that a sampling effect is not sufficientto account for positive abundance-range size relationships for two reasons. First, the effect is too small, in at least some cases, to account for the observed magnitude of change in geographical range size with increasing density. Second, the distributions of species in some assemblages are very well-known, and unlikely to be seriously underestimated. Neither argument denies the possibility that there could be a sampling component to observed abundance-range size relationships, rather they suggest that it is not the sole explanation for the patterns. A sampling explanation seems most likely to apply at small spatial scales, especially when the distribution of a species is determined from the proportion of samples in which it occurs (Hanski 1991a; Hanski et al. 1993), and when sampling intensity is moderate to low. PREDICTIONS The sampling explanation makes one simple prediction: adequate sampling will find no real interspecific abundance-range size relationship. Anything less admits that there must be a role for some aspect of species biology or some other artefact in generating a positive relationship, and hence that the sampling explanation alone is not sufficient. Those assemblages where independently of sampling a positive abundance-range size relationship exists beyond all reasonable doubt (e.g. British birds; Fuller 1982; O'Connor & Shrubb 1986; O'Connor 1987; Sutherland & Baillie 1993; Lawton 1996a; Gaston et al. 1997) falsify this prediction. Therefore, other explanations for the positive relationship must be sought. 2. Phylogenetic non-independence An artefactual positive interspecific relationship between abundance and range size could also result from the shared common ancestries of species in an assemblage. Because of their phylogenetic relatedness, species do not constitute independent data points for analysis, inflating the degrees of freedom available for testing statistical significance (Harvey & Pagel 1991; Harvey 1996). If sufficient, this inflation may falsely imply that relationships exist which in reality do not. Some of the clearest examples of such difficulties derive from analyses of morphological and life history traits. However, the same arguments apply to traits that affect ecological relationships among species (Harvey 1996). For example, Nee et al. (1991a) showed that the negative relationship between abundance and body mass in British birds resulted from a difference between passerines, which tend to be smallbodied and common, and non-passerines, which tend to be large-bodied and rare. Within each group there was no evidence for any association between abundance and body mass. Therefore, this relationship results from a single evolutionary difference between passerines and non-passerines, rather than any general tendency for abundance and body mass to be negatively related. The positive abundance-range size relationship could likewise represent a simple difference between taxonomic groups (say, one set of related taxa that are geographically restricted and rare, and another set of related taxa that are geographically widespread and abundant), rather than any general tendency for more abundant species to have larger range sizes. This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 582 EVALUATION Abundance-range size relationships In common with studies of most purported patterns in macroecology, the phylogenetic relatedness of species has seldom been controlled for in analyses of abundance-range size relationships. Those studies that have been performed suggest, however, that significant positive correlations do not result from the non-independence of data points. First, Gaston et al. (1997, in press) consistently recover significant positive abundance-range size relationships for British birds when controlling for phylogeny, when abundance and range size are calculated at a variety of spatial and temporal scales. Secondly, Blackburn et al. (1997) document positive interspecificrelationships between total population size and range size for both bird and mammal assemblages in Britain. Thirdly, Quinn et al. (in press) find positive relationships when controlling for phylogeny in analysing abundancerange size relationships for British macrolepidoptera. PREDICTIONS The phylogenetic non-independence explanation for the positive abundance-range size relationship, like that based on sampling effects, makes one simple prediction: there will be no interspecificabundance-range size relationship once the effects of phylogenetic relatedness among species have been controlled for. Those assemblages where a positive relationship has been demonstrated after accounting for phylogenetic effects (see above) falsify this prediction. For British birds in particular, neither of the first two, essentially artefactual, hypotheses for the abundance-range size relationship apply. As it is unlikely that this assemblage is unique in these respects, general biological explanations for the pattern must be sought. CONCLUSION ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 It is important to control for the phylogenetic relatedness of species in comparative analyses (Harvey & Pagel 1991; Harvey 1996). The failure of most studies of abundance-range size relationships to do so means that the reported statistical significance of positive correlations may potentially result from the non-independence of data points. We suggest, however, that on present evidence it seems highly unlikely that most such results are indeed artefacts of this kind. A biological (as opposed to artefactual) explanation for these relationships is required. However, of greater concern is that much of the evidence available with which to test possible biological determinants of abundance-range size relationships derives from analyses of interspecific relationships between various other variables, or between other variables and abundance or range size. In the vast majority of cases these analyses have not controlled for phylogenetic effects. In subsequent sections of this paper, in the absence of anything better (we cannot repeat the large numbers of analyses done by others), we will make use of the available evidence, taking it at its face value and largely ignoring problems of phylogeny. Nonetheless, we caution that this is an optimistic approach, and that the results of some of the studies which we cite may ultimately prove to have been misleading. 3. Range position If, on average, abundances decline towards the edges of the geographical ranges of species (Grinnell 1922), and species occupy a smaller proportion of a study area when they are closer to the edges of their ranges, then positive interspecific abundance-range size relationships could arise as a result (Bock & Ricklefs 1983; Bock 1984). Species closer to the edges of their ranges might have a smaller range size in the study area in two ways. First, they might only penetrate a relatively small way into the study area (e.g. they might be constrained to its northern parts). Second, if not only do abundances decline towards range limits but occurrence also becomes more patchy, then a species closer to the edge of its range might be widely dispersed through a study area but occupy a relatively small proportion of it. Whichever situation applied, the species for which the centres of their geographical ranges overlapped the study area would occur at relatively high abundance and be widely distributed, whilst those for which only their range edges overlapped the study area would occur at relatively low abundances and would be restricted in occurrence. EVALUATION The first step in evaluating this hypothesis is obviously to ask how good is the evidence that levels of abundance and occupancy indeed change across the ranges of species in the fashion postulated. Maps of abundance surfaces across parts or all of the geographical ranges of particular species illustrate that these are often very complex (e.g. Root 1988; Gibbons, Reid & Chapman 1993; Price, Droege & Price 1995), and may vary dramatically through time (e.g. Taylor & Taylor 1979; Taylor 1986; Cammell, Tatchell & Woiwod 1989) although this may not always be the case (Brown, Mehlman & Stevens 1995). Nonetheless, a number of studies have demonstrated declines in average abundances or occupancy towards range limits (e.g. McClure & Price 1976; Bock, Bock & Lepthien 1977; Hengeveld & Haeck 1981, 1982; Brown 1984; Bart & Klosiewski 1989; Roberts, Dawson Shepherd & Ormond 1992; Svensson 1992; Telleria & Santos 1993; Hengeveld 1994; Maurer 1994; Whitcomb et al. 1994; Brown et al. 1995; Carey, Watkinson & Gerard 1995). For example, Telleria & Santos (1993) observe such a pattern for species of insectivorous passerines in Iberian forests. Simple models of decline in average abundances seem inadequate, however, and a more This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 583 K.J. Gaston, T.M. Blackburn& J.H. Lawton appropriate model is one in which species near the edges of their ranges show uniformly low abundances, whilst those near the centres exhibit a wide range of abundances (Brown et al. 1995; Enquist, Jordan & Brown 1995). Hengeveld (1989) suggests that similar distributions of densities occur at local scales as at regional ones. Thus the abundance structures of the geographical ranges of species can be visualized as a series of abundance peaks, with the magnitudes of these peaks declining towards the range periphery. There are case studies that find conflicting patterns or less convincing evidence for declines in average abundance or occupancy (e.g. Rapoport 1982; Brussard 1984; Carter & Prince 1985; Woods & Davis 1989), and concerns have been expressed that results may, in part, rest on the spatial resolution of analysis (Wiens 1989). Moreover, it tends to be assumed that if abundance declines towards range limits so does occupancy, and vice versa, but there is no necessary reason that this should be so, and in some examples it plainly is not. Indeed, Carter & Prince (1988) argue that whilst, in general, there is evidence for a decline in the frequency of populations (occupancy) towards range limits, there is little evidence to support the view that populations become smaller. There have been very few studies which, for the same species, have sought to document spatial variation both in local abundances and occupancy towards range limits. PREDICTIONS ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 Despite these uncertainties and difficulties, if we accept that assumptions regarding the abundance and occupancy structure of the edge vs. the centre of species' ranges are reasonable, what predictions does this particular model make? 1. A positive interspecific abundance-range size relationshipwill not exist whenbased on measuresof the entire geographical ranges of species and their average abundancesacross those ranges. There is evidence that this is not so. Analyses of such data document positive abundance-range size relationships. For example, in determining abundance-range size relationships for some North American winter landbirds, Bock (1984) selected only species whose New World winter ranges appeared to be largely (> 75% by area) confined to the area for which good abundance data were available. A positive abundance-range size relationship was still recovered. 2. Thosespecies in an assemblage whichare locally rare or occupy a small range size will tend, on average, to be nearer the edge of their geographical range. Hengeveld & Haeck (1982) have argued that this is indeed so (see also Hodgson 1986). They have shown, for several assemblages, that there is an increase in the numbers of individuals or numbers of grid squares occupied by species for which an area is more central to their geographical range. Unfortunately, the interpretation of such analyses is complicated by more general positive correlations between the abundances or range sizes of species at different spatial scales (see Gaston 1994a for a review). If species which are closer to the edge of their geographical range in a study area are also those which have smaller geographical range sizes or lower range-wide local abundances, it is not always clear to what extent the lower abundances and more restricted distributions in the study area are a product of proximity to range edge and to what extent they are a product of self-similarityin abundances and range sizes. 3. Interspecificabundance-rangesize relationshipsmay tend to be lower triangular,such that widely distributed species may have either high or low densities, while geographically restrictedspecies can only have low densities. This prediction follows from the observation that some species which are close to the edge of their geographical ranges, and hence have low local abundances, may nonetheless be quite widespread in a study area. Triangularrelationships appear to be more typical of comprehensive analyses than partial ones, for assemblages of greater taxonomic and ecological diversity, and when range sizes are measured as extents of occurrence (the area within the outermost limits to a species' occurrence) rather than areas of occupancy (the area within the outermost limits that the species actually occupies; Gaston 1991). However, there are exceptions, and the pattern might be expected for a variety of other reasons (see 'Predictions in common' for discussion and references). Overall, the prediction finds moderate support. CONCLUSION In summary, while the predictions of the range position hypothesis are often upheld, controlling for its effects reveals that it cannot explain some documented interspecific abundance-range size relationships. This is not to say that the effect does not contribute to many documented patterns, especially in partial analyses. The extent to which it does will depend upon the proportion of between-species variation in abundances which can be accounted for simply by the position of the area in which those abundances were measured with respect to the centres of the geographical ranges of the different species. In discussing the range position hypothesis, we have not given reasons why population abundances and proportion of sites occupied might decline towards the edges of species ranges. Such a pattern might be generated by several of the processes discussed below (e.g. hypothesis 4; see Brown 1984). In other words, this hypothesis, and the hypotheses that follow are neither completely distinct nor independent. We will encounter this problem again at several points later in this paper. 4. Breadth of resource usage Brown (1984) took the possibility of a link between the abundance structure of species' geographical This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions ranges and the interspecific abundance-range size relationship a step further than the range position hypothesis. He argued that the decrease in the abundance of a species towards the periphery of its range and the interspecific abundance-range size relationship were united by a common theoretical explanation, based on three assumptions: (i) the abundance and distribution of each species is determined by combinations of many physical and biotic variables, and that spatial variation in population density reflects the probability density distribution of the required combinations of these variables; (ii) some sets of environmental variables are distributed independently of each other, and environmental variation is spatially autocorrelated; (iii) closely related, ecologically similar species differ substantially in only one or a very small number of niche dimensions. From the first two assumptions it follows that density should be highest at the centre of the range of a species and should decline towards the boundary. Other models of the abundance structure of ranges exist, although most seem closely related to Brown's model (e.g. Huffaker & Messenger 1964; Williams 1988; Hengeveld 1989, 1993; Hall, Stanford & Hauer 1992). If niches are multidimensional and variation in the environment tends to be spatially autocorrelated, there should also be a positive correlation between abundance and range size. Species that have broad environmental tolerances and are able to use a wide range of resources will in so doing achieve high local densities and will be able to survive in more places and hence over a larger area; the 'jack-of-all-trades' is master of all. Those that have a narrow environmental tolerance and are able to use only a narrow range of resources will be unable to attain either high local densities or extensive distributions; the specialist is never very successful. This has subsequently become known as 'Brown's hypothesis'. For present purposes we will, however, be more explicit and refer to it as the 'resource breadth' hypothesis. In so doing, and in subsequent discussion, we mean 'resource breadth' to embrace the sets of environmental conditions which a species exploits, as well as resources which are appropriated; it will thus be used interchangeably with 'niche breadth'. Brown's explanation of the interspecific relationship between local abundances and range sizes assumes that more abundant and widespread species have an ability to use a broader range of resources. There are both theoretical and empirical difficulties with this assumption. Theoretically, whilst it seems reasonable to presuppose that range size might increase with resource breadth, it is more difficult to see why resource breadth should affect local abundance in a similar fashion (Kouki & Hayrinen 1991; Hanski et al. 1993). There is no obvious reason why ? 1997British an ability to exploit a range of resources and hence EcologicalSociety occur more widely should enable species to attain a Journalof Animal 579-601 Ecology,66, greater local abundance (unless species with greater 584 Abundance-range size relationships niche breadths are able to exploit more kinds of resources locally and hence become more abundant; see below). Nonetheless, a positive relationship between niche breadth and abundance is assumed by many models of species-abundance distributions (e.g. Sugihara 1980; Kolasa 1989; Tokeshi 1990). EVALUATION: ABUNDANCE AND NICHE BREADTH Empirical tests seem to substantiate the theoretical difficulty of relationships between density and resource breadth. We will concentrate principally on the small number of studies carried out within the framework of 'niche pattern', a plot in three-dimensional space of the densities, niche breadths and niche positions of the species in an assemblage (Shugart & Patten 1972). Here, niche breadth measures the range of physical conditions or habitat used by a species, and niche position measures the availability or typicality of these conditions. We will also be concerned solely with more recent studies, which have accounted for many of the statistical inadequacies of earlierwork in this area (see Carnes & Slade 1982; Van Horne & Ford 1982). In virtually all published cases of which we are aware, studies of niche pattern fail to document a positive interspecific relationship between niche breadth and density (Table 2); many correlations are negative. There are several reasons why this result might be obtained. First, it could arise simply because of the small numbers of species typically involved. However, a meta-analysis reveals no significant overall relationship (population effect size [weighted mean r]= -0.048, NS, total n = 158, number of studies = 8) and no evidence that studies do not share a common effect size (%2 = 6.747, d.f. = 7, NS). Second, it has been suggested that the failure to find positive correlations between niche breadth and abundance could arise because analyses have been performed at an inappropriate spatial scale. Undoubtedly the habitat occupancy of a species changes with spatial scale (e.g. Wiens, Rotenberry & Van Horne 1987). Seagle & McCracken (1986) argue that the results of niche pattern analyses and explanations of positive abundance-range size relationships based on differences in niche breadth are not incompatible, because in the former niche breadth and abundance are measured at the same spatial scale, while in the latter this is not the case. However, their argument is based on the assumption that differences in niche breadth only directly determine differences in range size, not differencesin local abundance (because if they did determinedifferencesin local abundance, we would expect to see positive relationships between niche breadth and local density). If the resource breadth hypothesis is correct, niche breadth should determine both range size and abundance. This serves to highlight two additional implicit assumptions of This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 585 K.J. Gaston, T.M. Blackburn& J.H. Lawton Table 2. Summary of published studies of niche pattern (plots in three-dimensional space of the densities, niche breadths and niche positions of the species in an assemblage) and the documented interspecific relationships between density and niche breadth(seetext for details) P n -0.38 -0.35 -0.12 -0.31 -0.10 NS NS NS NS NS 7 8 7 13 7 MDS DFA DFA DFA 0.08 -0.51 -ve NS NS ? 92 11 13 14 DFA DFA 0.13 -0.85 NS <0.01 13 8 Taxon Technique Slugs Smallmammals Salamanders Birds Rodents PCA FA DFA DFA PCA Birds Rodents Lizards Lizards Rodents [Rodents* r Comments Source Abundancein optimalhabitat Meandensity Maximaldensity [Bukhara] A 'weak'relationship [Mapimi] Maximaldensity Maximaldensity Seagle& McCracken(1986) Seagle& McCracken(1986) Seagle& McCracken(1986) Seagle& McCracken(1986) Robey et al. (1987) Mac Nally (1989) Rogovinet al. (1991) Shenbrotet al. (1991) Shenbrotet al. (1991) Shenbrot(1992) Shenbrot(1992)] f Statisticsnot givenin originalpublication. * Common& abundantspeciesonly. 'Technique' is the ordination method used: (PCA, principal components analysis; DFA, discriminant function analysis; FA, factor analysis; MDS, multidimensional scaling); r is the correlation coefficient, P the probability and n the number of species. Brown's hypothesis: the niche breadths exhibited by species at local and regional scales should be positively correlated, and there should be little spatial variation in the use of resources made by individual species (i.e. there should be little local adaptation). These two points are closely related, and, put simplistically, concern where species tend to lie in the four cell matrix of local niche breadth (specialist or generalist) vs. regional niche breadth (specialist or generalist; Table 3). If a species shows local adaptation, so that individuals use a limited range of resources locally, but the species as a whole uses a wide range of resources across a region, then there is no reason why the local abundance of the species should be greater than that of a second species that uses an equally limited range of resources locally, but shows no variation across the region. The findings of studies of herbivorous insects on particular food plants confirm this point, with no evidence that species specializing on one or a small number of host species are less abundant than those which feed on a variety of hosts (Gaston & Lawton 1988; Root & Cappuccino 1992). Mac Nally (1995) notes a dearth of studies of relationships between local and regional ecological versatility, and the absence of a simple relationship in those studies which have been performed (e.g. Ford 1990; Mac Nally 1995). It has even been suggested that, entirely contrary to the requirements of the resource breadth hypothesis, relationships are likely, if anything, to be negative (Cody 1974); species which tend to have broad local niches will tend to have narrow regional ones, and vice versa. This concords with the large body of evidence that species do exhibit local adaptation, exploiting different resources and exhibiting different environmental tolerances in different areas (e.g. Machado-Allison & Craig 1972; Fox & Morrow 1981; Davidson 1988; Svensson 1992; Bertness & Gaines 1993; Ayres & Scriber 1994; Krebs & Loeschcke 1995); there is some evidence that niche breadth changes towards range limits (Svensson 1992). In fact, Brown (1984, p.275) admits the possibility of spatial variation in the niche of a species but assumes that niches are constant over space, an assumption he considers justified so long as ecological variation within species is small relative to that across species. A third reason for the failure to find positive correlations between niche breadth and abundance could be that these analyses are failing to measure the relevant niche axes (the appropriate axes have not been measured at all, or the wrong combinations of axes have been considered). This is difficult to refute, and Table3. Combinationsof the nichebreadthsof speciesat local andregionalscales,and theirimplications Niche breadthat local scale Narrow ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 Niche breadth at regionalscale Narrow [Use samenarrow resourcesin differentlocalities] Broad [Use differentresources in differentlocalities] This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions Broad [Makebroaduse of a smallrange of resources-an impossiblecombination?] [Usewiderangeof resourcesin all localities] 586 Abundance-range size relationships reflects a more general difficulty with the resource breadth hypothesis. The concept of an n-dimensional niche on which it is based, while a powerful heuristic tool, is impossible to make fully operational (Colwell & Futuyma 1971). This essentially makes Brown's hypothesis impossible to test. Failure to find appropriate relations between niche breadths and local abundances can always be explained away, and where such relations are documented it remains unclear how robust they would be if niche breadths were measured using alternative axes. One circumstance in which this problem would be reduced, although still not avoided, would be if it were to be demonstrated that, for the assemblage of concern, niche breadths on different axes were positively correlated. We are not aware of evidence that this is so. Indeed, it would be surprising if it were. EVALUATION: RANGE SIZE AND NICHE BREADTH Thus far, we have restricted discussion to the validity of assuming that locally more abundant species have greater niche breadths. Equally, however, the resource breadth hypothesis requires that more widespread species also have greater niche breadths. Unfortunately, many (perhaps most) empirical studies of interspecificrelationships between breadth of resource use and range size are confounded by sample size effects (Gaston 1994a). If environmental or habitat breadth is determined for more individuals or at a greater number of sites for abundant and widespread species than for locally scarce and restricted species, then a positive correlation would be expected. This effect particularly frustrates attempts to draw some general conclusion in the present context from studies of the relationship between the size of a species' geographical range and the number of habitats or breadth of environmental conditions which lie within that range (e.g. Jackson 1974; Thomas & Mallorie 1985; Stevens 1989;Pomeroy & Ssekabiira 1990;Pagel, May & Collie 1991; Shkedy & Safriel 1992; Mawdsley & Stork 1995), and of the relationship between the number or diversity of host species that a consumer exploits and the size of its geographical range (e.g. Hodgson 1993; Kitahara & Fujii 1994). Where sampling effects have clearly been accounted for, significant positive relationships between breadth of resource use and range size have not in the main been documented. Thus, Burgman (1989) found that the habitat volumes (environmental tolerances) of a suite of plants from southern Western Australia were not significantly different for regionally scarce and ubiquitous species once sample bias was taken into account, although they were if this bias was ignored. Likewise, the relationships between the number of ? 1997British sites inhabited by species and their habitat volumes EcologicalSociety 5% of variance when sample bias was Journalof Animal explained Ecology,66, 579-601 taken into account, but 40% when it was ignored. A similar pattern was observed for separate guilds of plants, negating any explanation of the results as a consequence of species being ecologically too dissimilar. Similarly, Kouki & Hayrinen (1991) found no relationship between local abundance and habitat specialization after standardizing for sample size. PREDICTIONS We conclude that the empirical evidence for the assumptions of the resource breadth hypothesis is weak. Nevertheless, following the logic adopted in considering the previous hypotheses, we can still ask what predictions it makes. Explicit predictions have not to date been derived from the resource breadth hypothesis. However, three pieces of information have been argued to be consistent with it. First, it has been found that when the local abundances of species are measured in habitats which are atypical of the spectrum of habitats in the geographical region of interest (i.e. that over which range sizes are determined), a negative abundance-range size relationship results (Ford 1990; Gaston & Lawton 1990a). This would follow from the resource breadth hypothesis if there were no spatial autocorrelation in environmental variables between the typical and atypical habitats. However, this argument implies that there are certain limits within which broad-niched species are 'master-of-all'. It is not clear whether those limits are set by features of the species or features of the habitat, and if it were the latter, the pattern would be more consistent with the resource availability hypothesis (hypothesis 5, below; Gaston 1994a). Second, Lawton (1993) suggests that the resource breadth hypothesis may also gain some support from the observation that introduced species are, in some studies at least, more likely to establish the more widespread and abundant they are in their native environments (e.g. Forcella & Wood 1984; Forcella, Wood & Dillon 1986; Moulton & Pimm 1986; Crawley 1987; Hanski & Cambefort 1991; Roy, Navas & Sonie 1991). This observation would result if ecological flexibility improves the likelihood of successful invasion. It might, however, equally be expected from several other hypotheses for the abundance-range size relationship. Third, it has been argued that some kind of hierarchical organization of the ecologies of species is a necessary condition for the existence of nested patterns of species composition, in which smaller assemblages contain successive subsets of species in larger ones, and that the best candidate may sometimes be a pattern of included niches (Patterson & Brown 1991). Here, species occupying fewer and fewer sites have narrower and narrower niche breadths. However, we are not aware of any rigorous tests of this version of the resource breadth hypothesis, and can see difficulties in designing unbiased field tests of its assump- This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 587 K.J. Gaston, T.M. Blackburn& J.H. Lawton tions for the reasons already outlined, for example sampling effects. CONCLUSION The resource breadth hypothesis is elegant and, in many respects, makes good intuitive sense. It has proven important and influential, providing a stimulus for many studies in community and population ecology. However, accepting the impossibility of a full test (embracing entire multidimensional niches), the evidence for the hypothesis as an explanation for positive interspecific abundance-range size relationships appears to us to be unconvincing. Others have reached similar conclusions (Burgman 1989; Kouki & Hayrinen 1991). 5. Resource availability Although this and the previous hypothesis are easily conflated, a second distinct explanation for a positive interspecific abundance-range size relationship based on resource usage has been suggested (we continue to maintain the broad application of 'resource' defined above). This is that those species that are locally abundant and widespread utilize resources which are themselves locally abundant and widespread, whilst those species that are locally rare and restricted in occurrence utilize resources with similar relative levels of abundance and distribution (Hanski et al. 1993; Gaston 1994a). The two hypotheses based on resource use may, of course, not be independent, especially if those species with broader resource use tended also to exploit the more abundant and widespread resources. However, there is no necessary link. EVALUATION ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 This mechanism escapes the difficulty of explaining why environmental generalists should attain higher local abundances, but necessitates that locally abundant resources are also widely distributed. For host specialist consumers this is obviously the case, because positive interspecific abundance-range size relationships are found for groups of organisms at different trophic levels. Thus, the distribution of the host plant of a specialist herbivore is likely to be widespread if the plant is locally abundant, and, on average, specialist consumers feeding on widespread and locally abundant hosts will themselves tend to be widespread and abundant. Given that the local abundance and distribution of the host plant set the upper bounds to the local abundance and range size of the consumer, positive relationships between the abundances or range sizes of host and consumer may be a more appropriate null model than no relationship. Indeed, several such relationships have been documented. At a local scale, Root's 'resource concentration hypothesis' (Root 1973) predicts that phytophagous insects will be more abundant on more abundant species of host plants, although the supporting evidence is weak (Karieva 1983; Strong, Lawton & Southwood 1984). On larger scales, Dixon & Kindlmann (1990) find a significant positive relationship between the rank abundances of 12 species of callaphid aphids and the rank abundances of their host plants. Similarly, Gilbert (1991) documents a positive correlation between the rank adult abundance of species of Heliconius butterflies and the rank of their host availability. Such cases serve, however, merely to shift the level of explanation for abundance-range size relationships from one species assemblage (that of the consumers) to another (that of the hosts). What about the resources used by other groups of species? Are those resources which attain high levels of local availability also widely distributed?Certainly some authors have claimed that they are. For example, Fuller (1982) argues that the most abundant and widespread species of breeding birds on saltmarshes in Britain are those which utilize the typical and common features of the marshes, while the least abundant and poorly distributed species are those which are restricted by their preference for special habitats. Likewise, there are examples demonstrating that locally more abundant or regionally less restricted species utilize resources which are themselves either locally more abundant or regionally more widespread (e.g. Hodgson 1986). Further indication of a relationship between resource availability and local abundance is provided from studies of niche pattern which document the correlation between niche position and local abundance. A large niche position means that a species occurs in habitats characterized by extreme values compared with the mean value of all habitats in the sample, and whilst some studies find no, or a weak positive, relationship with local abundance (Mac Nally 1989; Rogovin, Shenbrot & Surov 1991; Shenbrot, Rogovin & Surov 1991), others find negative relationships (Seagle & McCracken 1986; Robey, Smith & Belk 1987; Urban & Smith 1989; Shenbrot 1992). Blackburn, Lawton & Gregory (1996) found that British bird species with fast development, either absolutely or for their body size, generally have higher abundances. They suggested that this relationship may be related to resource availability. For a species to be able to rear offspring quickly relative to other species, adults will have to be able to achieve a high rate of resource provisioning. This, in turn, requires a reliable, abundant food resource. If taxa that can rear offspring quickly can do so because they have abundant resources available, these resources may also be reflected in higher population abundances. Some taxa have access to a larger resource base, and this is reflected both in the abundance a species can attain, and the rate at which it can provision offspring. Blackburn et al. (1996) noted that this idea is also consistent This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 588 Abundance-range size relationships with Brown's hypothesis, because species occupying broad niches may be able to rear offspring more quickly if niche breadth relates to the amount of resource available to a species. However, the resource availability hypothesis can explain the same patterns more parsimoniously, because it need make no assumptions about variation in niche breadths. PREDICTIONS The resource availability hypothesis makes the following predictions. 1. Species that share a common resource base will not exhibit a positive interspecific abundance-range size relationship. For example, monophagous species utilizing the same host plant should not exhibit a positive relationship because they should be able to attain the same range size (assuming some equivalence of plants in different regions). This is problematic to test, because of the paucity of taxonomically reasonably closely related species sharing a common resource base. 2. Resource specialists can be abundant and widespread. Indeed, specialists on widely distributed, abundant resources should be more abundant and widely distributed than either specialists or generalists that utilize limited resources. Evidence for this is provided by the failure of studies to document positive relationships between abundance or range size and niche breadth (see above). CONCLUSION In summary, although scattered, there is evidence, direct and indirect, that assumptions of the resource availability hypothesis are met, at least in some assemblages. This begs the obvious question of why widely distributed resources should also be locally more abundant. 6. Habitat selection ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 Brown's hypothesis is completely deterministic and contains no dynamics (Brown 1995, p.65). The local abundance of a species does not directly affect the size of its range. Rather, greater local abundance is associated with larger range size because the two are both determined by breadth of resource usage. Plainly, however, this is simplistic. It has long been known that some species exhibit density-dependent habitat selection (driven through intraspecific competition), occupying more habitats when densities are high and less when they are low (for a review see Rosenzweig 1991). Assuming some broad commonality between species in this dynamic, then locally more abundant species will tend to occupy more habitats and to be more widespread, without the necessity of local abundance being determined by niche breadth. Whatever the precise mechanism, the out- come will be a positive interspecific abundance-range size relationship (O'Connor 1987). EVALUATION The principal assumptions of this model are that density-dependent habitat selection is widespread, and that within a taxonomic assemblage the local abundance-habitat diversity relationships exhibited by different species are broadly similar. Both are difficult to assess. Whilst density-dependent habitat selection is known to be exhibited by several species in particular taxa (e.g. passerine birds, fish; O'Connor 1987; Wiens 1989; MacCall 1990; Marshall & Frank 1995), in other groups for which abundance-range size correlations are well established (butterflies, higher plants) there is no evidence for density-dependent habitat selection. Also, examples are known of assemblages for which species do not show broader habitat use at higher densities (Rogovin & Shenbrot 1995). Some of these problems can be circumvented if number of habitats is replaced by number of patches, so that increasing density is associated with an increase in patch occupancy, rather than in the types of patches occupied. A model in this form has been suggested by Maurer (1990), who examined the number of individuals of different species that can occupy a series of habitat patches. The critical parameter in his model is the probability that an individual can obtain sufficient resources to remain in a patch, which depends on attributes both of the species and of the patch. It predicts a non-linear increase in the average number of individuals of a species per patch as the proportion of patches occupied increases. Assuming that the distribution of resources was spatially autocorrelated, that the resources available in each patch were drawn from the same n-dimensional resource availability distribution, and that species resource use distributions were drawn uniformly from the overall resource distribution, this translated into a positive interspecific abundance-range size relationship, with slope proportional to resource number (n). Therefore, this model combines density-dependent habitat selection with aspects of the resource breadth hypothesis. PREDICTIONS The habitat selection hypothesis makes the following predictions. 1. Species that have undergonemajorreductionsin total population abundance (driven by extreme density-independent events-heavy overwinter mortality for instance) should not only have reduced ranges after the event, but also occupy fewer habitats Indeed, the resulting reduction in range size should be driven primarily by withdrawal from particular habitats. 2. Further to thefirst prediction, the first habitat to be abandonedwill be that in whichpopulationperformance is lowest, followed by the habitat with the next lowest This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 589 K.J. Gaston, T.M. Blackburn& J.H. Lawton populationperformance, and so on. The problem with testing this prediction is, of course, that if individuals are distributed at random across a landscape made up of different types of habitats in scattered patches, small populations may, by chance, occupy fewer habitats than large populations. Critical tests therefore require both the development of a suitable null model, and an assessment of population performance in different habitats. 'Population performance' also requires careful measurement. If density-dependent habitat selection generates an Ideal-Free Distribution (Fretwell & Lucas 1970) of individuals across habitats, then at equilibrium, and on average, all individuals have the same fitness; a more appropriate (but still not perfect) measure is the intrinsic rate of increase of the population in each habitat when rare. 3. This leads to an additional prediction (which is an inherent assumption of the model) that as populations decline, and habitats are abandoned, survivingpopulations in core habitats should show density-dependent increases in populationperformance. 4. Maurer's model predicts that the slope of the interspecific abundance-range size relationship should be proportional to number of resources (Maurer 1990). Maurer tested this prediction by comparing the slope of two bird communities, one each in low and high productivity boreal forests, on the basis that the high productivity region should have higher values of n. The community in the high productivity region did indeed have the higher slope. His interpretation is that unproductive environments show less variation in resources available in a patch, so that narrow-niched species can use most patches, and broad-niched species gain no advantage in higher densities by being able to use a wide range of resources. In contrast, productive environments show more variation in patch resources, so that only broad-niched species can occupy many patches, and their ability to exploit a range of resources leads to higher densities in the patches they do occupy. Clearly, the aspects of this model in common with the niche breadth hypothesis will suffer from identical problems. Exactly how the model performs with the niche breadth assumptions removed is unclear at present. CONCLUSION Although plainly postulated as a mechanism determining interspecific abundance-range size relationships (O'Connor 1987), the habitat selection hypothesis has subsequently largely been ignored or overlooked. It is unlikely to be of importance in determining these relationships for many taxa, but may perhaps play a role for some. ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 7. Metapopulation dynamics A positive abundance-range size relationship is an assumption of some metapopulation models (e.g. Hanski 1982), but is a prediction of other, often closely related, metapopulation models. Following Hanski (1991b), we can divide the latter models into two groups, respectively, termed the carrying capacity hypothesis and the rescue effect hypothesis. CARRYING CAPACITY HYPOTHESIS The carrying capacity hypothesis (Nee, Gregory & May 1991) assumes that different species in an assemblage have different local carrying capacities, and that those which attain higher local population sizes have a lower extinction rate and/or a higher colonization rate than those which attain small local population sizes. It follows that the locally more abundant species will occupy more patches at equilibrium. Hanski (1991b) argues that if we assume that the local carrying capacity of a species is a reflection of its ecological specialism, then the carrying capacity hypothesis is Brown's (1984) resource breadth hypothesis (see above) in another guise. There are, however, some important distinctions. First, the carrying capacity hypothesis embodies a dynamic link between local abundance and regional distribution. In contrast, Brown's model has no such requirement, the local abundance and regional distribution of a species are both determined independently by its breadth of resource use. Second, this genre of metapopulation models assume that all patches are equal, and hence that all species have the capacity to occupy all patches. Brown's (1984) hypothesis explicitly assumes that patches are very different and hence that not all species have the capacity to occupy all patches. Third, the carrying capacity hypothesis does not require that the interspecific variation in carrying capacities be determined by differences in breadth of resource use. It could equally be generated by differencesin resource availability alone. RESCUE EFFECT HYPOTHESIS The rescue effect hypothesis (Hanski 1991a, b; Gyllenberg & Hanski 1992; Hanski & Gyllenberg 1993; Hanski et al. 1993) does not assume interspecific differences in carrying capacities. Rather it assumes that immigration decreases the probability of a local population becoming extinct (the rescue effect), and that the rate of immigration per patch increases as the proportion of patches which are occupied increases. Here, for many parameter values, a positive relationship between local abundance and number of occupied patches can result. EVALUATION A significant difference between the carrying capacity and rescue effect hypotheses is that in the former local abundance affects distribution, but not vice versa, whilst in the latter local abundance affects distribution This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 590 Abundance-range size relationships and distribution affects local abundance; Hanski (1991b) suggests the two mechanisms may, in practice, complement one another. Whatever the details, foremost, metapopulation models predicting interspecific abundance-range size relationships require that most species in a given taxonomic assemblage exhibit metapopulation dynamics. They must exist as a series of discrete local populations within which most individuals are born and die, with the populations linked by the dispersal of individuals, and exhibiting extinctions and recolonizations (Hanski 1991a). Examples have been documented both of species that do (Harrison, Murphy & Ehrlich 1988; Kindvall & Ahlen 1992; Hanski 1994; Hanski, Kuusaari & Nieminen 1994; Nave et al. 1996) and do not (Gotelli & Kelley 1993; Harrison, Thomas & Lewinsohn 1995; Murdoch et al. 1996) appear to meet the assumptions of metapopulation structure. The balance of evidence at present is, however, probably against most plant and vertebrate species exhibiting metapopulation dynamics, although the models may be applicable to a number of insect species and although it remains unclear how good a caricature of the dynamics of species metapopulation dynamic models may provide even when all of their assumptions are not met. It has been suggested that the classical picture of a metapopulation needs to be broadened considerably if it is to become more realistic (Harrison 1994). If it were the sole mechanism, in those circumstances in which metapopulation dynamics were unlikely to apply a positive abundance-range size relationship should not exist. Hanski et al. (1993) argue that some support is provided by the finding by Gaston & Lawton (1990b) that there is no such relationship among freshwater fish in Britain. However, this is a rather weak test, given that the local abundances of species in that study were drawn from a single site. Indeed, reversing the argument, Brown (1995) suggests that his resource breadth model for the abundance-range size relationship is supported by the probable existence of such a pattern among islands of archipelagoes, where over-water dispersal is very low, and hence where metapopulation dynamics are very unlikely. PREDICTIONS If we accept that a metapopulation model may be appropriate under some circumstances, then metapopulation dynamic mechanisms for the positive abundance-range size relationship make several predictions. The first pertains to the carrying capacity ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 hypothesis. 1. The creation of new patches of suitable habitatfor a species will not alter its abundancein existing patches, and likewise the destruction of some existing patches will not alter its abundancein those that remain. This follows from the fact that, unlike the rescue effect hypothesis, under the carryingcapacity hypothesis the distribution of a species does not have an effect on its local abundance. The other predictions pertain to the rescue effect hypothesis. 1. There will be positive interspecificabundance-range size relationshipseven whenthereis no differenceamong species in breadths of resource use (Hanski & Gyllenberg 1993). This is a consequence of the prediction that frequency distributions of the levels of patch occupancy achieved by species should be bimodal, such that most species occupy either a small or a high proportion of the available sites. At its most simple, if the rate of colonization of empty patches (m) is greater than the rate of extinction in occupied patches (e), then patch occupancy (p) should tend to 100%. Conversely, if m < e, then p should tend to 0%. If (me) is a random variable with variance much greater than mean, p should tend generally to close either to 0 or 100%, leading to the bimodal distribution of occupancy within a species over a long period of time, or across species at any one point in time (Hanski & Gyllenberg 1993). Since occupancy affects abundance under the rescue effect hypothesis, then a positive interspecific abundance-range size relationship is expected, even given identical resource usage. Unfortunately, any evidence that might be presented in support of this prediction potentially suffers the same problem as evidence in support of the resource breadth hypothesis. A set of species exhibiting a positive abundance-range size relationship in the apparent absence of any differences in resource usage may always be argued to differ on some other, unstudied, niche axes, for example in their environmental tolerances. 2. Local abundance will decrease with the increasing isolation of habitat patches (Hanski 1991b). Isolated patches will incur lower levels of immigration, and hence benefit less from the rescue effect. They will therefore have higher extinction rates, and exhibit lower densities on average. Evidence for this prediction is equivocal. Hanski et al. (1993) cite one field and one laboratory example where increased isolation results in lower density in patches. The situation is confused, however, because populations occupying one set of patches that are clearly more isolated, offshore islands, often show density compensation in response to species-poor island faunas (e.g. MacArthur 1972; Blondel, Chessel & Frochot 1988; Blackburn et al. 1997). 3. Species that have large local populations but restricted distribution will have a high local growth rate in relation to emigration rate, and low mortality during dispersal; the opposite attributes will characterizespecies with low abundancebut wide distribution (Hanski et al. 1993). Hanski (1991a; Hanski et al. 1993) argue that the findings of Soderstrom (1989) in a study of epixylic bryophytes in late successional forest in northern Sweden are supportive of at least the first This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 591 K.J. Gaston, T.M. Blackburn& J.H. Lawton half of this prediction. Three species in Soderstrom's study had high local abundances but restricted distributions. These were the only species that regularly reproduced asexually (by producing gemmae), but were not observed to reproduce sexually (by producing spores). The dispersal rate of gemmae is likely to be low relative to spores, and Hanski argues that the three species in question are likely to have low dispersal rates relative to growth rates. 4. Species with high dispersalrates will show a negative deviation from abundance-range size relationships. That is, more dispersive species should have wider distributions than less dispersive species for the same local density. The only explicit test of this prediction of which we are aware is that by Hanski et al. (1993), who found that it was upheld in British butterflies, but not in four other assemblages. More recent comparative analyses of the interspecific abundance-range size relationships of British birds and mammals also bear on this issue (Blackburn et al. 1997). Here, the slopes of the positive relationships are approximately the same, but for any given range-size mammal species have densities w 30 times those of bird species. While this supports the dispersal rate prediction (birds have much greater powers of dispersal than mammals), contrary evidence is provided by British bats, which do not attain significantly lower population sizes for a given range size than do non-volant mammals. In summary, evidence for the dispersal rate prediction is equivocal at best. 5. There will be a positive relationship between the final' range of invadingspecies and their rate of spread. Explicit tests of this prediction based on intrinsic rates of increase are lacking. However, if we assume that these are correlated with initial rates of distributional spread (Skellam 1951), then it finds some support. Forcella (1985) documents a positive relationship between the initial rate of spread and 'final' size of distribution amongst 40 alien weed species in northwestern USA, although no abundance data are available to test explicitly for an abundance-range size relationship in this case. CONCLUSION ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 The literatureon metapopulation dynamics comprises an elegant body of theory which has contributed much to our understanding of the patterns of change in, and interdependence of, spatial and temporal abundances (e.g. Gilpin & Hanski 1991; Gotelli & Kelley 1993; Hanski & Gyllenberg 1993; Hanski 1994; Hanski & Thomas 1994; Hanski et al. 1996). A metapopulationbased mechanism seems unlikely to be the most frequent explanation for positive abundance-range size relationships given our present understanding of the proportions of species exhibiting metapopulations. However, there is some evidence for some of the predictions of the rescue effect hypothesis, and there may be certain taxa for which metapopulation structure is the rule, rather than the exception. 8. Vital rates One of the simplest biological explanations for abundance-range size relationships is also the most recent. This is the proposition by Holt et al. (1997) that if a set of species differ with respect to their responses to spatially independent, density-independent mortality factors, then a positive relationship will result. Consider a set of species distributed at a scale large enough that regular immigration is sufficientto permit colonization of suitable sites, whilst not a dominant determinant of local abundance (an assumption fundamentally different from that made by rescue effect metapopulation models). They will persist solely at those sites where their intrinsic population growth rate r (which equals birth rate minus death rate) exceeds zero. Assume that at low densities all these species have the same spatial patterns of birth rates, that they experience intraspecific density-dependence in birth rates in the same way, and that each species has a constant, spatially invariant density-independent death rate. Then, equilibrium local density varies directly with r, and any factor which tends to increase r across all sites for a species will simultaneously enlarge the number of sites potentially occupied and increase abundance at occupied sites (Fig. 2). More formally, Holt et al. (1997) derive the expression: <N> = sR/2u eqn 2 where <N> is mean abundance, R is range size, s is the slope of the spatial pattern of birth rates (Fig. 2), and u is the strength of density dependence. EVALUATION Whilst the principal assumptions of this model do not seem unreasonable, there is little explicit empirical evidence for or against them. In large part this reflects the difficulty in directly measuring the relevant quantities. Nonetheless, the following observations provide some limited support for the model: (i) various dimensions of birth rates do appear in some cases to decline towards range limits (e.g. Peakall 1970; Caughley et al. 1988; Carey et al. 1995) although the inverse pattern may also occur (Johansson 1994); and (ii) species with smaller ranges appear in some assemblages to have lower relative maximal population growth rates, or likely correlates thereof, than do species with larger range sizes (e.g. Glazier 1980; O'Connor 1987; Spitzer & Leps 1988; Sutherland & Baillie 1993; Blackburn et al. 1996). Conversely, if cases in which there is no coincidence between the areas in which species attain high reproductive rates and high densities (e.g. some source-sink systems) are preponderant, then the assumptions of This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 592 Abundance-range size relationships (a) bo(x) Environmental gradient (b) <N> S 2 Range 2. Birth rates at low Fig. (a) (bo) densityat eachsite(x) along an environmentalgradientdecline linearly(with slope s) awayfromthe optimumsite,withthe samegradients for all species.Note that this figureneed not indicatean actual spatialstructurein birthand death rates;the x-axis could denote an abstract orderingof sites that in reality are arrangedin a complexspatialmosaicof habitatsof varying quality (Lawton 1996a). Species 1 and 2 have different death rates (d1and d2),giving rise to density-independent (b) a positiverelationshipbetweenmean abundance(<N>) and rangesize (fromHolt et al. 1997). highly unlikely that sufficient data could ever be collected to make a test a practical possibility. 3. All else being equal, species with higher densitydependentbirth rates should have higher range sizesfor a given abundance.This prediction arises directly from the position of u in eqn 2. The exact form of the differencebetween two taxa in their interspecific abundance-range size relationship will depend on the way in which they vary in u and s. Relationships for two taxa that vary in s but not in u would be predicted to have differentregression slopes, but with the elevation of the slopes dependent on the exact pattern of difference in s. Relationships for two taxa that vary in u but not in s would be predicted to have identical regression slopes, but different slope elevations (as per prediction [3]). Interestingly, a situation where two taxa do indeed differ in the elevation of their abundance-range size relationships, but not in their regression slopes, has recently been demonstrated by Blackburn et al. (1997) for British breeding birds and mammals. The vital rates hypothesis would be supported if birds could be shown to have lower density-dependent birth rates than mammals. We know of no data to test this prediction. 4. Within a taxon showing positive interspecificabundance-range size relationships, all species have essentially similar values ofu (the strength of density-dependent changes in birth rate as afunction of density is the same in all species), but vary in r (their intrinsicgrowth rates) (Holt et al. 1997). If u varies among species, but density-independent factors do not, species will have the same range, but differentaverage abundances within their ranges. It is currently unclear to what degree these assumptions could be violated and still retain a positive abundance-range size correlation. The extent to which density-dependence is similar among populations within a species or across groups of related species is an important and untested question in comparative population ecology. CONCLUSION the model may not be generally valid (e.g. Van Horne 1983; Vickery, Hunter & Wells 1992). PREDICTIONS ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 1. If invadingspecies are established at a randompoint within their feasible geographical range, then initial population growth rates will be a goodpredictor of their ultimate range size. This prediction is also made by the rescue effect hypothesis, and the evidence, albeit limited, is discussed above. 2. The rate of change of birth rates across environmental space will be proportional to the slope of the abundance-range size relationship. This prediction arises directly from the position of s in eqn 2. It seems In summary, the vital rates hypothesis currently lacks significant evidence in its support. However, that may be more a function of its relative novelty than an indication of the extent to which its assumptions and predictions are realistic. No doubt, further investigation of this mechanism will serve to clarify which is the case. Predictions in common In addition to the predictions given separately for each hypothesis for the positive interspecific abundancerange size relationship, there are three predictions which are common to all six of the biological ones (and additionally to the sampling artefact mechanism). Evidence in support of these predictions alone obviously provides no basis for discriminating This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 593 K.J. Gaston, T.M. Blackburn& J.H. Lawton ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 between hypotheses, but allied with other information may help to do so. 1. Positive interspecificabundance-rangesize relationships will become weaker over progressively larger areas, and wherean assemblage embracesgreater taxonomic and ecological diversity. In all cases, the greater the heterogeneity of the environments and species embraced by a study, the weaker abundance-range size relationships should become. For example, at large spatial scales many of the assumptions of metapopulation dynamic models are unlikely to hold true (e.g. Lawton 1993; Gaston 1994a). There is evidence that this weakening of relationships indeed does occur (Gaston 1994a; Brown 1995), although positive abundance-range size relationships have been documented at large spatial scales for several assemblages (e.g. Bock 1984; Brown & Maurer 1997; Gaston 1994a), and across multiple spatial scales for a few (Bock 1987; Collins & Glenn 1990;Niemela & Spence 1994; Brown 1995). This prediction implies that positive abundance-range size relationships should also be recovered within taxa (using phylogenetic comparative methods), where variation is probably least. There is some evidence that this is the case (Gaston & Blackburn 1996b; Blackburn et al. 1997;Gaston et al. 1997). 2. Positive interspecificabundance-rangesize relationships will be weaker when range sizes are measured as extents of occurrence than when measured as areas of occupancy (sensu Gaston 1991, 1994b). This is because areas of occupancy contain more information on where individual species actually occur (Gaston 1991). Although there are suggestions that the prediction is supported (Gaston 1996), critical tests are wanting. These cannot readily be carried out from existing studies, because the two measures of range size have not been applied consistently across taxa. Comprehensive analyses tend to employ extent of occurrence measures, whilst partial analyses tend to employ area of occupancy measures (Gaston & Blackburn 1996a). Nevertheless, Gaston et al. (unpublished) demonstrated that abundance-range size relationships in a set of British birds were stronger when range size was measured as number of local sites occupied than when range size was measured as the number of occupied 10 x 10 km squares in the British national grid. The latter measure is closer to an extent of occurrence than the former. However, the local sites used for this study (Marchant et al. 1990) are not scattered evenly across the entire British Isles, so that the two range size variables arguably do not represent differentmeasures of the same quantity. 3. There will be positive intraspecificabundance-range size relationships. Intraspecific abundance-range size relationships are predicted by all the biological hypotheses and the sampling effect hypothesis under at least some circumstances (note that for the metapopulation dynamics mechanism such relationships are predicted by the rescue effect hypothesis [Hanski 1991b; Hanski & Gyllenberg 1993] and not the car- rying capacity hypothesis). These circumstances are listed in Table 6, and the existence of such relationships in the absence of the particular forms of specific or environmental variation identified may constitute powerful tests of the hypotheses. For example, positive intraspecific abundance-range size relationships are predicted by the vital rates hypothesis only when birth rates and/or death rates are changing. The loss of areas of the geographical range of a species in ways which do not affect these rates (e.g. habitat destruction without degradation of remaining habitat) will not result in reduction in local density. Positive intraspecific abundance-range size relationships may be quite widespread (Fig. 3). There is a growing body of evidence for synchronous increases and decreases in range sizes and local densities at sites where species persist (e.g. Gibbons et al. 1993; Marshall & Frank 1994, 1995; Hanski et al. (a) -1.4, ia) -1.45ca a) 0 I-1.5a) 0 0 -1 .55 - a) .0 0 0 0 0 S 0 :LIa) -1.6- 0 0 0 0 :L 0)- -1-65 (a) -o 0) 0 -1.7 0 -1.75 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Proportionof sites occupied (b) -0-45. - -0.475a) o -0.5. - -0.525- a) C) CL Co .a) S 0 6* I 0 0 -0.550 o -0.575CD 0 0 0 -0.6 S ?, -0-625 a) -o -0-65 0 - -0.675 S 0 0) 0 0 S _.7 0.93 0.94 0.95 0.96 0.97 0.98 0.99 Proportionof sites occupied Fig.3. The relationshipbetween local density (logo1territoriesha-') and the proportionof sites occupiedfor (a) long-tailedtit, Aegithaloscaudatus,and (b) chaffinch,Fringilla coelebs,on farmlandCommonBird Censusplots in Britainin 1968-91.For furtherdetailssee Blackburnet al. (unpublished). This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 1 594 Abundance-range size relationships 1995; Pollard, Moss & Yates 1995; van Swaay 1995; Gaston & Curnutt 1997, Blackburn et al., unpublished). For example, amongst farmland birds in Britain, those species that have undergone the strongest declines in numbers tend to have shown the most substantial range contractions (Fuller et al. 1995). Intraspecific abundance-range size relationships are not all positive. Positive relationships are exhibited by 71% of 75 species of British birds censused on farmland sites in the period 1968-91 (Blackburn et al., unpublished). However, in only 42% of species are these relationships positive and statistically significant, and the proportions are even lower for an overlapping set of species censused on woodland sites. Five percent of species on both farmland and woodland show significant negative intraspecific relationships. It is not obvious how these could be generated by some of the models for positive interspecific relationships. To give just one example, the resource breadth (Brown's) hypothesis predicts positive intraspecific relationships when there are temporal fluctuations in breadth of resource use (e.g. temporal fluctuation in climate affecting the size of a species' realized niche). A negative intraspecific relationship would require temporal fluctuations that simultaneously increased local abundance but decreased range size. Yet, Brown's hypothesis explicitly forges a positive link between variation in abundance and variation in range size. The example of a situation where it can produce a negative interspecific relationship (e.g. Gaston & Lawton 1990a; see below) does not apply intraspecifically. Negative interspecificcorrelations ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 Not all interspecific correlations between abundance and range size are positive. There are a few that are negative, and some that show no statistically significant relationship (e.g. Gaston & Lawton 1990a; Gaston 1996). Non-significant correlations are probably most likely to occur with poor data, but negative correlations can also be generated by some of the mechanisms giving rise to positive correlations, but for substantially different circumstances and parameter values. It is useful to review, briefly, which mechanisms can generate negative correlations, and under what circumstances. To avoid repetition, we do not explicitly discuss cases of zero correlation. Logically, these cases are bound to exist as conditions pass from those generating 'almost universal' positive correlations to those generating much rarer negative ones. Of the eight hypotheses discussed above that give rise to positive interspecific abundance-range size correlations, three cannot generate negative ones. They are the sampling artefact hypothesis (hypothesis 1), the range position hypothesis (3) and the densitydependent habitat selection hypothesis (6). Under hypothesis 1, sampling would have disproportionately to miss common species to generate a negative relationship. Under hypothesis 3, species would need higher levels of abundance and occupancy nearer to their range edge. Hypothesis 6 would require that species at higher densities occupy fewer habitats. It is difficult to see how any sensible modification of any of these models could change this situation. The phylogenetic non-independence hypothesis (hypothesis 2) could generate negative interspecific relationships in cases where the species compared belonged to distinct taxonomic groups, where species in the more widespread groups happened to be generally rarer. For example, the negative relationship between breeding density and geographical distribution found for birds breeding on Handa (Gaston & Lawton 1990a) could arise from a simple difference between seabirds (Ciconiiformes), which breed at high density but at a few restrictedlocalities, and passerines (Passeriformes),which are geographically widespread, but do not attain the high densities of nesting seabirds. The resource breadth hypothesis (hypothesis 4), as already noted, can generate negative interspecific relationships when the local abundances of species are measured in habitats which are atypical of the spectrum of habitats in the geographical region of interest (that over which range sizes are determined). A negative abundance-range size relationship indeed results under these circumstances (Ford 1990; Gaston & Lawton 1990a). It is conceivable under hypothesis 5 (resource availability) for widespread resources to be rare everywhere, and geographically restricted resources to be locally abundant. We know of no plausible demonstration of this possibility. Hypotheses 7 (metapopulation dynamics) and 8 (vital rates) are both capable of generating negative correlations for appropriate (and relatively restricted) ranges of parameter values. The necessary conditions are discussed in the relevant sources (Gyllenberg & Hanski 1992; Holt et al. 1997). Negative correlations deserve more attention. Despite their rarity, they offer an opportunity to explore the assumptions and predictions of the eight hypotheses in more detail than concentrating on positive relationships alone. If one subscribes to the view that we should seek the most parsimonious number of explanations for patterns in nature, then the suite of possible candidates yielding general explanations for abundance-range size correlation is reduced from eight to five, because three of them do not predict the existence of negative correlations. Synthesis We are in no doubt that the positive interspecificabundance-range size relationship is a real pattern, in that it is not simply a product of sampling artefacts or of phylogenetic non-independence (see also Brown 1984, 1995; Nee et al. 1991b; Lawton 1993; Gaston 1994a). Its underlying cause(s) are, however, less readily dis- This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions 595 K.J. Gaston, T.M. Blackburn& J.H. Lawton cerned. None of the six non-artefactual hypotheses summarized here has unequivocal support. There are four main reasons why this could be the case. First, the models have not been adequately tested, and if this were achieved one model would become clearly differentiatedas the explanation of the observed pattern. The relative dearth of evidence for some hypotheses (habitat selection, vital rates) may be more a function of the lack of attention they have so far received than of their intrinsic merits. By far the most effort has been expended testing the resource breadth and metapopulation dynamic models, to the extent that many authors seem not to recognize that there are several other potential explanations for interspecific abundance-range size relationships. One aim of this paper is to correct that narrow view. Nevertheless, given that the models concern some key issues in ecology (population dynamics, metapopulation dynamics, niche patterns) it is rather depressing how difficult it is, on present evidence, to discriminate amongst them or, at least, to determine the likely validity of their assumptions and predictions. Second, it is not possible to discriminate amongst hypotheses. In principle, and for most models, this should not be true. In Tables 4 and 5 we summarize the principal assumptions and predictions of the six biological mechanisms postulated to explain positive abundance-range size relationships, and provide a qualitative indication of the extent to which we believe there is empirical evidence (as discussed above) in support of them. Most of the hypotheses make either unique predictions, or unique combinations of predictions. Part of the problem to date has been the lack of rigour in defining what the different models really do predict. For example, the resource breadth hypothesis has sometimes been assumed not to predict positive intraspecific abundance-range size relationships (Lawton 1995, 1996a), because the niche breadth of a species is considered a fixed quantity. However, it is actually easy to envisage positive intraspecific relationships if a fixed fundamental niche translates into a variable realized niche under the influence of environmental variation. The conditions under which different hypotheses predict intraspecificrelationships (Table 6) are considerably more subtle than had been appreciated. The lack of rigour has also meant that predictions that have been tested to differentiate between competing hypotheses do not do so: the existence of positive intraspecific relationships per se does not invalidate the resource breadth hypothesis. Note also from Table 5 that the predictions for which there is most evidence are usually those that are the least useful in distinguishing between the different models. The relative difficulty in defining the predictions made by differenthypotheses seems, in large part, associated with whether the hypotheses have been expressed mathematically (e.g. metapopulation dynamics, vital rates) or not (e.g. resource breadth, resource availability). A third reason why no current theory has unequivocal support may be that none of the mechanisms are size relationTable4. Explicitassumptionsof mechanismspostulatedas determiningpositiveinterspecificabundance-range ships (see text and Table 1 for details of the hypotheses). 1, sampling; 2, phylogenetic non-independence; 3, range position; 4, resourcebreadth;5, resourceavailability;6, habitatselection;7, metapopulationdynamics;and 8, vital rates.'Evidence'is a qualitativeassessment(on a scale of 0-4) of the availableevidencein supportof the generalityof each assumptionin the context of abundance-range size plots (several assumptions may be true in a wider ecological context). Evidence involving severalspeciesis givengreaterweightthan evidencefromjust one, or a few, species- a low numberof crossesimpliesthat there is little evidencethat the assumptionholds widely, althoughthe evidencemay still be good for particularspecies assemblages. Some assumptions rate 0 (left blank), no evidence. No assumption warrants more than 2 from a maximum of 4 1 2 3 4 5 6 7 8 Evidence Thereis no real(biological)positiveabundance-range / size relationship Populations occur at lower densities near the edge of their ranges Localabundanceswill be greaterfor spp. withwider breadthof resource-use Distributionswill be greaterfor spp.withwider breadthof resource-use + + + + + Abundances will be greater for spp. with more abundant resources Distributions will be greater for spp. with more abundant resources ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 habitatselection Thereis density-dependent Spp.existas metapopulations Abundanceswill be greaterfor spp.withhigher intrinsicgrowthrates Distributionswill be greaterfor spp. withhigher intrinsicgrowthrates This content downloaded on Fri, 8 Mar 2013 13:56:10 PM All use subject to JSTOR Terms and Conditions ++ + + ++ + / + ++ 596 Table5. Predictions of mechanisms postulated in hypotheses to account for positive interspecific abundance-range size Abundance-range size relationships 3, rangeposition;4, resourcebreadth;5, resourceavailability; relationships.1, sampling;2, phylogeneticnon-independence; 6, habitat selection; 7, metapopulation dynamics; and 8, vital rates. 'Evidence' is a qualitative assessment (on a scale of 0-4) size relationships./ indicatesthat of the availableevidencein supportof eachpredictionin the contextof abundance-range the hypothesis heading the column produces the prediction in that row. ? indicates a prediction that may arise from a hypothesis,but whetheror not it does is currentlyunclear 1 size relationshipshouldbe stronger Abundance-range usingmeasuresof areaof occupancythanextentof occurrence Abundancesand distributionswill declinewhen distancesbetweenpatchesaregreater Specieswithgreaterdispersalabilitywill be more widelydistributedfor a givenabundance sizerelationshipwill be foundat Abundance-range scales verylarge/continental size relationshipshouldweakenas Abundance-range studyareaincreases Ultimaterangeof invadingspp. shouldbe positively correlatedwithrateof spread Spp.with smallrangesshouldhavelowerrelative maximalpopulationgrowthrates For invadingspp.,initialpopulationgrowthrates shouldbe a good predictorof ultimaterangesize / Generalistswill not be consistentlymorewidespread thanspecialists Localand regionalnichebreadthsarepositively correlated Thereis no abundance-range size relationshipfor spp. that sharea commonoverallresourcebase Thereis a positiveabundance-range size relationship for spp. that sharea commonoverallresourcebase Therewill be positiveintraspecific abundance-range size relationships Can also predictnegativeabundance-range size relationships // 2 3 4 5 6 7 8 Evidence ? / / / /, / ++ / / J ++ / + / / / / /? ++ + + / +++ + see below J / ,/ / / ++ / / + because arecorrelated withr ++ / ++++ / / / / I \/ / / / I / / v/ / + Table 6. Determinants of positive intraspecific abundance-range size relationships for the seven different hypotheses which predict such a pattern (relationships are based on the abundance and range size of the same species at different times) Mechanism Relationshipresultsfrom: 1. Samplingartefact of the rangesize of a specieswhenit occursat lowerlocal Systematicunderestimation abundances Temporalfluctuationsin the proximityof the studyareato the centreof the rangeof the species Temporalfluctuationsin breadthof resourceuse Synchronoustemporalfluctuationsin the localabundanceand distributionof resource availability Temporalfluctuationsin local abundancedrivechangesin habitatoccupancy,andhence distribution Metapopulationstructuresof the formof the rescueeffecthypothesis Temporalfluctuationsin birthand/ordeathrates 3. Rangeposition 4. Resourcebreadth 5. Resourceavailability 6. Habitatselection 7. Metapopulationdynamics 8. Vitalrates ? 1997British EcologicalSociety Journalof Animal Ecology,66, 579-601 appropriate. This is a depressing prospect, but impossible ever to dismiss out of hand, as it is the nature of science that even the most beautiful theory can always be killed off by one ugly fact. However, at present this conclusion is premature, at least until more rigorous tests of each individual hypothesis, or of combinations of hypotheses, have been performed. This leads to the fourth possibility, which is that some or all of the mechanisms are complementary (see also Collins & Glenn 1991; Holt et al. 1997), and that some or all may be appropriate somewhere. 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