Density–distribution relationships in British butterflies. I. The effect of mobility and spatial scale



  • 1 Positive relationships between the density and distribution of species in taxonomic assemblages are well documented, but the underlying mechanisms remain poorly understood. Two factors that are expected to be important in explaining variation in these relationships are the spatial scale of analysis and the relative mobility of the study species.
  • 2 We examined density–distribution relationships in British butterflies at a variety of spatial scales. Distributions were proportions of grid squares occupied: 50 m grid within 0·25 km2 areas (local), 500 m grid in 35 km2 (regional), 10 km grid across England, Wales and Scotland (national), 153 000 km2 grid squares across Europe (European), and also seven categories of international distribution (Global; 1 = European endemic to 7 = in 5 + continents). Densities were measured using transect counts at local, regional and national scales.
  • 3 Different relationships between density and distribution occurred at different scales of analysis. When we controlled for the effects of mobility and/or phylogenetic association, a positive relationship between density and distribution was apparent at local, regional and national scales. Species’ national densities in Britain were positively correlated with their European distribution sizes, but significantly negatively correlated with their global range sizes.
  • 4 Butterfly mobility had a positive effect on distribution and a negative effect on density at all spatial scales. For a given total abundance, more mobile species had lower densities but wider distributions, i.e. they were less aggregated than more sedentary species.
  • 5 The decreasing strength of the density–distribution correlation, and the eventual reversal of the pattern, with the increasing magnitude of difference between the scale at which density was measured relative to distribution, suggests that some element of niche may be important in determining densities and distributions. However, the measure of niche breadth analysed did not explain significant variation in density, distribution, or in the density–distribution relationship.


The local densities and regional distributions of species are not independent. Within an assemblage, species that are locally common tend on average to be more widespread than those that are locally rare. That is, there is a positive interspecific density–distribution relationship. This pattern has been observed in a variety of taxa, over a spectrum of spatial scales (for reviews see Hanski 1982; Brown 1984; Gaston & Lawton 1990; Hanski, Kouki & Halkka 1993; Lawton 1993; Gaston 1994a, 1996) and such is the volume of supporting evidence that it has been described as a general rule in community ecology (Hanski et al. 1993; Gaston 1996; Gaston, Blackburn & Lawton 1997). Eight principal mechanisms have been identified that could give rise to the correlation, of which six can be considered biological whilst two imply that the relationship is artefactual (for a review see Gaston, Blackburn & Lawton 1997; see also Gaston, Blackburn & Lawton 1998; Hartley 1998).

Many of the previous studies of interspecific density–distribution relationships have been concerned with establishing its generality (Gaston 1996) and identifying exceptions (Arita, Robinson & Redford 1990; Gaston & Lawton 1990). However, so many competing hypotheses predict a positive density–distribution relationship (Gaston, Blackburn & Lawton 1997; Gaston et al. 1998; Hartley 1998) that simply documenting such a relationship is of little help in distinguishing among the possible alternative causes. Thus, the exceptions provide particularly useful insights. The relationship has not yet been established for British butterflies, previous studies having reported positive, zero and/or negative relationships between density and distribution depending on the data and analyses used (Hanski et al. 1993; Thomas et al. 1998; Dennis et al. 2000).

One factor that has received little consideration, but that is likely to be important in determining when a positive relationship is observed, is the spatial extent of the study (e.g. Brown & Nicoletto 1991; Gaston 1994a; Gaston & Blackburn 1996; Thomas et al. 1998). It has been suggested that density–distribution correlations will tend to become weaker as spatial extent increases (Brown 1984; Brown & Maurer 1987; Gaston 1994a), but no consistent pattern has yet emerged. Variation in the form of the density–distribution relationship at different spatial scales may also help identify the role of the various explanatory mechanisms that have been proposed to explain the relationship. Only a few previous studies have attempted this, and none has simultaneously addressed the effects of species’ phylogenetic relatedness (Bock 1987; Collins & Glen 1990; Niemelä & Spence 1994; Brown 1995; Thomas et al. 1998). Phylogenetic relatedness should be examined because interspecific density–distribution relationship could represent simple differences between taxonomic groups, rather than any general tendency for locally common species to be more widely distributed (cf. Harvey & Pagel 1991).

Here, we consider patterns in the density and distribution of British butterflies at local (0·25 km2), regional (35 km2), national (229 797 km2), European (10 400 000 km2) and global scales. We test: (i) if the form of the density–distribution relationship varies at different spatial scales; (ii) if the relationship between density and distribution becomes weaker as one increases the magnitude of the difference between the scale at which density is measured relative to that at which distribution is measured; (iii) the extent to which distribution sizes are correlated with distribution sizes measured at other spatial scales; and (iv) whether densities are correlated when they are measured over different areas. The third and fourth questions are key issues in macroecology (Gregory & Blackburn 1998). If densities and distributions are scale dependent, then studies that only consider a small proportion of the area occupied by a species may not reflect broader patterns.

Understanding variation around the density–distribution relationship is also likely to help unravel the roles of the various explanatory mechanisms (Hanski et al. 1993; Blackburn, Gaston & Gregory 1997; Quinn et al. 1997). Measures of butterfly mobility and niche breadth are included in the analysis. Mobility is considered important in relation to suggested metapopulation dynamic mechanisms for the interspecific density–distribution relationship. These state that a positive density–distribution relationship may be generated as a consequence of migration: species with high local densities will have low local extinction rates, and generate more migrants, decreasing the probability of local extinction elsewhere (rescue effect) and increasing the colonization rate of empty habitats (Hanski 1991; Gyllenberg & Hanski 1992; Hanski et al. 1993). A resultant prediction is that more dispersive species should have wider distributions than less dispersive species of the same local density (Hanski et al. 1993).

Several studies have suggested or documented that more dispersive species do tend to have wider range sizes than less dispersive species (Kunin & Gaston 1993; Oakwood et al. 1993; Gaston 1994a; Gaston & Kunin 1997) and this has been demonstrated specifically for British butterflies (Hodgson 1993; Dennis & Shreeve 1996, 1997; Dennis et al. 2000). The effects of mobility on density–distribution relationships are less well established (Hanski et al. 1993).

Variation in species niche or resource breadth has also been proposed as an explanation for the interspecific density–distribution relationship. Brown (1984) argued that generalists able to use a wide range of resources would become both widespread and locally abundant, whilst more specialized species would be both local and rare even where they do occur. Tests of this hypothesis have demonstrated positive correlations between niche breadth and distribution, although few have demonstrated a positive correlation between niche breadth and density (for a collation of published studies, see Gaston, Blackburn & Lawton 1997). Thomas & Mallorie (1985) found a positive correlation between the habitat breadth of Moroccan butterflies and their European range sizes. Hodgson (1993) demonstrated that butterflies in Britain with a taxonomically wide range of food plants tend to be more widely distributed than butterflies that use only one species or genus of host plant. Similarly, Dennis & Shreeve (1996, 1997) and Dennis et al. (2000) attributed increased range size and incidence on offshore islands partly to host plant and habitat range.

Unfortunately, many of the published correlations between niche breadth and distribution suffer from sample size effects (Gaston 1994a; Gaston, Blackburn & Lawton 1997). For example, if two species have the same fundamental niche breadth, but differ in abundance because natural enemies set their abundance, the more abundant species is likely to be observed in more habitats than the less abundant species. If niche breadth is measured as the number of habitats occupied, this could lead to an non-causative positive correlation between niche and distribution. Where sampling effects have been accounted for, significant relationships between niche breadth and distributions have rarely been documented (Gaston, Blackburn & Lawton 1997). Intuitively, it seems reasonable to suppose that species with the ability to use a wide range of resources or with a wide ecological tolerance might be widely distributed, but it is not always so clear why they should also occur at higher density (Kouki & Häyrinen 1991; Hanski et al. 1993; Gaston, Blackburn & Lawton 1997).


Throughout the paper, we use the term ‘distribution’ to refer to the distribution size of species at each scale. At local, regional, national and European scales this refers to the number of occupied grid squares, and at a global scale to species’ entire geographical range sizes. In the terminology of Gaston (1991, 1994b) these are measures of ‘area of occupancy’ (grid square counts) and ‘extent of occurrence’ (range size).

The measure of density we employ is species’ mean density where present. We refer to this simply as species density. Most comparative studies compare densities where present or ‘ecological’ density as this avoids an artefactual relationship between density and distribution resulting from the inclusion of increasing numbers of zeros in calculations of mean density for species that occur in fewer and fewer sites (Gaston 1996).

In the analyses, we compare butterfly density data collected at local, regional and national scales with butterfly distributions measured at the corresponding scales. For correlations between density and distribution at European and global scales, we used species’ national densities (i.e. from within Britain) with European and global distributions; therefore, only a small subset of the European and global butterfly fauna is included.

Butterfly densities

All species density estimates were obtained using the butterfly transect method (Pollard 1977; Pollard, Hall & Bibby 1986; Pollard & Yates 1993). This involves a recorder counting the numbers of each species seen 2·5 m either side and 5 m in front of the recorder in weather suitable for butterfly activity. National, regional and local transect counts were all standardized using the same method (Pollard & Yates 1993) and reflect density where present, at the same resolution, in habitat-based sampling units. Differences in the form of the density–distribution relationship measured at different spatial scales must therefore be explained with reference to scale rather than to methodological differences.

The butterfly transect method was first developed by Pollard (1977) and was used solely for single species comparisons. This has also been the approach taken by all subsequent researchers, without actually testing its suitability for multiple species comparisons. For single species, the method is widely adopted and has been validated in several studies (e.g. Thomas 1983; Pollard & Yates 1993). Our unpublished distance-measurement analysis (D.M. Shuker & C.D. Thomas, unpublished) indicates that errors in density measures from the Pollard transect approach are no greater between species than within species. Furthermore, the error is small relative to the total range of densities seen both within and between species. Variation in visibility is also likely to be linked to phylogeny. Visibility would mainly be a cause for concern if positive density–distribution relationships disappeared or became weaker after carrying out phylogenetically controlled analysis (actually they became stronger).

The only species for which the method is unsuitable are five species that spend much of their time in the forest canopy (Satyrium pruni L., Satyrium w-album Knoch, Thecla betulae L., Quercusia quercus L. and Apatura iris L.) and are therefore under-recorded on transect walks (Pollard & Yates 1993). These species are excluded from all analyses in the current paper (only two of these species occur in the north Wales study area).

Variation in adult longevity also has the potential to effect the reliability of multispecies comparisons. However, as with visibility, the life span of individual butterflies is closely linked to phylogeny so this variation is effectively factored out in these analyses.

Two skipper butterflies, Thymelicus sylvestris Poda and Thymelicus lineola Ochsenheimer, are only distinguished by the colour of the underside of the tip of the antenna, and cannot be distinguished in flight, so density values are not used from transects where they co-occur. As there are no sites from which relative densities were obtained with only T. lineola, this species was excluded from the analysis but T. sylvestris could be included. Aricia agestis Denis & Schiffermüller and Aricia artaxerxes Fabricus are practically indistinguishable, but allopatric. A few 10 km distribution records may be attributed to the wrong species, but this is likely to represent a very low percentage of the total. Pieris rapae L. and Pieris napi L. are difficult to distinguish in flight and it is likely that mistakes will occur. Some of the national scale analyses were therefore repeated without them. At regional and local scales, only two recorders walked all butterfly transects, so the quality of recording is considered reliable enough to warrant their inclusion.

Local and regional densities and distributions

Local and regional butterfly density data were collected in an approximately 35 km2 area, the Creuddyn peninsula, located along the north coast of Wales, UK (53°18′N, 3°50′W) (Ordnance Survey, 10-km squares SH77–88). This area is bordered by sea to the north and west, and by land to the south and east. The landscape is extremely mixed and includes a variety of semi-natural habitats including limestone grassland, woodland, scrub, heath, coastal dune and bracken. The rest of the area consists mainly of agricultural and urban habitats.

To stratify the collection of butterfly density data, the study area was divided into major land-use types using a classification derived from Phase-1 land cover field data (JNCC 1990). Also included were additional habitats of relevance to butterflies that could be identified from Ordnance Survey maps, e.g. drains, woodland edge and road verge. In total, 16 coarse land-use (hereafter ‘habitat’) types were identified and in most cases 10 samples of each were selected (Table 1). A butterfly transect, usually 300 m in length, was located within each sample of a single habitat type. In total, there were 147 separate transect routes with a total length of 43·1 km. Transects were walked every other week from April through to October 1997 and a standardized yearly count was calculated for each site (total number of individuals per 300 m per year). Species’ regional densities were calculated as the mean of standardized yearly counts at each site at which one or more individuals were recorded per 300 m per year.

Table 1.  All major habitat types in the north Wales study area
Habitat typesArea (ha)PercentageNo. of samples
  • *

    Includes salt marsh, open water, scree and some cliff/quarry faces.

Amenity grassland  53 1·510
Bracken  43 1·210
Coastal dune  15 0·410
Ditches   6 0·210
Heathland  44 1·3 5
Hedgerows  69 210
Improved grassland110031·410
Lane  14 0·410
Limestone grassland 221 6·310
Non-habitat* 54115·5 –
Semi-improved grassland  78 2·310
Scrub  84 2·410
Urban areas 98728·210
Verges 987 0·510
Woodland 206 5·910
Woodland edges  21 0·610
Woodland rides   0 0·01 2

The distribution of the 16 coarse habitat types that were used to stratify the study area can be used to predict successfully the distributions and densities of individual butterfly species within the study region (Cowley et al. 2000). These habitats are therefore likely to be correlated with environmental differences of relevance to the distributions and densities of butterflies.

For the collection of regional distribution data, the study area was divided into 140 cells using a 500-m grid, based on Ordnance Survey Maps (Ordnance Survey 1994). Butterfly occurrences were collected at a 100-m resolution and expressed as species presence or absence in each of the 500 m grid cells. Distributions were collected over a 3-year period (1996–98) by a team of five researchers and are independent of the transect recording described above. During this sampling period more than 14 000 distribution records were collected: an average of over 100 records per grid square.

Five of the regional 500 m grid squares were selected at random. No single-habitat transects were located in these grid squares. Instead, each contained a 1 km butterfly transect that was monitored every other week from April through to October 1997. Transects were divided into sections according to habitat and a standardized year count (total number of individuals per 300 m, per year) was calculated for each section. Localdensity was species’ mean density on all transects sections on which one or more individuals were counted per 300 m, per year.

Within these five grid squares, butterfly distributions were collected at a 50 m resolution and local distribution was expressed as the proportion of 50 m grids occupied. Distributions were collected over a 3-year period (1996–98) and were independent of the transect recording described above. To ensure coverage of all 50 m squares, each was systematically searched every other week in 1997 in weather suitable for butterfly activity.

National densities and distributions

Species national distributions are taken from the maps contained in Heath, Pollard & Thomas (1984) and were expressed as the proportion of 10 km grid squares occupied. This measure of distribution is broadly correlated with other measures of butterfly distribution in Britain for which comparisons have been attempted (Quinn, Gaston & Arnold 1996).

National butterfly densities were derived from transect counts of adult butterflies made at over 100 sites across the UK as part of the British Butterfly Monitoring Scheme (BMS) (Pollard 1977; Pollard, Hall & Bibby 1986; Pollard & Yates 1993). BMS transects are divided into sections reflecting habitats and transect walks are conducted weekly during a 26-week period from April to October. Species’ national densities were calculated as the mean of all standardized yearly counts along each ‘occupied’ transect section. To make national densities comparable with those collected at local and regional scales, all butterfly section counts were divided by two (to standardize with the north Wales biweekly counts) and expressed as the number of individuals recorded per 300 m, per year, and a section was considered occupied if one or more individuals were counted per 300 m, per year.

Densities are considered for individual sections, rather than for entire transects to prevent systematic bias in favour of species that occurred on more habitats and therefore on more transect sections. Density must be sampled in an ecologically meaningful unit or it becomes in effect another measure of distribution (Bock & Ricklefs 1983).

Counts from all BMS transect locations were included with the exception of those considered to have unreliable or inconsistent recording (E. Pollard, personal communication). The largest numbers of distributional records used to generate the 1970–82 data class maps contained in Heath, Pollard & Thomas (1984) were collected from 1978 to 1982 and so only transect counts from these 5 years were included. Species’ densities and distributions can change over time so it is important that they are measured at a similar time (Hanski et al. 1993).

Four species, Carterocephalus palaemon Pallas, Melitaea cinxia L., Maculinea arion L. and Lycaena dispar Haworth were not recorded on any of the BMS transects between 1978 and 82 and could not be included. Five other species were excluded due to visibility or identification problems (see above). In total, a density term was calculated for 49 out of Britain’s 58 resident or regular migrant butterfly species. However, several of the rarest species are recorded on only a few BMS transect sections, thus increasing the likelihood that densities values could be strongly affected by one or more atypical sections. Certain analyses were therefore repeated excluding species that occurred on fewer than 10 transect sections between 1978 and 1982.

Some analyses were also carried out using data collected during only a single year. Those chosen were 1980 (the ‘median’ year of 1978–82) and 1990 (10 years after the median year). This provides an indication of how robust patterns are if only a single year’s data are used, or if density and distribution are measured at different times.

European and global distributions

European distributions are based on the maps contained in Higgins & Riley (1980) and Tolman (1997) and are expressed as the proportion of occupied 153 000 km2 grid squares. These grids were created by subdividing standard 611 000 km2 WORLDMAP squares (Williams 1992) into four.

To measure global range size, species distributions were given a value according to the number of broad biogeographic zones that are occupied (Higgins & Riley 1980; Tolman 1997). These zones and their scores are as follows: 1, endemic to Europe; 2, endemic to Europe and/or North Africa/near–Middle East and distributed no further east than the Ural Mountains; 3, zone two and elsewhere in Asia, but not reaching the Pacific; 4, zone three and reaching the Pacific; 5, occurring on three continents (counting Europe and Asia as two, but with North Africa and the near-Middle East included with Europe); 6, occurring on four continents (with North Africa and the near middle East included with Europe); 7, occurring on five or more continents.

Accuracy of distribution sizes

One frequently suggested explanation for the density–distribution relationship is that species that occur at low density will tend to be recorded at fewer locations, even when they occur widely (e.g. Brown 1984; Hanski et al. 1993). At national, European and global scales, the distributions of butterflies are sufficiently well known (at the resolution analysed) that the possibility of a purely artefactual basis for any density–distribution relationship is extremely unlikely. At regional and local scales, the 500 m and 50 m distributions recorded for the majority of species during the first year of field work remained more or less unchanged even after a further 2 years of sampling and three species were recorded from every 500 m square during the first year. An analysis of selected species by D. Gutiérrez et al. (unpublished) showed that estimated distribution sizes reached asymptotes during the study period. This suggests that our distributions are biologically meaningful and largely independent of species density.

Butterfly mobility

Several authors have attempted to classify British butterfly species according to their relative mobility; for example: Thomas (1984); Warren (1992); Pollard & Yates (1993) and Dennis & Shreeve (1996, 1997). For the current analyses, a more continuous index of mobility was desirable. Unfortunately, there does not appear to be any biological characteristic that can reliably be considered to reflect relative mobility; for example, wing size, relative thorax mass and wing loading have proved unsatisfactory (Lewis 1997). We therefore took a new and slightly unusual approach to this problem. Questionnaires were sent to leading butterfly ecologists in Britain and northern Europe and respondents were asked to rank butterfly species according to their experience of the relative mobility of each species. Given the experience that exists and the volume of mark–release–recapture data that has been collected, the approach seemed suitable. The results from all replies (n = 24) were used to generate a ‘consensus’ mobility ranking for each species (Appendix 1). This ranking reflects the proportion of replies that classified a species as more, less or equally mobile than every other species.

There are potential errors in seeking a single ranking of species’ mobility irrespective of year, part of range and sex. However, this method should be an effective way of ‘averaging out’ some of these errors: respondents are from a variety of locations, will have worked in many habitats and their judgement is based on many years experience. Whatever the uncertainties of the ranking, it should be unbiased with respect to the current analysis, and we are confident that the ranking is strongly correlated with real variation in mobility (it should not, however, be used to distinguish between particular pairs of species that lie close to one another within the ranking). We would expect the patterns observed to strengthen with increasingly accurate measures of relative mobility.

Niche breadth

The concept of the n-dimensional niche, while a powerful heuristic tool, is impossible to define (Colwell & Futuyma 1971), ultimately making it impossible to test the effect of niche on density–distribution relationships. Following previous authors, we took the approach of considering several important components of species’ relative niche breadth. The components chosen were larval host-plant specificity, larval feeding specificity (parts of plants) and the level of larval association with ants.

In the absence of knowledge of how to weight the relative importance of these aspects, we considered each to have equal weighting. Species were scored as follows. For larval host-plant specificity: 1, monophage (largely one species of host-plant); 2, restricted to one genus of host-plant; 3, feeding on one plant family; 4, feeding on plants from two to three families. For feeding specificity: 1, using only the seeds or the flowers of the plant; 2·5, using only specific vegetative parts, e.g. new growth; 4, using most parts of the plant. For ant association: 1, relationship with one genus only; 2, relationship with more than one genus; 4, no specific relationship with ants. These indices were summed such that each butterfly received a score in the range 3–12, with 3 representing the most specialized species.

Statistical analysis

All regressions between density and distribution were calculated using the ordinary least squares (model 1) method (McArdle 1990; Blackburn & Gaston 1998). Density was always used as the dependent variable. Before statistical analyses were conducted, we transformed both density values and distributions to homogenize variance. Density values were log10 transformed, whilst distributions were arcsine transformed (distributional data are proportions of all grid squares occupied). Inaccuracies in the data and violated statistical assumptions may add to unexplained variance in our analyses but should not yield spurious positive relationships.

The effects of phylogeny were tested using the Comparative Analysis by Independent Contrasts package (CAIC, see Purvis & Rambaut 1994, 1995). CAIC calculates the difference (or contrasts) in the traits of interest between extant pairs of species: this contrast represents the amount of evolutionary divergence since they speciated from their common ancestor. In addition, CAIC calculates contrasts at internal nodes of the phylogeny. Since we do not know what the ancestral species at these nodes were like, values at nodes are averages of the species (or nodes) that evolved from them. It is possible to weight these averages by the branch lengths but, in these analyses, all branch lengths were assumed equal. The standardized linear contrasts calculated by the CAIC programme can be analysed using standard regression techniques (Pagel & Harvey 1989; Harvey & Pagel 1991) although regressions must be forced through the origin (Garland, Harvey & Ives 1992).

An approximate phylogeny for British butterflies (Fig. 1) was produced using data from Geiger (1981); Martin & Pashley (1992); Aubert et al. (1996); De Jong, VaneWright & Ackery (1996); Weller, Pashley & Martin (1996); S. Nylin et al. (unpublished); A. Brower (unpublished) and N. Wahlberg (unpublished).

Figure 1.

Approximate phylogeny for British butterflies. Asterisks indicate species not included in any of the analyses.

Relatively few studies of the interspecific density–distribution relationship have controlled for phylogenetic effects (but see Arita 1993; Blackburn et al. 1997; Gaston, Blackburn & Gregory 1997; Quinn et al. 1997). Thus far, none of the positive relationships reported in these studies (in birds, mammals and macrolepidoptera) have arisen due to the non-independence of the data points (Gaston, Blackburn & Lawton 1997).


Simple pairwise comparisons between density and distribution reveal significant positive relationships at local and national scales and no relationship at a regional scale (Table 2a). These results were supported by a phylogenetically controlled analysis (Table 2b). Including mobility as a covariable in a multiple regression analysis had a marked effect on the form of these relationships and increased the strength of the relationship at each spatial scale (Table 3a and b). Mobility had a significant effect at regional and national scales (significant at local scale only after controlling for phylogeny): the negative effect of mobility shows that the more mobile species occur at lower local density, for a given distribution size. At a regional scale, controlling for the effects of mobility generated a significant positive relationship between density and distribution. Niche breadth had no significant effect (P < 0·05) on the form of the density–distribution relationship at any spatial scale and was therefore removed from all multiple regression analyses (Table 3).

Table 2.  The relationship between density and distribution at different spatial scales
(a) Treating species as independent data points
Dependent variableIndependent variableNSlopeSEInterceptSEr2P
Mean local densityLocal distribution192·8540·7920·9700·1720·4330·002
Mean regional densityRegional distribution260·1280·1980·6170·1690·0170·524
Mean national densityNational distribution490·2750·1060·6980·0620·1260·013
Mean national densityEuropean distribution490·1750·1220·6750·1070·0420·160
Mean national densityGlobal distribution49−0·1120·0291·1950·1070·2370·0004
(b) Controlling for phylogenetic non-independence, N is the number of independent contrasts
Dependent variableIndependent variableNSlopeSEr2P
Mean local densityLocal distribution173·1461·0310·3680·007
Mean regional densityRegional distribution240·1830·1630·0520·274
Mean national densityNational distribution450·3740·0910·2780·0002
Mean national densityEuropean distribution450·2410·1170·0880·045
Mean national densityGlobal distribution45−0·0920·0310·1700·004
Table 3.  Summaries of multiple regressions of distribution and mobility to predict mean density
(a) Treating species as independent data points
Dependent variableIndependent variableNSlopeSEInterceptSEr2P
Mean local densityLocal distribution192·7160·7541·3310·2660·5210·002
 Mobility −0·0260·015   0·106
Mean regional densityRegional distribution260·4540·1431·0510·1360·5890·004
 Mobility −0·0520·009   0·0001
Mean national densityNational distribution490·4520·1230·8360·0810·2280·017
 Mobility −0·0100·004   0·0006
Mean national densityEuropean distribution490·1750·1240·7040·1330·0450·163
 Mobility −0·0010·004   0·705
Mean national densityGlobal distribution49−0·1300·0321·1550·1100·2660·0004
 Mobility 0·0050·003   0·1840
(b) Controlling for phylogenetic non-independence, N is the number of independent contrasts
Dependent variableIndependent variableNSlopeSEr2P
Mean local densityLocal distribution173·3100·9350·5160·0030
 Mobility −0·0520·024 0·049
Mean regional densityRegional distribution240·4670·1300·5420·0016
 Mobility −0·0660·014 0·0001
Mean national densityNational distribution450·3940·1090·2800·0008
 Mobility −0·0020·005 0·734
Mean national densityEuropean distribution450·2320·1120·0920·060
 Mobility 0·0020·005 0·686
Mean national densityGlobal distribution45−0·1240·0330·2570·0005
 Mobility 0·0100·0040·031 

The national scale analyses were repeated without migrants, rarities or species with possible visibility problems, and using density data from only single years (Table 4a and b). A positive relationship between density and distribution remained despite any of these changes. However, when density data from single years were employed (1980 or 1990), the relationship only achieved statistical significance in phylogenetically controlled analyses (Table 4b).

Table 4.  The relationship between density and distribution at a national scale: (i) using density data from 1980 only (ii) using density data from 1990 only (iii) excluding species recorded on fewer than 10 BMS transect sections between 1978 and 82 (iv) excluding migratory species (Colias croceus, Pieris brassicae, P. rapae, Cynthia cardui and Vanessa atalanta) and (v) excluding P.rapae and P. napi
(a) Treating species as independent data points
Dependent variableIndependent variableNSlopeSEInterceptSEr2P
(i)Mean national density 1980National distribution470·2120·1130·7280·0680·0740·068
(ii)Mean national density 1990National distribution470·1550·0940·8270·0560·0560·108
(iii)Mean national density 1978–82, excluding raritiesNational distribution490·2460·1070·7230·0640·1050·026
(iv)Mean national density 1978–82, excluding migrantsNational distribution440·3590·1210·6980·0630·1730·005
(v)Mean national density 1978–82, excluding whitesNational distribution47−0·2820·1220·6940·0640·1060·025
(b) Controlling for phylogenetic non-independence, N is the number of independent contrasts
Dependent variableIndependent variableNSlopeSEr2P
(i)Mean national density 1980National distribution430·3190·1110·1630·007
(ii)Mean national density 1990National distribution430·2480·0840·1730·005
(iii)Mean national density 1978–82, excluding raritiesNational distribution430·2940·0880·2090·002
(iv)Mean national density 1978–82, excluding migrantsNational distribution400·3600·0980·2590·0007
(v)Mean national density 1978–82, excluding whitesNational distribution430·3750·0100·2520·0005

If species’ national densities are used with distributions measured at European and global scales, there is no relationship at a European scale and a significant negative relationship at a global scale (Table 2a). In phylogenetically controlled analyses, a significant negative relationship remains at the global scale and there is a significant positive relationship at a European scale (Table 2b).

The relationships between species density and mobility and between species distribution and mobility were also explored (Tables 5, 6). In general, mobility had a negative effect on density (Table 5a and b) and a positive effect on distribution (Table 6a and b) although these effects were not always significant. The same analyses were carried out using species’ niche breadth (Tables 7, 8). Niche breadth was not significantly related to density or distribution at any spatial scale. Host-plant specificity has been shown to be correlated with the distribution sizes of British butterflies (Hodgson 1993). For the subset of species included in the current paper no such correlation was evident (Spearman correlation of proportion of 10 km squares occupied and host plant specificity r = 0·26, n = 49, P = 0·67).

Table 5.  The relationship between density and mobility at different spatial scales
(a) Treating species as independent data points
Dependent variableIndependent variableNSlopeSEInterceptSEr2P
Mean local densityMobility19−0·0310·0191·8700·2880·1340·124
Mean regional densityMobility26−0·0400·0101·2230·1450·4080·0004
Mean national densityMobility49−0·0010·0030·8440·0910·0030·710
(b) Controlling for phylogenetic non-independence, N is the number of independent contrasts
Dependent variableIndependent variableNSlopeSEr2P
Mean local densityMobility17−0·0450·0310·1110·176
Mean regional densityMobility24−0·0480·0160·2710·008
Mean national densityMobility450·0060·0050·0290·260
Table 6.  The relationship between distribution and mobility at different spatial scales
(a) Treating species as independent data points
Dependent variableIndependent variableNSlopeSEInterceptSEr2P
Local distributionMobility19−0·0020·0050·1870·0690·0070·717
Regional distributionMobility260·0260·0120·3850·1770·1620·042
National distributionMobility490·0190·0040·0190·0960·3340·0001
European distributionMobility490·0000·0040·7970·1060·0000·987
Global distributionMobility490·0470·0142·3950·3590·4280·0021
(b) Controlling for phylogenetic non-independence, N is the number of independent contrasts
Dependent variableIndependent variableNSlopeSEr2P
Local distributionMobility170·0020·0060·0070·746
Regional distributionMobility240·0480·0200·2030·024
National distributionMobility450·0240·0060·2900·0001
European distributionMobility450·0070·0060·0330·225
Global distributionMobility450·0570·0180·1810·003
Table 7.  The relationship between density and niche at different spatial scales
(a) Treating species as independent data points
Dependent variableIndependent variableNSlopeSEInterceptSEr2P
Mean local densityNiche190·0810·0970·6800·9430·0390·417
Mean regional densityNiche26−0·0160·0690·8720·6890·0020·814
Mean national densityNiche490·0000·0290·8200·2820·0000·985
(b) Controlling for phylogenetic non-independence, N is the number of independent contrasts
Dependent variableIndependent variableNSlopeSEr2P
Mean local densityNiche170·1060·1490·0300·486
Mean regional densityNiche24−0·1270·0700·1260·082
Mean national densityNiche45−0·0190·0340·0070·590
Table 8.  The relationship between distribution and niche at different spatial scales
(a) Treating species as independent data points
Dependent variableIndependent variableNSlopeSEInterceptSEr2P
Local distributionNiche190·0350·020−0·1700·2010·1370·108
Regional distributionNiche26−0·0550·070 1·2550·6950·0250·442
National distributionNiche49 0·0390·037 0·0530·3600·0220·300
European distributionNiche49−0·0170·034 0·9620·3270·0050·616
Global distributionNiche490·0540·126 3·921·2270·0040·672
(b) Controlling for phylogenetic non-independence, N is the number of independent contrasts
Dependent variableIndependent variableNSlopeSEr2P
Local distributionNiche170·0260·029 0·0480·384
Regional distributionNiche24−0·1220·088 0·0780·177
National distributionNiche450·0330·041 0·0150·425
European distributionNiche450·0220·040 0·0070·583
Global distributionNiche450·1410·139 0·0230·316

The extent to which the densities and distributions of species are consistent over space appeared to be dependent on the magnitude of difference between the spatial scales being considered (Tables 9, 10). Densities or distributions measured at local, regional and national scales were all positively correlated (although the relationship between local and national distributions was not significant) but local and regional distributions were not correlated with European distributions and were negatively correlated with global distributions. National distributions were positively correlated with European distributions but not correlated with global distributions.

Table 9.  Matrix showing the Pearson correlation between species distributions at different spatial scales
1. Local distribution    
2. Regional distributionr = 0·56   
 n = 19    
 P = 0·012    
3. National distributionr = 0·41r = 0·72  
 n = 19n = 26   
 P = 0·08P < 0·0001   
4. European distributionr = 0·08r = 0·34r = 0·64 
 n = 19n = 26n = 49  
 P = 0·74P = 0·09P < 0·0001  
5. Global distributionr = −0·52r = −0·15r = 17r = 0·50
 n = 19n = 26n = 49n = 49 
 P = 0·02P = 0·47P = 0·24P < 0·0001 
Table 10.  Matrix showing the Pearson correlation between species densities at different spatial scales
1. Local density  
2. Regional densityr = 0·73 
 n = 19  
 P < 0·0001  
3. National densityr = 0·66r = 0·65
 n = 19n = 26 
 P = 0·002P < 0·0001 


The densities and distributions of British butterflies are positively related at local, regional and national scales (Table 2a and b), although a positive relationship is only detected at a regional scale if we control for the effects of mobility (Table 3a and b). These results, taken together, are broadly consistent with previous studies on other taxonomic groups that have demonstrated positive relationships between density and distribution regardless of the spatial scale considered (e.g. Bock 1987; Collins & Glenn 1990; Niemelä & Spence 1994; Brown 1995). Like the majority of previous studies, our r2 values are typically low, and the bulk of the variance remains unexplained (Gaston 1996).

Our results confirm and extend the findings of a previous analysis of density–distribution relationships in British butterflies (Hanski et al. 1993), and demonstrate that the reported relationship was not an artefact of treating species as independent data points. Controlling for phylogenetic association actually strengthened the relationship between density and distribution (Table 2b). Phylogenetic non-independence has been rejected as an explanation for the density–distribution relationship in all previous studies that have controlled for these effects (Gaston, Blackburn & Lawton 1997). Indeed, density and distribution are generally observed to exhibit rather little phylogenetic constraint (Gaston 1998; Gaston & Chown 1999). The positive relationship between density and distribution was also unaffected by using only a single year’s data, or by the removal of rare species, migrants or species with possible identification problems (Table 4a and b).

Within Britain, relative butterfly densities and distributions are reasonably consistent over space: those species that occur at high density and are widely distributed within 0·25 km2 tend to occur at high density and be widely distributed both in the surrounding 35 km2 and at a national level. However, increasing the spatial scale over which distributions are compared, especially beyond the national scale, results in a weakening and ultimately to a reversal of these positive relationships (Table 9).

As in other studies that consider densities and distributions measured across several spatial scales (see Hengeveld & Haeck 1982; Gaston & Lawton 1990; Gaston 1990, 1994a), species that occur at high density or are widely distributed at one scale tend to be so at larger scales, but there is some evidence to suggest that the strength of this correlation may decline as the difference between the spatial scales increases (Bock 1987). If we consider the relationship between density measured at one spatial scale and distributions measured over successively greater areas, we see a similar effect. The relationship between density and distribution moves from being positive, to absent, to negative as the magnitude of difference between the spatial scales increases (Tables 2, 3). Gaston & Lawton (1990) suggested that the strength of the density–distribution relationship in British birds was dependent on the similarity of the area in which species’ densities were measured (the reference habitat) compared to the area over which distributions were measured. In situations in which the reference habitat was atypical (based on factors such as structure, climate or range of available food resources) an inverse relationship between density and distribution was observed, whilst in intermediate cases, there was no relationship.

At a global scale, many British butterflies have range sizes that cover several continents: many stretch far into Asia and several into North America (Higgins & Riley 1980). In this context, Britain must be regarded as atypical due to: (i) the strong maritime influence on its climate; (ii) the relative scarcity of semi-natural habitat; and (iii) its position at the margins of the majority of species’ ranges. Species that are specialized in such a way as to achieve high density in Britain may not be so successful and widespread at a global scale. European distributions provide an intermediate case, and it appears that environmental conditions in Britain are sufficiently similar to those typical in Europe for national densities to be positively correlated (albeit weakly) with European distributions.

Species that are regionally dense and widespread (presumably in some way because of their adaptations) may occur at lower densities and have small distributions elsewhere in climates/environments to which they are less well suited. This explanation implies that some elements of niche are important in determining species densities and distributions. However, although niche per se might be an important factor, our specific measure of niche breadth failed to explain significant variation in density or distribution separately (Tables 7, 8) or significant variation in the density–distribution relationship. Niche-based explanations for the positive density–distribution relationship argue that generalist species should occur at high density and be widespread (Brown 1984). Previous studies have demonstrated a positive correlation between niche breadth and distribution, although many of these correlations may be due to sample size effects (Gaston 1994a). Few studies have demonstrated a positive relationship between niche breadth and density (Gaston, Blackburn & Lawton 1997). In this case, there is no evidence to support either prediction. A previous study of British butterflies found that niche breadth measured as host-plant specificity was positively correlated with species’ national distribution size (Hodgson 1993). However, for the subset of British species used in these analyses there was no significant relationship between host plant specificity and distribution (see Results). A recent study of British birds also found no relationship between niche breadth and density or distribution (Gregory & Gaston 2000).

Failure to find a positive relationship between niche and density or distribution might suggest that the relevant niche axis is not being measured. This is difficult to refute, and reflects the difficulty in making the concept of the n-dimensional niche operational (Colwell & Futuyma 1971). Brown’s hypothesis is therefore essentially impossible to test, as failure to find appropriate relations between niche breadth and density or distribution can always be explained away. Where such relationships are documented, it remains unclear how robust they would be if niche breadths were measured using an alternative axis (Gaston, Blackburn & Lawton 1997).

Some metapopulation dynamic models predict a positive relationship between distribution measured as the number (or proportion) of occupied patches and population density within patches (e.g. Hanski & Gyllenberg 1993). These predict that, for a given density, more mobile species should have a wider distribution than less mobile species, as dispersal may rescue small populations from extinction and increase the probability of unoccupied patches being colonized (Gyllenberg & Hanski 1992). The few studies that have directly tested the effect of dispersal ability on density–distribution relationships have demonstrated contradictory results, with more mobile species showing both negative and positive deviation from the underlying relationship (Hanski et al. 1993; Gutiérrez & Menéndez 1997, respectively).

In our analyses of British butterflies, the metapopution prediction is upheld as species that are more mobile show negative deviation from the density–distribution relationship (a lower density for a given distribution) at regional and national scales of analysis. However, other factors are also likely to be important: metapopulation theory is only applicable to the distributions and population dynamics of some British butterflies (Thomas 1995).

At a local scale, all species are likely to be relatively mobile within the context of a 0·25-km2 grid square, so mobility is unlikely to be very important, as we found. Sedentary species that persist within these small sampling units often occupy reasonably large areas (relative to 0·25 km2). More mobile species that occur in the surrounding region sometimes move rapidly through these areas resulting in only a few localized distribution records. These effects will weaken the impact of mobility, which barely achieved significance at this scale of analysis (Table 3).

At a regional scale, sedentary species have greater potential to be localized within the study area (Cowley et al. 1999). Mobile species have a higher probability of being recorded away from their main breeding habitats resulting in mobility having a positive effect on distribution. At a national scale, mobile, and particularly migratory species, are also likely to be recorded widely for similar reasons. At these scales, mobile species are less aggregated (see Wright 1991; Hartley 1998); for a given number of individuals in one landscape, they can be seen at lower densities in more locations. The effect of mobility reverses in the relationship between national density and global distribution size (Thomas et al. 1998): the combination of high density and high mobility increases global range size. There is no clear pattern at the intermediate, European scale.

Previous studies have demonstrated a positive relationship between mobility and distribution (Kunin & Gaston 1993; Gaston & Kunin 1997), but it is difficult to interpret the causation. Species may have narrow distributions because they fail to colonize suitable sites (low mobility causes limited distribution) (e.g. Gyllenberg & Hanski 1992) or low mobility could be a response to the low probability of migrants encountering suitable sites (limited distribution of suitable breeding areas causes evolution of low mobility) (e.g. Thomas, Hill & Lewis 1998).

Our results suggest that the positive density–distribution relationship in British butterflies is general and robust. The relationship is apparent at a variety of spatial scales and is not an artefact of species’ phylogenetic association. If density and distribution are analysed at different spatial scales, the relationship weakens as the magnitude of difference between scales increases, eventually becoming negative. This suggests that the interaction of niche and environment may be important, although niche breadth was not directly related to density or distribution, or to variation in the density–distribution relationship. Mobility was found to have a positive effect on distribution and a negative effect on density and more mobile species showed a negative deviation from the underlying density–distribution relationship (they were more ‘spread out’). Mobility also appeared to be responsible for some of the observed difference in the relationship between density and distribution at different scales of analysis. It was encouraging that phylogenetic control and inclusion of species’ mobility strengthened, rather than weakened the generality of the relationships between density and distribution.


We were supported by NERC (LSPE) grant GST/04/1211. M. Cowley has a NERC CASE studentship joint with ITE. J. León-Cortés was supported by a scholarship from the National Council of Science in Mexico (CoNaCyT, 92535), D. Gutiérrez was supported by a Marie Curie Training grant from the commission of European Communities (ERBFMICT 961523). We are grateful to Tim Blackburn for assistance with the CIAC analyses. We thank Rosa Menéndez, Roger Dennis and Caroline Wilmot for distribution records, all who completed the butterfly mobility questionnaire, the North Wales Wildlife Trust, NERC ARS 98/5 and the many landowners in the north Wales study area. Liz Howe at CCW provided Phase-1 survey data.

Received 15 November 1999; revision received 28 October 2000


Appendix 1 

Species density, distribution, mobility and niche breadth

Species nameNumber of local 50 m squaresMean local densityProportion of regional 500 m squaresMean regional densityNational density 1978–82National density 1980National density 1990Percentage of national 10 km squaresEuropean distributionGlobal distributionNiche breadthMobility score
Aglais urticae127 87100·0011·8210·10 6·68 9·46 97·43604 7·538
Anthocharis cardamines 25  1·6 67·14 2·60 4·64 5·00 6·14 67·39544 832
Aphantopus hyperantus  1  0  6·43 9·5013·1611·9015·01 53·784031116
Argynnis adippe     5·15 5·3511·03  6·835141028
Argynnis aglaja 20  2·8 25·71 2·25 3·84 3·7711·08 32·705941029
Argynnis paphia     6·77 6·61 7·89 19·135141031
Aricia agestis 78 47·6 53·57 9·72 6·49 6·36 5·67 17·704931012
Aricia artaxerxes     5·36 1·5011·96  3·35431 7 7
Boloria euphrosyne     7·70 7·3611·73 19·135141018
Boloria selene     7·21 6·06 9·66 33·094351019
Callophrys rubi     3·39 3·48 6·70 31·17685 8·514
Celastrina argiolus 60 26·3 86·43 2·43 2·30 2·36 7·48 36·78636 934
Coenonympha pamphilus109 61·1 48·5710·4014·9313·0616·27 88·266631117
Coenonympha tullia     2·28 1·19 6·46 14·6536510·5 4
Colias croceus     2·26 2·72 2·22 19·004521143
Cupido minimus     4·06 2·78 5·10 10·26503 4 1
Cynthia cardui 15  0  5·00 1·00 3·04 3·28 3·62 63·436571144
Erebia aethiops     5·74 7·0227·13 12·262431113
Erebia epiphron     5·64    1·43181 9 3
Erynnis tages  1  0 10·00 2·50 4·39 4·44 4·70 30·61493 9·510
Eurodryas aurinia    11·42 7·09 2·60 13·35492 913
Gonepteryx rhamni  6  0 27·86 1·40 5·99 5·59 8·72 43·70594 9·536
Hamearis lucina     3·43 1·77 3·61  7·0938210 9
Hesperia comma     1·86 2·18 6·60  1·39535 915
Hipparchia semele 55 26·1 41·4321·85 9·71 7·71 7·05 30·175021122
Inachis io 33 19 86·43 4·05 8·20 5·57 7·43 69·96524 7·539
Ladoga camilla     3·18 1·97 4·31 12·48324 927
Lasiommata megera 29  3 44·29 2·14 6·18 5·05 6·61 64·096031130
Leptidea sinapis     3·01 1·98 5·35  5·655331114
Lycaena phlaeas 31 11·8 68·57 2·82 4·79 4·39 5·94 76·96696 726
Lysandra bellargus    18·5319·5416·13  4·48392 7 8
Lysandra coridon    43·6544·8025·67  9·61321 711
Maniola jurtina293178·5 98·5719·4039·8436·5335·24 94·916321125
Melanargia galathea    16·9013·3310·69 19·654631124
Mellicta athalia     2·79 10·59  0·8748212 5
Ochlodes venata 28  0 50·71 3·83 5·39 5·47 6·63 57·705041120
Papilio machaon     3·66 1·92 3·89  0·96535 937
Pararge aegeria114242·1 72·1413·4710·86 8·5711·67 45·006531123
Pieris brassicae 98 15·2 91·43 2·06 6·82 5·33 4·55 85·966531041
Pieris napi 89 43·8 87·86 5·7817·3814·7611·39 88·096121135
Pieris rapae 94 24·25100·00 2·65 8·97 6·8210·59100·006331140
Plebejus argus 37 99·9 16·4392·86 8·18 9·37 5·04  6·74524 7·5 2
Polygonia c-album  9  0 40·00 2·27 3·64 2·98 4·22 40·2654410·533
Polyommatus icarus 76 54·7 92·8610·5212·2913·6313·59 86·96694 921
Pyrgus malvae     3·44 3·88 3·36 20·8749311 6
Pyronia tithonus173125·2 95·0018·0819·5714·2720·80 49·703521121
Thymelicus acteon     9·54 7·72   0·61452 9 5
Thymelicus sylvestris 10  0 23·57 3·9214·0311·0310·17 50·265031119
Vanessa atalanta 46 19·1 82·86 1·77 4·38 2·80 4·97 72·30656 9·542