The geographical range structure of the holly leaf-miner. I. Population density


  • Andrew M. Brewer,

    1. Biodiversity and Macroecology Group, Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK
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  • Kevin J. Gaston

    Corresponding author
    1. Biodiversity and Macroecology Group, Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK
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Kevin J. Gaston, Biodiversity and Macroecology Group, Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK. Tel.: 0114 2220030. Fax: 0114 2220002. E-mail:


  • 1The local population density structure of a phytophagous insect, the holly leaf-miner Phytomyza ilicis Curtis, was examined across its natural geographical range in Europe.
  • 2The frequency distribution of the number of sample sites at which the leaf-miner attained different densities per tree was strongly right-skewed, with the species being absent from a large number of sites at which its host occurred, particularly in southern regions.
  • 3There was a decline in the spatial autocorrelation of leaf-miner densities with increasing distance between sample sites, with negative autocorrelation at long lags resulting in part from high densities being attained at the north-eastern range limits and low densities at the southern range limits.
  • 4Partial regression analysis was used to model leaf-miner densities in terms of spatial position within the geographical range and the broad climate experienced at the sample localities. This accounted for between 40 and 65% of the variation in densities, dependent upon how the leaf-miner’s geographical range was defined.
  • 5While overall these results are at odds with common and intuitively appealing assertions about the abundance structure of geographical ranges, they can readily be interpreted in terms of a simple modification of a general model of such structures.


It has long been accepted that, at least to a first approximation, in general local population densities of a species can be regarded as tending to peak towards the centre of its geographical range and to decline towards the periphery (Shelford 1911; Kendeigh 1974; Hengeveld, Kooijman & Taillie 1979; Hengeveld 1989; Lawton 1993; Safriel, Volis & Kark 1994; Brown, Stevens & Kaufman 1996; Maurer 1999). Indeed, a number of theoretical models have been developed to explain why this should be so (Brown 1984; Williams 1988; Hengeveld 1989; Maurer & Brown 1989; Hall, Stanford & Hauer 1992; Maurer 1999), and the pattern provides a central presumption of many discussions in biogeography and macroecology (e.g. Hengeveld 1990; Brown 1995; Brown & Lomolino 1998; Maurer 1999). Perhaps surprisingly, however, it finds convincing support from rather few published empirical studies, even in an amended form that recognizes that low abundances may be found across the full breadth of a geographical range but maintains that mean or maximum densities will still tend to decrease towards range limits (see Brown, Mehlman & Stevens 1995; Enquist, Jordan & Brown 1995; Brown & Lomolino 1998). Mayr (1963) observed that the pattern itself had long been accepted by naturalists because of its intuitive appeal but that it was based on a general observation that lacked detailed quantitative support. Relatively little has changed since then.

Many assertions regarding patterns of local abundance are based on impressions derived from visual inspection of maps of abundance surfaces across all or parts of the geographical range of a species. These are problematic on the grounds that the human visual system is adept at seeing regularities in images that may not be present, particularly when there is some preconception as to what will be found. A variety of more formal analyses have suggested evidence for a decline in population abundances towards the edges of geographical ranges (e.g. McClure & Price 1976; Bock, Bock & Lepthien 1977; Hengeveld & Haeck 1981, 1982; Randall 1982; Emlen et al. 1986; Bart & Klosiewski 1989; Svensson 1992; Tellería & Santos 1993; Maurer & Villard 1994; Maurer 1994; Whitcomb et al. 1994; Brown et al. 1995; Carey, Watkinson & Gerard 1995; Curnutt, Pimm & Maurer 1996). A number of others have failed to find support for the pattern (e.g. Griggs 1914; Rapoport 1982; Brussard 1984; Carter & Prince 1985; Wiens 1989; Woods & Davis 1989; Blackburn et al. 1999).

A paucity of high quality data, the use of very indir-ect measures of abundance and complexities in the application of analytical techniques render the results of some of these studies difficult to interpret (see Grice, Caughley & Short 1986; Wiens 1989; Gaston 1994). In addition, a number of the analyses consider only portions, sometimes rather small, of the geographical ranges of species (e.g. Hengeveld & Haeck 1981, 1982; Griggs 1914; Randall 1982; Carter & Prince 1985; Woods & Davis 1989; Svensson 1992; Tellería & Santos 1993; Carey et al. 1995; Blackburn et al. 1999), raising concerns as to how well they reflect the pattern of change in local abundances across entire geographical ranges. The principal exceptions, and some of the studies providing the most convincing evidence for a peak in abundances towards the centre of geographical ranges, are those for North American birds, for which interpolated maps have now been published of variation in the abundances of both summering and wintering species across much of the continent, from data generated by the Breeding Bird Survey and Christmas Bird Counts (Root 1988; Price, Droege & Price 1995). Range-wide studies are required for other taxa on other continents, to see how general these findings are.

In this paper we examine the local abundance structure of a phytophagous insect, the holly leaf-miner Phytomyza ilicis Curtis (Diptera: Agromyzidae), across the bulk of its natural overall geographical range, in Europe. Previous studies of this species have revealed a great deal of variation in densities at small spatial scales (e.g. within a single host plant or between host plants within a small locality: Heads & Lawton 1983; Valladares & Lawton 1991; McGeoch & Gaston 2000). However, it is not known how this variability may contribute to or obscure any spatial structure that may be present at larger scales.

the study system

European (or English) holly Ilex aquifolium L. is a relatively small, dioecious, evergreen tree. It has distinctive, dark green, glossy leaves that are usually spiny with a relatively thick cuticle. Its natural range extends throughout north-western, central and southern Europe (Fig. 1; Peterken & Lloyd 1967; Hultén & Fries 1986). It can also be found less commonly in scattered localities in parts of North Africa and has been reported as having a narrow band of distribution extending into Asia Minor, although there is some doubt as to whether this is indeed so. European holly was also introduced to North America and Canada in the late nineteenth century, where it has been cultivated extensively (Cameron 1939).

Figure 1.

Interpolated surface of leaf-miner densities within the range of European holly. Geographic range of holly compiled from Hultén & Fries (1986) and our own observations. Points on the map indicate the positions of sites sampled. Filled circles indicate sites where leaf-miners were present on at least one tree. Open circles indicate where leaf-miners were absent.

Phytomyza ilicis, the holly leaf-miner, is the most common insect herbivore of European holly. It is strictly monophagous, so its geographical range is ultimately limited by the availability of holly trees. The life histories of P. ilicis and its natural enemies in Britain have been described in detail by Cameron (1939) and Lewis & Taylor (1967). Put briefly, the holly leaf-miner exhibits a univoltine life-cycle. Eggs are laid in June on new holly leaves (the tree has just one flush of new leaves per year) into the base of the underside of the midrib. The larvae eat through the midrib and enter the outer parenchyma of the leaf lamina during the autumn. They feed throughout the following winter months and pupate in the mine in March, emerging from the leaf as adults in late May or June.

Several factors contribute to making the holly leaf-miner an ideal model system for large scale population surveys. First, the larvae produce large, irregular mines that are clearly visible. Moreover, since holly is evergreen and its leaves typically stay on the tree for up to 5 years (Peterken & Lloyd 1967), leaves of a particular age can be sampled for a substantial period after the life-cycle of the leaf-miner is completed to give an estimate of the density for that generation. Therefore local population densities of this species can be relatively easily censused and mapped.


data collection

Between June and December 1998 we conducted a survey of leaf-miner densities throughout most of the natural range of holly. Our aim was to obtain a good coverage, sampling both the centre and the range edges. The survey was organized as a series of routes of varying duration: Spain and Portugal; Norway; Germany, Italy and France; United Kingdom; Ireland; Greece (Fig. 1). During each survey we sampled leaf-miner densities at as many sites as time allowed.

The abundance of the holly leaf miner on a given tree has been found to be quite stable from year to year, relative to the level of variation in densities between trees (Valladares & Lawton 1991; Brewer & Gaston, unpublished observations). Trees that are susceptible to attack tend consistently to be so, while those that are not remain largely free from miners. This seems to follow from the stability of the resource base represented by a particular tree, the tight linkage between the emergence of adult miners and leaf flush (reducing their vulnerability to seasonal variation when resources become available) and substantial differences between trees in their suitability as hosts. In consequence, while the present survey concerned only a single generation of leaf-miners, any patterns in densities revealed are likely to be representative of those to be found based on densities averaged over several generations.

Throughout its range, holly occurs naturally predominantly as a subordinate or understorey plant of deciduous woodland. Wherever possible it was sampled in this habitat type [in practice, this meant that the vast majority (> 85%) of trees were sampled from deciduous woodland, including from both the centre and the edge of its geographical range]. This served particularly to avoid the confounding effects of the planting of holly in heavily human modified environments (e.g. cemeteries, urbanized areas); holly trees in urban areas, for example, typically support higher mine densities than those in deciduous woodland (Brewer, unpublished data).

Leaf-miner density estimates were taken from 10 trees at each sampling site, or as many as possible where less than 10 trees were present. Following Heads & Lawton (1983) and Valladares & Lawton (1991), density was estimated on each tree by haphazardly sampling 200 1-year-old leaves (or all the leaves of this age if less than 200 were present on the tree) from all around the canopy, between ground level and a height of approximately 2 m. This protocol gives an estimate of density for the previous growing season. Leaves of a suitable age can readily be distinguished by their position between the annual nodes on the branch. For each leaf the number of mines present was recorded, although typically only one mine per leaf is found except in areas of very high leaf-miner density (Heads & Lawton 1983; Brewer, unpublished data).

For trees on which no mines were found in samples of 200 leaves of the appropriate age, an exhaustive search was made of the rest of the tree. In very rare cases some mines would be found, in which case densities were treated as an arbitrarily small number (0·1 mines per 200 leaves). This occurred for only four trees (at only one site, in Germany, where no mines were found on leaves of the appropriate age, were a few found on older leaves of the same trees).

The unit for the analyses was the density of holly leaf-miners at a site, calculated as the total number of mines recorded divided by the total number of leaves examined, across all trees that were sampled. The spatial relations of sites, which can be viewed as one form of potential non-independence of data points (Legendre 1993), were addressed explicitly in the analyses (see below). The geographical location (expressed as decimal degrees longitude and latitude) of each site and its altitude (m) were obtained from appropriate maps.

meteorological data

Regional climatic data over a 0·5° × 0·5° grid were obtained from a coverage of twentieth century terrestrial surface climate (New, Hulme & Jones 2000). From this coverage, mean values for winter (September–February) and summer (March–August) temperatures, precipitation and humidity were calculated from data for the 10-year period between 1986 and 1995, inclusive. All these factors are possible influences on the distribution and abundance of holly or the leaf-miner.

data analysis

A number of geostatistical techniques are available for handling data sets where each sample can be represented as a point estimate in two-dimensional space. We outline briefly those employed here, but for further details see Legendre & Fortin (1989), Rossi et al. (1992), Legendre (1993), Maurer (1994) and Legendre & Legendre (1998).

(i) Spatial autocorrelation

Spatial autocorrelation analysis (Cliff & Ord 1973) was used to establish whether local population densities of P. ilicis exhibited any simple spatial structure across the geographical range. Moran’s I was calculated for 15 equal distance intervals, and spatial correlograms were produced and tested for significant spatial dependence in the data. Since the survey covered a relatively large geographical area, site coordinates were not treated as Cartesian coordinates when measuring distances between them. Instead, distances along great circles were calculated to take into account the curvature of the earth’s surface. Bonferroni’s correction for multiple comparisons was used when assessing overall correlogram significance.

(ii) Interpolation

Leaf-miner densities were interpolated across space to estimate the overall local density structure of the geographical range of the species. Densities were entered into a geographical information system (GIS; ArcInfo & ArcView, Environmental Systems Research Institute Inc.) as point coverages, and interpolated using an inverse distance weighting technique (IDW) to create a grid comprising 0·1° × 0·1° cells over the study area (other interpolation methods give similar results). Following the recommendations of Isaaks & Srivastava (1989), 12 nearest neighbours were used to estimate the values with weights inversely proportional to the square of the distance from the estimated cell.

(iii) Partial regression analysis

Partial regression analysis is one of several techniques that can be used when attempting to model data showing spatial dependence (see Clifford & Richardson 1985; Clifford, Richardson & Hémon 1989; Getis 1990; Legendre 1993; Carroll & Pearson 1998; Legendre & Legendre 1998; for applications and reviews of the available techniques). Following the methodology suggested by Legendre (1993), we used the method to estimate how much variation in leaf-miner densities can be attributed to regional climatic variation and altitude once the effect of spatial location has been taken into account. The spatial component of the holly leaf-miner density data was modelled using a third-order polynomial of the form:

f(x,y) = b0 + b1x + b2y + b3x2 + b4xy + b5y2 + b6x3 +b7x2y + b8xy2 +b9y3

where x and y represent longitude and latitude, respectively. This expression is sufficient to extract any linear gradients from the data as well as more complex features such as patches or gaps (Legendre 1990; Borcard, Legendre & Drapeau 1992). Significant terms, determined by conducting a stepwise regression of leaf-miner densities on a matrix of all of the terms in the expression, were retained to construct a new matrix of spatial variables to be used in the subsequent analysis. To ensure that this matrix provided an adequate description of the spatial structure of leaf-miner densities, the residuals from the regression were checked for spatial dependence using autocorrelation analysis. Similarly, leaf-miner densities were regressed onto a matrix containing the climate and altitude data and significant terms determined after stepwise regression by elimination were retained.

The combined effect of both the environmental and spatial variables on leaf-miner densities was calculated by multiple regression of leaf-miner densities onto both sets of predictive variables combined. The explanatory potential of the environmental variables, after correcting for spatial dependence, was calculated by measuring the change in deviance accounted for the regression model after the environmental variables were removed. This fraction was then tested to determine whether the change in deviance was statistically significant.

At the end of the partial regression analysis, variation in leaf-miner densities could be divided into four components: (a) non-spatial environmental – the fraction that can be explained by the environmental variables independent of any spatial structure; (b) spatially structured environmental – spatial structuring in leaf-miner densities that is shared with the environmental data; (c) non-environmental spatial – spatial structure in leaf-miner densities that is not shared with the environmental variables; and (d) unexplained (residual) variation. These components and their associated probabilities allow several hypotheses about the causal relationships between environmental variation, spatial position and leaf-miner density to be tested.

The method employed here is essentially the same as Legendre’s (1993) third extension to partial regression analysis with some minor modifications. Since our leaf-miner abundance data were in the form of proportions (number of mines per number of leaves sampled), binomial errors were modelled. This results in proportions of deviance explained which are analogous to the partial r2 statistics at the end of the analysis that Legendre uses. In addition, during the stepwise regressions, any overdispersion in the residual deviance was corrected for using Williams’ procedure where appropriate (Collett 1991; Crawley 1993) before testing for parameter significance. All of the partial regression analyses were conducted using GLIM version 3·77 (Royal Statistical Society, London).


A total of 703 holly trees were sampled during the course of the survey at 96 sites. This resulted in the examination of 133 685 leaves. A total of 7284 mines of P. ilicis were found, giving a mean infestation rate of approximately 5·5% across all trees. However, no mines were recorded on nearly 50% of the trees sampled (Fig. 2a).

Figure 2.

Frequency histograms of P. ilicis densities across the natural geographical range (a) on trees sampled, and (b) taken from the interpolated surface (Fig. 1).

The holly leaf-miner was almost entirely absent from large regions of the geographical range of holly, particularly in Spain, Portugal, Greece and most of Italy. This was true even though in some of these areas (e.g. parts of Spain) holly itself is locally abundant. The overall frequency distribution of local densities at sample sites exhibits a strong right-hand skew, with most sites at which the miner was found being occupied at relatively low densities (Fig. 2a). Some of the highest densities were found at just two sites in Italy, but the peak densities were found consistently in the extreme north-east of the range, along the Norwegian coast. In some areas where holly leaf-miners attained high densities holly itself was scarce (e.g. Norway).

spatial autocorrelation

Since not all sites sampled supported populations of the holly leaf-miner, and it is rather difficult to define the boundaries of the range of a species exactly (Gaston 1994; Blackburn et al. 1999), there is some difficulty in deciding which sites to include in a spatial autocorrelation analysis. If all sites where the leaf-miner was absent are omitted from the analysis, we risk losing information about the spatial structure of the local populations since some of these sites lie well within the outermost boundaries of the geographical occurrence of the species. However, incorporating data from all of the sites sampled would result in the inclusion of a large number of sites from which P. ilicis was entirely absent, many of which are separated from one another by relatively short distances, and represent regions of the geographical range of holly which lie outside that of the leaf-miner. This could inflate artificially the value of Moran’s I obtained for short separation distances (lags). As a pragmatic solution, we present and compare both correlograms, one for all sites sampled and one which omits those sites where leaf-miners were absent.

The correlogram for all sites sampled shows that there is significant and relatively strong spatial dependence in the local densities of the holly leaf-miner across its geographical range (Fig. 3a). That is, sites relatively close together are more similar to each other than those further apart. Up to approximately 750 km, leaf-miner densities are positively autocorrelated. In addition, at lags of over 2000 km there is a sharp discontinuity in the autocorrelation profile and densities become negatively autocorrelated. This represents largely the relationship between sampling sites at opposite extremes of the geographical range and suggests a highly asymmetric abundance structure to the range of this species. The correlogram constructed only for those sites with leaf-miners present shows qualitatively the same spatial structure (Fig. 3b). However, note that Moran’s I falls to zero at a shorter lag of 500 km.

Figure 3.

Spatial correlograms of P. ilicis densities across the geographical range for (a) all sites sampled (P < 0·01), and (b) sites with leaf-miners present only (P < 0·01). Scale on the x-axis represents maximum distance in each distance class. Filled circles indicate significant values of Moran’s I (P < 0·05). Overall correlogram significance was tested using Bonferroni’s correction for multiple comparisons.


The interpolated map of leaf-miner densities shows clearly a strong spatial structure in the geographical distribution of local densities of P. ilicis (Fig. 1). High to moderate densities fall predominantly in a band running north-east to south-west, from the south-west coast of Norway, across Denmark, Holland, Belgium, northern France and southern Britain. Densities largely decline away from this band, with the principal exception of a peak of high density in central Italy. The interpolation also shows why at the longest lags (e.g. between Norway and Spain) Moran’s I was strongly negative, with the density peak in Norway contrasting with the absence of holly leaf-miners in Spain.

Summing under the interpolated surface also produces a strongly right-skewed frequency distribution of the extent of areas over which P. ilicis attains different local densities (Fig. 2b). This frequency distribution differs principally from that for the raw sample data in that the zero density class is significantly smaller (Fig. 2a).

partial regression analysis

Deciding which sites to include in the partial regression presents a similar problem to that encountered in the autocorrelation analysis. Again, we conducted analyses for all sites and also only for the subset of sites where leaf-miners were present. In an additional analysis the leaf-miner density data was simplified to a binary response variable, representing presence or absence from a site. This was considered to be another way of determining how well the geographical range of the holly leaf-miner could be explained by environmental variation after accounting for spatial dependence.

  • 1Regression over all sites (including zero densities). Including all 96 sites in the analysis, after stepwise regression by elimination the regional environmental variables that were found to contribute significantly in accounting for variation in leaf-miner densities were mean winter and summer temperatures, winter precipitation and humidity. When considered alone, these accounted for 48·0% of the deviance in leaf-miner densities (F4,91 = 19·9, P < 0·01). In addition, five terms from the coordinates polynomial contributed significantly to explaining the spatial structure of leaf-miner densities. These terms were x, y, xy, y2 and xy2 (F5,90 = 18·1, P < 0·01), where x and y represent longitude and latitude, respectively. When all of these variables were considered together, 55·2% of the total variation in leaf-miner densities was accounted for by the full model (Table 1). Once spatial position was taken into account, only 7·8% could be attributed to environmental variation alone, the rest was shared with the spatial component. However, this reduced fraction was still significant at the 5% level. Therefore, despite the spatial structure shared by both the local population densities of P. ilicis and environmental variation, a significant environmental effect on leaf-miner density could be discerned.
  • 2Regression over sites with leaf-miners present only (no zeros). In this analysis 61 sites which had at least one infested tree were included. After stepwise regression, winter and summer temperatures and winter precipitation were found to contribute significantly to the model and three terms from the coordinates polynomial; x, xy and xy2 (Table 1). When these variables were considered together in the partial regression, 40·0% of the total variation could be accounted for by the full model. However, the environmental variables were not found to contribute significantly after taking into account the spatial component. Moreover, the spatially structured environmental fraction was negative.
  • 3Binary response model. Finally, using a simplified binary response variable for all 96 sites, winter humidity was found to be the only environmental variable that contributed significantly to predicting whether leaf-miners would be present at a site (χ2 = 77·23, P < 0·01) (Table 1). From the coordinates matrix, the terms x, y, xy and x2 were significant (χ2 = 68·70, P < 0·01). After the partial regression, the total amount of variation explained was 65·4% with the environment only component accounting for just 4·1% of the variation. However, this component was significant at the 5% level.
Table 1.  Results of the partial regressions of Phytomyza ilicis densities on environmental data taking into account a spatial component. Environmental variables: wt = winter temperature; st = summer temperature; wp = winter precipitation; wh = winter humidity
Leaf-miner dataEnvironmental variablesCoordinate termsDeviance accounted for in leaf-miner data (%)Significance test
TotalEnvEnv × SpaceSpace
All siteswt, st, wp, whx y y2xy xy255·27·840·7 6·7F4,86 = 2·49
       P < 0·05
Occupied sites onlywt, st, wpx xy xy240·08·9−2·233·3F3,57 = 0·943
Presence/absence (binary response)whx y xy x265·44·150·410·9χ2 = 5·15
      P < 0·05


The holly leaf-miner occupies much of the geographical range of its host plant (Fig. 1). However, on the basis of extensive sampling (albeit for a single season, but see Methods) it is clear that it is also absent from large areas, particularly in the south (we predict that it will also be absent from the peripheral, but unsampled, host plant occurrences in North Africa). Leaf-miners in general might be expected to occupy a higher proportion of the geographical ranges of their hosts than do externally feeding insects because of their more intimate host associations (Cornell 1989). Given that many externally feeding herbivorous insects plainly occupy a rather small proportion of the range of their host (e.g. Strong, Lawton & Southwood 1984; Quinn, Gaston & Roy 1997, 1998), the data for the holly leaf-miner are not obviously at odds with this suggestion.

The strong right skew to the frequency distribution of estimated local densities of the holly leaf-miner across the geographical range of its host plant conforms to general expectations about the shapes of intraspecific abundance distributions (e.g. Taylor, Woiwod & Perry 1978; Perry & Taylor 1985, 1986; Strayer 1991; Gaston 1994; Brown et al. 1995). However, examples are scarce in which the pattern has been demonstrated for sample sites distributed across the majority of a species’ geographical range, and in which the zero class has been retained (Fig. 2a). The zero class may comprise sites at which the miner is genuinely absent (structural zeros) and sites at which it occurs but was missed during sampling (sampling zeros), but in this particular case the bulk are without doubt of the former kind. Where it occurs, most sites support relatively low densities of the holly leaf-miner, and only a very few support high ones. Of course, to some extent this is a biased estimate of the true population frequency distribution since the number of sites sampled was not equal between different regions. Rather, sampling intensity is more a reflection of the time available to sample in any one region. For example, since there were very few mines found in Spain and Portugal there was more time to visit further sites. Therefore one would expect bias to enter into any global estimate of the frequency–abundance histogram based on raw data alone and for this bias to make the sample histogram more right-skewed. Possibly, a more representative histogram is the one based on the interpolated surface of leaf-miner densities across the range of holly (Fig. 2b). Here we see a similar pattern to the raw data plot but with a much lower frequency of sites supporting no leaf-miners. However, even this is not necessarily completely representative since the density of holly trees, that is the number of suitable habitat patches available for the holly leaf-miner to colonize, also varies in space.

Correlograms are increasingly being used to check for spatial dependence in local abundance data. Koenig (1999) warns that despite the fact that a correlogram may be shown to be significantly non-random (due to the large number of comparisons – and hence degrees of freedom – between pairs of samples), individual values of Moran’s I may be so low within each distance class as to be biologically meaningless. However, the autocorrelation profiles for P. ilicis across its geographical range indicate very strong spatial structuring of local population densities. As documented here, positive autocorrelation has been found to be a common (albeit not ubiquitous, e.g. Koenig 1998, 1999) feature at short lags (e.g. Eber & Brandl 1994; Brown et al. 1995). As one expects intuitively, many species have similar densities at sites that are close to one another. Across an entire geographical range, Brown et al. (1995) suggested that autocorrelograms of densities may for many species show a characteristic bowl-shape, with marked positive autocorrelation at both short and very long lags (see also Villard & Maurer 1996). They argue that this reflects a symmetric unimodal abundance structure to ranges, with the high autocorrelation at long lags indicating the similarly low levels of density found at opposing range edges. The correlograms for leaf-miner densities do not show this pattern, and the abundance structure of its range plainly does not exhibit a central peak which declines towards the range limits (Fig. 1). However, it should also be noted that although a symmetric unimodal abundance distribution would have a bowl-shaped autocorrelation profile the converse is not necessarily true. Brown et al. (1995) give four examples of bird distributions that do show this autocorrelation pattern using data from the North American Breeding Bird Survey. However, reference to abundance maps for these species generated from the same data source (Price et al. 1995) reveal that arguably none of them have a central abundance peak. Most notably, the map for the Carolina wren Thryothorus ludovicianus is extremely asymmetric, with peak abundances toward the south-east coast of the United States, yet its autocorrelation profile is plainly bowl-shaped.

Despite the pitfalls present when interpreting such maps visually, even a cautious interpretation of the interpolated surface of densities of the holly leaf-miner suggests that it too has a strongly asymmetric spatial pattern of local abundance, with peak values being attained toward the north-eastern extremity of its geographical range (Fig. 1). However, the pattern is clearly quite complex. Across several regions, such as Britain, there appear to be gradients in densities that might, falsely, suggest simple trends of increasing density towards the range centre if these were considered in isolation. This raises the spectre that the results of previous analyses of abundance structure based on only parts of geographical ranges may indeed prove misleading (see Introduction).

As Legendre & Legendre (1998) point out, there are two motivations for analysing data using analyses related to the partial regressions we present here. One is that spatial structuring can be a major source of false correlations that do not indicate causal relationships between environmental variation and the response variable of interest. The other is that both the spatial and non-spatial components of the environmental variation may be considered to be causal and the magnitude of the spatially structured environmental effect or some other component of the variation in the response variable may be of interest in itself.

Taking the first more conservative approach, it is encouraging that despite the high degree of spatial dependence in our data that some effect of environmental variation on holly leaf-miner populations can be discerned when this is taken into account (Table 1). However, when considering the subset of the data that included only occupied sites, the amount of variation accounted for by the effect of environment alone was not found to be significant. This does not mean that there is no causal relationship between environmental variation and leaf-miner densities but it does indicate that if such a relationship exists, it cannot be disentangled from the confounding effect of space for this particular analysis. Considering all three analyses together, environmental variation has been shown to influence whether holly leaf-miner populations will be present at particular sites across the range of its host plant, although we have not demonstrated that there is a consistent significant effect on the internal density structure of the leaf-miner’s range itself. The partitioning of variation in an ecological response variable between spatial and environmental effects is an appealing approach yet since the components are not strictly additive (see Legendre & Legendre 1998 for a full account) some caution must be used in interpretation of the results. The small negative value obtained for the spatially structured environmental component in the second analysis indicates that the environmental and spatial variables together explain leaf-miner densities better than the sum of their individual effects and that the environmental variables themselves have significant spatial structure. However, the two sets of variables are having effects of opposite sign on holly leaf-miner densities. In the other two analyses the amount of spatially structured environmental variation is by far the largest proportion of the total explained variation. This is typical of the results found by others when analysing ecological data in this and similar ways. At a smaller, regional scale, in a study of the factors that affect the species composition of oribatid mite communities, Borcard et al. (1992) found that two-thirds of the variation explained by environmental variables could equally well be predicted by spatial position. Kitron et al. (1996) used the method proposed by Getis (1990) in their analysis of tsetse fly distribution using remotely sensed environmental data. They also found that the spatial component of their environmental data contributed more to explaining fly catches than the nonspatial component. The remaining spatial variation may be linked to unknown environmental variables that also contribute to the unexplained variation (Borcard et al. 1992). At smaller scales, it may reflect the effects of biotic processes between patches such as dispersal, predation or disturbance (Legendre 1993), although we feel that these effects are unlikely to be detected across an entire geographical range (see below).

The stepwise regressions for each of the data sets yielded different combinations of the environmental and spatial variables. We have not attempted to attribute any biological significance to this since the environmental variables themselves are often closely correlated (Table 2) and the results of a stepwise regression can be sensitive to the method used. Our intention here is simply to provide the minimum adequate model for explaining leaf-miner densities in terms of both environmental variation and spatial position. The results of our analyses demonstrate the difficulty in identifying important controlling factors on local population densities in the presence of correlated environmental variables and a high degree of spatial dependence. These are problems that will often be unavoidable in observational surveys of this nature, which ultimately can only help to formulate hypotheses about the regulation of abundance in space and would require subsequent testing by experimental studies.

Table 2.  Matrix of correlation coefficients between the regional environmental variables for all sites sampled during the survey
 Winter temperatureSummer temperatureWinter precipitationSummer humidityWinter precipitationSummer humidity
Summer temperature 0·71     
Winter precipitation−0·15−0·53    
Summer precipitation−0·45−0·52 0·77   
Winter humidity−0·38−0·62 0·24 0·25  
Summer humidity−0·36−0·75 0·51 0·51 0·86 
Altitude 0·19 0·36−0·34−0·33−0·77−0·71

Taking the rather less conservative approach to interpreting the results of the partial regression analysis, which is at least in part justified since some causal influence of environment on leaf-miner densities can be inferred, it is interesting to look at the findings reported here in the light of a popular ecological hypothesis for the structure of the geographical range. In so doing, it should, of course, be emphasized that the pattern of a unimodal symmetric spatial distribution of local abundances has long been emphasized to be a statistical one (Hengeveld & Haeck 1982; Brown 1995; Maurer 1999) with many exceptions to the general rule. That is, for any one species or at any one point in time the pattern may not be apparent, but when looking at many species averaged over longer periods it generally holds true. It would be naïve to dispute the existence or otherwise of the general pattern based on the data collected for one phytophagous insect species in Europe. However, in the case of North American birds we have seen that autocorrelation profiles may be interpreted rather differently. Moreover, in a study cited by Wiens (1989), Root found that only 4% of a sample of 48 species of birds wintering in North America could be said to have such a distribution according to her criteria. Other studies have also brought the pattern into question (see Introduction).

Brown (1984, 1995; see also Brown & Lomolino 1998) has argued that if (i) the abundance and distribution of a species are 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, and (ii) some sets of environmental variables are distributed independently of each other, and environmental variation is spatially autocorrelated, then density should be highest at the centre of the range of a species and should decline towards the boundary.

Examining each of these assumptions in turn, first, the abundance and distribution of the holly leaf-miner certainly seem likely to be determined by combinations of several physical and biotic variables. As a specialist herbivore, its occurrence at a site necessitates that of its host plant, holly. The northern and eastern extent of the distribution of holly are thought to be limited by minimum winter temperatures, where the trees can become prone to frost damage (Iversen 1944; Perring & Walters 1962). In addition, summer temperatures have to be sufficiently high to allow fruit production. In the most northerly parts of its range, holly is limited to low altitudes (e.g. < 200 m in Norway), whereas in southern regions it is confined to the mountains (usually in sheltered ravines with relatively high humidity) perhaps because drought stress poses an important limitation. In central areas, the tree is present throughout a large altitudinal range (Peterken & Lloyd 1967). A plot of the altitude of our sampling sites against latitude certainly reflects this trend in the distribution of holly (Fig. 4a). Within the geographical range of its host the holly leaf-miner does not occur in all regions. The results of the partial regression analysis show that this can be attributed in part to the effect of climatic variables. These effects may be direct, mediated through responses of the host plant, or may act upon agents of mortality across the geographical range of the leaf-miner (Brewer & Gaston, in preparation).

Figure 4.

Relationships between the latitude of each sample site and two of the environmental variables used in the partial regression analyses (a) altitude, and (b) winter relative humidity. The purpose of fitting the trend surface to the environmental data was to remove such trends before testing for an environmental effect on leaf-miner densities independent of space.

Secondly, spatial variation in the population density of the holly leaf-miner seems likely to also reflect the probability density distribution of the required combinations of physical and biotic variables (i.e. it is an optimum response surface; Hengeveld 1990), although the results of our analyses are not entirely consistent in this regard. The most obvious way in which this might not occur would be if the species exhibited some form of sink-source dynamics, such that in some areas immigration maintained densities at levels above those which could otherwise be sustained (Pulliam 1988). It is difficult to envisage that this could occur on the scale of the entire geographical range of this species. Thus, for example, it seems improbable that the high density of the holly leaf-miner in Norway (where the species is regarded, in some quarters, as a pest) is a product of immigration. In general, even small isolated populations appear to be self-sustaining, although the adult insects are probably good dispersers and may readily locate any unoccupied but suitable trees.

The third and fourth assumptions of Brown’s mechanism are that some sets of the environmental variables are distributed independently of each other and that environmental variation is spatially autocorrelated. Since our data set is comprised mainly of climatic variables, it is unsurprising that most of them show significant correlation with one another (Table 2). However, it is possible that some of the environmental variables we did not measure (e.g. aspects of soil type dependent upon underlying geology) may influence holly leaf-miner populations independently of climatic variation. We certainly found significant spatial structure in all of our environmental variables and in two out of the three partial regressions this structure was shared with holly leaf-miner populations. However, this spatial structure does not yield a simple Gaussian template of habitat suitability for P. ilicis. Population densities may well reflect local environmental conditions across the geographical range, but the spatial structure of the environment as it is presented to the species certainly does not appear to be a simple one.

In sum, examination of the local abundance structure of holly leaf-miner populations across the majority of its natural global geographical range suggests a rather different pattern from that which has been asserted to generally hold, namely a rather complex pattern of local density as opposed to a trend of increasing density towards the range centre. This result can be explained readily as a consequence of a violation of the assumptions about environmental structure underlying Brown’s (1984) general explanation for why such a peaked pattern should exist. Further investigation into environmental structure as it presents itself to local populations may prove to be a fruitful area of research into understanding the internal structure of the geographical range.


This work was supported by funding from the Natural Environment Research Council (GR9/03449/) and the University of Sheffield. We are grateful to Rob and Kerry Briers, Sian Gaston, Trond Hofsvang, Jens Rolff, Walter Wimmer and, most especially, John Marçal for assistance with the fieldwork.