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- Supporting Information
One of the most consistently observed patterns in ecology is a positive interspecific relationship between abundance and distribution: the locally most common species in a taxon or assemblage tend also to be the most widely distributed (Hanski 1982a,b; Brown 1984; Hanski, Kouki & Halkka 1993; Gaston 1994, 1996; Gaston, Blackburn & Lawton 1997a). This relationship has been observed for a wide variety of taxa, from diatoms (e.g. Soininen & Heino 2005) to mammals (e.g. Blackburn et al. 1997; Holt & Gaston 2003), in marine (e.g. Ellingsen 2001), freshwater (e.g. Tales, Keith & Oberdorff 2004) and terrestrial environments (e.g. Komonen 2003), and from most biogeographical regions (e.g. Bock 1987; Spitzer & Lepš 1988; Murray, Fonseca & Westoby 1998; van Rensburg et al. 2000). Positive relationships have also been observed within species (for reviews see Gaston et al. 2000; Gaston 2003), although we will not consider such intraspecific patterns further here. The interspecific relationship has been described as one of the general patterns on which, in the absence of hard and fast rules or laws, much of the foundations of ecology will be laid (Gaston & Blackburn 2000; Lawton 2000). Elucidating the mechanism that underlies them would thus represent a substantial advance in understanding the nature of ecological systems.
The simplest explanation for interspecific abundance–distribution relationships that has been suggested is that they are inevitable consequences of the frequency distributions of individuals of species across space following particular mathematical functions (e.g. Poisson, negative binomial; Wright 1991; Hanski et al. 1993; Hartley 1998; Holt, Gaston & He 2002). A number of relatively simple statistical models describe observed abundance–distribution relationships reasonably well, although their predicted forms are commonly not well differentiated over the range of abundances in such relationships (Holt et al. 2002). Such an explanation is, however, rather unsatisfactory, in that it is rooted in a mathematical description rather than the biology of the species concerned. Indeed, arguably, it is simply a rephrasing of one macroecological pattern in terms of another (Gaston, Blackburn & Lawton 1998).
In a related vein, it has been suggested that sampling errors may contribute to interspecific abundance–distribution relationships, through under-recording of the distributions of those species that are locally rare (Brown 1984; Wright 1991). However, it is generally accepted that for very many of the data sets that have been examined the spatial distributions of species are sufficiently well known that this bias is not sufficient to generate the observed pattern. Therefore, positive relationships between abundance and distribution appear to be a real feature of many ecological systems, requiring a mechanistic explanation.
Turning to ecological mechanisms, positive interspecific abundance–distribution relationships can result from a variety of processes, including niche characteristics, habitat suitability, vital rates, patterns of range overlap, and dispersal within a metapopulation framework (Gaston & Blackburn 2000; Gaston et al. 2000). For example, Brown (1984) hypothesized that species with broad niches could, through their ability to utilize a wider range of resources or conditions, both occupy more sites and attain higher abundances at occupied sites than species with narrow niches, giving rise to positive abundance–distribution relationships. Here, abundance and distribution are linked through variation in a third factor, niche breadth. Alternatively, such relationships could arise in the absence of niche differences through density-dependent habitat selection. It is well known that species will occupy more habitats when densities are high than when they are low, and assuming some commonality in this response across related species then positive abundance–distribution relationships can arise (Gaston & Blackburn 2000). Habitat selection models suggest that abundance drives distribution. Metapopulation dynamics can also generate positive abundance–distribution relationships under a variety of circumstances (Gaston & Blackburn 2000). For example, the rescue effect model suggests that immigration decreases the probability of local extinction, and that the rate of immigration per patch increases with the proportion of occupied patches (Hanski et al. 1993). This implies that distribution influences abundance and vice versa (Gaston et al. 1997a).
At present, while there is evidence that some specific abundance–distribution relationships have specific causes (e.g. Gonzalez et al. 1998), there is limited consensus about whether there is a general mechanism underlying such relationships. Further, it is unclear whether the same mechanism may apply in all situations, such as to assemblages of different taxa, in different habitats, or at different spatial scales. For example, while metapopulation dynamics explains the positive abundance–distribution relationship in a moss microecosystem, not all ecological systems show metapopulation structure, suggesting that multiple processes may be at work. Further evidence of this derives from the observation that although positive interspecific relationships between abundance and distribution are commonly observed, the strength of such relationships is highly variable. They are normally presented such that a measure of abundance is plotted as the dependent variable, with a measure of distribution as the predictor, although distribution may be dependent on abundance (Warren & Gaston 1997; Gaston 1999; Gaston & Blackburn 2000), depending on the mechanism at work (see above). It has been noted that, in many cases, distribution explains only 20–30% of the interspecific variation in abundance, albeit that this can rise to 70–80% in some cases (Gaston 1996; Gaston & Blackburn 2000). In a review of the form of interspecific abundance–distribution relationships, Gaston (1996) further showed that although about 80% of those relationships then published were significantly positive, about 5% were significantly negative and 15% showed no significant trend in either direction. Gaston (1996) suggested that much of this variation in the form of abundance–distribution relationships could be accounted for by differences in the spatial extent of studies, and in the measures of abundance and distribution used. However, an alternative possibility is that the variation is indicative of the action of different driving mechanisms in assemblages with different biological characteristics (e.g. dispersal modes, spatial structures). If so, variation in pattern could be informative about variation in process.
To date, Gaston's (1996) study is the only one to attempt a formal review of the form of abundance–distribution relationships. While this review has undoubtedly been helpful in developing an understanding of this ecological pattern, a significant shortcoming from the current perspective (although not from that prevailing at the time it was conducted) is that it takes a qualitative ‘vote-counting’ approach in summarizing the results of other studies. Gaston assessed the form of the relationship by counting the number of studies showing different forms. This approach does not take account of the fact that different studies may have different statistical power, or that results may be nonsignificant while still showing consistent effects of a variable (Osenberg et al. 1999). Thus, interpretation of a positive relationship where distribution explains 50% of the variation in abundance will be different if that relationship is based on data for five species or 50, yet vote-counting would treat both situations as equally informative on the form of the relationship. Moreover, even if there is indeed a positive effect of a species’ distribution on its abundance, sampling error can lead to nonsignificant or even negative relationships a proportion of the time. Thus, it is unclear at present whether the variability in abundance–distribution relationships shown by Gaston (1996) is indicative of sampling error in estimating a single effect, or of real heterogeneity in such relationships. In other words, whether underlying abundance–distribution relationships genuinely vary remains unknown.
A better approach to formal review is to use meta-analytical methods to synthesize quantitatively the results of multiple studies. These methods quantify the form of abundance–distribution relationships as the ‘effect size’– the strength and sign of the effect of distribution on abundance – and hence expose variation in form to rigorous analysis. These methods also allow the influence on abundance–distribution relationships of different classes of variables to be assessed in a rigorous and quantitative manner. Here, we use the meta-analytical approach formally to quantify variation in the form of the interspecific relationship between abundance and distribution, and to explore different hypotheses for variation in that form. Our aim is, first, to test whether observed variation in the form of abundance–distribution relationships is consistent with sampling error around a single, universal relationship, or whether abundance–distribution relationships show consistently different forms in different circumstances – and hence whether ‘the’ relationship is actually an amalgam of ‘multiple forms’ (Gaston 1996).
hypotheses for multiple forms
Heterogeneity in the form of abundance–distribution relationships may provide important clues as to mechanisms acting to drive that form. Heterogeneity may arise because different mechanisms act in different circumstances, because the same mechanism produces different effects in different circumstances, or because ecological responses are obscured by methodological effects. The first step towards distinguishing between these effects is to identify characteristics of abundance–distribution relationships that explain observed heterogeneity. This is the second aim of this paper.
Given that abundance–distribution relationships do indeed show considerable heterogeneity (see Results), we tested seven a priori hypotheses for causes of variation in interspecific abundance–distribution relationships.
First, we tested Gaston's (1996) suggestion that different abundance–distribution relationships pertain at different spatial extents. In fact, classifying spatial extent is not always straightforward. Some relationships are unambiguously local, such as Kemp, Harvey & O’Neill's (1990) plots of the density of grasshoppers vs. the number of habitat patches occupied, or unambiguously large-scale, such as Gaston & Blackburn's (1996a) plot of global population size vs. global range size for wildfowl. However, the extent of many other relationships is less clear-cut. For example, Owen & Gilbert (1989) plotted an abundance–distribution relationship for hoverflies where abundance was estimated from sites in Leicester while distribution was the range size of the species across several European countries (but not including England, where the abundances were sampled). We circumvented this problem by classifying the spatial extents of abundance–distribution relationships in two different ways: extent of the distribution measure, and extent of abundance measure. We also tested whether the strength of these relationships depended on whether abundance and distribution were measured at the same or different extents. Following Gaston (1996), we expect relationships to be weaker at larger spatial extents and when measured over different extents.
Second, we tested Gaston's (1996) suggestion that the form of the abundance–distribution relationship may depend on the measures of abundance and distribution used. Abundance is typically either measured as population size or population density (population size in some defined area), although other metrics are also used (e.g. per cent cover for plants; Söderström 1989). Depending on how density is calculated, it is possible that relationships with this abundance metric may be stronger as an artefact of plotting relationships of the form X vs. Y/X. Distribution is more variable in its measurement for abundance–distribution relationships, although the most common metrics are numbers of occupied sites, and numbers of occupied grid cells on a distribution map. Other measures include latitudinal range (e.g. Kouki & Häyrinen 1991), and prevalence for the distribution of parasite species across host species (e.g. Simkováet al. 2002). These measures can be broadly categorized as ‘extents of occurrence’ if they quantify the area between the outermost limits of the distribution, or ‘areas of occupancy’ if they quantify the area over which the species is actually found (Gaston 1991). We might expect relationships to be stronger using area of occupancy measures, as these more accurately represent the area over which a species is found.
Third, we tested whether the form of the abundance–distribution relationship depends on the extent of geographical coverage of the focal assemblage. Gaston & Blackburn (1996b) argued that macroecological studies can be divided into two types on this basis. ‘Comprehensive’ studies are those whose spatial extent embraces all, or the major proportion of, the geographical distributions of the species concerned. In contrast, ‘partial’ studies are those whose spatial extents embrace the geographical distributions of none or a low proportion of the species concerned. Different abundance–distribution relationships may result if the truncation of species’ distributions implicit in partial studies also influences the relationships of distribution to abundance. For example, a partial study that embraces only part of the range of several widespread, highly abundant species may suggest an association between high abundance and narrow distribution in these species, consequently producing a weaker abundance–distribution relationship.
At least two credible hypotheses for the existence of positive abundance–distribution relationships (Gaston et al. 1997a) implicate the spatial structure of populations within the environment as an important driving force (Hanski 1982a,b; Nee, Gregory & May 1991). In particular, there is experimental evidence that the dispersal of individuals between populations in a meta-population can maintain positive abundance–distribution relationships (Gonzalez et al. 1998; but see Warren & Gaston 1997). Freckleton et al. (2005) showed that the strength and shape of abundance–distribution relationships was affected by variation in the ability of species to colonize habitat. If so, we might expect to see different relationships where populations have different spatial relationships and patterns of dispersal. This leads us to test four related hypotheses.
Fourth, we tested whether relationships differ between the terrestrial, freshwater and marine environments. The relatively fragmented structure of freshwater populations may contrast with those in the terrestrial and, especially, marine environments, where opportunities for population mixing are, in theory at least, much greater. Fifth, we tested whether relationships vary with habitat, as the spatial structure of populations may differ between habitat types. Moreover, Freckleton, Noble & Webb (2006) show that the precise distribution of habitat suitability can affect the strength of abundance–distribution relationships. The distribution of habitat suitability may vary between habitat types. Sixth, we tested whether terrestrial abundance–distribution relationships vary with geographical location. Continents and regions vary in their evolutionary histories, and in their histories of human influence that may affect the degree to which habitats have been modified and/or fragmented. These effects may in turn influence the form of the abundance–distribution relationships found within them (Gaston 2006).
Seventh, we tested whether taxonomic affiliation can explain variation in abundance–distribution relationships. Different taxa have different modes and characteristic distances of dispersal, and may have very different population structures. Their abundances and distributions may be heavily influenced by other life-history characteristics, such as their body sizes and metabolic rates and consequent energy requirements, their mobility, and their rates and modes of reproduction. Our experience is that it is widely believed that most macroecological relationships in the literature relate to assemblages of birds or mammals. While it is certainly true that a large number of separate abundance–distribution relationships have been published for birds, these make up only about a quarter of those we located for this review. In fact, the largest proportion of relationships concern insects (see Methods), and plant assemblages are also well represented. Thus, there is significant potential for variation in the form of the abundance–distribution relationship as a consequence of biological variation among taxa.
In addition to these seven a priori hypotheses, we also tested for an effect of the statistical transform (if any) applied to the abundance and distribution data before analyses. Whether or how the data are transformed will clearly influence the effect size calculated for any given abundance–distribution relationship (at least using parametric statistics), and so may influence the distribution of effect sizes across studies.
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- Supporting Information
The relationship between transformed effect size (Zi) and sample size (Log10 Ni) is shown in Fig. 1. The overall mean effect size is 0·655 (95% CI 0·640, 0·669), positive, and highly significantly different from zero (Ztest = 89·79, P < 0·001). The number of missing results required to nullify this observed mean effect size is 570 519. In a random effects model the variance component of the population of correlation coefficients is particularly large (0·323) and a considerable amount of heterogeneity remains unexplained across the data (Q = 5266·28, d.f. = 278, P < 0·001), even though some of the abundance–distribution relationships in our data are not independent, which ought to reduce heterogeneity.
For each of the hypotheses listed in the Methods, we tested whether the average effect size differs across the classes into which different studies were classified. Table 1 shows an example for different classes of study scale. Hypothesis 1 was that abundance–distribution relationships are weaker at large spatial scales, for which there is not consistent support in our data. Although the mean effect size is lowest for both extent of distribution and extent of abundance at the Continental spatial scale there is no consistent trend across the other scales (Global, National, Regional, or Local). Mean effect sizes at all scales are significantly greater than zero (ZSTAT) but there also remains significant unexplained heterogeneity in effect size (CHI-stat) at all scales (Table 1). Our prediction that studies with different measurement extents should have lower effect sizes was not falsified (ZDIFF = 0·68, = 1574·79, P < 0·001; Table 1).
Table 1. Effect size statistics for different classes of study scale. In each case we tested whether significant heterogeneity exists within classes (CHI-stat) and whether the average effect size (Z+) is significantly different from zero (ZSTAT). s is the number of studies and k is the number of relationships included in each class. Note that some studies contribute data to more than one of the rows in each class of study scale, so that the s-values do not sum to the total number of studies
|National||21|| 78||0·80||0·77, 0·83||59·07***||2339·67***|
|Local||16|| 54||0·78||0·76, 0·81||60·13***|| 983·00***|
|Regional||29|| 82||0·49||0·46, 0·52||32·58***|| 749·38***|
|Global|| 3|| 5||0·41||0·32, 0·49|| 9·84***|| 191·26***|
|Continental||13|| 32||0·24||0·19, 0·28|| 9·81***|| 206·49***|
|National||18|| 72||0·99||0·96, 1·02||64·56***||1545·59***|
|Global|| 1|| 2||0·94||0·83, 1·06||16·29***|| 1·74|
|Regional||20|| 51||0·71||0·67, 0·75||33·12***|| 199·24***|
|Continental|| 7|| 9||0·46||0·39, 0·52||14·32***|| 43·68***|
|Same extent||54||185||0·83||0·81, 0·84||95·89***||2912·74***|
|different extent||17|| 64||0·13||0·10, 0·16|| 8·63***|| 618·19***|
|Total|| ||278||0·65||0·64, 0·67||89·79***||5266·28***|
Hypothesis 2 suggested that the measure of abundance or range size used could influence effect size. Indeed, for the measure of abundance, both Population Size [1·14 (1·11, 1·18)] and Percent Cover [0·93 (0·84, 1·03)] had significantly larger average effect sizes than Abundance Rank [0·65 (0·54, 0·75)] and Density [0·55 (0·53, 0·56)]. Similarly, for the measure of distribution, Number of Sites [0·82 (0·80, 0·84)] had a significantly larger average effect size than Number of Grid Cells [0·52 (0·50, 0·54)], which in turn had a significantly larger average effect size than Species Extent [0·04 (−0·04, 0·12)], which had an average effect size not significantly different from zero (ZSTAT = 0·93, P = 0·35).
Hypothesis 3 posited that studies embracing all, or the major proportion of, the geographical distributions of the species concerned may produce stronger abundance–distribution relationships. Average effect size was indeed significantly larger (ZDIFF = 0·06, = 8·01, P = 0·018) for comprehensive [0·71 (0·67, 0·75)] than for partial studies [0·65 (0·63, 0·66)].
Hypothesis 4 was that effect sizes differ between relationships in different realms. This hypothesis was also strongly supported (Table 2). The largest average effect sizes were for Intertidal [0·92 (0·83, 1·01)] and Marine assemblages [0·76 (0·66, 0·87)], and average effect sizes did not differ significantly between these two groups (ZDIFF = 0·15, = 4·93, P = 0·29). The smallest mean effect size was for Freshwater assemblages [0·54 (0·49, 0·59)], while effect sizes in Terrestrial [0·65 (0·63, 0·67)] and Parasitic assemblages [0·73 (0·65, 0·81)] were intermediate. Significant heterogeneity among effect sizes was unexplained in the Parasitic and Terrestrial classes, but not for Intertidal, Marine or Freshwater assemblages (Table 2).
Table 2. Effect size statistics for different realms, including the categories contained in subsequent nested classes. In each case we tested whether significant heterogeneity exists within classes (CHI-stat) and whether the average effect size (Z+) is significantly different from zero (ZSTAT). s is the number of studies and k is the number of relationships included in each class. Note that some studies include data from more than one realm, so that the s-values do not sum to the total number of studies
|Realm||Habitat||Distribution scale||Location||Taxa||s||k||Z+||95% CI||Z-stat||CHI-stat|
|Intertidal||Estuarine, Intertidal||Local, Regional, National||Palaearctic, Neotropical||Invertebrates|| 4|| 12||0·92||0·83, 1·01||20·61***||8·69|
|Marine||Benthos, Ocean||Regional|| ||Invertebrates, Fish|| 3|| 11||0·76||0·66, 0·87||14·42***||17·19|
|Parasitic||Lakes, Parasitic|| ||Palaearctic, Nearctic||Invertebrates, Insects|| 2|| 21||0·73||0·65, 0·81||18·12***||102·15***|
|Terrestrial||Bogs, Desert, Farmland, Grassland, Mountain, Savannah, Urban, Various, Woodland||Local, Regional, National, Continental, Global||Palaearctic, Nearctic, Neotropical, Afrotropical, Australasia||Plants, Invertebrates, Insects, Birds, Mammals||50||198||0·65||0·63, 0·67||81·26***||5012·50***|
|Freshwater||Lakes, Rivers, Streams||Regional, National, Continental||Palaearctic, Nearctic, Australasia||Plants, Invertebrates, Insects, Amphibians, Fish|| 9|| 34||0·54||0·49, 0·59||20·88***||45·60|
Hypothesis 5 posited differences between habitat types in abundance–distribution relationships. Because ‘Water’-related classes were not significantly heterogeneous we subsequently identified nine ‘Terrestrial’ habitat classes (Tables 2 and 3), and hence 36 interclass linear contrast comparisons, and so only summarize the key findings. Average effect sizes varied from 1·06 (0·96, 1·16) for Desert relationships, down to 0·50 (0·30, 0·70) for relationships from Mountain habitats. Average effect sizes differed significantly from zero for all habitats. Desert, Urban and Mountain assemblages showed no significant unexplained heterogeneity in effect size (Table 3). Average effect sizes for Desert and Bog habitats were consistently significantly greater than those from all other habitats (ZDIFF > 0·39, > 16·47, P < 0·05 in all cases) except woodland assemblages [0·90 (0·87, 0·93)].
Table 3. Effect size statistics for different nested distribution scales, locations, and taxa within habitats in the terrestrial realm. We tested the model specification that effect sizes are heterogeneous within classes by manually partitioning the classes across each of the nested classification dimensions in a stepwise manner to yield finer and finer groupings. The order in which classification dimensions were chosen was based on which hypothesis (when compared with the other remaining hypotheses) explained the most effect size heterogeneity within classes for each subsequent partition. To prevent over partitioning we used a conservative significance value (α = 0·01) for further division of the classes. Classes that are italicized are grouped at the level for which further partitioning does not significantly resolve their class heterogeneity. In each case we tested whether significant heterogeneity exists within classes (CHI-stat) and whether the average effect size (Z+) is significantly different from zero (ZSTAT). s is the number of studies and k is the number of relationships included in each class. Note that some studies contribute data to more than one of the rows, so that the s-values do not sum to the total number of studies
|Habitat||Distribution scale||Location||Taxa||s||k||Z+||95% CI||Z-stat||CHI-stat|
|Bogs||Regional||Palaearctic||Birds|| 1|| 5||1·31|| 1·12, 1·50||13·63***|| 2·76|
|Woodland||Local||Afrotropic||Birds|| 1|| 9||1·28|| 1·21, 1·35||34·89***|| 5·36|
|Desert||Local, Regional||Palaearctic, Nearctic||Plants, Birds|| 3|| 9||1·06|| 0·96, 1·16||21·47***|| 8·68|
|Various||National||Palaearctic||Mammals|| 2|| 7||1·05|| 0·88, 1·21||12·60***|| 5·84|
|Grassland||Local||Nearctic||Plants, Insects|| 3|| 5||0·95|| 0·84, 1·06||17·72***|| 8·72|
|Woodland||Local||Afrotropic||Plants|| 1|| 9||0·95|| 0·91, 0·99||43·08***|| 90·08***|
|Grassland||Regional||Palaearctic, Nearctic||Plants, Insects|| 4|| 6||0·94|| 0·82, 1·07||14·71***|| 6·35|
|Various||Global||Birds|| || 1|| 2||0·94|| 0·83, 1·06||16·29***|| 1·74|
|Woodland||Regional||Palaearctic||Plants, Insects, Birds|| 4|| 7||0·87|| 0·72, 1·02||11·57***|| 11·17|
|Various||National ||Palaearctic||Plants, Insects, Birds||11||25||0·85|| 0·82, 0·89||48·17***||233·54***|
|Woodland||Local||Afrotropic||Insects|| 1|| 9||0·73|| 0·64, 0·82||15·99***|| 17·40*|
|Woodland||National||Palaearctic||Birds|| 4||10||0·70|| 0·59, 0·77||15·27***|| 90·04***|
|Bogs||National||Palaearctic||Birds|| 1|| 4||0·64|| 0·34, 0·93|| 4·21***|| 3·37|
|Farmland||National, Continental||Palaearctic||Insects, Birds|| 5||13||0·61|| 0·54, 0·68||16·34***|| 46·48***|
|Urban||Regional, National||Palaearctic||Insects|| 1|| 4||0·59|| 0·48, 0·70||10·66***|| 0·10|
|Woodland||Local||Nearctic||Plants|| 1|| 4||0·51|| 0·40, 0·63|| 8·79***|| 1·91|
|Various||Continental||Nearctic||Birds|| 5|| 7||0·51|| 0·41, 0·62|| 9·48***|| 3·45|
|Various||Regional||Nearctic||Birds|| 1|| 2||0·50|| 0·32, 0·68|| 5·48***|| 0·24|
|Mountain||Local, Regional, National||Palaearctic, Nearctic||Insects|| 2|| 6||0·50|| 0·30, 0·69|| 4·90***|| 13·02*|
|Various||Local||Nearctic||Birds|| 1|| 2||0·45|| 0·27, 0·63|| 4·95***|| 2·14|
|Various||Continental||Australasia||Birds|| 1|| 2||0·23|| 0·14, 0·32|| 5·13***|| 13·15***|
|Grassland||Local||Palaearctic||Insects|| 1|| 2||0·19||−0·01, 0·39|| 1·81|| 0·02|
|Various||Regional||Palaearctic||Plants, Insects|| 6||10||0·19|| 0·14, 0·24|| 7·69***||335·87***|
|Woodland||Continental||Palaearctic||Insects, Birds|| 2|| 2||0·17||−0·01, 0·34|| 1·86|| 7·47**|
|Various||Continental||Palaearctic||Insects|| 2|| 2||−0·00||−0·22, 0·21||−0·04|| 4·37*|
|Various||Global||Mammals|| || 1|| 2||−0·07||−0·20, 0·05||−1·15|| 6·37*|
|Various||Continental||Neotropic||Mammals|| 1||13||−0·12||−0·24, 0·00||−1·91|| 16·01|
|Grassland||Continental||Palaearctic||Insects, Birds|| 2|| 2||−0·20||−0·37, –0·03||−2·26*|| 4·69*|
Hypothesis 6 suggests that the strength of abundance–distribution relationships might differ across biogeographical regions, and there are indeed biogeographical differences in average effect size. All terrestrial regions differed significantly from all other regions in terms of their average effect sizes. Average effect size was highest in the Afrotropics [0·97 (0·94, 1·01)], and then decreased through the Nearctic [0·69 (0·64, 0·74)], Palaearctic [0·57 (0·55, 0·59)], Australasia [0·27 (0·19, 0·35)] and the Neotropics [−0·12 (−0·24, 0·00)]. The mean effect size for this last region did not differ significantly from zero (ZSTAT = −1·91, P = 0·06). There was significant unexplained heterogeneity across effect sizes within all regions.
Finally, hypothesis 7 was that effect sizes differ between relationships for different taxonomic groups. This hypothesis also receives support. All mean effect sizes differ significantly from zero (ZSTAT > 4·66, P < 0·001). Mean effect sizes range from 0·18 (0·11, 0·26) for mammals to 0·98 (0·92, 1·05) for (mainly marine) invertebrates, and all these other mean effect sizes differ significantly from zero. Mean effect sizes do not differ between plants [0·48 (0·46, 0·51)], fish [0·61 (0·48, 0·73)] and insects [0·56 (0·53, 0·59)]. All other groups differ significantly in mean effect size (ZDIFF > 0·08, > 12·99, P < 0·05 in all cases). There was significant unexplained heterogeneity in effect size for most groups with the exception of other (noninsect) invertebrates ( = 25·84, P = 0·13), fish ( = 4·82, P = 0·78), and freshwater diatoms ( = 8·35, P = 0·21).
To assess model specification we first tested whether effect sizes are homogenous within classes across each of the seven hypotheses, separately. Large (highly statistically significant) overall within-class fit statistics (eqn 9) indicated that for each of the seven hypotheses effect sizes were significantly heterogeneous within individual classes. Note that the smallest within-class fit statistic was obtained for the test of differences among realms (QW 267 = 2184·37, P < 0·001), and that there is no heterogeneity in effect sizes for the marine, intertidal and freshwater realms (Table 2).
Second, we manually partitioned (in a stepwise manner) the classes across each of the classification dimensions (or hypotheses) to yield finer and finer groupings in an attempt to explain the remaining heterogeneity in the Terrestrial and Parasitic realms. The subsequent (final) categorical effect model for the Terrestrial realm is presented in Table 3. Note, however, that this model still contains 12 classes (a quarter of all relationships) for which the effect sizes within the classes are significantly heterogeneous (Table 3), and for which this heterogeneity is attributable to single source references such that there is no available information for further partitioning into subsequent smaller classes. For the Parasitic realm, further partitioning did not produce any classes that are homogeneous for effect size (and thus no improvement for this realm over the model in Table 2).
The data showed support for the idea that the transformation applied ought to influence effect sizes. Average effect size was highest for relationships with abundance logarithmically transformed and a logit transform applied to distribution [log-logit relationships: 1·77 (1·70, 1·85)] and with untransformed data [0·85 (0·83, 0·88)] and lowest for log-square root relationships [−0·04 (−0·08, −0·01)]. Mean effect sizes differed significantly between all groups except those with log-log [0·69 (0·66, 0·72)], log-arcsine [0·66 (0·56, 0·76)] and log-none [0·64 (0·61, 0·66)] transformations (ZDIFF < 0·055, < 7·2, P > 0·05 in all cases). However, categorizing relationships by the transformation applied was not necessary to explain heterogeneity in effect sizes in the marine, intertidal or freshwater realms, and did not help explain such heterogeneity in the Terrestrial (Table 3) or Parasitic realms.
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- Supporting Information
In a well-cited review of the strength of research findings in ecology and evolution, Møller & Jennions (2002) showed that the mean amount of variance in dependent variables explained in studies fell in the range 2·51–5·42%. r2 values of this magnitude equate to standardized effect sizes (from eqn 1) in the range 0·16–0·24. Thus, the mean effect size of 0·655 for the studies we review here is indicative of a strong general positive effect of spatial distribution on abundance across species, equating to a positive relationship with approximately one-third of the variance explained. Most individual effect sizes are also positive and lie above the upper significance line at α = 0·05 in Fig. 1. This confirms the conclusion of Gaston's (1996) original qualitative review of such studies that positive relationships greatly predominate, despite almost an extra decade being available for counter-examples (which should have been highly publishable) to accrue. Although we could not calculate effect sizes for some published relationships, and some of these effect sizes were apparently small, the fail-safe number indicates that more than half a million unpublished null results would be required to nullify an effect of this magnitude. We consider it highly unlikely that ecologists have so many null relationships stuffing their file drawers.
Despite the large positive mean effect size for abundance–distribution relationships, and the general tendency for individual effect sizes to be significantly positive, there is none the less considerable heterogeneity in the form of the relationship. Eighteen per cent of relationships lie within the α = 0·05 significance lines in Fig. 1 (cf. 15% found by Gaston 1996), and 29 relationships (10%) have negative effect sizes. Moreover, there is no tendency for effect sizes to converge on any given value as sample size increases, suggesting that studies are considering a relationship with multiple forms, as suggested by Gaston (1996). This thus begs the question of whether we can identify the cause(s) of this heterogeneity.
The results from univariate analyses show support for most of the hypotheses we test about sources of heterogeneity in abundance–distribution relationships. Most notably, relationships vary significantly in strength across realms, with the strongest in the marine and intertidal, intermediate relationships for terrestrial and parasitic systems, and the weakest relationships in freshwater systems (lakes, rivers and streams) (Table 2). Moreover, effect sizes in all of the aquatic realms are homogeneous (Table 2), suggesting both that realm is an important source of heterogeneity in the data, and that the relationships in each of these realms are estimating a common effect size.
We tested the effect of realm because of the hypothesis that the different spatial structure of the environment in each realm would affect the opportunity for the dispersal of individuals between sites: the ability to disperse between sites has been shown in theory and practice to influence the abundance–distribution relationship (Gonzalez et al. 1998; Freckleton et al. 2005; but see Warren & Gaston 1997). Some support for the importance of dispersal is provided by the observations that the lowest mean effect is for freshwater systems, which are often fragmented and where restricted dispersal between sites (e.g. ponds, lakes, river catchments) frequently leads to high compositional dissimilarity in local assemblages (e.g. Marchetti et al. 2001), while the highest mean effect sizes are for intertidal and marine studies. It is generally assumed that dispersal is particularly widespread in the marine realm, at least for species with pelagic larvae, with concomitant effects on range size and structure (Brown, Stevens & Kaufman 1996).
Tests of the remaining six hypotheses all revealed significant differences in effect sizes among different categories of abundance–distribution relationship, but where we had made predictions about the relative strengths of effects for different categories, these predictions received equivocal support at best. For example, we predicted that relationships should be weaker when abundance and distribution were measured over different spatial extents, and effect sizes are indeed significantly weaker in these circumstances (Table 1). However, we also predicted that smaller effect sizes would be found for larger-scale than for smaller-scale studies (hypothesis 1). Studies spanning local distributional extents did indeed have large mean effect size, but mean effect size for national scale studies was higher (Table 1). The ranking, with respect to mean effect sizes, of studies with abundance measured over different extents was also not from small-scale to large-scale (Table 1). Thus, while studies at different spatial scales did differ significantly in mean effect size, the pattern of differences does not suggest a simple increase in effect size from large to small scales. This ranking does not simply reflect the extent to which studies at different scales tend to concern the same scale for abundance and distribution.
We also predicted that effect sizes would differ for different types of abundance and distribution measure (hypothesis 2), with stronger effect sizes for abundance measured as density and distribution measured as area of occupancy (sensu Gaston 1991). Again, mean effect sizes differed among classes, and the ranking of distribution measures by effect size was as predicted: measures of occupancy had larger effect sizes than measures of range extent, presumably because the former more accurately represent the area over which a species is found. However, differences for abundance classes were not as predicted, with density measures having the smallest mean effect size. If there is an artefactual component to density-distribution relationships because of a range size component to both dependent and independent variables, it is not significantly inflating their effect sizes.
The prediction that comprehensive studies would have larger effect sizes than partial studies (hypothesis 3) was supported by our analyses. These analyses also supported our contentions that effect sizes should vary across habitats (hypothesis 5) and biogeographical regions (hypothesis 6), and with taxonomic affinity (hypothesis 7). For these last three hypotheses, no a priori predictions were made concerning the relative ranking of the various categories with respect to effect size. While the actual rankings could be the basis for subsequent hypotheses about effect size variation, three issues with these results complicate that possibility.
First, we can see no obvious reasons for the rankings observed within different variables. For example, mean effect sizes decrease across biogeographical region in the order Afrotropics, Palaearctic, Nearctic, Australasia and Neotropics. This ranking in effect sizes does not coincide with rankings in terms of human impacts, extent of natural habitat, climate, native species richness, hemisphere, or any other factor we can think of that might reasonably influence the form of abundance–distribution relationships. The same is true for rankings of habitats and taxa by effect size. Second, significant differences in mean effect size among these different classes of abundance–distribution relationship belie the fact that there is still considerable heterogeneity in effect sizes within the classes. Part of the reason for this may be the relatively uneven distribution of relationships into different classes. Thus, while comprehensive studies have a significantly larger mean effect size than partial studies, most studies are classed as partial (253 vs. 16). In these circumstances, it is unlikely that a distinction between comprehensive and partial studies is going to explain very much of the considerable variation in effect size observed for abundance–distribution relationships. Third, different classes are confounded by the nonrandom distribution of relationships with respect to different hypotheses. For example, a mean effect size not significantly different from zero is observed for terrestrial abundance–distribution relationships from South America, and a relatively low positive effect size for relationships concerning mammals. However, all of the terrestrial Neotropical studies in our data concern mammals, and so these classes are not independent.
These last two issues, at least, were addressed by the stepwise manual partitioning of the classes within each hypothesis variable, the aim of which was to try to explain the heterogeneity in effect size in the terrestrial and parasitic realms (recall that effect sizes are homogeneous in each of the aquatic realms) in terms of the other variables analysed. This partitioning could not produce any classes that were homogeneous for effect sizes for parasite abundance–distribution relationships. This is unsurprising, in that most of the relationships concern flea assemblages on mammal hosts (Krasnov et al. 2004), but there is one fish gill parasite assemblage (Simkováet al. 2002) and one duck parasite assemblage (Hanski et al. 1993). Each of these groupings is homogenous for most of the classes in all of our hypotheses, which in consequence cannot explain any of the effect size heterogeneity.
In contrast, some of the heterogeneity in effect sizes for terrestrial assemblages can be removed by dividing the relationships by, sequentially, habitat, scale at which distribution was studied, biogeographical region and taxon (Table 3). For example, continental-scale studies of Nearctic bird assemblages occupying various habitats exhibit homogeneous effect sizes that are significantly greater than zero. Habitat may be the first variable that enters the stepwise model for the same reason that we suggested realm to be the best predictor of effect size heterogeneity, through its influence on ease of dispersal. Terrestrial systems may show a variety of fragmentations, and hence degrees of dispersal limitation, that relate to habitat type. Dispersal effects may also explain the influence of location and taxon. Alternatively, Freckleton et al. (2006) show that the precise distribution of habitat suitability can affect the strength of the abundance–distribution relationship: presumably, this distribution will vary between habitat types. That said, even clustering studies into groups defined by several classes fails to remove all heterogeneity in several cases (e.g. national-scale Palaearctic woodland bird assemblages; Table 3). Moreover, most of the homogeneous groups comprise relatively few abundance–distribution relationships (typically n = 2–9) deriving from relatively few studies (K = 1–4; Table 3). It seems that heterogeneity in effect sizes in abundance–distribution relationships persists almost to the level of the individual study. At this level, the apparent homogeneity may be more to do with the nonindependence of relationships in given studies than with associations predicted by our various hypotheses.
One group for which effect sizes are homogeneous is that comprising continental-scale studies of Neotropical mammal assemblages occupying various habitats. This group of 13 relationships is unusual in that the mean effect size is negative, and while it does not differ significantly from zero, it comes close to doing so (Table 3). Why should this homogeneous group show a negative mean effect size? The most mundane answer is that all the relationships derive from a single study (Arita, Robinson & Redford 1990), and so may be a consequence of nonindependence combined with the precise methodology employed. However, Arita et al. (1990) themselves suggest that it could be due to the relationship being driven by associations of both variables to body size. Controlling for body size, they found no significant relationship between abundance and distribution in their full data set, and the lack of significance for relationships calculated among dietary and taxonomic subsets of the assemblage was argued also to be due to the reduced body mass variation in such groups. In fact, it is not the case that the sign of an association between two variables can be predicted from the sign of their relationships with a common third variable (unless the relationships are extremely strong). Abundance–distribution relationships are typically positive (Fig. 1), even though abundance–body size relationships are typically negative and distribution–body size relationships typically positive (Gaston & Blackburn 2000). Thus, the explanation for the form of the relationships found by Arita et al. (1990) may lie yet elsewhere. Whether it is methodological, derives from the influence of human exploitation on the density of large-bodied mammal species, or is perhaps a consequence of the unusually large body size of mammal species in general, cannot be determined from the available evidence.
In summary, the average effect size for published abundance–distribution relationships indicates an association that is positive and, for ecological data, unusually strongly so. Nevertheless, the considerable heterogeneity in effect sizes across individual studies supports Gaston's (1996) contention that the relationship has multiple forms. Identifying that this heterogeneity exists is an important step towards understanding the causes of abundance–distribution relationships. The challenge is now to explain it. Tests of the various hypotheses proposed to explain this variation revealed that forms differ across biological realms, and it would appear that realm is an important source of the heterogeneity observed across all studies. An obvious potential cause of this is the influence of environmental spatial structure on the opportunity for dispersal, but further tests, such as the comparison of relationships for marine taxa with different dispersal modes, are required to confirm this explanation. Moreover, much of the heterogeneity in effect sizes in parasitic and terrestrial assemblages could not be explained by the data available to us to test the various other hypotheses for this variation, and indeed it seems that this heterogeneity persists almost to the level of the individual study. The terrestrial environment in particular defies easy categorization, and for abundance–distribution relationships here there would appear to be almost as many answers as there are ecologists asking questions about them.