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Keywords:

  • diversity hotspots;
  • pattern matching;
  • scale invariance;
  • spatial autocorrelation;
  • species distribution;
  • species turnover

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  • 1
     Using data on the spatial distribution of the British avifauna, we address three basic questions about the spatial structure of assemblages: (i) Is there a relationship between species richness (alpha diversity) and spatial turnover of species (beta diversity)? (ii) Do high richness locations have fewer species in common with neighbouring areas than low richness locations?, and (iii) Are any such relationships contingent on spatial scale (resolution or quadrat area), and do they reflect the operation of a particular kind of species–area relationship (SAR)?
  • 2
     For all measures of spatial turnover, we found a negative relationship with species richness. This held across all scales, with the exception of turnover measured as βsim.
  • 3
     Higher richness areas were found to have more species in common with neighbouring areas.
  • 4
     The logarithmic SAR fitted better than the power SAR overall, and fitted significantly better in areas with low richness and high turnover.
  • 5
     Spatial patterns of both turnover and richness vary with scale. The finest scale richness pattern (10 km) and the coarse scale richness pattern (90 km) are statistically unrelated. The same is true of the turnover patterns.
  • 6
     With coarsening scale, locations of the most species-rich quadrats move north. This observed sensitivity of richness ‘hotspot’ location to spatial scale has implications for conservation biology, e.g. the location of a reserve selected on the basis of maximum richness may change considerably with reserve size or scale of analysis.
  • 7
     Average turnover measured using indices declined with coarsening scale, but the average number of species gained or lost between neighbouring quadrats was essentially scale invariant at 10–13 species, despite mean richness rising from 80 to 146 species (across an 81-fold area increase). We show that this kind of scale invariance is consistent with the logarithmic SAR.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

Patterns in the spatial turnover of species lie at the heart of many macroecological phenomena. Notwithstanding, they have received surprisingly little attention (but see, e.g. Harrison, Ross & Lawton 1992; Willig & Sandlin 1992; Blackburn & Gaston 1996a; Williams 1996; Mourelle & Ezcurra 1997; Willig & Gannon 1997; Ruggiero, Lawton & Blackburn 1998; Clarke & Lidgard 2000), at least in contrast with the large literature dealing with geographical gradients and other spatial patterns in species richness per se (e.g. Ricklefs 1987; Rohde 1992; Ricklefs & Schluter 1993; Rosenzweig 1995; Gaston & Williams 1996; Gaston & Blackburn 2000; Gaston 2000; and references therein). Spatial turnover at meso- and macro-scales has been described primarily in the rather restricted terms of the species–area relationship (e.g. Connor & McCoy 1979; Williamson 1988; Rosenzweig 1995; and references therein), in complementarity analysis in conservation biology (e.g. Pressey et al. 1993; Williams et al. 1996), and in nested-subset analysis (Wright & Reeves 1992; Worthen 1996; see also Cook & Quinn 1998). This relative neglect is reflected in the tendency for species richness and turnover to be considered separately, when strictly they are logically inseparable and interact through changes in spatial scale.

The scale dependence of species richness, the species–area relationship (SAR), is one of the oldest and well-known observations in ecology (Arhennius 1921; Williamson 1988; Rosenzweig 1995). Less familiar, although arguably still obvious, is that turnover is part of the same general phenomenon of autocorrelation within species distributions, i.e. all emergent patterns of species richness depend strongly on the spatial structure of occurrence of the component species. A SAR obviously implies turnover, in the sense of species gain with cumulative area. Simple theoretical species–area relationships imply simple relationships between area, endemism and turnover (Harte & Kinzig 1997).

Important as it is, the SAR is a relatively blunt instrument for studying turnover, summarizing as it does complex spatial variation as a few points on a bivariate graph. It has shortcomings as a measure of turnover too, because it focuses solely on species net gain with increasing area; species loss in the additional area is effectively invisible. To study turnover, it is necessary to consider explicitly the gain and the loss of species in space (Cody 1975; Wilson & Shmida 1984). This obviously requires more than simply the species numbers on which the majority of studies of macroecological phenomena are founded (and indeed, goes further than some of the simplest measures of turnover, e.g. Whittaker 1972; Harrison et al. 1992).

By definition, local gradients in species richness produce spatial turnover (Harrison et al. 1992), if turnover is defined in its broadest sense as any change in species composition between two locations. Therefore, there is the danger that in analysing spatial patterns of turnover, local species richness gradients are simply rediscovered. It is thus productive to think of turnover as having two components: one produced by local species richness gradients, and another independent of these gradients. A species richness gradient necessarily results in turnover of a sort, with the addition or loss of species in space. Nonetheless, turnover in the usual sense means the replacement of one set of species with another. This requires measures that are insensitive to richness gradients. Against this background, questions of the relationship between turnover and species richness have to be very tightly framed – probably more so than has been the case in past discussions concerning the relationship between latitudinal gradients in species richness and turnover, and the implications of this relationship for mechanisms generating high levels of tropical richness (e.g. Willig & Sandlin 1992; Blackburn & Gaston 1996a; Mourelle & Ezcurra 1997; Willig & Gannon 1997).

In this paper, we present the first detailed empirical analysis of spatial patterns of species richness and turnover across a series of spatial scales. Using data on the avifauna of Britain, we test the hypothesis that there is a relationship between richness and turnover. We show that local species richness gradients can distort measurements of turnover. We demonstrate that spatial patterns of both species richness and turnover depend strongly on scale, and that this is reflected in spatial patterns in the strength of the SAR. We break turnover down into its basic components (species gains and losses between quadrats), again at different spatial scales. We show that although spatial patterns of turnover change with scale, some important aspects of average turnover are close to being scale invariant. This scale invariance is in agreement with the type of SAR found.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

We take a spatial pattern-matching approach, by first generating spatial patterns of species richness and turnover at different scales, and then statistically matching these with each other. We have five main methodological objectives: (i) to fit two types of SAR model to the species distribution data, and to map spatial variation in the SAR model parameters; (ii) to map species richness patterns at different spatial scales; (iii) to define and discuss the various measures of species turnover we employ; (iv) to map species turnover patterns, using these measures, again across a series of spatial scales; (v) to statistically test for relationships between these maps of species richness, species turnover and SAR parameters. As mentioned in the Introduction, the latter are measures of turnover based on species accumulation with area; we go on to show that the two SAR models used imply two types of scale invariance for species richness.

species distribution data

We used the summer (breeding) distribution of the British avifauna recorded in April–July 1988–91 (Gibbons, Reid & Chapman 1993). These data are species presence/absence at a resolution of 10 km × 10 km quadrats on a continuous grid. We excluded 21 marine species and many vagrants (species recorded as a few individuals typically in only one or two quadrats), but retained the more naturalized introductions and some species that breed sporadically, giving a total of 196 species (as listed in Lennon et al. 2000a). Some initial filtering was performed on the distribution data: quadrats at this finest 10-km scale containing less than 50% land were excluded, leaving a total of 2406.

species richness and the species–area relationship

We generated maps of species richness at a series of successively larger quadrat sizes (coarser scales), using a moving-window algorithm: a larger quadrat was positioned centrally over each base 10-km quadrat (Fig. 1) and all species present counted. This introduces additional spatial autocorrelation into the species richness patterns, which is dealt with using appropriate statistical methods.

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Figure 1. The arrangement of quadrats used in the diversity and turnover calculations. To calculate diversity at a particular scale, say 30 km, we positioned a 30-km quadrat over all possible 10-km quadrat centres (nested quadrats of 10 km to 150 km shown on left). For the species–area relationship models, we used 15 nested quadrats (only eight shown here on left), again positioned over all possible 10-km quadrats, giving different fitted coefficients for each central 10-km quadrat. For turnover, pairwise comparisons between the focal quadrat (light shading) and up to eight neighbours were made at different scales: shown are 10 km (top), 30 km (middle) and 90 km (bottom). Again, the moving window algorithm applied this arrangement centred over all possible 10-km quadrats (dark shaded small quadrat at centre of focal quadrat), so a measurement of turnover was obtained at each 10-km quadrat over the whole study area.

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The process of generating these maps involves fitting SAR models, but we are also interested in these in their own right. At coarse scales there is clearly a problem caused by the encroachment of sea into the larger quadrats. We compensated for this by using a SAR model to correct upwards the species richness of these coastal quadrats to that expected if there was 100% land. We calculated a separate SAR for each of the 2406 10-km quadrats (Fig. 1). For each such quadrat, we gathered richness and area data points by expanding a ‘window’ around it (from 10 km × 10 km to 290 km × 290 km in steps of 20 km, giving 15 points). We then fitted two alternative SAR models to each quadrat’s set of 15 points. These were the familiar log(species)–log(area) relationship logR =c +z log A (the power SAR –Arhennius 1921), and the species–log(area) relationship R = k +m log A (the logarithmic SAR –Gleason 1922), where R and A are species richness and area, respectively. The richness of each coastal quadrat was then corrected (using the prediction for 100% land area) by applying whichever of the SAR models (power or logarithmic) that gave the best fit (i.e. highest r2) to its local data. We were able to map spatial variation in m and z by assigning the parameter estimates to their corresponding 10-km quadrat.

Applying this land-area correction raises some interesting problems. First, the species–area relationship is not spatially homogenous, i.e. the coefficients of the SAR vary spatially. So each fitted curve is an integration of different relationships. Secondly, the correction applied in each quadrat may be biased by the geometry of the surrounding landmass. For a given area, long strips of quadrats contain more species than a more compact arrangement (e.g. Goodall 1952; Kunin 1997). In the former circumstance, the correction applied may be too large. Thirdly, the richness data used to calculate each SAR are not independent. This affects all nested-design (rather than inter-island) species–area curves. The magnitude of these three problems is difficult to quantify precisely, but it is highly likely that the corrected patterns reflect true species richness at different scales more accurately. Unless otherwise mentioned, we use the corrected patterns in subsequent analyses.

measuring turnover

Components of turnover: species continuity, gain and loss

Fundamentally, turnover between two sample units (quadrats) is some measure of the difference between the lists of species present in each (e.g. Janson & Vegelius 1981). First, consider the presence/absence of species in a focal quadrat compared with one of its eight neighbours (Fig. 1). The total number of species that are each present in both quadrats is the pairwise matching component a′. The number of species that are present only in the neighbouring quadrat is b′, while the number present only in the focal quadrat is c′. We then define a, b and c as the averages of a′, b′ and c′ across the (up to) eight possible comparisons. The a component is the average number of species in common, or species continuity, the b component is the average number of species gained on entering an adjacent quadrat, while the c component is the average species loss. We mapped all three turnover components at different spatial scales (quadrat sizes).

We can make some simple predictions of the relationships between these turnover components and species richness. Continuity (a) should be positively correlated with richness: adjacent quadrats tend to have similar richness, and as richness increases we expect adjacent quadrats to contain an increasingly larger proportion of the local species pool, and so an increasingly similar list of species. We might also expect reduced opportunity for encountering ‘new’ species in high richness areas to result in a negative correlation with species gain (b), but a positive correlation with species loss (c). As a result, b and c are expected to be negatively correlated with each other, a and c to be positively correlated, and a and b to be negatively correlated. This reasoning relies on neighbouring quadrats sampling from the same species pool; at coarse scales, this might not be true.

turnover measured using indices

In contrast with the components of turnover that have units of numbers of species, turnover indices (essentially dissimilarity indices) implicitly correct for the number of pairwise comparisons (species) – they measure turnover on a ‘per-species’ basis. Two such indices that do not adjust for local species richness gradients are those of Whittaker (1960) and Sorenson. The first of these is the most widely used index of turnover:

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where R9 is the species richness of a large quadrat encompassing the focal quadrat and its eight neighbours (when all are available), and R1 is the species richness of the focal quadrat alone. It has a lower limit of zero but no upper limit. Clearly, areas with a stronger SAR will have higher βw values.

The second index is a composite Sorenson index, defined as the average dissimilarity of the focal quadrat with each of its neighbours:s

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where n is the number of pairwise comparisons (n = 8 when all neighbours are available). We use this index to show that the average pairwise dissimilarity (uncorrected for local species richness gradients) measures essentially the same property as βw. βsor has an upper limit of one (when the focal quadrat has no species in common with any neighbouring quadrat) and a lower limit of zero (if the focal quadrat and all neighbouring quadrats have identical species lists).

If there is a large difference in richness between quadrats, then βsor and βw will always be large. To focus more precisely on compositional differences, we introduce another turnover index:

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S2 resembles Simpson’s asymmetric index (Simpson 1943), but our form is symmetric. Any difference in species richness inflates either b′ or c′, so choosing the value of the smaller of these decreases the influence that any local species richness gradient has on dissimilarity. βsim has an upper limit of one (focal quadrat has no species in common with any neighbour) and a lower limit of zero (all have identical species lists).

We can empirically verify that βsim adjusts for local richness gradients (between adjacent quadrats), i.e. it is not influenced by local differences in richness, while βsor does not, i.e. is inflated by these differences. This can be done by comparing βg (below) with the difference between βsim and βsor. First, we subtract the maps of βsor from βsim on a quadrat by quadrat basis. Then we compare the resulting map of differences with a map of local species richness gradients. There should be a good match (strong correlation) if βsim removes the local species richness gradient component from βsor. As we expect βw to behave like βsor, this test can be applied to it, too. We define the local richness gradients for a focal quadrat as βg, the average proportional difference in richness between the focal quadrat and its neighbours:

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where αf and αn are species richness of the focal and neighbouring quadrats. βg has a lower limit of zero (identical richness throughout) and an upper limit of two (when the focal or all neighbouring quadrats have no species at all, so a and either b or c are zero).

As with species richness, all measures of turnover were calculated at different spatial scales: 10, 30, 50, 70 and 90 km. At each scale, we calculated turnover on the 3 × 3 neighbourhood basis (Fig. 1), and drew maps of each measure. Again, at coarser scales more quadrats have less than 100% land. In this case, we attempted no correction, because this is a much more difficult problem. The presence or absence of particular species would have to be predicted accurately. A related issue is that differences in land area and peninsularity will tend to produce differences in species richness between the quadrats and so inflate turnover for all measures except βsim. The magnitude of this effect will depend on the strength of the species–area relationship. It is not clear whether this effect, if real, will be evident in the spatial pattern of turnover, because variation in turnover caused by other factors may be large relative to variation produced by these area differences alone. For example, because values of the exponent z in R = cAz are relatively small (mean z = 0·12) in the present study, differences in species richness caused by differences in land area may be substantially less than those attributable to other causes of turnover. However, finding such a coastal effect is not necessarily evidence of a methodological artefact: there may be sound biological reasons for increased turnover at the coast. We check for coastal effects on the turnover maps.

Turnover as SAR model parameters

The strength of the SAR (magnitude of z or m) can reasonably be considered to be a measure of turnover based on species gain. Clearly z and m are affected by richness gradients. We estimated z and m using a nested set of 15 quadrats around each 10-km square, as described above.

pattern-matching and spatial autocorrelation

Spatial autocorrelation systematically distorts classical tests of association; it can make correlation coefficients, regression slopes and associated significance tests quite misleading (Clifford, Richardson & Hemon 1989; Cressie 1991; Lennon 2000). To avoid this, we implemented the modified correlation test of Clifford et al. (1989). This corrects the significance of the Pearson correlation coefficient for the spatial dependency within and between two patterns. It uses the concept of ‘effective sample size’ (ess). This is the equivalent sample size for the two variables when the redundancy produced by spatial autocorrelation is removed, and is a joint property of the two patterns, because the ess depends on the product of their autocorrelation functions. The ess can be considerably smaller (in the present study typically one or two orders of magnitude) than the observed number of data points.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

species richness patterns and spatial scale

Unsurprisingly, as quadrat size increases so does average species richness. However, the spatial pattern of species richness alters considerably (Fig. 2). Generally, there is a relative increase in richness in the north and a decrease in the south-west. The spatial distribution of the most diverse 5% of quadrats also changes with coarsening scale (Fig. 2). This change is particularly pronounced between scales of 10 km and 30 km. Although this movement slows down at coarser scales, the scattered high diversity quadrats in the south of Britain still tend to drift northwards (Fig. 2). The centre of the single most diverse quadrat moves north by 160 km between scales of 10 km and 90 km. This trend toward higher species richness in the south may be continued at scales finer than 10 km. A 2-km scale map of bird species richness shows an even higher concentration of species richness in the south-east of Britain (Fig. 11 in Gibbons et al. 1993).

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Figure 2. Spatial patterns of species richness at a series of spatial scales: 10 km, 30 km, 50 km and 90 km, left to right. Top row: species richness. Bottom row: diversity hotspots, as the most diverse 5% of quadrats (i.e. the highest 5%‘peaks’ of the richness map immediately above). There is a northwards shift in the most diverse areas with coarsening scale. Note that the shading legend is different for each map (preserves detail within rather than between maps). See Fig. 1 for moving window algorithm.

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As might be expected, correlations between species richness patterns at different measurement scales diminish with increasing difference in those scales (Table 1). Strictly there is no reliable statistical test available for this trend in correlation coefficients, because the patterns at different scales are clearly not independent. However, on comparing the most extreme scales considered (10 km and 90 km), the two species richness patterns become statistically unrelated (Table 1).

Table 1.  The cross-scale correlation of spatial patterns of species richness calculated at different scales. The correlation coefficients were calculated between the pairs of patterns measured at different scales. Effective sample sizes are shown in parentheses. NS = not significant at P = 0·05, corrected for spatial autocorrelation
 10 km30 km50 km70 km90 km
10 km0·62 (28)0·47 (30)0·31 (42)0·13 (74) NS
30 km 0·81 (13)0·63 (15)0·45 (23)
50 km  0·84 (11)0·66 (15)
70 km   0·84 (12)

turnover and local species richness gradients

The argument that βw and βsor combine or confuse two sources of turnover, local richness gradients and species replacement, is confirmed empirically. Our measure of richness gradients (βg) is strongly correlated with the difference between maps of βw and βsim (at 10-km scale: r = 0·75, ess = 140, P < 10−35), and with the difference between maps of βsor and βsim (at-10 km scale r = 0·98, ess = 55, P < 10−48; test for homogeneity of r, t = 8·13, P < 10−15). The strength of the latter correlation in particular demonstrates that βsor is essentially βsim plus a local species richness gradient component βg.

turnover and spatial scale

Mean turnover

Average turnover, as measured by the indices βw, βsor, and βsim, declines with coarsening scale (Fig. 3a). The greatest decline is between scales of 10 km and 30 km, after which the decline is shallower. In contrast, turnover as measured by numbers of species gained and lost between quadrats (b and c) is essentially scale-invariant (Fig. 3b): the mean level is roughly 10–13 species across a change in quadrat area of just under two orders of magnitude (81-fold), over which mean richness rises from 80 to 146 species.

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Figure 3. The decay of mean turnover (average of quadrat values within turnover maps, Fig. 4) with coarsening scale: (a) for the turnover index measures – all three ‘per-species’ measures decline with coarsening scale; (b) turnover as species continuity and as absolute numbers of species gained or lost. Species gain and loss remains approximately invariant at between 10 and 13 species across all scales.

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Turnover patterns and scale

As is the case with species richness, changing scale markedly alters spatial patterns of turnover. The distribution of βsim changes from having most high-turnover quadrats in the north at the finest scale to a geographically much wider distribution of high-turnover quadrats at the coarsest scale; the same is true, perhaps to a lesser extent, of βsor and βw (Fig. 4). Similarly, while species continuity a remains relatively static, species gain and loss b and c (negatively correlated as expected) shift pattern with coarsening scale dramatically (Fig. 5). The association between b and c (at least as measured by correlation) is not as strong as is perhaps suggested by Fig. 5: the correlations are between −0·48 and −0·61 across scales from 10 km to 90 km (all P < 0·05).

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Figure 4. Maps of turnover measured at three spatial scales using the three turnover indices: βw, top row (eqn 1); βsor, middle row (eqn 2); and βsim, bottom row (eqn 3); each index at scales 10 km, 30 km and 90 km, left to right. Generated using moving window algorithm (Fig. 1).

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Figure 5. Maps of the components of turnover a, b and c at three spatial scales. Top row = the turnover component a, species continuity, the number of species in common between neighbouring quadrats; middle row = the turnover component b, number of species gained in neighbouring quadrats; and bottom row = the turnover component c, the number of species lost in neighbouring quadrats, all at scales 10 km, 30 km and 90 km, left to right. See Fig. 1 for moving window algorithm.

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Like species richness, patterns of species turnover are less similar to each other as scale difference increases (Table 2). The patterns in βsor and βsim become statistically unrelated after relatively small changes in scale, with βsim changing more rapidly than βsor. The same is true of turnover measured as absolute species gain and loss (Table 3); the dissimilarity of patterns at different scales is more pronounced for species gain than for species loss.

Table 2.  The cross-scale correlation of spatial patterns of turnover measured with indices. The correlation coefficients were calculated between pairs of patterns measured at different scales. Effective sample sizes are shown in parentheses. The upper triangle is for βsor and the lower is βsim. NS = not significant at P = 0·05, corrected for spatial autocorrelation
 10 km30 km50 km70 km90 km
10 km0·40 (19)0·33 (20) NS0·39 (16) NS0·36 (17) NS
30 km0·30 (27) NS0·53 (26)0·44 (22)0·35 (23) NS
50 km0·20 (47) NS0·42 (54)0·57 (17)0·44 (18)
70 km0·13 (84) NS0·17 (100) NS0·39 (61)0·78 (11)
90 km0·06 (117) NS0·05 (116) NS0·19 (65) NS0·53 (23)
Table 3.  The cross-scale correlation of spatial patterns of species gain and loss (b and c). The correlation coefficients were calculated between pairs of patterns measured at different scales. The upper triangle is for species gain b and the lower is for species loss c. Effective sample sizes are shown in parentheses. NS = not significant at P = 0·05, corrected for spatial autocorrelation
 10 km30 km50 km70 km90 km
10 km0·06 (660) NS0·04 (372) NS0·03 (272) NS0·01 (334) NS
30 km0·21 (422)0·45 (155)0·15 (286)0·07 (378) NS
50 km0·11 (424)0·49 (121)0·58 (45)0·43 (51)
70 km0·09 (377)0·24 (247)0·61 (44)0·81 (17)
90 km0·07 (321) NS0·14 (498)0·47 (55)0·67 (23)

the species–area relationship, species richness and turnover

Logarithmic and power SARs

The logarithmic SAR outperformed the power SAR (had a higher model r2) in 76% of quadrats (Fig. 6). So although the spatial patterns of z and m are very similar, one SAR model dominates. The difference on a quadrat by quadrat basis in r2 between these two models (subtraction of the map of r2 for the power SAR from that for the logarithmic SAR) is negatively associated with βsim at the 10-km scale (r = −0·37, ess = 144, P = 0·0002). This shows that the logarithmic SAR tends to be a better fit in areas with more turnover at the 10-km scale. It is also a better fit in areas of low species richness at the 10-km scale (r = 0·68, ess = 391, P < 0·0001), and where z of the power SAR is smaller (r = −0·62, ess = 39, P < 0·005).

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Figure 6. Spatial patterns in SAR parameters: the ‘rate’ parameters (z and m) for the two models show similar spatial distributions. Left map: The exponent z of the power SAR. The SAR model was fitted to different data centred around each base 10-km quadrat. Quadrats of successively larger size were centred over each base 10-km quadrat, and the observed diversity and area at each scale used to fit the scaling exponent z (see Fig. 1). Middle map: m of the logarithmic SAR, same method. Right map: Spatial distribution of the identity of the SAR model giving the better fit in terms of regression model r2; dark-shaded quadrats indicate that the power SAR is a better fit, light-shaded quadrats indicate the logarithmic SAR is a better fit.

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The logarithmic SAR is also a better fit when the average species richness (across all quadrats) at each scale is fitted using least-squares regression to quadrat area (i.e. each map becomes a single point in the richness-scale plot); it does not matter whether or not the adjustment for land area in coastal quadrats is made (Fig. 7). In the absence of significance testing (not possible here – the data points are not independent), we follow Connor & McCoy (1979) in defining ‘better fit’ as meaning the model that best linearizes the relationship and minimizes the residuals.

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Figure 7. The relationship between average quadrat diversity and quadrat area (scale). Average quadrat diversity is the average of the mapped values in Fig. 2 (plus a 70-km scale not shown): each map is condensed to a single point on the diversity–area plot. (a) The power SAR model. (b) The logarithmic SAR model. The logarithmic SAR has a higher r2 than the power SAR, irrespective of whether or not the adjustment for the land area of coastal quadrats is made.

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species richness patterns and sar parameters

The strength of the SAR varies geographically, with both regional and local trends evident (Fig. 6). These spatial patterns of both z and m are negatively associated with richness, and the degree of pattern-matching declines at coarser scales. For z, at the 10-km scale: r = − 0·94, P = 0·006, ess = 23, at 30 km: r = − 0·72, P = 0·03, ess = 21, at 50 km: r = − 0·59, P = 0·06, ess = 21, at 70 km: r = − 0·45, P = 0·08, ess = 25, at 90 km: r = − 0·32, P = 0·13, ess = 32. The figures for m are almost identical, as might be expected from the similarity of the patterns of z and m (Fig. 6).

Turnover patterns and SAR parameters

The spatial pattern of βw (Fig. 4) is expected to reflect local spatial variation in the strength of the species–area relationship, since both are measures of turnover based on species gain (see Methods). Its strong associations with z of the power SAR and with m of the logarithmic SAR confirm this: the correlations of both z and m with βw are strong and positive (at 10-km scale r = 0·71, ess = 65, P < 10−13 and r = 0·59, ess = 57, P < 10−7, for z and m, respectively). Both SAR parameters show a very similar spatial distribution to species richness, confirmed by their strong correlations with species richness (at 10-km scale r = − 0·94, ess = 22, P = 0·006 and r = −0·93, ess = 21, P = 0·008, for z and m, respectively).

Turnover patterns and species richness patterns

There is more turnover in low richness areas, although this weakens at coarser scales. βw is strongly negatively associated with species richness measured at the same scale (Fig. 8). In contrast, although βsor is negatively correlated with richness, only at the two finest scales is this significant at P < 0·05. βsim is negatively correlated with species richness at the 10-km scale (r = −0·54, ess = 25, P = 0·04), but this correlation diminishes and is not significant at coarser scales. There is therefore some evidence that the association becomes increasingly positive with coarsening scale when measuring turnover with βsim.

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Figure 8. The scale-dependency of the correlation between turnover and diversity. All correlations between diversity and turnover are relatively constant in strength across scales except for the case of βsim, which is marginally significant (P = 0·04) for the finest scale only.

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The components of turnover a, b and c (mapped in Fig. 5) show systematic associations with species richness which are in accord with expectations (Fig. 8). The continuity component a is strongly positively associated with richness. The b component, species gain, is negatively associated with richness. The c component, species loss, is positively associated with richness, and positively associated with a. The strength of these associations between a, b or c and species richness holds relatively steadily across scales.

Coastal effects

Visual inspection of turnover maps (Figs 4 and 5) reveals no obvious indications of inflated turnover near the coast. This is confirmed for the three per-species indices by correlation of turnover patterns with maps of (log-transformed) distance from the coast. Only one correlation out of 15 is marginally significant (for βsor 50 km; r = 0·29, ess = 63, P = 0·05), indicating lower turnover in coastal areas. However, for b and c, four out of 10 comparisons are significant; all are negative, indicating more turnover nearer the coast (for b at 50 km, r = −0·20, ess = 126, P = 0·04; at 70 km, r = −0·33, ess = 66, P = 0·03, at 90 km, r = −37, ess = 52, P = 0·03, and for c at 30 km, r = −0·14, ess = 308, P = 0·02). Of course, these correlation tests are not independent, because each variable is correlated across scales (Tables 2 and 3). Had we included marine birds in our assemblage these coastal effects would have been more pronounced, because they inflate coastal richness and all turnover measures but βsim are affected by local richness gradients.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

species richness, turnover and scale

Spatial patterns are sensitive to scale

Patterns in the species richness of British birds are strongly scale-dependent. This is illustrated by our results in several ways. Spatial variation in the strength of the SAR (Fig. 6) shows that the rate at which species are accumulated with increasing area (coarsening scale) depends on the location of the area. Similarly, maps of our various measures of spatial turnover (Figs 4 and 5) show geographical structure (local and regional trends) at all scales. This means that the spatial pattern of species richness, in the sense of where the peaks and troughs of a species richness surface are, depends strongly on the scale at which it is measured (Fig. 2). Consequently, the location of richness ‘hotspots’ for a single taxon, in the present study, or the spatial coincidence of hotspots across multiple taxa (e.g. Prendergast et al. 1993), is inextricably linked to the spatial scale of analysis (see also Curnutt et al. 1994). For hotspots in different taxa to remain coincident across several scales would require the scale-dependency of species richness for each taxon to be identical. This implies a matching spatial distribution of turnover across taxa, such that the growth of species richness with increasing quadrat size is qualitatively the same. This strict condition is unlikely to be met. We can therefore extend the conclusion of Prendergast et al. (1993), that hotspots do not coincide across taxa at a fixed scale, by saying that hotspots at different scales within a single taxon tend not to coincide either. This has implications for the identification of richness and rarity hotspots for conservation (e.g. Williams et al. 1996; Reid 1998): locations or areas identified as having complementary sets of threatened species may, effectively, move as the scale of analysis (e.g. size of reserve) is changed. In a similar vein, Pearson & Carroll (1999) found that scale influences the relationship between the numbers of butterfly and bird species in quadrats across western North America.

Given this statistical disconnection of species richness patterns (termed ‘scale decay’ by Palmer & White 1994) across what is a relatively small change in scale (relative to the range of quadrat sizes used in published species richness analyses), clearly there is considerable room for doubt about the universality of the conclusions drawn from studies performed at a single scale. See Scheiner et al. (2000) for an interesting discussion on this theme.

Coastal and altitudinal trends in turnover

Our finding of weak evidence of increased turnover nearer the coast (only for b and c), despite excluding marine species, is intriguing. If this is not an artefact produced by more variable land area nearer the coast (see Methods), it might suggest some general habitat or climatic heterogeneity effect that is stronger at coarser scales.

Inspection of turnover maps (Figs 4 and 5) suggests a potential association of some measures with altitude or topographic variation (for maps of these and source of data, see Lennon & Turner 1995). Correlation with mean altitude is significant for βw and βsor at the 10-km scale (r = 0·32, ess = 66, P = 0·002, and r = 0·45, ess = 15, P = 0·04, respectively), but βsim is not significantly correlated with altitude at any scale. That the two indices sensitive to richness gradients are associated with altitude while βsim is not suggests that the association is caused mainly by these local richness gradients (Fig. 2). For the British avifauna, altitude and topographic variation are not the best predictors of species richness (at the 10-km scale; summer temperature is more important, Lennon et al. 2000b). Clearly, a more detailed analysis of associations between environmental factors and turnover is worthwhile, both in terms of the environmental factors considered and in terms of assemblage definition.

Turnover, randomness and local-regional effects

Low species richness areas have more spatial turnover as measured by βw and βsor, b and c, and most importantly by βsim. The latter in particular implies that low species richness areas tend to have relatively more random mixtures of species than high species richness areas. It is worth remembering here that all patterns (except fractals) are scale-dependent: a pattern viewed at one scale can look more aggregated or less aggregated at another (e.g. Dale 1999). The low richness, high turnover areas also have high values of the two SAR model rate parameters z and m. This makes sense, given that z and m are measures of species gain, and species are accumulated relatively quickly as a quadrat is expanded around a species richness ‘hole’.

Is this higher turnover in lower richness areas inevitable? We know that regional-scale processes may be more important for local-scale species richness than hitherto thought (e.g. Cornell & Lawton 1992; Cornell & Karlson 1997; Rosenzweig & Ziv 1999). Random sampling of a fixed species pool should produce lower turnover in high species richness areas, simply because there is less room for differences in species composition when a higher proportion of the pool is already present. But it is not quite as simple as this. If some species tend to be associated with low species richness areas (which, we suggest, is likely), it would mean that low species richness areas are sampling from a subset of the regional pool. This reduced pool size would produce lower turnover in low species richness areas. Since we observe that low species richness areas do have higher turnover, the latter process does not dominate – perhaps surprisingly. It would certainly be worthwhile to measure the relative strengths of these two opposing trends by quantifying affinities of particular species for areas of low or high species richness.

sar, turnover and scale

Two kinds of scale invariance

Mean turnover measured with all three indices βsor, βw and βsim (Fig. 3a) diminishes with coarsening scale – this may reflect the growth of species continuity (Fig. 3b) with scale. In striking contrast, the mean numbers of species gained and lost between quadrats (b and c) are effectively scale-invariant (Fig. 3b). This is a necessary consequence of a particular species–area relationship. The logarithmic SAR implies one kind of scale invariance but the power SAR indicates another. When we expand a quadrat area by a constant factor f in a nested design (in the present study f = 2 for all cases except βw, where f = 9), the power SAR implies that the ratio of species in the larger quadrat to that in the smaller is a constant, independent of area: R2/R1 =c(fA)z/cAz = fz. If we do the same area expansion but the logarithmic SAR applies, then the difference in species richness between the larger and smaller quadrat is a constant: R2−R1 = k + m log(fA) − [k + m log(A)]= m log (f). So our observation that mean numbers of species gained and lost between adjacent quadrats is approximately scale-invariant is consistent with the logarithmic SAR. This is confirmed by the result that the logarithmic SAR is a better fit overall than the power SAR (Figs 6 and 7).

SAR models: an unsolved puzzle

There is no really convincing theory of the circumstances that produce different types of SAR. Clearly, this makes it difficult to answer the question of why the logarithmic SAR should be a better fit overall than the power SAR in our study (Figs 6 and 7), although such a finding has also been reported elsewhere (Connor & McCoy 1979; Williamson 1988). The dominance of the power SAR is obvious in the recent literature (e.g. Rosenzweig 1995). It probably arises from the comparative study of different models of SARs done by Connor & McCoy (1979) and the apparent solidity given by the earlier ground-breaking theoretical work of Preston (1962; but see Leitner & Rosenzweig 1997). The logarithmic SAR was more popular with plant ecologists earlier in the last century because it often gave a better fit than the power SAR (e.g. Gleason 1922; Evans, Clarke & Brand 1955). Rosenzweig (1995) argues that the superior fit of the logarithmic SAR could be an artefact of the typically small sample sizes in those cases. May (1975) observes that small samples from a log-series species abundance distribution result in the logarithmic SAR (see Connor & McCoy 1979; Leitner & Rosenzweig 1997). However, it is unlikely that our finding is a sampling artefact – if any taxon has been reliably mapped it is the British avifauna. A possible artefact in our nested-quadrat design is the effect of coastal quadrats at coarse scales. As discussed above, these coastal quadrats may contain relatively more species for their area. Our richness-area correction does not take this into account, so richness maps at coarse scales may have inflated coastal richness. But, if this matters, it would not favour the logarithmic SAR. We would expect this effect to make a SAR curve more convex (steeper at high richness on log–log axes) while the logarithmic SAR is favoured if a linear log (species)–log (area) relationship is made more concave (less steep at high richness – see Fig. 7a).

turnover and scale: the big picture

Methodological issues: disentangling turnover from richness, scale and area differences

There are several coarse-scale analyses of turnover and richness (e.g. Willig & Sandlin 1992; Blackburn & Gaston 1996a, 1996b; Mourelle & Ezcurra 1997; Willig & Gannon 1997; Gregory, Greenwood & Hagemeijer’s 1998) that seem directly relevant to our study but, in practice, making a comparison both between them and with our results is not straightforward. One reason is the variety of different methods of measuring turnover used in these studies. More importantly, however, in several of these studies turnover measures have been applied in such a way as to effectively confound issues of spatial scale with the richness-turnover relationship. This has been done mainly by measuring turnover between unequal sized or numbers of quadrats. Moreover, none of the studies use measures of turnover that take into account the potentially overwhelming impact of local richness gradients, which as we demonstrate in the present study, cannot be ignored. Clearly, a generally agreed framework is needed for the measurement of turnover (Koleff, Gaston & Lennon, unpublished).

Turnover, endemism and scale

Will our observed negative relationship between richness and turnover continue to apply at even coarser scales? Probably not. At fine (landscape) scales, turnover is high between areas of low species richness for the reasons suggested in the present study. But at very coarse (approaching regional) scales, at which whole or substantial proportions of species ranges are contained within single quadrats, turnover is high between adjacent areas of high species richness simply because there are more species present to differ between quadrats. At these very coarse scales, moving between neighbouring quadrats means moving between areas with different sets of endemics. At both extremes of scale, high turnover results from spatial discontinuity of species presence, but the unit of presence ranges from local populations at fine scales up to whole or substantial parts of species ranges at very coarse scales. A switch is therefore expected in the sign of the diversity–turnover relationship at some intermediate scale. At very coarse scales, one obvious prediction is that turnover should be positively associated with latitudinal trends in endemism (e.g. Major 1988; Rosenzweig & Sandlin 1997).

Conclusions

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

For British birds, there is more turnover in areas of low species richness – but once local gradients in species richness have been filtered out, this is only statistically significant for the finest scale considered (10 km). Spatial patterns of species richness show weak connections across scales. After a roughly tenfold change in (linear) scale, richness patterns become statistically disconnected. In contrast, the average properties of species richness patterns at different scales show much more regular behaviour – most notably the scale invariance of species gains and losses. It is clear that species richness patterns can be very sensitive to scale, such that the location of richness hotspots changes radically depending on the scale of observation. This sensitivity has obvious consequences for macroecological analyses of spatial trends in patterns of species richness or turnover, attempts to detect meaningful associations between patterns of richness and environmental factors, and identification of target areas in conservation biology. Our results reinforce the point that species richness is not a concept or a measure that can be divorced from spatial scale.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

Particular thanks are due to the many thousands of volunteers whose efforts in collecting the data made this work possible, and the staff of the British Trust for Ornithology for making the data available to J.J.L. electronically. The referees were outstandingly helpful with this paper, and we extend our sincere gratitude for their efforts. J.J.L. acknowledges the support of a University of Leeds Fellowship and a Joint Venture Agreement with the Pacific North-west Research Station of the U.S. Forest Service (PNW 99–1006–1-JVA). P.K. acknowledges the support of Conacyt (51822/12228). K.J.G. is a Royal Society University Research Fellow.

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  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
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