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RESEARCH ARTICLE © 2002 Blackwell Science Ltd. http://www.blackwell-science.com/geb Global Ecology & Biogeography (2002) 11 , 363–375 Blackwell Science, Ltd The relationships between local and regional species richness and spatial turnover PATRICIA KOLEFF and KEVIN J. GASTON Biodiversity and Macroecology Group, Department of Animal & Plant Sciences, University of Sheffield, Sheffield S10 2TN, U.K. ABSTRACT Aim To determine the empirical relationships between species richness and spatial turnover in species composition across spatial scales. These have remained little explored despite the fact that such relationships are fundamental to understanding spatial diversity patterns. Location South-east Scotland. Methods Defining local species richness simply as the total number of species at a finer resolution than regional species richness and spatial turnover as turnover in species identity between any two or more areas, we determined the empirical relationships between all three, and the influence of spatial scale upon them, using data on breeding bird distributions. We estimated spatial turnover using a measure independent of species richness gradients, a fundamental feature which has been neglected in theoretical studies. Results Local species richness and spatial turnover exhibited a negative relationship, which became stronger as larger neighbourhood sizes were considered in estimating the latter. Spatial turnover and regional species richness did not show any significant relationship, suggesting that spatial species replacement occurs independently of the size of the regional species pool. Local and regional species richness only showed the expected positive relationship when the size of the local scale was relatively large in relation to the regional scale. Conclusions Explanations for the relationships between spatial turnover and local and regional species richness can be found in the spatial patterns of species commonality, gain and loss between areas. Key words beta diversity, birds, local–regional relationships, Scotland, spatial scale, spatial turnover, species richness. INTRODUCTION Ecologists have long distinguished between different compon- ents of species diversity. Commonly, three such components are recognized: local species richness, regional species richness and spatial turnover or differentiation diversity (Whittaker et al ., 2001). Local species richness may or may not equate to alpha diversity, depending on how fine is the spatial resolution of the localities concerned and how heterogeneous they are; both Whittaker (1960, 1972, 1975) and Cody (1975, 1993) regard alpha diversity as species richness within local patches of a given vegetation or habitat type (i.e. within-habitat diversity). Similarly, regional species richness may or may not equate to gamma or epsilon diversities, depending on the authority followed; while gamma diversity is employed widely to refer to richness in sample or inventory units of any large area (e.g. Rosenzweig, 1995; Calow, 1998), some constrain the term much more tightly to refer to species richness of a landscape unit or to a measure of the rate of species turnover between sites of the same habitat type (e.g. see Whittaker, 1960, 1977; Cody, 1975, 1993). Finally, spatial turnover is equated frequently with beta diversity, with changes in species composition being determined between spatial units that may be small or large in area, and may be relatively homogeneous in habitat or very heterogeneous (e.g. Harrison et al ., 1992; Blackburn & Gaston, 1996; Gregory et al ., 1998; Lennon et al ., 2001). However, again, some limit the latter term simply to the turnover in composition between vegetation or habitat types, or to the turnover between the alpha diversities of a vegeta- tion or habitat type that gives rise to the gamma diversity of that type (e.g. Whittaker, 1960, 1977; Cody, 1975, 1993). Despite wide application of the terms and associated concepts, exploration of the relationship between spatial turnover and species richness at different geographical scales has been surprisingly fragmentary (but see Loreau, 2000; Moreno & Halffter, 2001; Sweeney & Cook, 2001). The relationship between species richness and spatial turnover Correspondence: P. Koleff. E-mail: P.Koleff@sheffield.ac.uk

The relationships between local and regional species richness and spatial turnover

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RESEARCH ARTICLE

© 2002 Blackwell Science Ltd. http://www.blackwell-science.com/geb

Global Ecology & Biogeography

(2002)

11

, 363–375

Blackwell Science, Ltd

The relationships between local and regional species richness and spatial turnover

PATRICIA KOLEFF and KEVIN J. GASTON

Biodiversity and Macroecology Group, Department of Animal & Plant Sciences, University of Sheffield, Sheffield S10 2TN, U.K.

ABSTRACT

Aim

To determine the empirical relationships betweenspecies richness and spatial turnover in species compositionacross spatial scales. These have remained little exploreddespite the fact that such relationships are fundamental tounderstanding spatial diversity patterns.

Location

South-east Scotland.

Methods

Defining local species richness simply as the totalnumber of species at a finer resolution than regional speciesrichness and spatial turnover as turnover in species identitybetween any two or more areas, we determined the empiricalrelationships between all three, and the influence of spatialscale upon them, using data on breeding bird distributions.We estimated spatial turnover using a measure independentof species richness gradients, a fundamental feature which hasbeen neglected in theoretical studies.

Results

Local species richness and spatial turnover exhibiteda negative relationship, which became stronger as largerneighbourhood sizes were considered in estimating the latter.Spatial turnover and regional species richness did not showany significant relationship, suggesting that spatial speciesreplacement occurs independently of the size of the regionalspecies pool. Local and regional species richness onlyshowed the expected positive relationship when the size ofthe local scale was relatively large in relation to the regionalscale.

Conclusions

Explanations for the relationships betweenspatial turnover and local and regional species richness can befound in the spatial patterns of species commonality, gain andloss between areas.

Key words

beta diversity, birds, local–regional relationships,Scotland, spatial scale, spatial turnover, species richness.

INTRODUCTION

Ecologists have long distinguished between different compon-ents of species diversity. Commonly, three such componentsare recognized: local species richness, regional species richnessand spatial turnover or differentiation diversity (Whittaker

et al

., 2001). Local species richness may or may not equate toalpha diversity, depending on how fine is the spatial resolutionof the localities concerned and how heterogeneous they are;both Whittaker (1960, 1972, 1975) and Cody (1975, 1993)regard alpha diversity as species richness within local patchesof a given vegetation or habitat type (i.e. within-habitatdiversity). Similarly, regional species richness may or maynot equate to gamma or epsilon diversities, depending on theauthority followed; while gamma diversity is employed widelyto refer to richness in sample or inventory units of any largearea (e.g. Rosenzweig, 1995; Calow, 1998), some constrain

the term much more tightly to refer to species richness of alandscape unit or to a measure of the rate of species turnoverbetween sites of the same habitat type (e.g. see Whittaker,1960, 1977; Cody, 1975, 1993). Finally, spatial turnover isequated frequently with beta diversity, with changes in speciescomposition being determined between spatial units that maybe small or large in area, and may be relatively homogeneousin habitat or very heterogeneous (e.g. Harrison

et al

., 1992;Blackburn & Gaston, 1996; Gregory

et al

., 1998; Lennon

et al

.,2001). However, again, some limit the latter term simply to theturnover in composition between vegetation or habitat types,or to the turnover between the alpha diversities of a vegeta-tion or habitat type that gives rise to the gamma diversity of thattype (e.g. Whittaker, 1960, 1977; Cody, 1975, 1993).

Despite wide application of the terms and associatedconcepts, exploration of the relationship between spatialturnover and species richness at different geographical scaleshas been surprisingly fragmentary (but see Loreau, 2000;Moreno & Halffter, 2001; Sweeney & Cook, 2001). Therelationship between species richness and spatial turnover

Correspondence: P. Koleff. E-mail: [email protected]

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, 363–375

has been explored principally in the context of latitudinalgradients in species richness, and the proposition that hightropical richness results proximately from high levels ofspatial turnover in species identities (Willig & Sandlin, 1992;Blackburn & Gaston, 1996; Bowman, 1996; Gaston &Williams, 1996; Mourelle & Ezcurra, 1997; Willig & Gannon,1997; Gregory

et al.

, 1998; Williams

et al.

, 1999). The resultshave been very variable, with only some studies findingpositive correlations between species richness and turnover,and others finding negative relationships or none at all.Assuming no biases in sampling effort, these inconsistenciesmight be attributed to differences in the taxa that have beenexamined, or in the geographical regions where the studieswere conducted. Unfortunately, however, interpretation ofthe findings is greatly complicated, if not rendered impossible,because different measures of spatial turnover have beenemployed in a variety of ways by different studies (Koleff

et al.

submitted). It is thus extremely difficult to disentanglemethodological from biological differences.

There is also evidence that the relationship between speciesrichness and spatial turnover varies systematically withspatial scale (Lennon

et al

., 2001). Moreover, attention in theliterature has fallen on measures of spatial turnover thatemphasize the level of sharing of species between areas(exemplified by measuring spatial turnover as the relationshipbetween alpha and gamma diversities as suggested originally,see below) rather than the pattern of turnover as reflectedby species gains and losses. This is particularly importantbecause measures of spatial turnover should capture thenotion that turnover is high when the proportion of speciesshared between two areas is low, and the proportions lostand gained moving from one to the other are similar. However,this has not been achieved in previous studies, where turnoverincluded differences in richness gradients. Thus, overall,understanding of the empirical relationship between speciesrichness and spatial turnover remains limited.

A substantial literature has sought to document what hascome to be termed the local–regional richness relationship(for reviews see Ricklefs, 1987; Cornell & Lawton, 1992;Cody, 1993; Cornell, 1993, 1999; Ricklefs & Schluter, 1993;Caley & Schluter, 1998, 1998; Lawton, 1999; Blackburn &Gaston, 2000; Gaston, 2000). Two basic types of patterns aredistinguished commonly. The first is a proportional-samplingor type I model in which local richness is directly proportionalto, but less than, regional richness. In the second, or type IImodel, as regional richness increases local richness attains aceiling above which it does not rise despite continuedincreases in regional richness. Empirical data seem to exhibitmost frequently (although not exclusively) an underlying typeI relationship (Cornell & Lawton, 1992; Caley & Schluter, 1997;Lawton, 1999) with, not uncommonly, regional richnessexplaining a large proportion (> 75%) of variance in localrichness, and local richness constituting a marked proportion

(> 50%) of regional richness (Gaston, 2000). For example,type I relationships have been documented for fig wasps andtheir parasitoids in southern and central Africa (Hawkins &Compton, 1992), tiger beetles in North America and in India(Pearson & Juliano, 1993), lacustrine fish in North America(Griffiths, 1997) and primates in Africa and South America(Eeley & Lawes, 1999). The predominance of type I relation-ships is supported by the observation that some spatial gradientsin species richness are documented both for localities and forregions across those gradients.

As with relationships between local species richness andspatial turnover, those between local and regional richnessseem to be influenced by spatial scale (Caley & Schluter,1997; Zobel, 1997; Huston, 1999; Loreau, 2000; Godfray &Lawton, 2001). Thus, Caley & Schluter (1997) reported thatconsidering larger local spatial scales in relation to the regional,local species richness accumulates faster as a function ofregional diversity.

Defining spatial turnover following Whittaker’s (1960)original definition of beta diversity (but broadening itsconstituent parts to local and regional richness as employedhere), as regional richness/ local richness (i.e. from the multi-plicative relationship

γ

=

αβ

, where

γ

is gamma diversity,

α

ismean alpha diversity, and

β

is beta diversity), regions havingthe same ratio of local to regional richness should have thesame spatial turnover (Srivastava, 1999). However, this arguablypoints more to the limitations of this measure of spatialturnover (which does not exhibit the intuitively appealingproperties identified earlier) than it provides valuable insight.If spatial turnover is defined so as to account for the level ofsharing of species between areas and the pattern of speciesgains and losses, the relationship between spatial turnoverand regional richness could take a wide range of differentforms. Once again, spatial scale might also be expected toinfluence the patterns observed.

In this paper we determine, for the first time for a singlespecies assemblage, the pairwise relationships between spatialturnover, local species richness and regional species richness,using a measure of spatial turnover based on species gain andloss, and document the influence of spatial scale on therelationships.

METHODS

Our analyses are based on the distribution of the breedingbirds of south-east Scotland recorded in 1988–94 in a surveycarried out on behalf of the Scottish Ornithologists’ Club(Murray

et al

., 1998). Data are at a resolution of 2

×

2 kmquadrats (tetrads) on a continuous grid, and comprise recordsobtained mainly between 1 April and 31 July (with the exceptionof those for species breeding earlier than this). They constitutethe most comprehensive and accurate information currentlyavailable on the distribution of birds in the region, with

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coverage among the best of the regional ornithological atlasesfor Britain and for one of the larger regions over which birdshave been mapped at this resolution. For a detailed descriptionof the methods used in the survey see Murray

et al

. (1998).From the survey, presence/absence data were available for

125 breeding species (from a total of 189 species recorded,excluding marine birds, vagrant, marginal, escaped speciesand confidential occurrences from the analysis) distributedacross 1756 tetrads. For these species there was a total of68 599 species–tetrad records (i.e. records of the occurrenceof a given species in a given tetrad, ignoring duplicates).

These data were manipulated using the Worldmap software(Williams, 1996). Local species richness was measured as thetotal number of species recorded in each tetrad. FollowingLennon

et al

. (2001), spatial turnover was measured as:

(eqn 1)

where

n

is the number of pairwise comparisons. For eachpairwise comparison, S

i

, between the focal tetrad and a singleneighbouring tetrad (

i

),

a

is the total number of species whichare each present in both tetrads;

b

is the number of specieswhich are present in the neighbouring tetrad but not in thefocal tetrad, while

c

is the number present in the focal tetradbut not its neighbour.

β

sim

is independent of species richnessgradients, i.e.

β

sim

reflects compositional differences ratherthan differences in species richness between two units undercomparison (Lennon

et al

., 2001). Additionally, this measureis highly sensitive to small changes either in species gain (

b

) orspecies loss (

c

) between the focal cell and its neighbourhood(Koleff

et al

., in press).

β

sim

was calculated for each focal tetrad and separatelyfor neighbourhood sizes of 9 (36 km

2

), 25 (100 km

2

), 49(196 km

2

), 81 (324 km

2

), 121 (484 km

2

), 169 (676 km

2

) and225 (900 km

2

) tetrads (Fig. 1; see Williams

et al

., 1999).Regional species richness was measured at the same

seven different scales, as the total number of species recordedin the focal tetrad and each of the seven neighbourhoods(36–900 km

2

) used in calculating spatial turnover. Whencomparing results for different regional scales, we consideronly those 441 tetrads for which the largest neighbourhood(900 km

2

) lies completely within the boundaries of the studyregion. This avoids both systematic changes in sample sizes withdifferent sized neighbourhoods and excludes neighbouringareas that include sea or lie in adjacent regions for which datawere unavailable. However, patterns of local and regionalrichness and spatial turnover for all tetrads with completeneighbourhoods were also analysed for every scale, i.e. 1495tetrads for the 36 km

2

scale, 1276 tetrads for the 100 km

2

,1057 tetrads for the 196 km

2

, 866 tetrads for the 324 km

2

,695 tetrads for the 484 km

2

and 554 tetrads for the 676 km

2

.To correct for the possible effects of spatial autocorrelation

on classical tests of association (including those effects resultingfrom the overlapping of neighbourhoods for different tetrads),we employed the modified correlation test of Clifford

et al

.(1989; see also Lennon, 2000). This corrects the significanceof the standard product–moment correlation coefficientfor the spatial dependency within and between two patterns,and uses the concept of ‘effective sample size’ (

ess

), theequivalent sample size for the two variables when theredundancy produced by spatial autocorrelation is removedand is a joint property of the two patterns. The

ess

dependson the product of their autocorrelation functions, and can

Fig. 1 Area of study and scales considered to assess spatial turnover and regional species richness. For each focal tetrad (central, in black) anincreasing number of surrounding tetrads was considered.

βsim S S ( ); min( , )

= − =+=

∑11

1na

a b cii

n

ii

i i i

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be considerably smaller than the observed number of datapoints.

RESULTS

The frequency distributions of local and regional speciesrichness, spatial turnover and of the three matching components,

a

,

b

and

c

were all unimodal over the region of south-eastScotland, although with some evidence of skewness for all scalesconsidered. The frequency distributions were all left-skewedfor local richness (

g

1

=

0.11, NS), the matching component

a

(36 km

2

,

g

1

=

0.41; 100 km

2

,

g

1

=

0.62; 196 km

2

,

g

1

=

0.69;324 km

2

,

g

1

=

0.73; 484 km

2

,

g

1

=

0.77; 676 km

2

,

g

1

=

0.80;900 km

2

,

g

1

=

0.82; for all

P

< 0.001) and regional richness,with the exception of regional richness at the 196 km

2

scale, which was slightly right-skewed (36 km

2

,

g

1

=

1.48;100 km

2

,

g

1

=

0.62; 196 km

2

,

g

1

= 0.38; 324 km

2

,

g

1

=

0.41;484 km

2

,

g

1

=

0.42; 676 km

2

,

g

1

=

0.57; 900 km

2

,

g

1

=

0.49; for all

P

< 0.001). At the largest scale variation inregional richness decreased dramatically, as tetrads exhib-ited very similar species composition (Fig. 2a). On the otherhand, frequency distributions were right-skewed for theturnover components,

b

(36 km

2

,

g

1

= 0.82; 100 km

2

,

g

1

=0.62; 196 km

2

,

g

1

= 0.61; 324 km

2

,

g

1

= 0.67; 484 km

2

,

g

1

= 0.75;676 km

2

,

g

1

= 0.81; 900 km

2

,

g

1

= 0.87; for all

P

< 0.001) and

c

(36 km

2

,

g

1

= 0.77; 100 km

2

,

g

1

= 0.84; 196 km2, g1 = 0.83;324 km2, g1 = 0.79; 484 km2, g1 = 0.77; 676 km2, g1 = 0.75;900 km2, g1 = 0.72; for all P < 0.001) and for spatial turnoverat all scales except for 324 and 484 km2 (36 km2, g1 = 0.273,P < 0.001, 100 km2; g1 = 0.03, NS; 196 km2, g1 = 0.03, NS,324 km2, g1 = −0.03, NS; 484 km2, g1 = −0.03, NS; 676 km2,g1 = 0.07, NS; 900 km2, g1 = 0.22, P < 0.001). In the main,however, all these skew values are small, their statisticalsignificance results from the large samples, and they are notsufficient to invalidate subsequent analyses.

Local species richness and spatial turnover

Considering the 1495 tetrads with complete neighbourhoodsof eight surrounding cells, local species richness exhibits acomplex pattern of variation across the study area (Fig. 3a),with peak values often being associated with the occurrenceof river valleys and other lowland areas. Spatial turnover atthis scale tends to show the obverse pattern (Fig. 3b). Indeed,

(a)

(b)

(c)

10

100

1000

1 100010010Size of the neighbourhood, km2, log

Mea

n nu

mbe

r of

spe

cies

, log

10

20

30

40

Size of the neighbourhood, km2

Size of the neighbourhood, km2

Size of the neighbourhood, km2

Mea

n a

0.15

0.18

0.21

0.24

0.27

0.3

0.33

0 200 400 600 800 1000

0 200 400 600 800 1000

0 200 400 600 800 1000

0 200 400 600 800 1000

Size of the neighbourhood, km2

Mea

n β s

in

(d)

(e)

0

5

10

15

20

25

Mea

n b

0

5

10

15

20

25

Mea

n c

Fig. 2 Mean values of (a) species richness, (b) βsim, (c) the matchingcomponent a, (d) the matching component b, and (e) the matchingcomponent c, for each neighbourhood considered. Dark circles arefor tetrads for which the largest neighbourhood (900 km2) liescompletely within the boundaries of the study region (N = 441).Open circles are for the total number of tetrads with completeneighbourhoods of different sizes (see methods for numbers). Barsindicate ±1 SD.

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the spatial pattern of variation in local species richness wasweakly negatively related to that in spatial turnover whenconsidering a 36 km2 neighbourhood (Table 1). However, asthe size of the neighbourhood used to estimate spatial turnoverwas increased, this relationship, while remaining negative,became progressively stronger (Table 1).

Mean local species richness was c. 36 species across allthe tetrads (1756) in south-east Scotland; 86 species wererecorded in the richest tetrad, and one in the poorest. For thesubset of 1495 tetrads with complete 36 km2 neighbourhoodsthe mean number of species was c. 38, the maximum 84 andthe minimum was five (Figs 2a and 3a). For the subset of

Fig. 3 Patterns of variation for the birds of south-east Scotland in (a) local species richness (LSR), (b) spatial turnover (β), (c) the matchingcomponent a, (d) the matching component b, and (e) the matching component c. (b–e) were estimated for a nine-cell neighbourhood, 36 km2.

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tetrads each having a complete neighbourhood of 900 km2,the maximum and minimum species richness values were,respectively, 76 and six, while the mean local species richnesswas 40. These differences reflect high variability in the speciesrichness of peripheral tetrads (those toward the edges ofsouth-east Scotland), because these were eliminated whenconsidering complete areas for the regional scales andlarge neighbourhoods (e.g. the richest tetrads located in thenorthernmost area of the region were excluded).

Mean values of spatial turnover increased for largerneighbourhoods (Fig. 2b), presumably because of a distanceeffect (i.e. assemblages become more divergent when com-paring the focal tetrad with, on average, progressivelymore distant tetrads; Figs 2c and 4). Consistently, as thesize of the neighbourhood was increased, the values of band c also increased (Fig. 2d,e) while those of a decreased(Fig. 2c). For all three matching components, the meanchange across the full range of neighbourhood sizes was,however, only about three species. Figure 4 shows howpatterns of spatial turnover changed spatially with differencesin neighbourhood size, e.g. some areas of low spatial turnoverat the 36 km2 scale, become areas of high diversity at the900 km2 scale.

For the 36 km2 neighbourhood, local species richnesswas significantly positively correlated with matching com-ponents a and c, and negatively with component b (Table 2,Fig. 3). Conversely, spatial turnover was negatively correlatedwith a and c, and positively with component b (Table 3, Fig. 3).For both local richness and spatial turnover, the strengths ofthese correlations increased with the size of the neighbourhoodused to calculate the components (Tables 2 and 3).

Spatial turnover and regional species richness

Spatial turnover and regional species richness did not exhibitany significant relationship when the former was calculatedfor a 36-km2 neighbourhood, regardless of the scale used tocalculate regional richness (Table 4).

As expected, mean values of regional richness increasedwith neighbourhood size (Fig. 2a; log species richness =1.51 + 0.202 log area, r = 0.89, P < 0.0001). Correlation

coefficients between regional richness and the matchingcomponent a were initially high but declined dramaticallyas the neighbourhood size at which both were calculatedincreased (Table 5). This effect was also apparent for thematching components b and c, although the relationships atthe 36 km2 neighbourhood were not as strong as that withcomponent a (Table 5).

Local and regional species richness

Local species richness was correlated positively with regionalspecies richness when the latter was calculated for smallscales, but no relationship was observed as neighbourhoodsize increased (Table 6). This decline was associated with adecline in the variance in regional diversity (Fig. 5), but alsowith an area effect (i.e. a smaller focal area is considered inrelation to a larger regional pool).

DISCUSSION

Local species richness and spatial turnover

The negative relationship between local species richnessand spatial turnover documented for the breeding birds ofsouth-east Scotland (Table 1) is consistent with findings forthe breeding birds of Britain at a scale of 10 × 10 km usingthe same measure of spatial turnover (Lennon et al., 2001).However, such a relationship may not generalize to other areas,taxa or scales. For example, high species turnover mightcontribute to high diversity in the tropics (e.g. Blackburn &Gaston, 1996), giving rise to a positive relationship betweenlocal richness and spatial turnover. Nevertheless, on a perspecies basis species turnover could remain constant andthere still be many more species of restricted distribution intropical regions.

In the present case, areas of low local species richnesstend to have higher species turnover than do areas of highspecies richness. This effect is reflected in the marked positiverelationships between local richness and matching componentsa and c (Table 2), and the negative relationship betweenlocal richness and the matching component b (Table 2). In

Table 1 The correlation coefficients between spatial patterns of local species richness and spatial turnover calculated at different neighbourhoodsizes. All are significant at P < 0.005, corrected for spatial autocorrelation. Effective sample sizes are shown in parentheses. Complete = values forthe tetrads for which the largest neighbourhood (900 km2) lies completely within the boundaries of the study region (N = 441). All = values forthe total number of tetrads with complete neighbourhoods of different sizes (see Methods for numbers)

Neighbourhood size tetrads (area, km2) 9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete −0.288 (216) −0.365 (207) −0.478 (212) −0.576 (147) −0.646 (108) −0.686 (90) −0.713 (78)All −0.386 (89) −0.446 (80) −0.489 (91) −0.534 (103) −0.604 (86) −0.683 (81)

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Fig. 4 Patterns of spatial turnover considering differentneighbourhood sizes (a) nine tetrads, 36 km2; (b) 25tetrads, 100 km2; (c) 49 tetrads, 196 km2; (d) 81tetrads, 324 km2; (e) 121 tetrads, 484 km2; (f) 169tetrads, 676 km2; and (g) 225 tetrads, 900 km2. Mapsshow the tetrads for which the largest neighbourhood(900 km2) lies completely within the boundaries of thestudy region (N = 441).

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other words, as local species richness increases so does thenumber of species shared between two tetrads and the numberpresent in the focal tetrad but not in its neighbourhood, whilethe number in the neighbouring tetrad but not in the focalone declines. The observed higher turnover in lower speciesrichness areas for the breeding birds of south-east Scotlandalso suggests that differences in species composition willtend to be low when a high proportion of the species pool isalready present.

The strength of the relationship between local speciesrichness and spatial turnover increases with the size of the

neighbourhood over which spatial turnover is calculated(Table 1). That is, the relationship between local speciesrichness and spatial turnover becomes stronger as the value ofthe latter increases (Fig. 2b) but also as the patterns in spatialturnover change spatially (Fig. 4). Higher values of spatialturnover are expected to be obtained when comparing thefocal tetrad with more distant ones (Whittaker, 1975; Harrisonet al., 1992), as more distantly separated tetrads are expectedto show more differences in species composition. As the sizeof the neighbourhood increases, the number of species incommon (a) between each focal tetrad and remote neighbouring

Table 2 Coefficients of correlation between local species richness and the matching components, a, b and c, estimated at different neighbourhoodsizes. All are significant at P < 0.0001, corrected for spatial autocorrelation. Effective sample sizes are shown in parentheses. Complete = valuesfor the tetrads for which the largest neighbourhood (900 km2) lies completely within the boundaries of the study region (N = 441). All = valuesfor the total number of tetrads with complete neighbourhoods of different sizes (see Methods for numbers)

(a)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete 0.934 (31) 0.927 (30) 0.926 (31) 0.930 (32) 0.931 (33) 0.934 (34) 0.939 (34)All 0.911 (28) 0.901 (28) 0.900 (28) 0.917 (28) 0.926 (28) 0.935 (31)

(b)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete −0.555 (139) −0.757 (109) −0.864 (84) −0.911 (64) −0.929 (56) −0.935 (52) −0.936 (50)All −0.480 (357) −0.681 (313) −0.779 (295) −0.848 (162) −0.892 (93) −0.922 (69)

(c)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete 0.891 (80) 0.917 (71) 0.927 (65) 0.934 (59) 0.937 (56) 0.941 (55) 0.945 (55)All 0.803 (298) 0.846 (247) 0.873 (189) 0.908 (120) 0.926 (81) 0.938 (72)

Table 3 Coefficients of correlation between spatial turnover and the matching components, a, b and c, estimated at different neighbourhoodsizes. All are significant at P < 0.05, corrected for spatial autocorrelation. Effective sample sizes are shown in parentheses. Complete = values forthe tetrads for which the largest neighbourhood (900 km2) lies completely within the boundaries of the study region (N = 441). All = values forthe total number of tetrads with complete neighbourhoods of different sizes (see Methods for numbers)

(a)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete −0.716 (52) −0.733 (48) −0.742 (48) −0.758 (50) −0.771 (50) −0.780 (51) −0.786 (51)All −0.467 (47) −0.535 (36) −0.579 (42) −0.612 (50) −0.684 (44) −0.752 (45)

(b)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete 0.406 (209) 0.559 (190) 0.653 (150) 0.710 (113) 0.742 (95) 0.761 (86) 0.773 (81)All 0.377 (716) 0.439 (739) 0.497 (528) 0.572 (273) 0.648 (194) 0.721 (135)

(c)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete −0.570 (179) −0.576 (170) −0.578 (156) −0.572 (156) −0.565 (141) −0.561 (141) −0.562 (142)All −0.144 (969) −0.214 (694) −0.271 (624) −0.357 (413) −0.434 (275) −0.529 (200)

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ones decreases (Fig. 2c), while higher values of the matchingcomponents b and c are observed (Fig. 2d,e).

A novel approach to evaluating the contribution of the threematching components to spatial turnover is to express thesecomponents as percentages of the total number of species occur-ring in a focal quadrat and/or its neighbours (Koleff et al.,in press). Ternary plots can then be used to show the relative valuesof the components (Fig. 6). As employed here, the magnitudeof a increases from the base of the ternary plot towards its apex,and for a given value of a the lateral position of a point reflectsthe relative contribution of b and c. For βsim, low values ofspatial turnover are produced if there is a high proportion ofspecies in common (a) between the focal cell and the neigh-bourhood, while the highest values are reached when both band c are high in relation to a (see eqn 1; Koleff et al., in press).

This approach reveals first that, as mentioned before, thelarger neighbourhoods show a decrease in the mean valuesand the proportion of the component a (Figs 2c and 6).Secondly, mean values of component b are consistently higherthan those of c, as neighbourhood sizes increase (Fig. 6).However, many of the species can be found throughoutsouth-east Scotland, as most major habitat types are to someextent available in all tetrads across the region, e.g. waterbodies, woodlands, grasslands, lowlands or uplands. Themean increase in b and c across all neighbourhoods was thusonly about three species (Fig. 2d,e). In consequence, relativelylow values of species turnover were observed even for largeneighbourhoods (Fig. 2b), although more importantly, peaksof spatial turnover and low turnover sites change spatiallywith neighbourhood size (Fig. 4).

Table 4 The correlation coefficients between spatial patterns of spatial turnover and regional species richness, both calculated at differentneighbourhood sizes. No values were significant at P = 0.05, corrected for spatial autocorrelation. Effective sample sizes are shown in parentheses.Complete = values for the tetrads for which the largest neighbourhood (900 km2) lies completely within the boundaries of the study region(N = 441). All = values for the total number of tetrads with complete neighbourhoods of different sizes (see Methods for numbers)

Neighbourhood size, tetrads (area, km2) 9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete 0.055 (161) 0.056 (68) −0.044 (253) −0.071 (116) −0.060 (66) −0.001 (54) 0.095 (60)All −0.071 (79) −0.074 (52) −0.097 (58) −0.085 (90) −0.067 (61) −0.036 (57)

Table 5 Coefficients of correlation between regional species richness and the matching components, a, b and c, estimated at differentneighbourhood sizes. NS = not significant at P < 0.05, corrected for spatial autocorrelation. Effective sample sizes are shown in parentheses.Complete = values for the tetrads for which the largest neighbourhood (900 km2) lies completely within the boundaries of the study region(N = 441). All = values for the total number of tetrads with complete neighbourhoods of different sizes (see Methods for numbers)

(a)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete 0.055 (1785) 0.056 (620) 0.058 (418) 0.057 (742) 0.050 (442) 0.047 (442) −0.009 (369)NS NS NS NS NS

All 0.674 (22) 0.518 (18) 0.417 (18) 0.329 (29) 0.248 (43) 0.173 (73)NS NS

(b)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete −0.065 (251) −0.059 (517) −0.034 (530) 0.007 (322) 0.045 (168) 0.072 (119) 0.088 (100)NS NS NS NS NS NS NS

All 0.307 (220) 0.213 (233) 0.143 (251) 0.072 (415) −0.003 (165) 0.010 (109)NS NS NS

(c)Neighbourhood size, tetrads (area, km2)

9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete −0.035 (358) −0.028 (431) −0.029 (436) −0.026 (414) −0.019 (362) −0.015 (342) −0.009 (369) NS NS NS NS NS NS NS

All 0.342 (278) 0.187 (313) 0.077 (426) 0.061 (238) 0.088 (153) 0.018 (362)NS NS NS NS

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Spatial turnover and regional species richness

For the breeding birds of south-east Scotland, there was nosignificant relationship between spatial turnover and regionalspecies richness, no matter what neighbourhood sizes thesediversities were determined over (Table 4). However, variationin regional species richness at the largest scales is limited(Fig. 5). In other words, the size of the regional pool (thesum of species in local assemblages) is largely independentof spatial patterns of species replacement. A high regionaldiversity might not result because there is a high level ofturnover in species identities between localities, in the sensethat turnover is captured by βsim. There is little informationavailable with which to judge how general such a result mightbe, because studies of spatial turnover seldom break turnoverdown into its basic components of species gains and losses

Table 6 The correlation coefficients between spatial patterns of local and regional species richness calculated at different neighbourhood sizes.NS = not significant at P < 0.05, corrected for spatial autocorrelation. Effective sample sizes are shown in parentheses. Complete = values for thetetrads for which the largest neighbourhood (900 km2) lies completely within the boundaries of the study region (N = 441). All = values for thetotal number of tetrads with complete neighbourhoods of different sizes (see Methods for numbers)

Neighbourhood size, tetrads (area, km2) 9 (36) 25 (100) 49 (196) 81 (324) 121 (484) 169 (676) 225 (900)

Complete 0.613 (33) 0.388 (35) 0.195 (42) 0.096 (53) 0.058 (71) 0.037 (119) 0.016 (897)NS NS NS NS NS

All 0.621 (36) 0.422 (34) 0.289 (38) 0.217 (56) 0.181 (73) 0.101 (153)NS NS NS

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across the landscape (but see Lennon et al., 2001). In fact,most widely used measures of spatial turnover do not employsuch a decomposition of turnover into its constituent parts,and when it is performed it reveals that some such measuresare plainly not capturing the features of turnover that havebeen claimed for them (Koleff et al., in press). Koleff et al.(in press) identified 25 measures that have been used tomeasure spatial turnover for presence–absence data. Theseexhibit widely differing properties, reflecting different aspectsof species turnover, and consequently produce differentspatial patterns.

Local and regional richness

As far as we are aware, the only previously documentedlocal–regional richness relationship for birds in Britain wasa moderately strong linear relationship (with no statisticalevidence for curvilinearity) determined between the numbersof species breeding in tetrads and the number in those countiesin which tetrads lay (Gaston & Blackburn, 2000). At the fineresolution at which the breeding birds of south-east Scotlandhave been mapped, there was no simple relationship betweenlocal and regional species richness. Rather, the relationshipappeared to change with variation in the ratio between the sizesof locality and region (Fig. 5). For the smallest neighbourhoodconsidered in estimating regional species richness (36 km2),local species richness increases roughly linearly with regionaldiversity, despite some variation. It might reasonably bedescribed as following a type I relationship (see Introductionfor the distinction between type I and II local–regionalrelationships). However, for the largest regional scale (900 km2),a range of values of local species richness is observed forsimilar values of regional richness, as most of the tetradsexhibit similar-sized regional species pools. This emphasizesthe importance in studies of local–regional relationships ofthe size of the region considered, and the potential that differentstudies at different scales may or may not support differentmodels for the relationship (Cornell & Lawto n, 1992; Pärtelet al., 1996; Caley & Schluter, 1997; Dupré, 1999; Huston,1999; Srivastava, 1999; Loreau, 2000; Ricklefs, 2000).

A component of the pattern for small neighbourhoods mayresult from the moderate to high proportion of species commonto both local and regional species richness (although this isno greater than documented in other studies; Gaston, 2000).Excluding those species comprising the local assemblagefrom the estimation of the size of the regional pool (that isregional minus local species richness), and plotting thesevalues against local diversity, results in a significant negativerelationship between the two, which becomes stronger as theneighbourhood size increases (Fig. 7).

The majority of previous studies of local–regional richnessrelationships have been concerned with the evidence theymay provide as to whether local assemblages are or are not

saturated with species. Type I relationships have beenregarded as supplying evidence for a lack of saturation andfor an important role of regional processes in determininglocal richness, and type II relationships as supplying evidencefor species saturation (e.g. Cornell & Lawton, 1992; Cornell& Karlson, 1996). The extent to which such inferences canindeed be drawn has been much debated, and it is clear thatthis is at best problematic (Caley, 1997; Caley & Schulter,1997; Griffiths, 1999; Srivastava, 1999; Herben, 2000;Loreau, 2000; Winkler & Kamplicher, 2000). Therefore, noconclusion about the extent to which local assemblages aresaturated is drawn from this study.

CONCLUSIONS

In combination, local and regional species richness andspatial turnover capture much of the spatial variation inspecies diversity. For the birds of south-east Scotland localspecies richness and spatial turnover were negatively related,local and regional species richness were positively relatedand spatial turnover and regional species richness showedno significant relationship. Any constraint on one pairwiserelationship occasioned by the existence of the other twoshifts with changes in spatial scale, with the correlationbetween local species richness and spatial turnover becomingstronger towards coarser resolutions and that betweenlocal and regional species richness becoming weaker. Therelationships can be understood in terms of the commonality,gains and losses in species between areas (matching com-ponents a, b and c), the levels of which move in space with theresolution of analysis, giving rise to the spatial dependency

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of the relationships between spatial turnover, local andregional species richness.

ACKNOWLEDGMENTS

We are grateful to P. Vandome and colleagues for providingus with access to the south-east Scotland bird data. We thankP.H. Williams and J.J. Lennon for analytical assistance,particularly in making available, respectively, Worldmap andmethods of addressing spatial autocorrelation. We also thankA. Bonn, S.L. Chown and P.H. Williams for comments on themanuscript. P.K. is funded by CONACyT (51822) and SEP.

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BIOSKETCHES

Patricia Koleff has research interest in the study of patterns and processes of species distribution from a macroecological perspective and in biodiversity information management and conservation biology.

Kevin J. Gaston has research interest in the fields of biodiversity, conservation biology, and macroecology, with particular emphasis on the ecologies of rare organisms, the structure of geographical ranges and patterns in species richness.

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