Are there latitudinal gradients in species turnover?

RESEARCH PAPER

© 2003 Blackwell Publishing Ltd. http://www.blackwellpublishing.com/journals/geb

Global Ecology & Biogeography

(2003)

12

, 483–498

Blackwell Publishing Ltd.

Are there latitudinal gradients in species turnover?

PATRICIA KOLEFF*, JACK J. LENNON† and KEVIN J. GASTON‡

*

C

omisión Nacional para el Conocimiento y Uso de la Biodiversidad, Liga Periférico — Insurgentes Sur 4903, Parques del Pedregal, Tlalpan 14010 México, D.F., México;

†

Macaulay Institute, Craigiebuckler, Aberdeen, Scotland AB15 8QH, U.K.;

‡

Biodiversity and Macroecology Group,

Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, U.K.Contact details. E-mail: [email protected]

ABSTRACT

Aim

To examine the effect on the observed relationshipbetween spatial turnover and latitude of both the measure ofbeta diversity used and the method of analysis.

Location

The empirical analyses presented herein are for theNew World.

Methods

We take the spatial distributions of the owls of theNew World as an exemplar data set to investigate the patternsof beta diversity across latitudes revealed by different analyt-ical methods. To illustrate the strengths and weaknesses ofalternative measures of beta diversity and different analyticalapproaches, we also use a simple random distribution model,focusing in particular on the influence of richness gradientsand landmass geometry.

Results

Our simple spatial model of turnover demonstratesthat different combinations of analytical approach and meas-ure of beta diversity can give rise to strikingly different rela-tionships between turnover and latitude. The analyses of thebird data for the owls of the New World demonstrate thatthis observation extends to real data.

Conclusions

For the particular assemblage considered, wepresent strong evidence that species richness declines at higherlatitudes, and there is also some evidence that species turnoveris greater nearer the equator, despite conceptual and practicaldifficulties involved in analysing spatial patterns of speciesturnover. We suggest some ways of overcoming these difficulties.

Key words

Beta diversity, birds, diversity modelling, latitude,macroecology, New World, owls, species turnover, Strigidae,Tytonidae.

INTRODUCTION

The latitudinal gradient in species richness is among the mostwidely documented of macroecological patterns (see Lawton,1999; Gaston & Blackburn, 2000; and references therein).Numerous mechanisms have been postulated to explain whythere are more species in tropical realms (e.g. Pianka, 1966;Huston, 1979, 1999; Stevens, 1989; Currie, 1991; Rohde, 1992,1997, 1998; Rosenzweig, 1992, 1995; Jablonski, 1993; Colwell& Hurtt, 1994; Gaston, 1996, 2000; Rosenzweig & Sandlin,1997; Davidowitz & Rosenzweig, 1998; Kaufman & Willig,1998; Shepherd, 1998; Willig & Lyons, 1998; Gaston &Blackburn, 2000; Roy

et al

., 2000). However, one proximatecontributor has been thought to be a higher level of spatialturnover in species identities (beta diversity) towards lowerlatitudes, associated with a higher level of endemism (Major,

1988; Stevens, 1989; Gaston & Williams, 1996; Rosenzweig& Sandlin, 1997; Brown & Lomolino, 1998; Williams

et al

.,1999; Stevens & Willig, 2002). Certainly, higher levels of suchturnover at microscales or mesoscales could serve to increaserichness at mesoscales and macroscales, respectively.

A number of studies have sought to document the relation-ship between species turnover and latitude (Table 1)

.

Theresults have, however, been extremely variable. Some studieshave reported increases in turnover with latitude, some havereported decreases, and others have found no relationship atall. This variation might possibly be attributed to differencesin the taxa that have been examined (a variety of plant andanimal groups), in the latitudinal span of analyses (hundredsto thousands of km), in the sizes of the geographical units (thescale) between which comparisons of species compositionhave been made, or in the biogeographical or geopoliticalregions considered (including Afrotropical, Nearctic,Neotropical, Australasian, Atlantic) (Table 1). Certainly, thesedifferences imply variation in important features both ofspecies and of environments, which could well have profoundimplications for observed patterns of turnover.

Correspondence: Patricia Koleff,

C

omisión Nacional para el Cono-cimiento y Uso de la Biodiversidad, Liga Periférico — Insurgentes Sur4903, Parques del Pedregal, Tlalpan 14010 México, D.F., México.E-mail: [email protected]

http://www.blackwellpublishing.com

484

P. Koleff, J. J. Lennon and K. J. Gaston

© 2003 Blackwell Publishing Ltd,


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12

, 483–498

Important as these potential sources of variation might be, interms of establishing whether there is any general pattern aperhaps more troubling feature of the studies that have examinedrelationships between beta diversity and latitude is the diversityof analytical approaches that have been taken (Table 1). First,the geographical units whose species composition is beingexamined have been compared in a number of different ways(Fig. 1). In particular, beta diversity has been calculated (1)between pairs of contiguous quadrats along a latitudinal transect(2) between pairs of contiguous latitudinal bands (3) betweenquadrats within latitudinal bands, and (4) with reference to

focal quadrats and their neighbourhoods (Fig. 1). Whilst anyone of these approaches might be appropriate in a given cir-cumstance, they seem likely often to yield different relation-ships between beta diversity and latitude (Koleff

et al

., 2003).Second, studies have frequently employed different measures

of beta diversity (Tables 1 and 2). Indeed, the 11 studies listedin Table 1 have between them employed nine such measures,with rather little commonality in this usage. This variation issignificant, because different measures reflect different aspectsof spatial turnover in species identities (and not always thosethat the authors of studies seemed to intend) and possess different

Table 1 Studies that have explored the relationship between beta diversity and latitude

Source Taxon Region Scale Method* Measure†

Trend of the relationship between beta diversity and latitude

Willig & Sandlin (1991)

bats New World quadrats 5° × 5° 3c βt Positive

Harrison et al. (1992) plants andanimals‡

Britain quadrats50 km × 50 km

1b β−1 β−2 No correlation

Blackburn & birds New World quadrats 3b, 3c βw β−1 βt NegativeGaston (1996) c. 611 000 km2 β−2 No correlationBowman (1996) plants

(woodyspecies)

Australia quadrats 3.5°longitude × 1°latitude

1a DCA§ Positive

Willig & Gannon (1997) marsupials North andSouthAmerica

quadrats5° × 5°

3c βt No correlation

Mourelle & Ezcurra (1997) cacti Argentina quadrats1° × 1°

3c βw

βme

No correlationNegative

Gregory et al. (1998) birds Europe quadrats≈ 50 km × 50 km

1a βw Negative

Rodríguez (1999) mammals Mexico quadrats0.5° × 0.5°

3b βME No correlation

Williams et al. (1999) birds Afrotropical region

quadrats 1° × 1°

4b βrs Negative¶

Clarke & Lidgard (2000) bryozoan North Atlantic latitudinal bands 10°and biogeographical provinces

2a βw βj Negative

Koleff & Gaston (2001)

parrots andwoodpeckers

New World latitudinal bands 5° 2a βw β−1 βt β−2

βc

No correlationNegative

Stevens & Willig (2002) bats New World 32 communities intothree geographical zones: tropical (12°N to 12°S), subtropical (13°N to 23.45°N and 13°S to 23.45°S) and temperate (> 23°N or 23.45°S)

Other** βw Negative

* See Fig. 1, † See Table 2, ‡ 15 taxa of plants (composites, ferns, mosses, orchids, Rosaceae, umbellifers, native trees) and animals (bees, breeding birds, butterflies, dragonflies, freshwater fishes, nonmarine molluscs, moths, woodlice). § DCA = first ordination axis scores of a detrended correspondence analysis. ¶ On turnover dominated by species replacements, because on turnover caused by richness gradients (measured with another index) the opposite trend was observed. ** number of bat species whose geographical distributions overlapped at that site.

Latitudinal gradients in species turnover

485



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statistical properties (some of which are problematic; Koleff

et al

., 2003). Thus, on the few occasions on which more thanone measure has been used to examine the relationshipbetween beta diversity and latitude for the same set of data,different patterns have usually been documented (Table 1).

In this paper we examine how the measure of beta diversityused and the method of analysis affects the observed relation-ship between beta diversity and latitude. We take the spatialdistributions of the owls of the New World as an exemplar dataset to consider the patterns of beta diversity across latitudes

as revealed by different analyses. We also develop a simplerandom distribution model to illustrate the strengths and weak-nesses of different measures of beta diversity and differentanalytical approaches, focusing in particular on the influenceof richness gradients and landmass geometry.

METHODS

Empirical analysis for the owls of the new world

Data on the geographical distribution of 79 species of owls(Strigidae and Tytonidae) occurring in the New World wereobtained from König

et al

. (1999). The occurrence of eachspecies was recorded within equal area quadrats of about152 750 km

2

(Fig. 2), a resolution at which their distributionsare sufficiently well known and documented.

Fig. 1 Illustration of main methods used to determine variation inbeta diversity, although not all of them have been applied to the studyof beta diversity in relation to latitude. (1) Between contiguous equal-sizeareas along latitudinal gradients: (a) at the same longitude (b) at differentlongitudes. (2) Between contiguous latitudinal bands: (a) without con-sidering differences in area (b) taking into account the number ofquadrats within the band. (3) Within latitudinal bands across longitude:(a) depending on the measure applied the number of quadrats in eachband might or might not be considered in calculating the total variation,and (b) consecutive across longitude calculating variation betweencontiguous quadrats in each latitudinal band. (4) Neighbourhood, whereeach quadrat is evaluated in relation to the surrounding neighbouringquadrats: (a) depending on the measure applied, the whole neighbour-hood is considered as a unit, although some measures attempt to makea correction considering the number of quadrats in the neighbourhood,and (b) averaging each pairwise comparison — as illustrated with thewhite arrow — between the focal quadrat and each neighbour. Lightshading shows units compared.

Fig. 2 Grid used to record species occurrences of the New World owls.The transect used to evaluate beta diversity for method 1 (see text) isshown in grey. Cells within the transect lie in the 42 bands consideredfor methods 2 and 3.

486

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We considered turnover calculated using three different spatialcomparisons encapsulating all turnover measures previouslyused (see Table 2). We do not report explicitly the ‘neighbour-hood’ method (Fig. 1, method 4a,b), since method 4a is conceptu-ally similar to 2a in that different-sized areas may be compared,while 4b is an omnidirectional, constant-area pairwise com-parison approach, essentially combining methods 1a and 3b.

Method 1.

Between pairs of quadrats along a transect

,from about 75

°

N to 55

°

S (Fig. 2). Because of the shape of theNew World, the transect chosen was displaced to the eastfrom North America to Central America, once within CentralAmerica, and from Central America to South America (Fig. 1,method 1b). This maximizes the numbers of quadrats at thesame longitude. The displacements do not strongly influencethe patterns documented (see below), and are irrelevant to thecomparisons of different methods and measures.

Method 2.

Between pairs of latitudinal bands

, where eachof the 42 bands was considered as a unit (Fig. 1, method 2a), andwhere appropriate (for

β

−

1

,

β

−

2

and

β

ME

, see below) the numberof quadrats in the band was taken into account (Fig. 1, method2b).

Method 3.

Within latitudinal bands

, where turnover wasobtained from E-W across each latitudinal band (Fig. 1,method 3a) or (for

β

j

,

β

sim

and

β

gl

, see below) as the averagevalue derived from pairwise comparisons of adjacent quad-rats within a latitudinal band (Fig. 1, method 3b).

Measures of turnover

Distinct from the spatial arrangement of sampling units, betweenwhich turnover is quantified, is the measure of turnover itself,i.e. how the presence/absence of species across the sample unitsis translated into a quantitative index. We considered all eightof the measures of beta diversity (Table 2) employed in previ-ous studies of the relationship with latitude (Table 1), withthe exception of Detrended Correspondence Analysis (DCA),which constitutes a rather different approach. Some of thesemeasures produce identical values for pairwise comparisons(Fig. 1, methods 1a,b and 2a) of the species composition ofquadrats (

β

t

=

β

−

1

;

β

t

=

β

M

), while

β

t

exhibits the same patternof variation as

β

w

. In addition, we considered two other meas-ures,

β

sim

, which accounts for the spatial replacement of spe-cies independently of any species richness gradient, and

β

gl

,which has been shown to detect turnover exclusively causedby local species richness gradients (Lennon

et al

., 2001).For method 1 (Fig. 1), between pairs of quadrats, we calcu-

lated the values of each of the seven measures of turnoverin terms of the matching components used in dissimilarityindices, as suggested by Koleff et al. (2003) (Table 2). Thesedissimilarity indices are functions of the basic matching/mismatching components a, b and c, where a is the totalnumber of species that are present in both quadrats, b is thenumber of species that are present in the neighbouring

Table 2 Measures of beta diversity previously used to study variation in spatial turnover along latitudinal gradients. Measures are identified bysubscripted ‘β’s and given in terms both of their original formulation and of matching components for a pair of quadrats (see Koleff et al., 2003)

Abbreviation Original formulation* Measure re-expressed† Source of original description

βw S/a (a + b + c)/[(2a + b + c)/2] Whittaker (1960)β−1 [(βw − 1)/(N−1)] βw − 1 Harrison et al. (1992)

βc [g(H) + l(H)]/2 (b + c)/2 Cody (1975)βt [g(H) + l(H)]/2a (b + c)/(2a + b + c) Wilson & Shmida (1984βME βt /(N − 1) βt Mourelle & Ezcurra (1997)βj a/(α1 + α2 – a) a/(a + b + c) Jaccard index (see Magurran, 1988

and Southwood & Henderson, 2000)β−2 [(S/αmax) − 1/(N − 1)] min(b,c)/[max(b,c) + a] Harrison et al. (1992)‡

βrs rs + 1/[(S2 − S)/2] 2(bc + 1)/[(a + b + c)(a + b + c + 1)] Williams et al. (1999)

βsim 1 − (a/[min(b,c) + a]) min(b,c)/[min(b,c) + a] Lennon et al. (2001; based on Simpson, 1943)

βgl 2 |b − c|/(2a + b + c) same as original formulation Lennon et al. (2001)

* Original formulations are described in common algebraic notation. † See methods for the meaning of a, b, and c. ‡ β−1 = β−2 when a = αmax.S = total number of species recorded for both quadrats (S = a + b + c).a = average number of species found within the quadrats, α1 = total number of species found in the focal quadrat, α2 = total number of species found in the neighbouring quadrat, αmax = maximum value of species richness for the two quadrats.N = number of quadrats, g = cumulative gain in species, l = cumulative loss in species.H = range of habitat gradient, rs = number of cases in which there is no species overlap (number of unique pairwise species comparisons without co-occupancy of any quadrat).a = total number of species which are each present in both quadrats, b = number of species which are present in the neighbouring quadratbut not in the focal one, c = number present in the focal quadrat but not in the neighbouring one.

Latitudinal gradients in species turnover 487

© 2003 Blackwell Publishing Ltd, Global Ecology & Biogeography, 12, 483–498

quadrat but not in the focal one and c the number present inthe focal quadrat but not in the neighbouring one.

We used the original formulations (Table 2) of the meas-ures of species turnover that have previously been applied forassessing latitudinal gradients (Table 1), calculated betweenpairs of latitudinal bands (Fig. 1, methods 2a,b) and withinlatitudinal bands (Fig. 1, methods 3a,b), although these for-mulations have some undesirable properties (see below).

Detecting latitudinal gradients in diversity and turnover

Establishing the statistical significance of a latitudinal trend indiversity or turnover using a single spatial series is notstraightforward, mainly because it is so difficult to specify thecorrect null model. Simple regressions of latitudinal trends inrichness or turnover assume that these are statistically inde-pendent between quadrats, in the sense that the error term inthe regression model is spatially uncorrelated. But we knowthat this is not true, or at least is unlikely to be true — mostif not all species distributions are spatially autocorrelated(aggregated occurrences), and the superposition of thesedistributions (generating richness patterns) will consequentlytend to be autocorrelated in turn. While it is perhaps expect-

ing too much that nonexperimental data should exactly fit theassumptions of routine statistical methods, this simple prop-erty presents a surprisingly difficult analytical challenge, aproblem distinct from the issue of how beta diversity is meas-ured in the first place.

If we test the hypothesis that there is a significant latitudi-nal trend in beta diversity, for example, erroneously makingthe assumption of uncorrelated errors, we will tend to findmore significant trends than we should (e.g. Lennon, 2000).This is one extreme: to assume independence of successivepoints in space. That is what is usually assumed in analyses ofthis kind, and is likely to produce significant relationshipswhere there are none. The opposite extreme is to assume thatonly the differences between adjacent points in a spatial seriesare independent; if these increments tend to be consistentlybiased in one direction (i.e. many more and/or larger increasesrather than decreases), one can be confident of detecting asystematic spatial trend in the data. In contrast, this approachmay find lack of significance when there really is a relation-ship. We apply both of these approaches to the New Worldowl data (Tables 3, 4 and 5). Empirical data such as thoseexamined here will likely have behaviour intermediatebetween these limits, but practically, when presented with a

Table 3 Method 1 (between pairs of quadrats along a transect). Coefficients of correlation (r) between the species richness of the transect andbeta diversity, and coefficients of determination (r2) between latitude and beta diversity for different models, for the owls of the New World.Overall = all latitudes across the region, distinguishing between North and South hemispheres by assigning an arbitrary negative value to northernlatitudes. All = considering all latitudes ignoring the hemisphere, i.e. regardless of geographical position, north or south. For both n = 41.N = Northern hemisphere, n = 22. S = Southern hemisphere, n = 18. Under the assumption of uncorrelated errors between spatially adjacent datapoints, two-tailed significance levels are marked as * P < 0.05, ** P < 0.01, *** P < 0.001 and **** P < 0.0001. Alternatively, a much moreconservative test is made by assuming that variables follow a first-order autoregressive spatial process (with no systematic spatial trend). In thiscase, the significances (by differencing — taking first differences between adjacent points, south minus north) of the cross-correlations or latitudinaltrends are indicated as before. For regression, the lower of the pairs of numbers is the Student’s t for these differences (testing H0: meandifference = 0), for the cross-correlations it is the correlation coefficient calculated between the spatial series of these differences. Positive valuesof t for N or negative values of t for S indicate an excess of increases over decreases towards the equator

r Regression r 2 against latitude or Student’s t of differences

SR a b c Overall All N S

SR — 0.924**** 0.655*** 0.658*** 0.01 0.553**** 0.730**** 0.674****0.348* 0.143 0.271 0.162 1.863 1.268 −1.368

βw 0.422** 0.139 0.596*** 0.722*** 0.099* 0.032 0.034 0.1360.206 −0.616*** 0.402** 0.636*** 0.246 0.132 0.284 0.074

βj −0.433*** −0.170 −0.610*** −0.690*** 0.118* 0.031 0.035 0.151−0.194 0.575*** −0.404** −0.595*** −0.287 −0.172 −0.356 −0.073

βc 0.795**** 0.565*** 0.773**** 0.868**** 0.035 0.237*** 0.358** 0.335**0.349* −0.528*** 0.488** 0.718*** 0.113 0.340 0.280 −0.187

β−2 0.502*** 0.218 0.440*** 0.711**** 0.052 0.106* 0.116 0.453**0.284 −0.533*** 0.112 0.525*** 0.000 0.168 0.086 −0.322

βrs −0.260 −0.460*** −0.11 0.194 0.089 0.134* 0.254* 0.0640.205 −0.524*** 0.029 0.526*** −0.831 −0.916 −0.951 0.103

βsim 0.541*** 0.250 0.441*** 0.763**** 0.065 0.110* 0.097 0.382**0.359* −0.507*** 0.062 0.582*** 0.000 0.228 0.124 −0.266

488 P. Koleff, J. J. Lennon and K. J. Gaston


Table 4 Method 2 (between pairs of latitudinal bands). Caption as Table 3

Table 5 Method 3 (within latitudinal bands). Caption as Table 3

r Regression r2 of factor against latitude or Student’s t of differences

SR Overall All N S

SR — 0.007 0.818**** 0.849**** 0.887****0.237 2.712** 1.915 −1.875

βw −0.060 0.162** 0.043 0.152** 0.0790.110 −0.671 −0.294 −0.810 −0.229

β−1 −0.248 0.511**** 0.000 0.604**** 0.855****0.193 1.71 0.241 0.357 2.106*

βME 0.163 0.003 0.024 0.112 0.0010.220 −0.209 0.041 −0.187 0.892

βj −0.013 0.159** 0.019 0.109 0.114−0.147 0.611 0.174 0.668 0.794

βc 0.589*** 0.007 0.202** 0.200* 0.336**0.348* −0.139 0.418 0.234 0.738

β−2 0.403** 0.003 0.165** 0.262* 0.1670.079 0.000 0.405 0.235 0.707

βrs −0.069 0.048 0.020 0.023 0.0000.091 −0.045 −0.049 −0.055 0.997

βsim 0.304 0.052 0.045 0.035 0.251*0.177 0.000 0.386 0.221 0.711

βgl −0.311* 0.094 0.174** 0.331** 0.0050.034 −0.728 −0.728 −1.109 0.000

r Regression r2 of factor against latitude or Student’s t of differences

SR Overall All N S

SR — 0.007 0.818**** 0.849**** 0.887****0.814 2.712** 1.915 −1.875

βw 0.694*** 0.006 0.241** 0.049 0.692****0.501*** 0.003 0.791 0.428 −0.983

β−1 0.492*** 0.302*** 0.316*** 0.623**** 0.0070.337* 0.209 0.505 0.534 −0.374

βt 0.756**** 0.003 0.328*** 0.122 0.726****0.509*** −0.129 1.053 0.519 −1.278

βME 0.366* 0.379**** 0.254** 0.622**** 0.0630.110 0.237 0.456 0.477 −0.371

βj −0.646*** 0.168** 0.468*** 0.641**** 0.122−0.276 −0.212 −0.893 −0.761 0.493

βc 0.981**** 0.007 0.752**** 0.738**** 0.876****0.889*** 0.000 2.360* 1.515 −1.822

β−2 0.077 0.451**** 0.047 0.471*** 0.0830.298 0.000 0.344 0.435 −0.300

βrs −0.550*** 0.127* 0.290*** 0.264* 0.333**−0.384* −0.676 −0.957 −0.860 0.559

βsim 0.418** 0.160** 0.181** 0.295** 0.0030.296 0.000 0.422 0.254 −0.212

βgl 0.527*** 0.020 0.268*** 0.354** 0.159−0.025 0.121 0.247 −0.244 −0.244



single spatial series, there is no way of determining with con-fidence where this intermediate point lies; formal significancetesting is thus difficult. While there seems to be no easy wayout of this conundrum when there is only a single spatialseries, when there are multiple latitudinal series (within asingle species or across species within an assemblage) thisreplication provides the element of independence, allowing,for example, the general global latitudinal gradient in speciesrichness to be established beyond any reasonable doubt.

Modelling landmass geometry, turnover and richness gradients

We now discuss a simple spatial model of turnover that helpsto clarify its behaviour in response to different turnovermeasures or spatial arrangements of sample units, and theeffects of spatial gradients in species richness. We expect thatthe geometry of the study region and the way it is subdivided,strongly influence measurement of turnover; in some cases,we expect latitudinal turnover gradients to be generated bythe measurement procedure itself.

We illustrate the behaviour of the 10 beta diversity meas-ures using simulated species distributions in a hypotheticallandmass that either (i) narrows (increasingly shorter longitu-dinal bands) from high to low latitudes or (ii) is of constantwidth (Fig. 3). The landmass is divided into quadrats of equalsize. Each species is either present or absent in each quadratprobabilistically as the outcome of an independent Bernoullitrial with probability of success P. We consider three sce-narios for spatial trends in P: (a) a linear decrease in P fromlow to high latitudes (b) a linear increase in P, and (c) no changein P with latitude. For simplicity, all species are defined ashaving identical P and so all behave similarly. For case (i)combined with (a) or (b) this generates a richness gradientthat runs either in parallel or in opposition to the direction ofthe trend in landmass width. For cases (i) or (ii) combinedwith (c) there is no expected richness gradient. These fivecombinations allow the effect of landmass width on turnovermeasurement to be isolated from that of richness trends. Wethen apply beta measures to these artificial data, consideringcomparison scenarios for which beta measures have beendefined: 1a, 2a, 2b, 3a, and 3b (Fig. 1).

The main analyses for the owls were done using SPSS.

RESULTS

Turnover models

The results of the simple stochastic model show how turnovervaries when different arrangements of quadrats are combinedwith and without simple gradients of species richness andlandmass width.

Between pairs of cells at different latitudes

Figure 4 shows turnover calculated between adjacent pairs ofcells in the north–south axis. Variation in landmass width canhave no effect on these comparisons, since cells are ofuniform size. Consequently Fig. 4(a) is the same as Fig. 4(c),Fig. 4(b) is the same as Fig. 4(d), and Fig. 4(e) is the reverse ofthe latter two cases. All measures (except βc, which indicatesgreatest turnover at middle latitudes) indicate that turnoverincreases as richness decreases (a fall in βj represents greaterdissimilarity/turnover) — with for several measures a smalldecrease at extremes of latitude.

Between pairs of bands at different latitudes

Figure 5 shows turnover calculated between adjacent bandsof cells (at the same latitude) in the north–south axis. For thescenarios with varying landmass width, turnover is being

Fig. 3 Models of species distribution and landmass geometry. (a) Nogradients in per-quadrat probability of species occurrence (synonymouswith richness, since all species have the same probability of occurrence)or landmass width (numbering is ‘latitude’), (b) linearly decliningprobability of occurrence (from 1 to 0) with increasing latitude (bottomof figure) but no landmass width gradient, (c) narrower landmasswith latitude but no richness gradient, (d) narrower landmass withparallel linear gradient in richness and, (e) narrower landmass withopposite linear richness gradient. Assemblages were defined ashaving 50 species; turnover was measured on 500 replicates of eachassemblage.



calculated between areas of different size, and so species-areaeffects are introduced. When landmass width is constant butrichness decreases with latitude (Fig. 5b), all turnover measuresindicate an increase in turnover at high latitudes (a fall in βj rep-resents greater dissimilarity/turnover); some measures show adecrease in turnover for comparison of the ‘most southerly’ pair

of bands (the last of which contains no species). However, withthe exception of the latter detail, the same general pattern ofresponses is produced by introducing a width gradient to anassemblage with or without a richness gradient; narrowingthe landmass increases turnover between bands (Fig. 5c,d).Reversing the richness gradient reverses these trends (Fig. 5e).

Fig. 4 Turnover model, between-cell comparisons. Results for the five different richness and land width gradient scenarios shown in Fig. 3,comparing pairs of adjacent quadrats in the north-south axis as Fig. 1, method 1a. βc is multiplied by scaling factor 0.1.



Within bands (between cells) at different latitudes

Figure 6 shows mean turnover calculated within latitudinalbands (Fig. 1, comparison 3b). The measures used are βw, β−1,βc, βt, βME and β−2, all as expressed in the ‘original formulation’

column of Table 2. For the scenarios with varying landmasswidth, again turnover is being calculated between differentnumbers of quadrats at different latitudinal bands. Depend-ing on the landmass geometry and richness gradients,measures of turnover can increase, decrease or stay constant.

Fig. 5 Turnover model, between-band comparisons. Results for the five different richness and land width gradient scenarios shown in Fig. 3,comparing pairs of bands at adjacent latitudes as Fig. 1, method 2a. βc is multiplied by scaling factor 0.1.



When richness increases with latitude in a landmass of con-stant width (Fig. 6b) all measures increase with latitude,except βc which is unimodal, and β−2 which is constant. Iflandmass width is varied but richness is constant (Fig. 6c),then within-band turnover measures can either increase (β−1,β−2), decrease (βw, βc, βt) or remain constant (βME). Combina-tion of the landmass width and richness trends (Fig. 6d,e) canreverse these trends.

EMPIRICAL PATTERNS FOR NEW WORLD OWLS

Species richness

The owls of the New World show a decrease in species richnesstoward higher latitudes, i.e. from the Equator to the Poles(Fig. 7, Tables 3, 4 and 5). For methods 2 and 3 (i.e. richnesswithin bands), the maximum values are at around 17.5°N

Fig. 6 Turnover model, within-band comparisons. Results for the five different richness and land width gradient scenarios shown in Fig. 3,calculating turnover within bands as per Fig. 1, method 3a. Lettering (a–e) corresponds to that of the land geometry and richness gradientscenarios in Fig. 3. Some measures are multiplied by scaling constants: βc × 0.01, βt × 0.1 and βw × 0.1.



and 5°S (Fig. 7a), and the trend is statistically significant evenwhen using the probably over-conservative difference test.For method 1 (richness within the transect), species richnesspeaks at 15°N (Fig. 7b). Of course, the quadrats exhibitingthe maximum number of species recorded in each latitudinalband do not lie completely on the transect, but the pattern ofspecies richness is very similar to that observed considering allspecies present in each band (r = 0.725, n = 42, P < 0.001).

Species turnover components

For method 1, the turnover components, a, b and c measuredon the owl data show higher values towards lower latitudes(Fig. 8). The pattern for a is very similar to that of species

Fig. 7 Latitudinal pattern of species richness for the owls of theNew World considering all species recorded (a) across latitudinalbands, and (b) along the transect (Fig. 2). Latitudes in the northernhemisphere are arbitrarily designated as negative.

Fig. 8 Values of the turnover components (a) a (b) b and (c) c for theowls of the New World, estimated between each pairs of contiguousequal area quadrats along a latitudinal transect. Latitudes in thenorthern hemisphere are arbitrarily designated as negative.



richness (r = 0.924, n = 41, P < 0.001, difference test alsosignificant, see Table 3). Although the patterns of b and c aremore variable, they too show significant relationships withspecies richness (respectively, r = 0.655 and r = 0.658; n = 41,P < 0.001, but the difference tests are not significant; seeTable 3).

Species turnover

As anticipated, a wide variety of patterns of variation in betadiversity with latitude were found using the 10 measures ofbeta diversity and different methods of analysis (Fig. 9, Tables 3, 4and 5). For a given method, different measures showed peak

Fig. 9 Values of beta diversity for the owls of the New World estimated for the three methods of analysis (see text for details). (a) βw, (b) β−1,(c) βc, (d) βt, (e) βME, (f) βj, (g) β−2, (h) βrs, (i) βsim and (j) βgl. Latitudes in the northern hemisphere are arbitrarily designated as negative. Methods:• 1, � 2, 3 as per Fig. 1.



values at different latitudes, whilst the same was true of thesame measure calculated using different methods. Whilstsome latitudes were fairly consistently identified as havinghigh or low turnover, in this respect the similarity in resultsbetween the different measures and methods of analysis waslow. Whilst it is the statistical test that is usually applied, vari-ation in the occurrence and strength of simple linear relation-ships between beta diversity and latitude only serves partiallyto capture these differences.

Using method 1, significant correlations between beta diversityand latitude across all latitudes were seldom apparent, andwhere they did occur were rather weak and not statisti-cally significant when difference tests were applied (Fig. 9,Table 3). Moderate to weak significant correlations were foundusing βc, β−2, βrs, and βsim when hemisphere was ignored, andin one or other hemisphere for all of these measures, althoughagain these were not significant using difference tests(Table 3).

Using method 2, the most marked patterns were shown forβ−1, with moderate to strong highly significant correlationsbetween turnover and latitude across all latitudes, and sepa-rately in both the northern and southern hemispheres, with

the last result remaining significant using a difference test(Fig. 9b, Table 4). These correlations are much stronger thanthose exhibited by βw (Table 4), demonstrating the effect ofattempting to ‘correct’ for variation in the width of the latitu-dinal bands embodied in the formulation of β−1 (Harrisonet al., 1992). Using method 2, other measures of beta diver-sity exhibited a variety of patterns of correlation with latitude,across all latitudes, ignoring hemisphere, or in the northernor southern hemisphere only (Table 4).

Of the different analytical approaches, method 3 generallygave rise to the strongest correlations between beta diversityand latitude (Table 5). However, it was evident that many ofthese correlations followed from the close relationshipsbetween the measures of turnover and the species richnessassociated with different latitudinal bands, which were fre-quently statistically significant even using difference tests(Table 5).

DISCUSSION

Our simple spatial model of turnover demonstrates that dif-ferent combinations of analytical approach and measure of

Fig. 9 Continued



beta diversity can give rise to strikingly different relationshipsbetween turnover and latitude. The analyses of the bird datafor the owls of the New World demonstrate that this observa-tion extends to real data. Clearly, the question remains as towhat is the most appropriate way in which to test for rela-tionships between turnover and latitude?

The most widely used measure of beta diversity, and onethat has been used on a number of occasions in studies oflatitudinal variation in turnover, is βw (Whittaker, 1960), theratio of local and regional species richness (see Table 1). Thisis a ‘broad-sense’ measure of turnover (as are βc, β−1, βj, βt, βME

and βgl) in that it implicitly incorporates differences in compo-sition attributable to diversity gradients, but ignores the rela-tive magnitude of species gains and species losses betweensample units (Lennon et al., 2001; Koleff et al., 2003). Assuch, it is highly responsive simply to patterns of variation inspecies richness, as evidenced in the simulations (Figs 4, 5 and6). This would seem generally to be an undesirable propertyin a measure of beta diversity, which rather should reflect pat-terns of species gain and loss (Koleff et al., 2003). This said,the expectation that there should be higher levels of turnovertowards low latitudes may owe much to consideration ofturnover in terms of βw. The strong latitudinal gradient in spe-cies richness means that a latitudinal gradient in this turnovermeasure would be expected commonly to be observed (e.g.Blackburn & Gaston, 1996; Gregory et al., 1998; Clarke &Lidgard, 2000).

The measures βrs, β−2 and βsim, depend on a (number ofspecies in both quadrats) and on the relative magnitude of b(number of species in neighbouring but not focal quadrat)and c (number of species in focal but not neighbouringquadrat). These can be considered as ‘narrow-sense’ measuresof turnover, in that they focus on compositional differencesmore than differences in species richness. As such, theycapture the notion that turnover is high when the propor-tion of species shared between two quadrats is low and theproportions lost and gained moving from one to the otherare similar; that is, they take into account differencescaused by unequal numbers of species. These three measuresdiffer in the details of the function relating changes in theproportions of species gained and lost to the value of betadiversity, and in the particular statistical properties thatthey possess (Koleff et al., 2003). On balance, βsim perhapsperforms best overall since it is relatively sensitive to speciesreplacement.

As far as the method of analysis goes (the number, size andgeometrical arrangement of quadrats), it seems essential tomeasure turnover using pairs of quadrats of consistent size.Each of the pair need not necessarily be the same size, but ifone is larger than the other then all larger quadrats should bethe same size, and all smaller quadrats must be the same sizetoo. If this is not adhered to, it seems all too easy to unwit-tingly generate trends in turnover caused by variation in

quadrat area. For example, β−1 was originally proposed as analternative measure to βw (Harrison et al., 1992) with theintention of correcting for the effect of different transect areason turnover. Effectively, this was done by dividing βw by thenumber of quadrats (Table 2). However, dividing the ratio ofthe species in a larger area to a small one by what is essen-tially the area of the transect introduces an over-correctionfor the positive dependency of βw on area (Koleff et al., 2003).This is because the exponent of the species-area relationshipis typically much less than one, i.e. doubling area does notdouble species richness. In fact, this difficulty is a generalissue affecting all measures of turnover, and indicates that it isparticularly desirable to avoid comparing sample units ofvarying area, e.g. latitudinal bands consisting of a singleelongated quadrat, since this entails variation of sample unitarea with latitude that cannot reliably be taken into accountin turnover analyses.

In conclusion, have we answered the central question —are there latitudinal gradients in turnover? It has to be said,generally speaking, because of the methodological difficultiesdiscussed here, for the most part we do not know. However,for the particular bird group we consider, we present strongevidence that species richness declines at higher latitudes.We also present some evidence that species turnover is alsogreater nearer the equator (the conceptual and practical dif-ficulties involved in analysing a single spatial series notwith-standing) as has been shown for birds overall (Blackburn &Gaston, 1996) and for other bird taxa (e.g. Koleff & Gaston,2001). By analogy with the situation where the nonrandom-ness of latitudinal richness gradients is best established bytreating multiple species distributions as independent piecesof evidence, the nonrandomness of species turnover gradientsis undoubtedly best established robustly by measuring turnovertrends in multiple assemblages.

ACKNOWLEDGMENTS

We are grateful to P.H. Williams for assistance and discus-sion, and A. Bonn and M. Huston for comments on themanuscript. P.K. acknowledges the support of CONACYT(51822/12228) and SEP (204-4-19440), and J.J.L. the sup-port of a University of Leeds Fellowship and a Joint VentureAgreement with the Pacific North-west Research Station ofthe U.S. Forest Service (PNW 99-1006-1-JVA).

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BIOSKETCHES

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

Jack Lennon has broad interests in macroecology and spatialecology. Particular interests include diversity gradients, speciesturnover, cross-scale analysis and spatial scaling of species distri-bution patterns and other ecological phenomena, metapopulationecology, conservation biology and spatial statistics.

Kevin J. Gaston has research interest in the fields ofbiodiversity, conservation biology, and macroecology, withparticular emphasis on the ecologies of rare organisms, thestructure of geographical ranges and patterns in species richness.

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Are there latitudinal gradients in species turnover?