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Ecology, 86(9), 2005, pp. 22632277q 2005 by the Ecological Society of America

GLOBAL MODELS FOR PREDICTING WOODY PLANT RICHNESSFROM CLIMATE: DEVELOPMENT AND EVALUATION

RICHARD FIELD,1,4 EILEEN M. OBRIEN,2 AND ROBERT J. WHITTAKER3

1School of Geography, University of Nottingham, NG7 2RD UK2Gainesville College, Watkinsville, Georgia 30677 USA, and Institute of Ecology, University of Georgia,

Athens, Georgia 30602 USA3Biodiversity Research Group, School of Geography and the Environment, University of Oxford, Mansfield Road,

Oxford OX1 3TB UK

Abstract. There have been few attempts to generate global models of climaterichnessrelationships, and fewer still that aim to predict richness rather than fitting a model to data.One such model, grounded on theory (biological relativity to waterenergy dynamics) isthe interim general model (IGM1) of the climatic potential for woody plant richness. Herewe present a second-generation model (IGM2), and genus and family versions of bothmodels. IGM1 describes horizontal climaterichness relationships based on climate stationdata and systematic species range maps, with IGM2 additionally incorporating verticalchanges in climate due to topographic relief. The IGMs are mathematical transformationsof empirical relationships obtained for the southern subcontinent of Africa, whereby there-described regression models apply to the full range of global variation in all independentclimate parameters. We undertake preliminary validation of the new IGMs, first by mappingthe distribution and relative spatial variation in forecasted richness (per 25 000 km2) acrossthe continent of Africa, then by evaluating the precision of forecasted values (actual vs.predicted) for an independent study system, the woody plants of Kenya. We also comparethe IGMs with a recent example of purely statistical regression models of climaterichnessrelationships; namely, the global model of A. P. Francis and D. J. Currie for angiospermfamily richness. We conclude that the IGMs are globally applicable and can provide afundamental baseline for systematically estimating differences in (woody) plant richnessand for exploring the hierarchy of subordinate relationships that should also contribute todifferences in realized richness (mostly at more discrete scales of analysis). Further, wefound that the model of Francis and Currie is useful for predicting angiosperm richness inAfrica, on a conditional basis (somewhere, sometime); we examined the relationship thatit describes between climate and richness. Lastly, we found that indices of available soilwater used in water-budget or water-balance analyses are not proxies for availableliquid water as a function of climatological dynamics.

Key words: Africa; climate; climatic potential for richness; diversity gradients; interim generalmodel; Kenya; model evaluation; species richness; waterenergy dynamics; woody plant diversity.

INTRODUCTION

It has long been known that global gradients in rich-ness covary with global gradients in climate. The de-velopment of statistical models of this relationship thatapply globally is an important but elusive goal for ecol-ogists. In addition to improving our understanding ofdiversity patterns, such models could prove useful forpredicting reasonable values of plant or animal richnesswhere actual values are unknown, and for modelinghow changes in climate could alter the richness (andvegetation) patterns we see today.

Attempts to apply models, developed in particularregions, to other regions have produced some success

Manuscript received and accepted 16 December 2004; finalversion received 1 February 2005. Corresponding Editor:B. A. Hawkins. For reprints of this Special Feature, see footnote1, p. 2261.

4 E-mail: [email protected]

but have tended not to result in globally applicablemodels (e.g., Currie and Paquin 1987). Such work tendsto focus on mid to high latitudes; regions for whichdata availability is better, but which contain relativelyfew of the worlds species. An exception is an interimgeneral model (IGM) of the climatic potential for(woody) plant richness (OBrien 1998). Rather thanusing a purely statistical approach, OBrien workedfrom first principles to develop a first-order mechanisticexplanation for covariation between climate and rich-ness globally: biological relativity to waterenergy dy-namics (OBrien 1989, 1993, 1998). This idea effec-tively links waterenergy dynamics (work done by wa-ter) to fundamental parameters of both climatologicaland biological dynamics, at all scales of analysis: liquidwater and solar energy (e.g., hydrologic cycle and pho-tosynthesis, respectively). In accord with energys dy-namic relationship with the state of water, the modeldescribes the relationship of climate to woody plant

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2264 RICHARD FIELD ET AL. Ecology, Vol. 86, No. 9

richness as a linear function of rainfall and an optimal(parabolic) function of insolation (OBrien 1993,1998).

Empirically, model development was based on cli-mate and richness data for the southern subcontinentof Africa (from 158 S to 358 S latitude) at the macroscale (25 000 km2 grain), which spans tropical to tem-perate climate and vegetation. Regression analyses sug-gested that the best climate variables for describingavailable liquid water and optimal energy con-ditions were annual rainfall (Ran) and minimum month-ly potential evapotranspiration (PETmin), respectively:species richness } Ran 1 (PETmin 2 (PETmin)2). An em-pirically based global model of this relationship de-pends on the availability of qualitatively similar ac-tual richness data with global coverage. Because ofthe lack of such data (see Appendix B), the southernAfrican model (SAF1) was mathematically trans-formed so that it applies to the full global range ofvariation in Ran and PETmin (OBrien 1998). The trans-formation was necessary because energys parabolicfunction prevents extrapolation to climates where en-ergy values fall outside the range sampled in southernAfrica. OBrien (1998) showed that the resulting in-terim general model (IGM1) of the climatic potentialfor richness generates reasonable estimates for woodyplant species richness elsewhere in the world (UnitedStates, South America, Africa, China) in terms of bothrelative differences (gradients) and actual values (forthe United States).

Since development of the IGM1 for species richness,we have investigated two other implications of biolog-ical relativity to waterenergy dynamics: (1) the samerelationship should apply over time, and (2) inclusionof vertical changes in climatological dynamics as afunction of topographic relief should improve modelfit. First, if waterenergy dynamics are fundamental tolife, the same dynamics that apply over space today,should apply over time. If so, the same climaterich-ness relationships applying to species should apply togenera and families. OBrien et al. (1998) found thisto be true for southern Africa; the strength of the re-lationship being almost identical at species and genuslevels, but significantly weaker for family richness. Thelast is unsurprising for the following reasons (see alsoQian and Ricklefs 2004). Since terrestrial life began,both climatological and biological dynamics have beensubject to change due to independent geological dy-namics (e.g., plate tectonics and diastrophism). Theseprocesses necessarily alter the location of land and searelative to both the horizontal and vertical vectors ofclimatological dynamics. The effects are evident todayin continental disjunctions and taxonomic vicariance,and in the idiosyncratic effects of topography on theprevailing climate and richness of an area (e.g., oro-graphic rainfall and rainshadows, and hot spots andrefugia, respectively). Although the horizontal vectoris inherent in IGM1, the vertical vector is not. The

second implication that we tested has two parts: (1)inclusion of the vertical vector should increase thestrength and precision of climaterichness relation-ships; and (2) given the more recent evolution of mod-ern genera and species, the increase should be greatestwith regard to family richness. On adding topographicrange to the species, genus, and family models forsouthern Africa, the strength and precision of climaterichness relationships increased from 78.8, 79.8, and69.7% (SAF1 models) to 85.6, 86.8, and 81.5% (SAF2models), respectively; the greatest improvement beingin family richness (OBrien et al. 2000). Herein wepresent IGMs for species, genus, and family richnessthat were developed from these findings.

This and other evidence reviewed elsewhere (e.g.,Whittaker et al. 2001, Hawkins et al. 2003) has con-tributed to a growing shift from a traditional emphasisonly on the relationship of energy with richness, to onewhereby both liquid water and energy are consideredwhen describing climaterichness relationships. Onerecent example of this shift is a global statisticalmodel of the relationship of climate with angiospermfamily richness developed by Francis and Currie (2003;hereafter, F&C model). They found that their modelaccounts for a greater portion of the variation in familyrichness (;84%) than does the IGM1 when its param-eters are regressed using their data (;63%). However,such a discrepancy is expected given differences inrichness (woody plant vs. angiosperm families) andclimate data, and especially given that IGMs are ex-planatory regression models, rather than simply statis-tical regression models. In addition to meeting morestringent statistical criteria, the IGMs had to meet the-oretical and empirical criteria, with the latter takingprecedence over statistical strength (R2) when selectingthe best model. As a consequence, the best explan-atory model may not be the best-fit statistical model.These and other important differences mean that theIGMs describe a general climaterichness relationship(everywhere, always); by comparison, given the apriori conditional nature of its water variable, the F&Cmodel describes a conditional one (somewhere, some-time). (See Results: Model terms and global applica-tion.)

Our aims are therefore twofold. First, we present thesecond-generation IGMs (IGM2) for species, genus,and family richness, along with the hitherto unpub-lished IGM1s for genus and family richness. We ex-amine their ability (1) to estimate absolute values ofwoody plant richness outside of southern Africa, spe-cifically in Kenya, and (2) to describe the relative var-iation in predicted richness across the continent of Af-rica. The predicted pattern should reflect expected orknown differences in richness and vegetation. The fo-cus on Africa is in keeping with the paucity of con-vincing empirical relationships between richness andenergy within the tropics, where rainfall seems to dom-inate. Africa is also suitable for generating a global

September 2005 2265LATITUDINAL GRADIENTS

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model since virtually the full range of variation in IGMclimate parameters occurs there. Secondly, we comparethe IGMs with the F&C model. We illustrate the sim-ilarities, but also the difference between explanatoryand purely statistical regression models of climaterichness relationships. We focus attention on theoret-ical and empirical discrepancies between models, rath-er than purely statistical ones.

For reasons of limited space, and to save duplication,we do not attempt to review relevant literature. Thishas burgeoned in recent years, and contains richly con-trasting views of controls on diversity (notably Huston1994, Whittaker et al. 2001, 2003, Blackburn and Gas-ton 2003, Hawkins et al. 2003, Colwell et al. 2004,Currie and Francis 2004, Qian and Ricklefs 2004).

Conceptual basis: biological relativityto waterenergy dynamics

The following is drawn from E. M. OBrien (un-published manuscript) and briefly summarizes what ismeant by biological relativity to waterenergy dynam-ics and how it applies to terrestrial life.

Theoretically, the idea follows from first principlesgoverning climatological, biological and ecologicaldynamics that can be gleaned from standard refer-ences and texts. The key is liquid water.

In terms of climatological first principles, giventhe Earths energy regime, water is the only matterat the Earths surface that is fully dynamic as afunction of energymatter exchange. Like all othermatter at the Earths surface, water is subject tochanges in form and location. In addition, however,water occurs in and moves through all three states,primarily via climatological (atmospheric) dynam-icsthe hydrologic cycle. When this is combinedwith waters physical properties, the resulting wa-terenergy dynamics (work done by water) accountfor almost all work done at the planets surfacethroughout geological time. In terms of terrestriallife, climatological waterenergy dynamics deter-mine the very existence of water on landmasses, aswell as its state, amount, duration and, in conjunc-tion with topography, its distribution.

In terms of biological first principles, liquid wateris the essential matter and matrix of life (see detailsin Franks 2000). Its physical properties make it thekey agent of biological dynamics, driving all bio-logical processes and functions, everywhere and al-ways. Since the state of water varies as a functionof ambient energy conditions, this a priori meansthat biological dynamics are restricted to optimalenergy conditionsthe range in which water is liq-uid and energy (light/heat) is still available for work.Outside this envelope biological dynamics cease(plant dormancy, aestivation, hibernation, death,etc.). Within this range the capacity for biologicaldynamics should vary as a function of both energy

and water availability, reaching maximum capacitywhere surface water from precipitation remains ina liquid state year-round and its amount exceeds theclimatological demand (evaporation).

In terms of ecological first principles, the directand primary relationship between climate and ter-restrial life should be its relationship with plants,whereby raw energy, water and essential abioticmatter are transformed into biotic energy and mat-ter. There should be a strong secondary relationshipbetween climate and animal richness, via trophicplantanimal exchange, as found by Andrews andOBrien (2000) for the distribution and richness ofmammals in southern Africa. Finally, climatologicaldynamics are independent of life. Although second-ary and tertiary feedbacks develop if life exists (e.g.,vegetation cover decreasing albedo), life per se isnot necessary to the operation of climatological dy-namics. Crucially, however, climatological dynam-ics are necessary for terrestrial biological dynamics.Thus realized climate limits the capacity for terres-trial biological dynamicsand over time we expectrichness to respond to this.

Other independent and dynamic parameters (e.g.,geomorphological waterenergy dynamics) also lim-it the capacity for biological dynamics (e.g., via dis-solved nutrients), and must form part of a completeexplanation for spatial richness patterns. However,given both the smaller distances over which theseparameters exhibit measurable heterogeneity andtheir dependence on climatological waterenergydynamics, their inclusion must await the develop-ment of trans-scalar modelling (OBrien 1989,OBrien et al. 2000, Whittaker et al. 2001). In theinterim the IGMs describe only the first-order cli-matic potential for richness and assume all else tobe equal or non-limiting.

MATERIALS AND METHODSThe thrust of regression analysis can be explanation

or simply statistical description. In either case, rela-tionships need to be empirically plausible and basedon analyses carried out at an appropriate scale (grainsize). Sampling area should be held constant. If glob-ally applicable predictive models are a goal, then thesampled variation in independent model parametersshould be representative of (or reasonably extrapolatedto represent) their full range of variation globally, andspatial autocorrelation in richness values should beminimized, if not eliminated, to avoid biasing modeldevelopment, a priori, towards particular richness andassociated climate conditions. Unlike purely statisticalmodels, explanatory models explicitly test potential ex-planations for phenomena rather than simply docu-menting their existence. They should be both empiri-cally and theoretically plausible in terms of how ex-planatory variables relate to each other and to the re-sponse variable. Correlation between explanatory

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FIG. 1. Spatial correlograms for the south-ern African (SAF) data used in Interim GeneralModel (IGM) development (N 5 65 grid cells,each 25 000 km2): woody plant species richness;SAF1 residuals (rainfall [Ran] 1 PET model);and SAF2 residuals (rainfall 1 PET 1 topog-raphy model). The species richness correlogramis significant (P , 0.001, Bonferroni approxi-mation), with the two smallest and two largestdistance classes being significant at P , 0.05after Bonferroni correction. The SAF1 corre-logram is significant (P 5 0.011), but the onlysignificant point on this is the smallest distanceclass. The SAF2 correlogram is not significant(P 5 0.597).

variables should be minimized to avoid (1) misleading(inflated) R2 values resulting from redundancy, and (2)the problem of unstable parameter estimates, which canobscure the role of important missing environmentalvariables. Thereafter, selection of the best explan-atory models should be based on theoretical criteria(plausibility, generality, simplicity, parsimony) andlastly on statistical strength.

Development of second-generationInterim General Models (IGM2s)

All of the southern African models (SAFs) and IGMsare explanatory regression models. Empirically theydescribe with minimal redundancy how waterenergydynamics relate to both climatological and biologicaldynamics. The capacity for atmospheric waterenergydynamics and biological waterenergy dynamics (e.g.,photosynthesis) should tend to increase with insolation(and evaporation off oceans), but only as long as avail-able liquid water meets or exceeds the atmosphericenergy demand for water and evapotranspiration off oflandmasses. Theoretically the models describe one fun-damental outcome of biological relativity to wateren-ergy dynamics; that is, the relative capacity for changesin the form (richness) or location (distribution) of ter-restrial life, over space and time.

Multicollinearity was minimized, first by restrictingmodels to one water variable and one energy variable,both of which had to be dynamic first-order climato-logical parameters. Secondly, the energy and water var-iables used are as weakly correlated as possible (r 0.5 in southern Africa, and in Africa in general), andempirically they are temporally independent of eachother. The minimum monthly amount of potentialevapotranspiration (PETmin) usually occurs in winter,when rainfall tends to be least. This is consistent withmost seasonal changes in climate globally. The topog-raphy variable, ln(topographic range), models the po-tential effects on richness of vertical variation in cli-mate, such as environmental and adiabatic lapse rates.It is weakly correlated with the other explanatory var-iables (r 5 0.409 and r 5 20.032 [not significant] with

Ran and PETmin, respectively, in southern Africa). Notethat the natural logarithm of topographic range is onlyslightly better statistically than a linear function; butit is more reasonable than the simpler linear functionbecause of the increase in surface area (and habitats)that can be occupied as topographic relief increases(OBrien et al. 2000).

The potential effects of spatial autocorrelation werefirst reduced by using only richness samples associatedwith climate stations (SAF1), and then eliminated bythe addition of the topography variable, as indicatedby the spatial distribution of residuals for SAF1(OBrien et al. 2000). No spatial autocorrelation re-mains in the residuals of SAF2 (Fig. 1).

Finally, we argue that the intercept should be neg-ative, both theoretically and empirically. A negativeintercept indicates that the relationship originates fromthe explanatory variables. Richness should be zero inthe absence of liquid water, even when energy condi-tions are optimal (e.g., Peruvian coastal desert), sinceno life can exist without liquid water. Positive inter-cepts can be taken to indicate deficiency of the model,such as a missing variable. Negative predicted valuesshould be treated as predictions of zero taxa. They canbe taken to indicate the degree of increase in water and/or energy needed before any richness is expected (e.g.,Antarctica).

Mathematical transformation of the best southern-African models (SAF1 for genus and family; SAF2 forspecies, genus, and family) into IGMs followed exactlythe same methods as those detailed in OBrien (1998),except that topographic range was included in IGM2s(see Appendix B). For the mathematical transformationto be reasonable, there should be strong correlation (r. 0.7 and ideally r . 0.9) between forecasted richnessvalues generated using the three empirical SAF modelsand those generated using IGMs, with minimal changein the unexplained variance. This was the case forIGM1 for species richness: r 0.97 (OBrien 1998).Thus it is reasonable to assume that the strength (R2)and associated error term (RMSE) of the relationship of


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FIG. 2. Maps of Kenya showing: (a) the locations and identification numbers of the climate stations and the 25 000-km2circles surrounding them; (b) woody plant family richness per circle; and (c) residuals from IGM2 family level (i.e.,forecast minus observed family richness). Large lakes (Turkana and Victoria) are indicated (stippled fill). Circles that have,80% of their area as land in Kenya, although shown here, are excluded from consideration in the paper; these are numbers13, 17, 19, 21, 22, 25, 26, 27, and 28.

climate with richness in southern Africa also apply withrespect to IGMs. As demonstrated for species richnessby OBrien (1998), this assumption is supported math-ematically if there is little difference between the idealSAF model (based on PETmin) and the correspondingIGM in terms of the coefficients for annual rainfall and,in the case of IGM2, topographic relief. (Compare idealSAF models in OBrien et al. [1998] with IGMs re-ported here.) Given the increased range in PETmin val-ues, IGM coefficients for PETmin should markedly de-crease relative to ideal SAF model coefficients. And,given the greater range of positive (potential) richnessvalues, the intercept value should increase but remainnegative.

African climate and topography dataWe used Thornthwaite and Mather (19621965) for

climate data from 980 stations in Africa (i.e., meanannual rainfall and potential evapotranspiration, bothof which are dynamic climate variables). Thornth-waites PET is a proxy for the intensity of insolationat the Earths surface. It measures the energy demandfor liquid water (mm), and thus the role of energy inclimatological dynamics (evaporation and transpira-tion). The data were calculated using a formula he de-rived from experimental data on the amount of waterevaporated and transpired from samples of grass-cov-ered land never suffering from lack of water. The for-mula requires data on prevailing temperature and in-tensity of insolation at a given time (date) and place(latitude). Unlike many measures of PET, his is notadjusted to sea level and thus measures the energy(heat/light) regime actually influencing vegetation atthe Earths surface.

Following OBrien et al. (2000), topography datawere extracted from the USGS DEM of Africa, and

resampled to 0.18 resolution, giving .200 elevationpoints/25 000-km2 grid cell. The minimum value wassubtracted from the maximum to give the topographicrange (in meters), for each grid cell. Values were as-signed to the 980 climate stations according to the gridcell that they occupied

Examination of the spatial patternof model predictions

All IGMs were used to predict the climatic potentialfor richness across the continent of Africa, based ondata from the 980 climate stations. The same was donefor the F&C model at the family level (using theThornthwaite climate data). Examination of the re-sulting patterns in forecasted richness, and how theyrelate to variation in vegetation and physiography, wasundertaken following OBrien (1998).

Actual vs. predicted richness for KenyaAll the IGMs forecast richness for a circular area of

25 000 km2 (i.e., within a radius of 90 km of a climatestation), the same area as the grid cells used in modeldevelopment (e.g., OBrien 1993). Actual woody plantrichness data for Kenya were calculated accordingly,based on presenceabsence data per circle, with eachcircle centered over a climate station (Fig. 2). Pres-enceabsence data were obtained using a comprehen-sive set of distribution maps and site location data forKenyan woody plants (Beentje 1994). Following thesame criteria as in OBrien (1993) to determine whichspecies to include, 1417 out of 1862 species were re-tained; these represented the largest and longest livedof plant species, and thus those most likely to be robustindicators of climate conditions. Those eliminated werenon-native species, plants #2.5 m in height, and/orplants that are not truly woody. The distributional rang-

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es of higher taxa were determined by aggregating rang-es of species within genera (635 genera in total), andwithin families (126 families).

Distribution maps from Beentje (1994) consist ofpresence/absence data per pixel, with pixel resolutionof half a degree (309). Given that Kenya lies on theequator, the spatial resolution of the distribution datais ;55.5 km and pixel area is effectively constant at;3080 km2. Distribution information for ;30% of thespecies in Beentje (1994) is given only as named col-lecting localities. For these, all the named places wereassigned latitude and longitude coordinates using var-ious sources, including Polhills (1988) checklist ofcollecting localities, Microsoft Encarta CD-ROM, anda Kenyan postal districts booklet. These locations werethen rasterized into the same 309 grid system. We cal-culated actual richness per circle using MapInfo Pro-fessional (MapInfo, Windsor, Berkshire, UK) by amal-gamating the species data from those pixels whose cen-ters lie within each circle. Circles with ,80% of theirarea as land within Kenyas borders were removed fromthe data set, leaving a total of 28 circles (Table 2a).

We also calculated actual woody plant family rich-ness for 34 900-km2 circles (105-km radius) using thesame protocol as for the 25 000-km2 circles (Table 2b).This corresponds to the sampling area used by Francisand Currie (2003) for their model (see Table 1b forerror terms). Of the 37 circles centered on Kenyan cli-mate stations, 27 met the equal-area criterion at thisgrain size.

Woody plant family richness differs from angio-sperm family richness, which includes nonwoody fam-ilies and excludes gymnosperm and pteridophyte fam-ilies. A comprehensive series of species range mapsdoes not exist for Kenyan angiosperms. This preventsdirect comparison between the IGMs and the F&Cmodel, but some testable implications exist. We knowthere to be 245 plant families in Kenya (H. Beentje,personal communication.). Excluding gymnosperm (3)and pteridophyte (31) families, this leaves 211 as amaximum for angiosperm family richness in any circle.According to the Francis and Currie richness data (notall derived from range maps) the global maximum an-giosperm family richness in 34 900-km2 grid cells is201 (Francis and Currie 2003: Fig. 1). So, in the Ken-yan test, predicted angiosperm family richness per34 900-km2 circle can be seen as reasonable if it isgreater than actual woody plant family richness but,211 and preferably no more than 201. Similarly, forAfrica in general, predicted family richness values us-ing the F&C model should be ,202. It is difficult togive a lower bound, but comparison with IGM forecastscould be informative.

The climate data used by Francis and Currie are fromglobal climate databases (i.e., interpreted/interpolateddata). The formulation of PET that they used is that ofAhn and Tateishi (1994). Annual water deficit (WDan)was calculated as PETan minus mean annual actual

evapotranspiration (AETan). When using the F&C mod-el to forecast richness in Kenya we used the climatedata (and formulations) used by Francis and Currie.This was necessary because the two PETan measuresare very different, with ranges of 6681938 mm and11771727 mm, respectively (Appendix A: Fig. A1).Only in terms of the higher PETan values, which occurin low-elevation interior (xeric) basins and coastalplains, are the two measures similar. For climate sta-tions at higher elevations, and in the mountains anduplands of eastern Africa (.1000 m above sea level),Thornthwaites PETan is markedly lower than the PETanvalues of Ahn and Tateishi. Each Kenyan climate sta-tion was assigned WDan and PETan values from thelocation closest to its geographic location (the Ahn andTateishi data were kriged over a 0.58 grid; these climatedata were kindly provided by A. P. Francis and D. J.Currie).

Many of the Kenyan circles overlap (Fig. 2). Thiswould be a problem in model development, but is ir-relevant in generating forecasted richness. It is also notimportant when we consider each circle individually:we simply compare the predicted richness with the ac-tual richness. Similar to confidence intervals, forecastswithin one error term (root mean square error) of theoriginal model can be classed as a close fit; those outby 12 error terms, a reasonable fit; and those out by.2 error terms, a poor fit. Overlapping circles are aproblem, however, if we try to compare predicted withactual values by considering more than one circle at atime (e.g., by correlation). To avoid such pseudorep-lication when performing correlation, we generated 30different random samples of the circles, such that notwo circles in any sample overlapped; this producedsample sizes ranging from seven to nine. We correlatedactual and forecasted richness values within each sam-ple and report the mean results.

RESULTS

New IGMs

Model coefficients for IGM1 species richness(OBrien 1998) and all new IGMs are reported in Table1a, which also gives the R2 and root mean square error(RMSE) values for the empirical southern AfricanPETmin models. In addition, Table 1a gives correlationcoefficients for the mathematical transformation of thesouthern African models into global models (IGMs).In all cases, statistical synonymy (r . 0.9) is indicated,making it reasonable to assume that empirical R2 andRMSE for ideal PETmin models also apply to the re-spective IGMs. In all cases the expected mathematicalchanges occurred, supporting this assumption (see Ma-terials and Methods: Development of second-genera-tion Interim General Models; compare with SAF modelcoefficients in OBrien et al. 2000). Furthermore, com-parison between IGM1 and IGM2 model coefficientsindicates that, consistent with comparisons between


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empirical SAF1 and SAF2 models (OBrien et al.2000), the addition of topographic range independentlyincreases precision and strength of the model. In allcases, this is shown by an increase in predictive power,reduction in unexplained variance, and the more neg-ative intercept, while the Ran and PETmin coefficientsremain nearly the same.

Statistical resultsSpatial pattern of model predictions.As expected

(given the strong correlations between species, genus,and family richness in southern Africa), the patterns ofpredicted genus (especially) and family richness acrossAfrica were very similar to those for species richness(Figs. 3, 4a, and Appendix A: Fig. A2). Visual com-parison of these maps with topographic maps of Africaindicate, consistent with the changes in coefficients(see Results: New IGMs and Table 1), that IGM2 pre-dictions result in an increase in forecasted richness val-ues in areas with high topographic relief and a decreasefor areas with relatively flat terrain, especially for fam-ily richness. For example, Mt. Cameroon, the AfricanRift Valley, the Ethiopian Highlands, and the TibestiDome all exhibit increases in predicted richness, whilethere are notable decreases in portions of the interiorplateaus of eastern and southern Africa, and portionsof the Congo and Chad Basins. In between these areas,predicted values remain similar to those generated byIGM1. This emphasizes the independent and idiosyn-cratic nature of vertical changes in climate and reflectsthe increased strength and precision of the models.Again in line with the greater contribution that topo-graphic relief makes to the strength and precision ofIGM2 for family richness, the most pronounced chang-es occurred for family richness.

The pattern generated by the F&C model (using theclimate station data) is similar to that generated by theIGMs for family richness in that the ordering of pre-dictions is similar (compare Fig. 4a with Fig. 4b). Whenthe 980 climate stations are ranked from lowest to high-est predicted value for each model, the mean differencein ranks between the two models is only 65 (althoughthis difference is significant; Wilcoxon signed rank testZ 5 3.6, P , 0.001). The main distinction between thetwo sets of predictions is in the spread of values. TheF&C model predicts high numbers of families underextremely arid conditions (see also Fig. 5). Indeed, allF&C model predictions for Africa are .50 angiospermfamilies and only 11 points are ,70. The maximumpredicted value is 186.4, which is only just below themaximum possible from the model (186.8; Fig. 5); 55predicted values are .175 (there would have been morehad we used Ahn and Tateishi PET data in this exer-cise). In contrast, IGM1 produces 255 predictions be-low 35 woody plant families, the lowest being 5.8. Themaximum predicted value for Africa is 263.9, but only12 predictions are .175. Some of these differencesbetween the two models relate to the different response

variables, especially at the lowest predicted values.However, the fact that IGM1 predicts substantiallymore woody plant families in rich cells than the F&Cmodel predicts angiosperm families is a notable dif-ference. IGM2 produces lower predicted family rich-ness at the top end (only six .175, maximum 226.0),and also in the least rich cells (e.g., 12 predictions ofzero), but not overall. Mean predictions for the 980climate stations across Africa are 134.0 (F&C model),62.6 (IGM1), and 63.0 (IGM2).

Kenyan test.Predictions of actual woody plantrichness values using the two generations of IGMs aremostly reasonable or close fits [within 2 or 1 errorterm(s), respectively], with a slight increase in preci-sion being found among IGM2 predictions (Table 2a).Using the random sample protocol (see Materials andMethods: Actual vs. predicted richness for Kenya) toeliminate pseudoreplication caused by circle overlap,the mean values for residuals (forecast minus actualvalues) were very small. Mean observed species rich-ness was 307.2 6 3.0 (mean 6 SE); the mean residualof the species forecasts for IGM1 was 24.3 6 3.7 (SDof residual sizes 5 71.5 6 2.4 [SD 6 SE]), and forIGM2 it was 23.1 6 3.3 (75.2 6 2.2). Mean genusrichness was 172.5 6 1.4; IGM1 mean residualwas21.4 6 1.8 (34.0 6 1.2), and IGM2 mean residualwas 10.6 6 1.6 (34.7 6 1.0). Mean family richnesswas 65.4 6 0.25, IGM1 mean residual was 29.7 60.45 (10.9 6 0.19), and IGM2 mean residual was 22.76 0.34 (6.2 6 0.22).

The mean Pearson correlation coefficients betweenactual and forecast values were high: IGM1 species r5 0.71 6 0.008; IGM2 species r 5 0.78 6 0.007; IGM1genera r 5 0.72 6 0.007; IGM2 genera r 5 0.80 60.006; IGM1 families r 5 0.68 6 0.006, IGM2 familiesr 5 0.81 6 0.005. Significance values based on thesemean r values and a sample size of eight are marginalfor IGM1 (P 0.05) and significant for IGM2 (P 0.02). Further, the best-fit lines between observed andforecast values for IGM2 approximated the ideal 1:1line in the cases of species and genera, suggesting nosystematic errors in relation to richness levels: meanslope did not differ significantly from 1 nor mean in-tercept from 0. For families, and for all IGM1 forecasts,the slope (observed values arbitrarily on the y-axis)was flatter than 1. (For IGM2, species: mean slope 50.95 6 0.03, mean intercept 526.3 6 7.3; genera:mean slope 5 0.99 6 0.03, mean intercept 527.8 64.3; families: mean slope 5 0.82 6 0.02, mean inter-cept 5 14.0 6 0.9.) Thus the correspondence betweenobserved and forecast richness values was good. In-terestingly, ln(topographic range) correlated verystrongly with richness values in the random samples:r 5 0.80 6 0.005, 0.83 6 0.005, 0.86 6 0.003, re-spectively, for species, genera, and families (P 0.01).

Geographically there was a broad pattern of over-prediction in west and northeast Kenya and under-prediction in south and central Kenya (Fig. 2). Possible

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TABLE 1. Predictive global model specifications for (A) Interim General Models (IGM1 and IGM2), and (B) F&C 28potential evapotranspiration (PET) model, with values taken from Francis and Currie (2003) and residual mean squareerrors (RMSE) provided by D. J. Currie.

Model

IGM coefficients (N 5 980)Intercept(constant) Ran (mm)

PETmin(mm)(PETmin)2(mm2)

ln(topographicrange) (m)

Transformation(Pearson

correlation r)A) Interim general models of the climatic potential for richness: predicting number of woody plant taxa

IGM1Species 2150 0.3494 5.6294 20.0284 0.973Genera 270 0.1836 2.9008 20.0141 0.974Families 21 0.0473 0.7197 20.0039 0.963

IGM2Species 2371 0.2987 5.1186 20.0257 42.7155 0.971Genera 2170 0.1597 2.6250 20.0127 19.6916 0.971Families 257 0.0372 0.6455 20.0034 10.1120 0.966

B) Francis and Currie (28 latitude/longitude spatial resolution) global PET model: predicting the number of angiospermfamilies (N 5 4224)

Families 8.8 20.0641 0.2199\ 26.79 3 1025Notes: The correlation coefficients indicate statistical singularity (r . 0.9) between predictions generated using southern

African (SAF) models and those generated using the IGMs, making it reasonable to assume that each IGM is a globallyapplicable redescription of the ideal empirical relationship obtained for southern Africa (see OBrien 1998). For the southernAfrican models, numbers in parentheses are the values when negative predictions are converted to zero values (see Materialsand Methods: Development of second-generation Interim General Models); the first numbers result when the negative valuesare retained. Ran is annual rainfall; PETmin and PETan are minimum monthly and annual potential evapotranspiration, respec-tively; WDan is annual water deficit (see OBrien 1998).

Reported for the IGMs are both the empirical relationships obtained for the southern subcontinent of Africa (R2, adjustedR2, and RMSE; OBrien et al. [1998]), and those obtained from mathematical transformation into global models (IGMs forthe full range of variation globally in PETmin).

See OBrien (1998). Value reported is WDan (mm), not Ran.\ Value reported is PETan. Value reported is (PETan)2.

contributing factors are likely to be edaphic ones, withunderprediction being associated with richer-than-nor-mal soils (basalt derived) and higher-than-normal soilmoisture (presence of lakes, underground water re-sources, and/or exotic rivers [i.e., rivers bringing waterfrom rainfall elsewhere]), and overprediction being as-sociated with relatively poor soils and low soil moisture(high leaching, lack of exotic rivers or undergroundwater resources). In some cases, overprediction couldalso be a function of undercollection of botanical spec-imens (e.g., from remote parts of Kenya), which werethe basis for Beentjes maps.

The F&C model appears not to grossly underpredictangiosperm family richness in Kenya (Table 2b). Fore-casted values are greater than the number of actualwoody plant families in every 34 900-km2 circle, andgreater than the IGM-predicted woody plant familyrichness (for 25 000-km2 circles). Given the maximumpossible prediction of 187 associated with the F&Cmodel, all forecasted values are less than the total num-ber of angiosperm families known to occur in Kenya(211) and also less than the global maximum number(201) of angiosperm families per 34 900 km2 reportedby Francis and Currie.

Model terms and global applicationIn terms of global application, the range of variation

in annual rainfall and PETmin across Africa is repre-

sentative of the global range of variation in these pa-rameters. Even where PETmin 5 0 (mid latitudes topoles) the IGMs plausibly describe how climate relatesto richness, given the use of rainfall rather than pre-cipitation (which includes solid water) as the measureof available liquid water. In other words, if there israinfall then the energy conditions for liquid water nec-essarily exist at some time(s) during the year (e.g.,summer). Thus Ran implicitly (and statistically) mea-sures the amount and/or duration of optimal energy, aswell as plant growth, under these conditions (seeOBrien 1998). Thus, where PETmin 5 0, the IGMs stillmodel waterenergy dynamics, despite reducing to

richness } 2a 1 R [1ln(topographic range)]anwhere 2a is the (negative) intercept and Ran is the meanannual rainfall. Where Ran also equals zero, the IGMsreduce to

richness } 2a[1ln(topographic range)].In this case zero woody plant richness is expected (e.g.,Antarctic), which is empirically plausible.

The IGMs and the F&C model differ primarily interms of the water variable used and in the sign of theintercept. Francis and Currie use a water-budget vari-able, water deficit, one of the basic indices of availablesoil moisture derived from climate (precipitation minusPET). Others are actual evapotranspiration (AET) and


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TABLE 1. Extended.

Southern African model fits (N 5 65)R2 adj. R2 RMSE

0.788 (0.804) 0.778 (0.794) 73.7 (70.8)0.798 (0.808) 0.788 (0.798) 36.7 (35.8)0.697 (0.697) 0.683 (0.683) 11.8 (11.8)

0.856 (0.868) 0.846 (0.859) 61.2 (58.6)0.868 (0.874) 0.859 (0.865) 29.9 (29.3)0.815 (0.815) 0.803 (0.803) 9.3 (9.3)

0.837 0.837 17.40

FIG. 3. Predicted species richness for Africa based on (a) IGM1 and (b) IGM2. Values were calculated using the Thornth-waite climate data for all 980 African climate stations (source of climate data: Thornthwaite and Mather 19621965). Thisfigure is reproduced in color in Appendix A.

water surplus. All are conditional indices of availablesoil moisture for plant growth; none is a dynamic cli-mate variable. AET 5 precipitation only when precip-itation , PET. Otherwise, when precipitation $ PET,AET 5 PET. WD 5 PET 2 AET when precipitation, PET. When precipitation $ PET, WD 5 0, becauseAET 5 PET. Water surplus 5 precipitation 2 PETwhen precipitation . PET (i.e., when AET 5 PET andWD 5 0). For a detailed analysis of how these indicesstatistically relate to richness, to climate variables, and

to each other in southern Africa or Africa in general,see OBrien (1993, 1998).

Since WD 5 0 when PET 5 0 or when precipitation$ PET, the F&C model is a priori conditional. Andwhen WDan 5 0, the model reduces to an optimal en-ergy model of the relationship of climate with richness,with no water component. For Condition 1, the soilwater-budget model, when Pan (mean annual precipi-tation) , PETan, then AETan 5 Pan and WDan . 0:

2richness } a 2 (PET 2 P ) 1 [PET 2 (PET ) ]an an an an25 a 2 (PET 2 AET ) 1 [PET 2 (PET ) ]an an an an

25 a 2 WD 1 [PET 2 (PET ) ].an an anFor Condition 2, the optimal energy-only model, whenPan $ PETan or when PETan 5 0, then AETan 5 PETanand WDan 5 0:

2richness } a 2 (PET 2 PET ) 1 [PET 2 (PET ) ]an an an an25 a 2 (PET 2 AET ) 1 [PET 2 (PET ) ]an an an an

25 a 1 [PET 2 (PET ) ].an anThus the F&C model is a soil moistureenergy modelwhere soil moisture deficits limit plant growth and ispurely an energy model where water deficits do notoccur. Where there is no available water, it predictsbetween nine and 98 angiosperm families (within theglobally observed range of PETan; Fig. 5). This aspectof the model, which derives from both the positive

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FIG. 4. Predicted family richness for Africa based on (a) IGM1 and (b) F&C model. Parentheses indicate that the categoryis empty, i.e., no climate stations in Africa have predicted richness within the specified range.Values were calculated usingthe Thornthwaite climate data for all 980 African climate stations (Thornthwaite and Mather 19621965). This figure isreproduced in color in Appendix A. Also, see Fig. A2 in Appendix A for IGM1 and IGM2 predictions at the genus andfamily levels.

intercept and the values of the other coefficients, sug-gests that unmodeled effects are subsumed within thestatistical fit to the data, and is true for all the Francisand Currie global PET models (from 28 to 108 spatialresolution; Francis and Currie 2003: Table 2). Simi-larly, interpretation is hindered by the redundancy thatresults from the collinearity between PETan and WDan.

DISCUSSIONAn empirical global model of the climatic potential

for richness depends on the quality of the data on whichit is based. Systematic and exhaustive species rangemaps do not exist for humid tropical regions of theworld. They do exist for parts of mid to high latitudes(e.g., parts of Western Europe, United States). And theyexist for the transition between them (southern Africa,Australia). However, model development also requiresregions where we know or can reasonably assume spe-cies richness to be on a par with its environmentalpotential; where recolonization after deglaciation andmajor volcanic eruption, for example, is most likely tobe complete. This assumption seems reasonable withregard to the flora of Africa, given the absence of majorphysical barriers to migration of species during Plio-Pleistocene ice-age oscillations. It is unreasonable inmany parts of the mid to high latitudes. Thus the em-pirical basis for the IGMs can be considered reason-able.

Empirical performance of the modelsThe results support the global applicability of the

new IGMs of the climatic potential for richness at threetaxonomic levels. They support the idea that the re-lationship between climate and richness stems from thedependence of both climatological and biological dy-namics on waterenergy dynamics, and that consequentgeographic variation in the climatic capacity for bio-logical waterenergy dynamics could cause the co-variation between realized climate and realized rich-ness. Given that the IGMs apply to the full range ofglobal variation in Ran and PETmin, reasonable fore-casting of the climatic potential for richness is possiblefor elsewhere in the world. The good fit between actualand predicted richness in Kenya supports this, as doesthe realistic pattern of relative variation in predictedrichness across Africa (see OBrien 1998). Empirically,the addition of vertical changes in climate in IGM2salter forecasted richness values almost exclusively inareas of high or low topographic relief, in a positiveor negative fashion, respectively. The same should ap-ply globally. Since the IGMs only describe the climatepotential for richness, gross over- or underpredictionof richness by the models should highlight other var-iables that need inclusion in a more complete expla-nation (see Discussion: Some applications and impli-cations of predictive models).


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FIG. 5. (a) Envelope of possible predictions from the F&Cmodel (Francis and Currie 2003). The solid line shows thecondition of no water deficit (WD) and represents the upperlimit of predictions for this model. The dashed line showsthe condition of no precipitation and thus represents the lowerlimit of predictions for this model. All model predictions fallwithin the area bounded by the two lines. A plot showing therange of predictions of IGM1 can be found in Whittaker etal. (2003: Fig. 7.2b). (b) Predicted values from IGM2 plottedagainst minimum monthly potential evapotranspiration(PETmin) when there is no rainfall and no topography (i.e.,completely flat terrain), at the species, genus, and family lev-els. Note that all are negative, which means that no woodyplants are predicted to exist under such conditions, even whenoptimal energy conditions exist (see Introduction: Conceptualbasis: biological relativity to waterenergy dynamics)incontrast to the F&C model.

Annual water deficits are common in Kenya and ourfindings support the predictive usefulness of the F&Cmodel where annual water deficits occur, even in lowlatitudes.

Comparison of IGMs and the F&C modelTo be a general, globally applicable description of

the first-order (and ideally causal) relationship of cli-mate with richness, a model should generate reasonablepredicted richness values (without regional refitting),and the resulting distribution of relative predicted rich-ness should be similar in pattern and relative magnitude

to observed or expected differences in richness, es-pecially the latitudinal gradient in richness. All workto date suggests that the IGMs meet these and otherempirical and theoretical criteria. Our results, togetherwith those of Francis and Currie, suggest that the F&Cmodel also tends to produce a good fit to empirical datain a range of climatic conditions. However, its upperprediction limit of 187 angiosperm families and its pos-itive, often high lower limit (depending on PETan; Fig.5) suggest that its predictive usefulness is best in mod-erate (e.g., temperate), rather than harsh (e.g., veryarid) or benign (e.g., equatorial humid), climatic con-ditions.

The F&C model is a purely statistical regressionmodel, which its authors interpret via the importanceof secondary or tertiary biotic relationships to climate,such as the correlation of productivity with richness.We have only compared the F&C model with IGM1,since it applies only to the horizontal relationship ofclimate with richness. Like the other models, the F&Cmodel was limited to a single water variable and asingle energy variable (Table 1). In both cases the en-ergy variables are similar (aspects of PET) and relatedto richness in a functionally similar fashion: an optimal(parabolic curve) function, modeled as PET 2 PET2.Thus according to both sets of models, richness initiallyincreases and then decreases as energy increases. Interms of climate, such an optimal relationship is em-pirically plausible with regard to rainfall: as we movefrom the poles to the tropics, rainfall increases as re-alized evaporation and the capacity for atmosphericsaturation (dew point) increase up to some global op-timum. At this point the capacity for evaporation con-tinues to increase but subsequent condensation, satu-ration, and rainfall decrease as dew point increases.Instead, more and more (and eventually all) evaporatedwater is held in the atmosphere: the same amount ofatmospheric moisture can keep Holland green, but theSahara a desert.

These similarities between the F&C model and theIGM1 model are considerable and, along with otherrecent findings (e.g., Hawkins et al. 2003), could sug-gest that we are close to determining which climaticvariables tend to be responsible for constraining plantrichness. If so, the differences between the models maybe even more instructive and important for advancingour knowledge. In the F&C model, a conditional, non-dynamic soil water-budget variable (WDan) representsavailable liquid water, as opposed to the dynamic cli-mate variable (Ran) in the IGMs. The result is a modelof how energy, coupled sometimes with an insuffi-ciency of soil moisture, relates to richness. The con-ditional rather than general nature of the F&C modelcan be attributed to at least two factors; (1) the lack ofa theoretical or empirical explanatory framework inmodel development, and (2) statistical issues includingmulticollinearity between the variables chosen to de-fine climate and how it relates to richness.

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TABLE 2. (A) Interim General Models (IGMs): actual, predicted, and residual values for woody plant species, genus,and family richness/25 000 km2 (N 5 28 climate stations). (B) F&C model: actual woody plant richness and predictedangiosperm family richness/34 900 km2 (N 5 28 climate stations).

A) IGMs

Climatestation Area (%)

Actual valuesWoody plant richness

Species Genus Family

Model predictionsIGM1

Species Genus FamilyIGM2

Species Genus Family1 100 410 236 83 488 265 83 507 273 882 100 508 279 87 437 238 76 468 252 843 99 414 237 83 462 251 80 483 260 854 100 561 291 91 501 272 84 547 292 965 100 160 93 47 187 115 38 182 112 376 100 526 286 93 321 179 59 397 213 777 100 525 274 87 404 221 72 446 240 828 100 560 291 92 347 191 63 417 223 809 100 435 247 84 379 207 68 429 230 80

10 95 469 269 84 625 337 101 621 334 10211 96 413 239 81 720 387 114 704 378 11212 100 525 274 87 400 218 71 445 239 8214 88 411 252 79 542 295 89 545 295 9115 82 408 227 81 486 264 82 528 282 9316 100 480 249 82 456 248 78 477 257 8418 88 143 101 56 88 66 23 145 92 3720 98 460 244 89 322 178 60 368 199 7123 100 313 184 72 289 160 56 345 186 6924 100 208 124 58 379 208 68 389 212 7029 100 525 274 87 383 209 69 427 229 7930 100 404 232 81 284 157 55 343 185 6931 100 350 201 78 394 216 70 441 237 8132 100 486 272 88 318 175 60 386 206 7633 100 391 220 77 304 168 58 360 194 7134 100 368 202 81 310 171 59 372 199 7335 100 477 270 87 359 197 65 422 226 8036 90 529 277 86 314 175 58 344 188 6537 100 70 40 24 181 110 38 185 111 39

Notes: Area 5 percentage of the area of a circle that is land within Kenya. Residuals 5 predicted minus actual richness.

In the first case, given an explanatory framework,models can be accepted, rejected, or modified based ontheoretical grounds (generality, parsimony, simplicity)and empirical observation, as well as on statistical cri-teria. Without an explanatory framework, only statis-tical descriptions of how input data relate to each otherare generated, and discrimination of the best modelis restricted to statistical criteria. Empirically the pos-itive intercept of the F&C model suggests that the pos-itive effect of some missing explanatory influence onrichness is subsumed in the intercept (when there is nowater and no energy, nine angiosperm families aremodeled as being present). Within an explanatoryframework, this would suggest model rejection, evenif alternatives are less powerful statistically.

In the second case, we consider that the F&C modelis biased by the fact that water deficit conditions dom-inate terrestrial systems, as does the vegetation asso-ciated with them, with associated richness values con-stituting the bulk of any global database on richness.A priori redundancy between WDan and PETan increasesthe statistical precision of this particular relationshipat the expense of other possible relationships. Togetherthese biases could account for the high statistical

strength of the F&C model, despite its poor perfor-mance under other climatic conditions. Climatic andwater-budget variables are meaningful and these mean-ings need to be considered when modeling how climaterelates to biological phenomena; rainfall always mea-sures available liquid water as a function of climate.

Despite these issues, the Francis and Currie (2003)study contributes in several important ways to a betterunderstanding of the relationship of climate with rich-ness. First, their model emphasizes the negative effectsof energy in its relationship with richness. It does soin a fashion that is empirically consistent with the op-timal relationship between energy and the potential forrainfall (as energy increases, dew point increases whilethe potential for atmospheric saturation decreases). Thesame applies with regard to biological dynamics, asshown by the empirical increase and decrease in pho-tosynthesis during the course of a day, and seasonallyduring the course of a year.

Second, their study highlights an assumption com-mon to many studies of the relationship of climate withrichness; that water-budget variables are climate var-iables. This assumption is similar to treating primaryproductivity as though it were a dynamic parameter of


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TABLE 2. Extended.

A) IGMsResiduals

IGM1Species Genus Family

IGM2Species Genus Family

B) F&C model

Area (%)

Actual valuesWoody plant

richnessFamily

ModelpredictionsAngiosperm

richnessFamily

78 29 0 97 37 5 100 85 175271 241 211 240 227 23 98 88 179

48 14 23 69 23 2 97 87 172260 219 27 214 1 5 100 91 156

27 22 29 22 19 210 100 56 772205 2107 234 2129 273 216 100 94 1582121 253 215 279 234 25 100 87 1522213 2100 229 2143 268 212 100 94 150256 240 216 26 217 24 100 85 153156 68 17 152 65 18 92 87 183307 148 33 291 139 31 95 86 185

2125 256 216 280 235 25 100 87 152131 43 10 134 43 12 60 NA NA

78 37 1 120 55 12 85 84 186224 21 24 23 8 2 100 89 145255 235 233 2 29 219 88 59 87

2138 266 229 292 245 218 95 89 130224 224 216 32 2 23 100 79 151171 84 10 181 88 12 100 69 155

2142 265 218 298 245 28 100 87 1522120 275 226 261 247 212 100 85 151

44 15 28 91 36 3 100 82 1582168 297 228 2100 266 212 100 90 159287 252 219 231 226 26 95 83 152258 231 222 4 23 28 100 87 150

2118 273 222 255 244 27 100 90 1572215 2102 228 2185 289 221 85 87 141

111 70 14 115 71 15 99 25 95

photosynthesis. The fundamental, dynamic parametersof climate are atmospheric moisture, energy, wind, andpressure. Since derived water-budget variables are sub-ordinate and conditional corollaries of realized cli-matesoil interactions, it follows that they should beconditional correlates of associated richness. But be-cause they are not parameters of climatological dy-namics, it does not follow that they should describehow climate per se relates to richness.

Third, the Francis and Currie (2003) study docu-ments the fact that, when the global variation in PETanis sampled, which is not possible using only Africandata, an optimal relationship between richness and en-ergy pertains. Thus, Francis and Currie provide the firstindependent empirical corroboration of the optimal re-lationship between richness and energy first docu-mented by OBrien (1989, 1993). It is therefore puz-zling that Francis and Currie (2003) argue that theirfindings refute the existence of such a relationship. Vir-tually all plant growth depends on liquid water, andsince liquid water availability depends on ambient en-ergy conditions, some form of optimal relationship be-tween energy and richness should be expected (to ac-count for the solid and gaseous states of water). It has

only recently been documented because few studiessample a sufficient range in climate and richness toobtain the relationship empirically. Most only examineportions of the curve, documenting positive, negative,or insignificant (humid tropics) statistical relationshipsbetween energy and richness. These results tend to betreated as competing hypotheses, but our findings andthose of Francis and Currie show that they can be rec-onciled when energy is described as an optimal func-tion.

Fourth, the Francis and Currie study highlights theissue of using only statistical strength to refute a hy-pothesis. To test the global applicability of IGM1 inprinciple (see Appendix B), they regressed their familyrichness data accordingly, as a function of increasingannual rainfall and optimal energy (PETmin) conditions.(Note that Francis and Currie cite Legates and Willmott[1992] and Ahn and Tateishi [1994] as the sources oftheir data; the IGM was derived using climate data fromThornwaite and Mather [19621965]). Despite the dis-crepancies in climate and richness data, they found thatthis relationship accounted for 63% of the global var-iation in angiosperm family richness (Francis and Cur-rie 2003:530). This is close to the 68% accounted for

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by SAF1/IGM1 for woody plant family richness(OBrien et al. 1998). Although they rejected IGM1 infavor of the statistically stronger F&C model in thiscase, their study can be seen as providing the first in-dependent evidence that the IGMs are globally appli-cable and empirically plausible in principle.

Some applications and implicationsof predictive models

The most obvious use of predictive models is to pre-dict richness where actual values are unknown. Otherapplications are also possible. First, if Africas flora isassumed to be near equilibrium with its climatic po-tential, the IGMs provide a line of evidence for eval-uating whether or not this is the case elsewhere in theworld. Second, given that they invoke dynamic cli-matological parameters, the IGMs can be linked di-rectly to Global Climate Models (GCMs) and used toexamine how past and/or future changes in climatecould alter present-day richness patterns. Alternatively,being independent of GCMs, they could be used fortesting GCM predictions. Perhaps most importantlythey can contribute to the development of trans-scalarmodels, and to making hierarchy theory operational.In essence, when working at more discrete scales ofanalysis, predictions at the macro scale can be incor-porated as constants (potential richness) in analysesof how other variables and factors (e.g., edaphics,shade) relate to richness (OBrien 1989, OBrien et al.2000, Whittaker et al. 2001, 2003). In so doing, thefirst-order effects of climate can be eliminated as activefactors, focusing analyses on the residual variation notexplained by climate.

In terms of future test implications, gross differencesbetween predicted and actual richness values in Kenyaemphasize that climate is not the only factor influencingrichness. Consistent with findings for southern Africa(OBrien et al. 2000), visual examination of topograph-ic, hydrological, and soil maps for Kenya points toedaphic and associated hydrological factors as the nextindependent parameters that need to be included in amore complete explanation of global variations in plantrichness, especially exotic rivers, permanent andephemeral lakes (pans), ground water reserves, soilparent material, and nutrient content. Of these, exoticrivers, ground water reserves, and soil parent materialprobably make the most important edaphic contributionto woody plant richness in Africa today, as in the past(OBrien and Peters 1999a, b). IGMs should grosslyoverpredict richness where extant richness is below itsclimatic potential (e.g., where soils are poorer thannormal or lower in moisture than that expected as afunction of rainfall, and especially where perenniallakes and rivers are scarce). Gross underprediction isexpected where perennial lakes and rivers (especiallyexotic rivers) exist, soils are richer than normal, or soilmoisture is greater than that expected as a function ofrainfall alone (e.g., due to meltwater).

CONCLUSIONS

The results of this study both support and extend theglobal applicability of OBriens (1998) interim generalmodel of the climatic potential for woody plant rich-ness, thereby providing operational versions at threetaxonomic levels, for use with or without topographicdata. They also support the idea that biological rela-tivity to waterenergy dynamics explains the covari-ation between climate and richness globally, one out-come of which should be a latitudinal gradient inrichness. IGM2 invokes parameters that reflect both thehorizontal and vertical vectors of change in climate andshould contribute to a better understanding of observedelevational gradients in richness in mountainous re-gions, as well as idiosyncratic hot spots of highdiversity. Lastly, by providing a systematic and glob-ally applicable model of how first-order differences inclimate relate to woody plant richness, we are now ina position to eliminate it as an active factor (hold itconstant) when analyzing other causes for differencesin richness at more discrete scales of analysis.

ACKNOWLEDGMENTSMany thanks to David Currie and Anthony Francis for an-

swering our questions regarding their models and for sup-plying unpublished climate data and model parameters. Weare grateful to the University of Oxford for funding to RJWat an early stage of our collaboration on climaterichnessrelationships. We also thank Lucy Stevens for assistance withGIS and Bradford A. Hawkins for assistance in producingcorrelograms. Finally, we thank Bradford A. Hawkins, OleVetaas, David Currie, and one anonymous reviewer for theircomments on earlier versions of this paper.

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APPENDIX AFigures showing the relationship between PET data used for IGMs and PET data used for the F&C model for Kenyan

climate stations (Fig. A1), the predicted genus richness for Africa based on (a) IGM1 and (b) IGM2 (Fig. A2), colorreproductions of Figs. 3 and 4, and associated literature citations are available in ESAs Electronic Data Archive: EcologicalArchives E086-120-A1.

APPENDIX BA description of the general methodological constraints, a summary of transformation of southern African models into

IGMs, and associated literature citations are available in ESAs Electronic Data Archive: Ecological Archives E086-120-A2.

field etal 2005

Documents

global model of

forecasted richness

realized richness

angiospermfamily richness

model of francis

global gradients

angiosperm richness

climate stationdata