PHYSIOLOGICAL ECOLOGY

Seasonal and daily climate variationhave opposite effects on specieselevational range sizeWei-Ping Chan,1* I-Ching Chen,1,2* Robert K. Colwell,3,4,5 Wei-Chung Liu,6

Cho-ying Huang,7 Sheng-Feng Shen1†

The climatic variability hypothesis posits that the magnitude of climatic variabilityincreases with latitude, elevation, or both, and that greater variability selects fororganisms with broader temperature tolerances, enabling them to be geographicallywidespread. We tested this classical hypothesis for the elevational range sizes ofmore than 16,500 terrestrial vertebrates on 180 montane gradients. In supportof the hypothesis, mean elevational range size was positively correlated withthe scope of seasonal temperature variation, whereas elevational range sizewas negatively correlated with daily temperature variation among gradients.In accordance with a previous life history model and our extended versions of it,our findings indicate that physiological specialization may be favored undershorter-term climatic variability.

Changes in patterns of climatic variabilitywith globalwarming are progressivelymoreconspicuous (1). Increasing seasonal varia-bility and asymmetric changes of dailymax-imum and minimum temperatures have

altered the thermal environment that organismsexperience (2–4). So far, little is known abouthow species respond physiologically to climatevariation (5, 6), yet these responses are crucial forsurvival in an era of rapid climate change. Theclimatic variability hypothesis suggests that or-ganisms experiencing higher thermal variability,and thus having broader physiological thermaltolerances, tend to be geographically widely dis-tributed as a consequence (7). This hypothesisis regarded as a broad macrophysiological prin-ciple, as it brings together climate patterns andmechanisms of adaptation to explain macro-ecological phenomena (8, 9). Although speciesface environmental fluctuations on the scale ofhours to days to years to decades and beyond,how the interplay between climatic variabilityat these various temporal scales contributes toshaping the evolution of species’ physiologicaltraits and geographical range sizes has rarelybeen addressed.Consideration of how species range size relates

to climatic variation has deep roots (10). Janzen(11) explained that “mountain passes are higherin the tropics” because species inhabiting tropi-

calmountains experience relatively lower seasonalvariation in temperature than species at com-parable elevations at higher latitudes and maytherefore evolve narrower physiological toler-ances. Temperature gradients in tropical moun-tains thus become effective dispersal barriersand result in relatively smaller elevational rangesizes (11, 12). Stevens went on to propose Rapo-port’s rule, which postulates a positive correla-tion between species range size and latitude orelevation, suggesting that climatic variability maybe the underlying mechanism (13, 14). Empir-ical support for these components of the cli-mate variability hypothesis has been equivocal(15–17), partly due to the use of latitude or elevationas a rough proxy for climatic variability (18–21).Previous studies often neglected considerablevariation in climate componentswithin latitudes(22), as well as associated distinct biologicalinfluences.Here we assess how climatic variability on con-

trasting temporal scales—seasonal and diurnal—influences the elevational range size of terrestrialvertebrates across the world. We obtained datafor climatic variables potentially associated withspecies range size fromCRUTS2.1 and other opensources (23) (table S1) and adopted McCain’scarefully vetted database of elevational range sizefor 16,592 species of rodents, bats, birds, lizards,snakes, salamanders, and frogs on 180 montanegradients spanning from36.5°S to 48.2°N latitude(19) (fig. S1). We calculatedmean elevational rangesize for each taxonomic group on each gradient.These means, not individual ranges, formed thebasis for all analyses and are henceforth referredto simply as “elevational range size.”We first applied hierarchical partitioning (24)

to select the environmental and geographic var-iables with the highest explanatory power forelevational range size. The nine variables retainedwere daily temperature maximum, diurnal tem-

perature range (DTR), mean annual temperature,seasonal temperature range (STR), minimum andmaximummonthly mean temperature, mean an-nual precipitation (MAP), latitude, and mountainheight (fig. S2). We then applied structural equa-tion modeling (SEM) (25) to assess the relation-ships among these variables in explaining rangesize. SEM is capable of including non–mutuallyexclusive hypotheses in a system of relationships(25) and, hence, is particularly suitable to struc-ture the multiple pathways of highly correlatedclimatic variables that shape elevational rangesize (23) (fig. S3).On the basis of the preliminary hierarchical

partitioning and subsequent SEM analysis, wefound that latitude alone explained little of thevariation in elevational range size (Fig. 1, A andB), in accordwith other studies that used latitudeas a proxy for climatic variability (15, 17, 19). How-ever, when we considered all possible combina-tions of proxies, drivers, and relevant climatecomponents, the final model retained latitude,MAP, STR, and DTR as the best model (Fig. 1, Aand C). In this model, STR had a significantlypositive relationship with elevational range sizefor our vertebrate data set (correlation coefficientR = 0.29, probability P = 0.006) (Fig. 1A and tableS3). Not surprisingly, latitude had a strong andsignificant positive relationship with STR (R =0.88, P < 0.001) (Fig. 1A and fig. S4A) and thusindirectly influenced elevational range size throughits effect on STR in the model. Together, theseresults support the climate variability hypothesisand corroborate previous results (11, 12, 19).However, elevational range size had a signifi-

cantly negative relationshipwithDTR (R= –0.25,P = 0.012) (Fig. 1, A and D). Moreover, DTR andSTR are each negatively correlated with MAP(fig. S4,D andE;R= –0.54,P<0.001 andR= –0.07,P = 0.025, respectively; panels A, B, and C in fig.S4 display the global patterns between each cli-matic factor and latitude). In contrast,MAPshowedonly a weak correlation with elevational range sizeitself (Fig. 1E), as demonstrated previously byMcCain (19). Our final model fits better than amodel with only latitude and STR [root meansquare error of approximation = 0.076; compar-ative fit index = 0.981; standard root mean squareresidual = 0.073 (table S2); note that SEM pen-alizes for each additional parameter]. When weused climate variables for which climate data arecurrently available at finer spatial resolutions(5 arcmin and 30 arc sec) (fig. S5), the structuredrelationships remained robust, except that theeffect of STR became insignificant in one modelvariant.In our analysis, latitude and MAP emerged as

the geographical and environmental factors thatindirectly shape elevational range size throughtheir influence on climatic variability (DTR andSTR). We used a stationary bootstrap method toassesswhetherSTRand/orDTR ismoreexplanatorythan expected at random along latitude andMAPgradients (23). We found that MAP gradients, butnot latitude, influenced the relative importance ofDTR versus STR with regard to the elevationalrange size (Fig. 2, A and B). The explanatory

SCIENCE sciencemag.org 25 MARCH 2016 • VOL 351 ISSUE 6280 1437

1Biodiversity Research Center, Academia Sinica, Taipei 11529,Taiwan. 2Department of Life Sciences, National Cheng KungUniversity, Tainan 70101, Taiwan. 3Department of Ecologyand Evolutionary Biology, University of Connecticut, Storrs,CT 06269, USA. 4University of Colorado Museum of NaturalHistory, Boulder, CO 80309, USA. 5Departmento de Ecologia,Universidade Federal de Goiás, CP 131, 74.001-970 Goiânia,Goiás, Brazil. 6Institute of Statistical Science, AcademiaSinica, Taipei 11529, Taiwan. 7Department of Geography,National Taiwan University, Taipei 10617, Taiwan.*These authors contributed equally to this work. †Correspondingauthor. E-mail: shensf@sinica.edu.tw

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power of MAP was generally higher than ran-dom expectation along the precipitation gradient,whereas latitude showed considerably less devi-ation from random expectations. Because precip-itation influences global energy flow through itscorrelation with cloudiness and latent heat flux,MAP has been identified as a dominant factorgoverning Earth’s thermodynamics (26). At low-er precipitation levels, DTR was the dominantinfluence on geographic variation in mean eleva-tional range size, whereas STR dominated atmoderate precipitation levels. At high precipi-tation levels, the effects of both DTR and STRwere diminished (Fig. 2A). This complex relation-ship was generally concealed when the proxyapproach was directly applied. As shown by theblue lines in Fig. 2, A and B, the locally weightedscatterplot smoothing (LOESS) lines for eleva-tional range size did not respond noticeably toeither gradient.Our structural equation model demonstrated

that STR and DTR have opposite effects on spe-cies elevational range size. Although organismsmust evolve to survive all conditions that theyexperience (tolerance range), they can nonethelessfocus reproductive activity on a narrow range ofconditions (optimum performance range), as longas they experience those conditions often enoughwithin their life span (27). Using a phenotypicoptimality model, Gilchrist (27) demonstrated thatgreater among-generation temperature variationshould favor a wider performance range (thermalgeneralists), whereas a narrower performancerange (thermal specialists) will be favored by se-lection when within-generation temperature var-iation is great. Recent empirical studies also showthat the scope of tolerance range limits for motorfunction and survival, as determined experimen-tally, may be a poor predictor of elevational rangesize for thermal generalists (28).Nevertheless, becauseGilchrist’smodel focused

on within- and among-generation environmentalvariation, an organism’s life span should have apronounced influence on the evolution of thermalperformance range. Thus, it is perhaps surprisingto see the strong relationships among STR, DTR,and range size for the vertebrate species in ouranalysis, given that most have multiyear genera-tion times. We therefore extended Gilchrist’s ap-proach to general forms of environmental variationto investigate the expected effects of longer- andshorter-term environmental variations on the ex-pected evolution of performance range (23) (figs.S6 to S9). We found that Gilchrist’s principalpredictions still hold, even when we replacedamong- and within-generation variations witha more general form of longer- and shorter-termvariation, respectively. This result arises simplybecause longer-term variation (including STR)occurs more frequently among generations thanwithin generations, whereas shorter-term varia-tion (e.g., DTR) tends to occur within genera-tions (23). Moreover, we found that average STRwas highly correlated with multiyear temper-ature variation (R= 0.87, P< 0.001) (23) (fig. S10).Together, these results help to explain the im-portant roles of STR and DTR in shaping the

elevational range sizes of the vertebrate speciesin this study.In addition, taxon-specific analysis showed

that MAP and DTR synergistically shape ele-vational range sizes of rodents and birds (butnot bats, the third endotherm group consid-ered), with increasing range size associated withgreater MAP (fig. S11). For endotherms, wateravailability is crucial for evaporative cooling in

a hot environment (29). The role of water inadaptation to cold remains largely unexploredin ecological studies, but water may be impor-tant in blood circulation and metabolic heat(30). Further studies of the relationship betweenwater availability and shorter-term temperaturevariation could prove fruitful, especially for en-dotherms, including bats (see supplementary textand fig. S12).

1438 25 MARCH 2016 • VOL 351 ISSUE 6280 sciencemag.org SCIENCE

Fig. 1. Relationships among MAP, DTR, latitude, and STR in explaining the elevational range sizesof terrestrial vertebrates. (A) Structural equation statistical model. N, number of mountain gradients;RMSEA, root mean square error of approximation; SRMR, standard root mean square residual; CFI, com-parative fit index. (B) Direct relationship between elevational range size and latitude. The blue line rep-resents the LOESS mean; the red dashed line represents a significant linear relationship. (C) Conceptualscheme of this study. Plus and minus symbols represent positive and negative relationships, respectively.(D) Partial residual plots of elevational range size and DTR.The red line represents the regression curve,which controls for the effect of STR and the interaction between DTR and STR. The gray shaded arearepresents the smoothed 95% confidence interval. (E) Direct relationship between elevational range sizeand MAP. The blue line represents the LOESS mean. In (A), the structural equation model, numbersnext to arrows and boxes are unstandardized slopes and intercepts, respectively. The double-headedarrow indicates correlations between factors. For this analysis, taxonomic differences were statisticallycontrolled by setting taxon as a variable, but taxa were also analyzed separately (fig. S11). For details,see tables S3 to S5.

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On the basis of our empirical and modelingresults, we propose a new macroecological prin-ciple. Introducing temporal scale offers a newperspective on the physical influence of climaticvariability. STR dominates the thermal profile athigh latitudes in theNorthernHemisphere, where-as tropical areas with high amounts of rainfallweaken the contrast betweenDTRandSTR (Fig. 3).DTR dominates the majority of the rest of theland surface, including arid land masses, moun-tainous areas, and most of the terrestrial South-ern Hemisphere (Fig. 3D). We conclude that therelevance of each climatic factor to the rangesize of species should be carefully evaluated fororganisms of different taxonomic groups, char-acterized by different generation times and ther-moregulatory systems.

Our study may have implications for under-standing biological responses to climate change.For example, tropical species are expected to bethermal specialists because they are adapted tolow STR (5, 6). Nevertheless, because of theiradaptation to higher DTR, both tropical and tem-perate montane species (of some groups) maybe thermal specialists and, thus, vulnerable tochanging climates.

REFERENCES AND NOTES

1. IPCC, “Summary for policymakers,” in Climate Change 2013:The Physical Science Basis. Contribution of Working Group I tothe Fifth Assessment Report of the Intergovernmental Panel onClimate Change, T. F. Stocker et al., Eds. (Cambridge Univ.Press, 2013), pp. 1–30.

2. D. R. Easterling et al., Science 277, 364–367(1997).

3. T. R. Karl et al., Geophys. Res. Lett. 18, 2253–2256(1991).

4. G. Wang, M. E. Dillon, Nat. Clim. Chang. 4, 988–992(2014).

5. I. Khaliq, C. Hof, R. Prinzinger, K. Böhning-Gaese, M. Pfenninger,Proc. Biol. Sci. 281, 20141097 (2014).

6. D. A. Vasseur et al., Proc. Biol. Sci. 281, 20132612(2014).

7. J. Spicer, K. Gaston, Physiological Diversity and Its EcologicalImplications (Blackwell Science, 1999).

8. F. Bozinovic, P. Calosi, J. I. Spicer, Annu. Rev. Ecol. Evol. Syst.42, 155–179 (2011).

9. K. J. Gaston et al., Am. Nat. 174, 595–612(2009).

10. K. J. Gaston, The Structure and Dynamics of GeographicRanges (Oxford Univ. Press, 2003).

11. D. H. Janzen, Am. Nat. 101, 233–249 (1967).12. C. K. Ghalambor, R. B. Huey, P. R. Martin, J. J. Tewksbury,

G. Wang, Integr. Comp. Biol. 46, 5–17 (2006).13. G. C. Stevens, Am. Nat. 133, 240–256

(1989).14. G. C. Stevens, Am. Nat. 140, 893–911 (1992).15. K. J. Gaston, S. L. Chown, Oikos 84, 309–312

(1999).16. C. M. McCain, K. Bracy Knight, Glob. Ecol. Biogeogr. 22,

750–759 (2013).17. F. J. Whitton, A. Purvis, C. D. L. Orme, M. Á. Olalla‐Tárraga,

Glob. Ecol. Biogeogr. 21, 179–190 (2012).18. A. Addo-Bediako, S. L. Chown, K. J. Gaston, Proc. Biol. Sci. 267,

739–745 (2000).19. C. M. McCain, Ecol. Lett. 12, 550–560 (2009).20. A. Ruggiero, V. Werenkraut, Glob. Ecol. Biogeogr. 16, 401–414

(2007).21. J. M. Sunday, A. E. Bates, N. K. Dulvy, Proc. Biol. Sci. 278,

1823–1830 (2011).22. K. S. Sheldon, J. J. Tewksbury, Ecology 95, 2134–2143

(2014).23. Materials and methods are available as supplementary

materials on Science Online.24. U. Grömping, J. Stat. Software 17, 1 (2006).25. J. B. Grace, Structural Equation Modeling and Natural Systems

(Cambridge Univ. Press, 2006).26. J. T. Kiehl, K. E. Trenberth, Bull. Am. Meteorol. Soc. 78,

197–208 (1997).27. G. W. Gilchrist, Am. Nat. 146, 252–270 (1995).28. J. M. Sunday et al., Proc. Natl. Acad. Sci. U.S.A. 111, 5610–5615

(2014).29. L. B. Buckley, A. H. Hurlbert, W. Jetz, Glob. Ecol. Biogeogr. 21,

873–885 (2012).30. C. M. Beall, N. G. Jablonski, A. Steegmann, Human Biology: An

Evolutionary and Biocultural Perspective (Blackwell Science,2012).

ACKNOWLEDGMENTS

We thank T. Amano and anonymous referees for insightfulcomments and Y.-S. Jang for help with assembling thedata for fig. S10. The sources for the data sets used inthis paper can be found in table S1. S.-F.S. wassupported by Academia Sinica (Career DevelopmentAward) and the Ministry of Science and Technology,Taiwan (grant NSC101-2313-B001-008-MY3). I.-C.C. wasfunded by the Ministry of Science and Technology,Taiwan (grant 103-3114-C-006-001-ESR). R.K.C. wassupported by the U.S. NSF (grants DEB-0639979 andDBI-0851245) and Coordenacão de Aperfeiçoamentode Pessoal de Nivel Superior (CAPES, Brazil). C.H. wassponsored by National Taiwan University and the Ministryof Science and Technology, Taiwan (grant NSC100-2621-B-002-001-MY3).

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/351/6280/1437/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S12Tables S1 to S5References (31–37)

23 April 2015; accepted 17 February 201610.1126/science.aab4119

SCIENCE sciencemag.org 25 MARCH 2016 • VOL 351 ISSUE 6280 1439

Fig. 2. Influence of DTR andSTR alongenvironmental gradients. Panels show the relative explanatorypower of DTR and STR for elevational range size along (A) the MAP gradient and (B) the latitudinalgradient. In the upper panels, blue lines represent LOESS lines of the plots in Fig. 1, B and E. Total ex-planatory power is indicated by bars in the lower panels, plotted against randomexpectations (black lines).Rng Sz., range size; r2, coefficient of determination.

Fig. 3. Global maps of temperature variability. (A) Seasonal temperature range (STR). (B) Diurnaltemperature range (DTR). (C) Mean annual precipitation (MAP). (D) RGB (red-green-blue) colorspectra presenting STR, DTR, and MAP. For example, the northern Amazon basin within the tropicalregion has very high MAP with low STR and DTR, yielding bluish pixels in (D). All maps are at 0.5° spatialresolution.

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DOI: 10.1126/science.aab4119, 1437 (2016);351 Science

et al.Wei-Ping Chanelevational range sizeSeasonal and daily climate variation have opposite effects on species

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www.sciencemag.org/content/351/6280/1437/suppl/DC1

Supplementary Materials for

Seasonal and daily climate variation have opposite effects on species

elevational range size

Wei-Ping Chan, I-Ching Chen, Robert K. Colwell, Wei-Chung Liu, Cho-ying Huang,

Sheng-Feng Shen*

*Corresponding authot. E-mail: shensf@sinica.edu.tw

Published 25 March 2016, Science 351, 1437 (2016)

DOI: 10.1126/science.aab4119

This PDF file includes:

Materials and Methods

Supplementary Text

Figs. S1 to S12

Tables S1 to S5

Full Reference List

-2-

Index

Materials and Methods (p. 3)

Range size data (p. 3)

Climate data (p. 3)

Structural equation modeling (p. 4)

Latitude and MAP as proxies for climatic variability in the CVH (p. 5)

Gilchrist model description and modification (p. 6)

Step by step SEM used to construct the best model of range sizes (p. 8)

The correlation between average STR and multi-year temperature variation (p. 10)

Supplementary Text (p. 11)

Figs. S1 to S12 (p. 12)

Tables S1 to S5 (p. 25)

References (31 to 37) (p. 32)

-3-

Materials and Methods

Range size data

We adopted McCain’s (19) species elevational range database and attempted to update this

data set by searching on the keywords “elevational range” in the Google Scholar online

archive in December, 2012. The published datasets from this search were carefully filtered to

avoid bias from insufficient sampling effort, limited spatial extent and habitat destruction (19),

which resulted in no suitable additional data. Spatial extents of individual elevational

gradients usually exceeded 30 kilometers. Using the average range size of species for each

taxon, within each mountain gradient, enabled us to include all species in the analysis to test

adaptation to climatic variability at global scale, while partially controlling for the

phylogenetic relationships among species. Although mountain height does not vary

systematically with latitude (R2 = 0.002, P < 0.001), to reduce any effects of mountain height

(because higher mountains allow wider elevational ranges [17, 19]), we restricted our

analyses to mountain gradients spanning more than 2000m that had been at least 70%

surveyed (see 19 for details), but in this study we also statistically assessed any remaining

effect of mountain height.

Climate data

We computed seasonal temperature range (STR) from CRU TS2.1 as the difference between

maximum and minimum monthly temperature within each year, and we then averaged over

years. Diurnal temperature range (DTR) was computed as the difference between daily

maximum and minimum temperature, averaged, first, within months, then among monthly

means to obtain annual values (31). Both STR and DTR were derived from local weather

stations and subsequently averaged across coarse spatial extent to obtain the final values.

Thus, 0.5° grid climatic variability data represented means of local values rather than the

-4-

differences between maximum and minimum values spanning an entire grid cell. DTR data

from CRU in Greenland is not included in the analysis because of the systematic errors noted

(32).

Diverse causes have been suggested to explain species range sizes and species richness, such

as mean climatic conditions (15), ambient energy (17, 33), topographic heterogeneity (10, 17,

32), climatic extremes (13, 17) and area effect (15, 17). We included potentially explanatory

climatic and topographic variables to assess their effects in our framework (Table S1). To test

the climatic variability hypothesis, climate data were re-sampled at the approximate spatial

resolution of the elevational gradients (0.5°or roughly 50km, as explained above), so that the

climate data could be linked to mean elevational range sizes. In other words, we did not

compare range sizes of particular taxonomic groups within elevational gradients or patterns

of range size and climatic variability as a function of elevation but, instead, mean values of

range size for particular mountain gradients, worldwide. Gridded values encompassing a

georeferenced point of a mountain gradient were extracted using ENVI IDL 4.7 (ITT Visual

Information Solutions).

Structural equation modeling

Unlike exploratory approaches, such as multiple regression, which assumes no causal

relationships among variables, SEM incorporates existing knowledge or proposed hypotheses

to assess the roles of statistically intercorrelated variables (25). To find the model that best

explained elevational range sizes using structural equation modeling, given our variables, we

retained variables with higher explanatory power in the hierarchical partitioning using

“relaimpo” package in R (24) (Fig. S2B). We defined two hierarchies in the SEM－primary

and secondary levels, in which a primary variable served as proxy or causal factor for

secondary variables. We tested variable combinations ranging from two to the complete set

-5-

and determined the corresponding indices of model fit. Models that failed in the fitting

process were excluded from further test, for they were unlikely to remain in the best model

(see below for full details). Model-fitting criteria included root mean square error of

approximation (RMSEA) < 0.08, comparative fit index (CFI) > 0.95, and standard root mean

square residual (SRMR) < 0.1 (34). The best model was the set maintaining the lowest

SRMR. Taxonomic differences were statistically controlled by setting taxon as a variable in

the model. Model-fitting was carried out using AMOS 18.0 (SPSS, Inc).

Latitude and MAP as proxies for climatic variability in the CVH

In discussions of the climatic variability hypothesis (CVH), latitude has been treated as major

proxy of climatic variability, representing STR. The final SEM in this study suggested,

however, that DTR and STR may jointly affect observed elevational range sizes of terrestrial

vertebrates, together with a strong effect of precipitation. In fact, mean annual precipitation

(MAP) may be as important as latitude (11, 19)—based on the statistical relation of MAP and

latitude as gradients associated with climatic variability (both STR and DTR)—in explaining

species range sizes. To determine whether latitude (with its complex climate gradients) and

the MAP gradient might serve as good proxies for understanding range size patterns, we

carried out further analysis to delineate the role of these two variables. We conducted

stationary bootstrapping (35) (10,000 times) to create pseudo-climate data and range size data

series along latitudinal and MAP gradients. We then applied hierarchical partitioning to the

data to estimate the relative importance of DTR and STR in explaining elevational range

sizes. Furthermore, to assess the potential influences of geographical patterns (mountain

height) and data structures, which may bias our results, randomly simulated data series were

created for each gradient. At any given latitude or level of MAP, elevational range size was

replaced by a randomly simulated value. In the case of latitude, the simulated value took into

account the constraint of mountain height at the latitude of interest.

-6-

Gilchrist model description and modification

General model formulation

We generalize the phenotypic optimality model of Gilchrist (27). Our model assumes N

generations, each occupying M time steps. The fitness of a species over one generation g, i.e.

lifetime fitness, is the sum of the organismal performance rates at different times t:

, Eq.1

where the function f, which describes the performance rate, has three arguments: θg,t is the

temperature of the surrounding environment at time t of generation g, while Tmax and Tmin are

respectively the maximum and minimum temperatures at which an organism has a positive

performance rate. As suggested by life history evolution theory, the appropriate measure of

phenotypic fitness in a fluctuating environment is the geometric mean over time (36). Thus,

fitness values across different generations are combined multiplicatively and their geometric

mean is thus:

, Eq.2

Performance rate

Thermal performance (niche) breadth Tbr of a species is simply the difference between Tmax

and Tmin; and the performance rate f is assumed to be a positive constant if θg,t falls

within the interval [Tmin, Tmax]. Thus, the sum of performance rates over the interval [Tmin,

Tmax] is always 1, which imposes a tradeoff between performance rate and performance

breadth. For instance, if a species evolves to have a narrow performance breadth (i.e. small

Tbr), then its performance rate at any given tolerable temperature will be high. In contrast, if a

species has a wide performance breadth (i.e. large Tbr), then its performance rate will be low

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despite the fact that it can survive within a broader temperature range.

Within- and among-generation variation in temperature

The temperature experienced by a species at time t by the gth

generation, θg,t, is assumed to be

a uniformly distributed random variable sampled from the interval [θg,mid – x/2, θg,mid + x/2],

where x is the interval width and θg,mid is the temperature at the middle of this interval. θg,mid

in turn is also a uniformly distributed random variable sampled from the interval [θmid –

y/2,θmid + y/2], where y is the interval width and θmid is the midpoint of this interval. Here, x

and y represent shorter-term and longer-term variations in temperature, respectively (Fig. S6).

Model exploration

Following Gilchrist (27), we plot the fitness landscape in the Tmax-Tbr parameter space with

various combinations of shorter-term and longer-term variations in temperature (i.e., all

combinations of and ). Here, for each parameter combination,

we simulate the model with N =100 (i.e., 100 generations), M = 500 (i.e., 500 time steps per

generation), and θmid = 50. From Fig. S7, it can be observed that, as shorter-term variation

increases, the best fitness values tend to occur for shorter performance breadths, implying

that thermal specialists are more advantageous than thermal generalists. However, as

longer-term variation increases, the best performance breadth now shifts to a higher value,

indicating that specialists are no longer at an advantage over their generalist counterparts.

These results are qualitatively the same as the results found in Gilchrist’s model (27), which

uses a specific sine function to describe the within-generation and among-generation

variation in the environment. Taken together, we believe our result—showing the opposite

influences of longer-term and shorter-term environmental variability on the niche width of

species—is qualitatively general and may help explain the macroecological patterns revealed

by our study.

}80,40,0{x }80,40,0{y

-8-

The effect of timing of changes in longer-term environmental variation

The model of Gilchrist (27) and our general model, above, both assume that longer-term

variation changes for each new generation. In nature, it is possible that longer-term

environmental fluctuations might occur within a generation, and we therefore further

investigate this issue here. Our extended model in essence is the same as the general model

proposed above, with the following exception. Here, we assume that longer-term variation

changes every E time steps. Specifically, after E time steps have elapsed, we then sample a

new θg,mid from the interval [θmid –y/2, θmid +y/2] to be used during the next E time steps. We

simulate this extended model with E = 400 time steps and explore the model in the same way

as before. The results of this extended model were qualitatively the same as the Gilchrist (27)

and our above general model, when we replaced among- and within- generation variations

with longer-term and shorter-term variations, respectively (Fig. S8 and S9).

Step by step SEM used to construct the best model of range sizes

Step 1. We started with two-variable models, assigning “geographic” variables (either

latitude or MtH2 [Mountain heights at survey sites]) at the primary level and a single

climatic variable at the secondary level. This design treats the geographic variables

as climate proxies. In Fig. S3, we illustrate the model structures of Models No.1 and

No.5. Note that the two-level hierarchical structure considered all links among

variables. This two-variable state (Models No.1-14 in Table S2) retained five

variables: latitude and MtH2 at the primary level, and STR (No. 1); DTR (No. 2),

and MAP (Nos. 3 and 10) at the secondary level. Assigning both latitude and MtH2

at the primary level also met model criteria (No. 15). Using these five variables, we

tested two- to five-variable combinations and compared their model fitting indices to

select the best model.

-9-

Step 2. For the climate variables retained in step 1 (STR, DTR, and MAP), we also tested

their two-variable combinations, as these variables could influence one another (Nos.

16-18) (37). The DTR-STR set (No. 18) failed the model fitting criteria and was

excluded from further test. Note that in the two-variable SEM, exchanging the

hierarchy (e.g., DTR-STR vs. STR-DTR) necessarily yielded the same indices of fit.

Step 3. Subset No. 5, representing “mean climatic condition theory,” (15) failed in the model

fitting process. We further tested MAP and MAT (No. 19) as a possible substitute but

this model also failed the fitting criteria.

Step 4. An additional variable was added to each qualified two-variable model (Nos. 1-3, 10,

15-17) to form three-variable models. Note that the third variable and the new

structure need to be in agreement with the previous findings, because subsets models

failing the fitting criteria were unlikely to form the final, best model. In this step, we

added MAP, but not DTR, as a primary variable to model No. 1 to form model No.

20, since DTR-STR had been rejected in Step 2 (No. 18). For the same reason, we

added only MAP to No. 2 that to form No. 21. For No. 10, latitude, STR and DTR

were added one by one to form Nos. 24-26. For No. 16 and 17, the only extension

was No. 27, for the same reasons mentioned above.

Step 5. All three- variable models fulfilled the fitting criteria, but the only acceptable four-

variable model was No. 28 (obtained by adding DTR to No. 20 or STR to No. 21).

For No. 22 and No. 23, neither DTR nor STR could be the secondary variable, as

discussed for Step 4. For Nos. 24-26, in which MtH2 served as the primary level

variable, STR or DTR were not qualified to be the secondary factors (see Nos. 8-9).

For No. 27, it did not make sense to set latitude or MtH2 as the secondary factors,

because geographic variables are not influenced by climate.

-10-

Step 6. Based on the findings in Table S2, the only possible five-variable model was

established by adding MtH2 as an independent variable, i.e. no links to STR and

DTR, but directly influencing species elevational range sizes (No. 29). This model

failed in the fitting criteria, indicating that the structured climate relationship

influencing range sizes (No. 28) was not a compound effect through mountain

height.

Step 7. Comparing all qualified models (marked * in Table S2), No. 28 maintained the

lowest SRMR, hence was identified the best model. This model suggested that

Latitude and MAP were the primary-level factors that influenced STR and DTR,

which directly mediated species elevational range sizes. The coefficients in the

structured relationships and their ecological significances are discussed in the main

text.

The correlation between average STR and multi-year temperature variation

We analyzed 20-year daily temperature data derived from 986 climatic stations globally. By

randomly drawing a temperature sequence based on a given temporal scale (minimal unit:

one year) from a station, we calculated temperature variance and paired it with the averaged

STR within the same temporal scale. This procedure was iterated 10 times for each station

(total number of samples is 9,860, for each temporal scale), and the correlation coefficients at

different temporal scales were then computed. For each scatter-plot figure (Fig. S10c-h), we

plotted at subset of 986 points, randomly chosen data from all stations, for clarity.

Author contributions: S.-F.S. and W.-P. C. conceived the idea for the study. W.-P. C.,

S.-F.S., I.-C.C. and R.K.C. designed and performed research; W.-C.L. and S.-F.S.

constructed and analyzed the models; C.-Y.H. contributed new analytic tools; W.-P. C.,

S.-F.S. I.-C.C., C.-Y.H. and W.-C.L. analyzed data; and W.-P. C., S.-F.S., I.-C.C. and R.K.C.

wrote the paper.

-11-

Supplementary Text

Discussion of Taxonomic differences

To assess the possible influence of taxonomic differences on our results, we performed

taxon-specific analyses. The results are consistent with our original SEM analysis, which

shows that mean annual precipitation (MAP) indirectly influences elevational range sizes

through altering diurnal temperature range (DTR) and seasonal temperature range (STR),

except for rodents and birds. The positive relationships between STR and elevational range

size and the negative relationships between DTR and elevational range size remain consistent

through all taxonomic groups, in spite of the limited statistical power for each sub-analysis

arising from reduced sample sizes. Both MAP and DTR directly shape elevational range sizes

of rodents and birds. For both groups, range sizes increase with larger MAP (Fig. S11).

Importantly, diurnal temperature range has substantially higher explanatory power than the

sum of minimum and maximum daily temperature (Fig. S12), despite the fact that DTR is

determined jointly by maximum and minimum daily temperature. Taken together, these

results suggest that MAP and DTR synergistically influence rodent and bird range sizes. The

different pattern for bats, compared with birds and rodents, may be caused by the strong STR

effect on their distribution which is, thus, indirectly influenced by MAP.

-12-

Fig. S1. The geographical location of elevational gradients in this study for each

vertebrate group (19). Note that no data are available in the highest latitudes regions

because of the lack of studies.

-13-

Fig. S2. Relative importance of all explanatory variables for elevational range size,

using hierarchical partitioning. (A) Preliminary analysis with the full dataset. (B) Analysis

restricted to mountain gradients higher than 2000 m for which at least 70% of the gradient

was surveyed. This criterion retained 137 of 180 mountain gradients for this study.

-14-

Fig. S3. Examples of SEM for variable subsets representing relationships among (A)

latitude, seasonal temperature range (STR), and range sizes; and (B) latitude, mean

annual temperature (MAT) and range sizes. Solid and dashed arrows connecting boxes

show significant (P < 0.05) and non-significant effects, respectively. Numbers next to arrows

and boxes are unstandardized slopes and intercepts, respectively.

-15-

Fig. S4. Relationships among key variables. Climatic variables are shown as a function of

latitude for (A) seasonal temperature range (STR), (B) diurnal temperature range (DTR), and

(C) mean annual precipitation (MAP). Panel (D) shows DTR as a function of MAP, and (E)

plots STR as a function of MAP. The observed number of samples is indicated by colors.

Shown for each plot is the square of the linear or curvilinear correlation coefficient, R2 (P<

0.005*** for all panels).

-16-

Fig. S5. SEMs with four major variables (MAP, DTR, latitude, and STR) from CRU 2.1

and WorldClim data at three spatial resolutions. (A) CRU 2.1 datasets at 0.5 arc-degrees,

as shown in the main text; (B) WorldClim datasets at 0.5 arc-degrees; (C) WorldClim data

sets at 5 arc-minutes; and (D) WorldClim data sets at 30 arc-seconds. Model fits for all four

SEMs are satisfactory (RMSEA < 0.065, CFI > 0.991 and SRMR < 0.025). Solid and dashed

arrows connecting boxes show significant (P< 0.05) and non-significant effects, respectively.

Numbers next to arrows and boxes are unstandardized slopes and intercepts, respectively.

Double-headed arrows indicate correlations between factors. For details, see Tables S3-S5.

-17-

Fig. S6. Variation in environmental conditions used in the generalization of Gilchrist’s

model (27). Both shorter-term and longer-term environmental variations were modeled

stochastically. Error bars represent shorter-term environmental variation. The hypothetical

environmental condition here, standardized from a minimum of 0 to a maximum 100,

represents a key explanatory factor for the performance breadth of species, such as

temperature tolerance range.

-18-

Fig. S7. Fitness landscapes corresponding to the patterns of environmental conditions

shown in Fig. S6. Color represents different levels of fitness. The triangle in each fitness

landscape marks the location of the highest fitness peak. These figures show the generality of

Gilchrist’s model (27) predictions: greater longer-term environmental variation selects for

wider fitness performance breadth (generalists), whereas greater shorter-term environmental

variation favors the evolution of narrower performance breadth (specialists).

-19-

Fig. S8. Variation in environmental conditions used in the extension of Gilchrist’s model

(27). Both shorter-term and longer-term environmental variations were modeled

stochastically. Error bars represent shorter-term environmental variation. The number of time

steps within a longer-term variation cycle was shorter than that within a generation. (Here,

400 time steps were used for a longer-term variation cycle, and a generation time equaled 500

time steps. See also Materials and Methods). The hypothetical environmental condition here,

standardized from a minimum of 0 to a maximum 100, represents a key explanatory factor for

the performance breadth of species, such as temperature tolerance range.

-20-

Fig. S9. Fitness landscapes corresponding to the patterns of environmental conditions

shown in Fig. S8. Color represents different levels of fitness. The triangle in each fitness

landscape marks the location of the highest fitness peak. These figures show the extension of

Gilchrist’s model (27) predictions. Despite the fact that longer-term environmental

fluctuations might occur within a generation, the main predictions of Gilchrist’s model still

hold.

-21-

Fig. S10. Correlation between average STR and among-year temperature variation

from 986 weather stations globally. (A) Examples of 3 stations from 3 continents

demonstrate 20-year temperature fluctuations. (B) Correlation coefficient (r) between average

STR and temperature variation at different temporal scales. (C-H) The relationship between

average STR and temperature variation at a range of multi-year temporal scales.

-22-

Fig. S11. Relationships among seasonal temperature range (STR), diurnal temperature

range (DTR), and mean annual precipitation (MAP) in explaining the elevational range

sizes of different taxonomic groups. (A) For each taxon, the relationship between STR and

-23-

elevational range size, represented by a partial residual plot, controlling for the effect of DTR.

(B) Similarly, the relationship between DTR and elevational range size, controlling for the

effect of STR. (C) Linear regression of MAP on elevational range size, to show the direct

effect. (D) The relative importance of explanatory variables for elevational range size

determined by hierarchical partitioning..

-24-

Fig. S12. Relative importance of climatic variables for mean elevational range size of

rodents and birds, using hierarchical partitioning. Tmin and Tmax represent daily minimum

temperature and daily maximum temperature, respectively. The second column of graphs

includes Tmin and Tmax (together with DTR) in the analysis.

-25-

Table S1. Climatic and topographic variables used in this study.

Variables Abbreviation Original

Resolution

Temporal span Data source a

Seasonal temperature range STR 0.5° 1901-2000 CRU TS2.1

Diurnal temperature range DTR 0.5° 1901-2000 CRU TS2.1

Mean annual temperature MAT 0.5° 1901-2000 CRU TS2.1

Mean annual precipitation MAP 0.5° 1901-2000 CRU TS2.1

Maximum of diurnal temperature Tmax (daily) 0.5° 1901-2000 CRU TS2.1

Minimum of diurnal temperature Tmin (daily) 0.5° 1901-2000 CRU TS2.1

Maximum of monthly mean

temperature

Tmax (monthly) 0.5° 1901-2000 CRU TS2.1

Minimum of monthly mean

temperature

Tmin (monthly) 0.5° 1901-2000 CRU TS2.1

Seasonal precipitation range SPR 0.5° 1901-2000 CRU TS2.1

Net primary productivity NPP 0.25° 1995-2006 SEDAC

Actual evapotranspiration AET 1km 1950-2000 CGIAR-CSI

Potential evapotranspiration PET 1km 1950-2000 CGIAR-CSI

Topographic heterogeneity b Topo_SD 10’ CGIAR-CSI

Mountain height c MtH1 10’ CGIAR-CSI

Mountain height

(at survey sites) d

MtH2 Original

papers (19) a The Climate Research Unit (CRU) database (http://www.ipcc-data.org/obs/cru_ts2_1.html); the Socioeconomic

Data and Applications Center (SEDAC) database (http://sedac.ciesin.columbia.edu/); the Consultative Group on

International Agricultural Research Consortium for Spatial Information (CGIAR-CSI) database

(http://www.csi.cgiar.org/).

b Topographic heterogeneity was measured as the standard deviation of elevation within a grid cell.

c Mountain height was measured as elevation above sea level.

d Mountain heights at survey sites were derived from original papers (19).

-26-

Table S2. Subsets of variables assessed in structural equation models (SEM).

No. Theory Subset of SEMa RMSEA

b

(95% confidence

interval)

CFIb SRMR

b

Primary

level

Secondary

level

1* Climatic variability

hypothesis

Latitude STR 0.076

(0.00,0.14)

0.98 0.0727

2* Latitude DTR 0.066

(0.00,0.17)

0.96 0.0666

3* Latitude MAP 0.000

(0.00,0.11)

1.00 0.0416

4 Latitude Tmax

(daily)

0.490

(0.42,0.56)

0.00 0.2963

5 Mean climatic

condition theory

Latitude MAT 0.217

(0.14,0.31)

0.83 0.1183

6 Climatic extreme

hypothesis

Latitude Tmin

(monthly)

0.192

(0.12,0.27)

0.90 0.1012

7 Latitude Tmax

(monthly)

0.146

(0.08,0.23)

0.63 0.1102

8 MtH2 STR 0.093

(0.00,0.19)

0.87 0.0742

9 MtH2 DTR 0.098

(0.00,0.20)

0.72 0.0747

10* MtH2 MAP 0.000

(0.00,0.14)

1.00 0.0508

11 MtH2 Tmax

(daily)

0.274

(0.21,0.35)

0.00 0.1760

12 MtH2 MAT 0.182

(0.10,0.27)

0.47 0.1233

13 MtH2 Tmin

(monthly)

0.172

(0.09,0.26)

0.64 0.1041

14 MtH2 Tmax

(monthly)

0.227

(0.15,0.32)

0.51 0.1129

15* Latitude

MtH2

0.062

(0.00,0.19)

0.97 0.0525

16* MAP STR 0.076

(0.00,0.18)

0.97 0.0679

17* MAP DTR 0.066

(0.00,0.17)

0.97 0.0654

-27-

18 DTR STR 0.095

(0.00,0.19)

0.93 0.0849

19 Mean climatic

condition theory

MAP MAT 0.160

(0.09,0.24)

0.72 0.1188

20* Latitude

MAP

STR 0.059

(0.00,0.13)

1.00 0.0600

21* Latitude

MAP

DTR 0.000

(0.00,0.07)

1.00 0.0587

22* Latitude

STR

MAP 0.059

(0.00,0.13)

0.99 0.0600

23* Latitude

DTR

MAP 0.000

(0.00,0.72)

1.00 0.0586

24* MtH2

Latitude

MAP 0.000

(0.00,0.03)

1.00 0.0482

25* MtH2

STR

MAP 0.000

(0.00,0.92)

1.00 0.0645

26* MtH2

DTR

MAP 0.000

(0.00,0.95)

1.00 0.0657

27* STR

DTR

MAP 0.007

(0.00,0.10)

1.00 0.0727

28* Best model Latitude

MAP

STR

DTR

0.062

(0.00,0.13)

0.99 0.0236

29 Latitude

MAP

MtH2

DTR

STR

0.147

(0.08,0.23)

0.97 0.0305

a Variable abbreviations: mountain height at survey site (MtH2), seasonal temperature range

(STR), diurnal temperature range (DTR), mean annual precipitation (MAP), maximum of

diurnal temperature (Tmax [daily]), mean annual temperature (MAT), maximum monthly mean

temperature (Tmax [monthly]), and minimum monthly mean temperature (Tmin [monthly])b.

Model fitting criteria: root mean square error of approximation (RMSEA) < 0.08,

comparative fit index (CFI) > 0.95, and standard root mean square residual (SRMR) < 0.1.

The best model was the set maintaining the lowest SRMR.

-28-

Table S3. Unstandardized and standardized parameter estimates for the structural

equation models presented in the Figures specified.

Unstandardized Standardized

Estimate Standard

error

Critical

ratio P Estimate (r)

Fig. 1 & Fig. S4A

DTR <--- MAP -0.452 0.077 -5.889 <0.001 -0.540

STR <--- Latitude 0.830 0.039 21.118 <0.001 0.881

STR <--- MAP -0.074 0.033 -2.236 0.025 -0.071

DTR <--- Latitude 0.045 0.070 0.647 0.518 0.059

Mean Range Size <--- DTR -0.233 0.093 -2.505 0.012 -0.248

Mean Range Size <--- STR 0.219 0.080 2.737 0.006 0.288

Mean Range Size <--- MAP -0.097 0.078 -1.249 0.212 -0.124

Fig. S4B

DTR <--- MAP -0.311 0.107 -2.897 0.004 -0.278

STR <--- Latitude 0.876 0.036 24.076 <0.001 0.949

STR <--- MAP 0.057 0.066 0.858 0.391 0.034

DTR <--- Latitude 0.126 0.059 2.156 0.031 0.207

Mean Range Size <--- DTR -0.303 0.101 -2.997 0.003 -0.262

Mean Range Size <--- STR 0.192 0.072 2.652 0.008 0.251

Mean Range Size <--- MAP -0.292 0.125 -2.335 0.020 -0.227

Fig. S4C

DTR <--- MAP -0.708 0.118 -5.988 <0.001 -0.569

STR <--- Latitude 0.789 0.038 20.763 <0.001 0.890

STR <--- MAP -0.078 0.064 -1.222 0.222 -0.052

DTR <--- Latitude -0.030 0.070 -0.425 0.671 0.040

Mean Range Size <--- DTR -0.256 0.091 -2.819 0.005 -0.270

Mean Range Size <--- STR 0.152 0.082 1.843 0.065 0.192

Mean Range Size <--- MAP -0.287 0.138 -2.076 0.038 -0.243

Fig. S4D

-29-

DTR <--- MAP -0.630 0.095 -6.651 <0.001 -0.619

STR <--- Latitude 0.789 0.038 20.922 <0.001 0.885

STR <--- MAP -0.076 0.052 -1.442 0.149 -0.061

DTR <--- Latitude -0.096 0.068 -1.407 0.159 -0.131

Mean Range Size <--- DTR -0.229 0.093 -2.480 0.013 -0.239

Mean Range Size <--- STR 0.163 0.082 1.992 0.046 0.208

Mean Range Size <--- MAP -0.173 0.116 -1.491 0.136 -0.177

-30-

Table S4. Sample covariance and correlation used for the structural equation models

presented in the Figures specified.

Covariance Correlation

Estimate Standard

error

Critical

ratio P Estimate (r)

Fig. 1 & S4A

MAP <--> Latitude -0.049 0.003 -15.457 <0.001 -0.647

Fig. S4B

MAP <--> Latitude -0.028 0.002 -12.490 <0.001 -0.595

Fig. S4C

MAP <--> Latitude -0.033 0.002 -15.889 <0.001 -0.653

Fig. S4D

MAP <--> Latitude -0.039 0.003 -14.697 <0.001 -0.635

-31-

Table S5. Intercepts for variables in the structural equation models in the Figures

specified.

Estimate Standard error Critical ratio P

Fig. 1 & S4A

DTR 0.541 0.056 9.636 <0.001

STR -0.094 0.014 -6.830 <0.001

Mean Range Size 0.462 0.060 7.748 <0.001

Fig. S4B

DTR 0.636 0.046 13.967 <0.001

STR -0.110 0.028 -3.903 <0.001

Mean Range Size 0.583 0.080 7.296 <0.001

Fig. S4C

DTR 0.703 0.059 11.919 <0.001

STR -0.072 0.032 -2.258 0.024

Mean Range Size 0.555 0.081 6.820 <0.001

Fig. S4D

DTR 0.780 0.059 13.207 <0.001

STR -0.065 0.033 -1.991 0.046

Mean Range Size 0.527 0.088 5.991 <0.001

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