Are leaf functional traits invariant with plant size and what is invariance anyway?

14 Pages·2014·0.89 MB·English

FunctionalEcology2014 doi:10.1111/1365-2435.12298
‘ ’
Are leaf functional traits invariant with plant size and
‘ ’
what is invariance anyway?
€
Charles A. Price*,1, Ian J. Wright2, David D. Ackerly3, Ulo Niinemets4, Peter B. Reich5,6 and
Erik J. Veneklaas1
1SchoolofPlantBiology,UniversityofWesternAustralia,Perth,WesternAustralia6009,Australia;2Departmentof
BiologicalSciences,MacquarieUniversity,Sydney,NewSouthWales2109,Australia;3DepartmentofIntegrative
Biology,UniversityofCalifornia,3060ValleyLifeSciencesBuilding,Berkeley,California94720-3140,USA;4Instituteof
AgriculturalandEnvironmentalSciences,EstonianUniversityofLifeSciences,Kreutzwaldi1,Tartu51014,Estonia;
5
DepartmentofForestResources,UniversityofMinnesotam1530,ClevelandAvenueNorth,St.Paul,Minnesota
6
55108;USA;and HawkesburyInstitutefortheEnvironment,UniversityofWesternSydney,LockedBag1797,Penrith,
NewSouthWales2751,Australia
Summary
1. Studies of size-related plant traits have established a suite of mathematical functions
describing whole plant investment and allocation. In parallel, studies of plant ‘economic spec-
tra’ have measured the scaling and variance composition of traits related to the major dimen-
sions of both structure and function. Here, we explore the intersection of these two broad
areas by exploring the notion that many leaf economic traits are invariant with species differ-
ences in adult plant size. Invariant traits are those that do not change with plant size and are
invoked as a key simplifying assumption of prominent models that purport to explain the scal-
ing of plant size and metabolism. Unfortunately, leaf trait invariance is neither well defined
nor understood andhasneverbeen critically evaluated.
2. Using a global plant trait data set, we evaluated whether nine key traits can be considered as
effectivelyinvariantasafunctionofthemaximumheightofplantspecies,withinandacrossplant
growth forms and within and across broad taxonomic groups. We also examine the influence of
habitat,biomeandglobalspatialscalesonthesize-relativevarianceinplantfunctionaltraits.
3. We suggest that while invariance is an intuitive concept, an objective statistical definition is
elusive. Expanding on ideas drawn from the study of life-history invariants, we propose five
criteria toidentifytraits that are effectively invariant, dependingon the research question.
4. We show that all studied ‘leaf economic spectrum’ (LES) traits approach invariance within
and between herbaceous and woody plant groups, angiosperms and gymnosperms, and within
most biome and habitat types. Individual leaf area, however, shows a modest increase with
plant size, and there are significant shifts in the average LES trait values at a given plant maxi-
mum height, among the plant growthforms and taxonomicgroups.
5. Our resultsdemonstrate thatgenerally, LEStraitsshowlittleinterspecific variation withmax-
imumplantheight,whichprovidessomesupportforattemptstomodelplantswith‘average’leaf
properties. Our work also highlights the need for a better understanding of the drivers of leaf
sizevariationwithinandacrossindividuals,functionalgroups,clades,biomesandhabitats.
Key-words: leaf area, leaf economic spectrum, metabolic scaling theory, metabolic theory of
ecology, plant functionaltraits, plant height
1932; Brody 1945). The publication of several compendia
Introduction
ofallometricrelationshipsforanimals(Peters1983;Calder
Biologists have long recognized body size as one of life’s 1984; Schmidt-Nielsen 1984; Charnov 1993) and plants
principal dimensions (Galilei 1638; Rubner 1883; Kleiber (Niklas1994)andthedevelopmentofanarrayofsynthetic
theoretical approaches (Kooijman 1993; West, Brown &
*Correspondenceauthor.E-mail:[email protected] Enquist 1997; Brown et al. 2004) have further established
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety
2 C.A.Priceet al.
body size as one of the principal drivers underlying vari- associatedwithsomeleaftraits,suchasleafarea,thickness
ability in organismal metabolic requirements, biomechani- or leaf mass per area (Diaz et al. 2004), or leaf mass per
cal demands and life-history strategies, both within and area and leaf mean area (Wright et al. 2007), are orthogo-
across clades. This has led to increased efforts aimed at nal to the principal component associated with plant can-
understanding the mechanistic drivers of the allometry of opy height. Similarly, leaf economic traits and wood
metabolism and mass, and the suite of biological phenom- economic traits have also been shown to be orthogonal in
enathataretiedtothiscentralpattern. some systems (Baraloto et al. 2010) but not necessarily in
One prominent recent approach, known as the Meta- general(Reich2014).
bolic Theory of Ecology (MTE, Brown et al. 2004), pro- Here, we explore the intersection of MTE and LES. On
poses a mechanism for the origin of quarter power scaling theonehand,theinfluenceofbodysizeasadriverofmor-
of metabolism with mass and numerous related scaling phological and physiological variability is well-established.
phenomena. MTE has generated strong interest and con- On the other hand, a growing body of work has estab-
troversy (e.g. Dodds, Rothman & Weitz 2001; Kozlowski lished that plant size and suites of physiological or ‘eco-
&Konarzewski2004;Glazier2006)andhasbeenlinkedto nomic’ traits are often orthogonal to one another. We
numerouspatterns acrossplants including (but notlimited propose that plant body size and LES traits can be linked
to) metabolic allometry (Reich et al. 2006; Enquist et al. by evaluating the variance in plant functional traits and
2007; Mori et al. 2010), ontogenetic growth (West, Brown plant body size, relative to one another. It has been sug-
& Enquist 2001), biomass partitioning (Enquist & Niklas gested that some leaf traits and plant size represent inde-
2002;Price,Enquist&Savage2007),morphologicalallom- pendent axes of ecological and evolutionary diversity
etry (Price, Enquist & Savage 2007) and forest structure (Ackerly 2004). But to what leaf functionaltraits does this
(Enquist, West & Brown 2009; West, Enquist & Brown apply, at what spatial scale, and are those traits invariant
2009). For more information on MTE, we direct readers withplantsize?Theuseoftheterminvariancehere(which
to recent reviews (Coomes 2006; Muller-Landau et al. wediscussindetailbelow)meansthatthetraitinquestion
2006a,b;Savage,Deeds& Fontana2008; Priceet al.2010, showslittlevariabilityandthatvariabilitydoesnotchange
2012;Sibly,Brown&Kodric-Brown2012). systematically withplant size.Invariant traits are orthogo-
Biologists have also long held an interest in the nature nal, but orthogonal traits may, or may not be, invariant.
of functional trait variability within and across organisms. Further, with natural selection acting locally and differen-
Functional traits have been defined as ‘morpho-physio- tially across habitats, how is it that a global pattern of
phenological traits which impact fitness indirectly via their invariancemightemerge?
effects on growth, reproduction and survival’ (Violle et al. These two areas have been linked previously via a cen-
2007). For plant leaves, the analyses of both continental tral assumption of the MTE plant model [a.k.a. WBE
(Reichet al.1999)andglobalscaledatasets(Wrightet al. (West, Brown and Enquist) model] that the size and func-
2004) have identified a series of trade-off curves known as tional traits of leaves are invariant with plant size (West,
the global leaf economic spectrum (LES) (Wright et al. Brown&Enquist1999).Thespecificassumptiondescribed
2004). The spectrum represents a set of leaf physiological intheoriginalmodelpresentationisthat‘...thenumberof
traits and trade-offs that are strongly indicative of species tubes in a petiole which is taken to be an invariant.’, that
growth patterns and life-history strategies. A series of key is, the number and size of conduits in a leaf petiole is
papers has shown that this suite of traits covaries strongly invariantwithplantsize (West,Brown&Enquist1999)or
across plants and represents, coarsely, a slow-growth to that both conduits and leaf size are invariant (West,
fast-growthcontinuum(Reichet al.1999;Diazet al.2004; Enquist&Brown2009).Inotherwords,theterminalunits
Wright et al. 2004; Reich 2014). Multi-dimensional analy- onaplant–leaves,suppliedbypetiolarvasculature–were
ses of global data compilations of six of these traits have assumed to vary little (or at least not systematically) with
shownthatastriking74%ofthevariabilityacrossasetof plant size. An implicit assumption is that other leaf func-
core traits is explained by the first principal axis (Wright tionaltraitsarealsoinvariant,forexamplethoserelatedto
et al. 2004). Plants at the slow end of the continuum typi- metabolism such as those described within the leaf eco-
cally have high leaf mass per area (LMA), long leaf life nomic spectrum. How do we evaluate these simplifying
span, low mass-based photosynthetic capacity and dark assumptions? Clearly, most biological traits are variable
respiration and low nitrogen and phosphorus concentra- (and leaf traits are known to vary ontogenetically with
tions per unit mass, when compared to the fast end of the size), so our question becomes in essence, is the variability
continuum(Reich,Walters&Ellsworth1997;Wrightet al. uncorrelated with species differences in size, or if it is cor-
2004). Nevertheless, within this broad spectrum, plants related, is the correlation weak enough that it will have
with similar ecological strategies tend to cluster in groups littleinfluenceonmodelpredictions?
defined by: growth habit, life-form, leaf habit and toler- Here,weexpanduponpreviousworkbycombiningtwo
ance to drought and shading (Reich, Walters & Ellsworth large data sets, one containing measurements for several
1997;Hallik,Niinemets&Wright2009). measures of plant size including height, stem diameter and
The analyses of several large regional or global data canopy spread (www.americanforests.org/our-programs/
sets have demonstrated that the principal components bigtree), and a global data set of plant economic traits
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
Areleaftraits‘invariant’withplantsize? 3
(GLOPNET; Wright et al. 2004) containing measurements typicallylacksuitesofhomologouslandmarks,suchasthe
for a number of LES traits: leaf mass per area (LMA), location of bone features, that have proven useful in the
photosynthetic capacity per unit mass (A ) or area analysis of coordinate transformations in animal evolu-
mass
(A ), dark respiration rate (R ), leaf life span (LL), tionary studies (Thompson 1917; Bookstein 1991), the
area mass
nitrogen content per unit mass (N ) or area (N ), transformation of coordinates can be thought of as an
mass area
phosphorus content per unit mass (P ) or area (P ). increase in body size with regularly collected measures
mass area
The data set also contains data on individual leaf size suchasplantheight,stemdiameterorcanopyspreadserv-
(measured as leaf area) and maximum plant height, which ingasgeneralproxiesforplantsize.
arenottypicallyconsideredLEStraitsperse. Invariant means ‘non-variable’ or ‘lacking’ variance.
We discuss the reasons why an objective statistical defi- Clearly, mostbiological traits,from conduitdimensionsto
nition of invariance is challenging, despite its intuitive leaf size, exhibit variability. Certainly, the leaf traits we
appeal, and argue that a more productive approach is to discuss hereall vary: withinindividual plants, among indi-
quantifyanddiscuss the relativevariance intraits of inter- viduals within a species and across plant species. Thus,
est. We then utilize the combined data sets to evaluate the statements such as the assumption of invariant conduit
variance in eight LES traits and leaf area, all relative to dimensions in West, Brown & Enquist (1999) or conduit
plant height, a proxy for overall plant size. Looking at dimensions and leaf size in West, Enquist & Brown (2009)
woody and herbaceous species together and separately, must be viewed as simplifying model assumptions (Price
withinangiospermsandgymnosperms,andwithindifferent et al.2012).But,howmuchvariability canexistinagiven
biome and habitat types, we find that most leaf functional trait for it still to be considered invariant? Unfortunately,
traitsaresubstantiallylessvariablethan,andshowlittleto the exact meaning of invariance in biology is not well
nosystematicvariationwith,plantsize.Importantly,how- defined, creating confusion regarding its definition
ever, individual leaf area itself increases modestly with and interpretation (Charnov 1993; Nee et al. 2005, 2006;
plantsize,bothwithinwoodyspeciesandacrossallplants. Savage et al. 2006). As biology and ecology are largely
In addition, we find an increase in the amount of variance concerned with the study of variability, the adoption of
in LES traits explained by plant height, at smaller spatial the term ‘invariant’ from mathematics and physics will
scales. We speculate on some possible drivers of these pat- likelycontinuetoleadtoconfusion.Werecognizetheutil-
terns and discuss the implications of our findings for ity of viewing traits as ‘invariant’ within some modelling
understandingecological distributions of leaftraits and on approaches; however, we offer that it is more accurate to
futureattemptstomodelthegeneralpropertiesofplants. describe traits as ‘approaching invariance’ or ‘effectively
invariant’, which recognizes invariance as a theoretical
ideal,butpreservestheinherentvariablenatureofbiologi-
ARE BIOLOGICAL TRAITS INVARIANT?
cal traits. Moreover, as the concept of an invariant trait is
Within biology, the idea of invariant quantities can be poorly understood, we emphasize the relative nature of
found in many areas from food web studies (Briand & this concept: invariance in a biological context is always
Cohen 1984) to species–area relationships (Preston 1960). relativetoanothertrait.
One area where they have garnered considerable attention We expand upon earlier work (Charnov 1993; Savage
is in the study of organism life histories (Charnov 1993). et al. 2006) and propose five criteria that can help in iden-
Thesetraitsareusuallyreferredtoasdimensionlessinvari- tifyingtraitsthatapproachinvariance:
ants, and examples include the ratio of weaning mass to 1. Lowvarianceinthe y-variablerelativetothex-variable
adult mass or the ratio of the age at maturity to average (Charnov1993;Savageet al.2006).Asistypicalwithin
life span. In all of these studies, variability exists in the the field, we treat size as the x-variable and the trait of
biological quantities in question, but the variability is interest as the y-variable. Coming up with an a priori
much less than that of body size. In an attempt to add guideline for exactly how much more variability is
clarity to the issue, Savage et al. (2006) discuss two types expected in the x-variable than the y-variable is chal-
of invariance: ‘type A’ invariance, in which a biological lenging. We suggest that, rather than using some arbi-
characteristic does not vary systematically with another trary cut-off value for invariance, investigators simply
characteristic,suchasbodysize,and(lesscommonly)‘type reportthe ratioof variancesandinterpret theirfindings
B’ invariance, in which a biological characteristic exhibits in the light of this value. This approach is valid only
a unimodal central tendency, suggestive of an optimal or whenvariableshavethesameunitsoriftheyareexam-
constrained value, and varies over a limited range, relative ined on logarithmic scales. Note that the ratio of vari-
to the variable to which it is being compared. However, ances also corresponds to the standardized major axis
whilewerecognizethattheideaofinvarianttraitsissome- slope of the relationship between the variables, and so
what intuitive, coming up with a rigorous definition for approaches zero as variance in the y-variable declines
quantifyingitischallenging. relativetosize(seeCriterion4).
Within mathematics or physics, invariance is clearly 2. Modalvarianceinthey-variable,whichmaybesugges-
defined as a system unaffected by a designated operation, tive of an optimal value (Charnov 1993; Savage et al.
such as a transformation of coordinates. While plants 2006). In practice, it is likely that due to the inherent
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
4 C.A.Priceet al.
multiplicative nature of growth, most traits of interest considered, where maximum height corresponds to the maximum
will have frequency distributions that are close to nor- observedheightwithinastudylocationordataset.Atotalof540
recordsinthedatabasehadheightandleafarea(cm2)oratleast
malonlinearorlogarithmicscales(Kerkhoff&Enquist
one of the following LES trait measurements: leaf mass per area
2009). Thus, for many traits, the distribution of vari- (LMA, gm(cid:1)2), photosynthetic capacity on a mass (A ,
mass
ance might be consistent with the expectation of the nmolg(cid:1)1s(cid:1)1) or area basis (A lmolm(cid:1)2s(cid:1)1), leaf life span
area
normal curve, that is, 95% of the observations will fall (LL, months), nitrogen content per unit mass (N , ) or area
mass %
within two standard deviations. However, it is also (Narea, gm(cid:1)2), phosphorus content per unit mass (Pmass,%) or
area(P ,gm(cid:1)2).
likely that some traits will have frequency distributions area
Additional maximum tree height data comes from the registry
that depart from normality, yet still contain much less
ofBigTreeswhichismaintainedby thenon-profitgroupAmeri-
variabilitythanplantsizeforexample. can Forests (www.americanforests.org). Tree species within the
3. Low coefficient of determination (R2 value). Regression registryareconsideredchampionsbasedonthefollowingcompos-
fits to bivariate plots should show that size has little to itescore: circumference at breastheight(in),plustree height (ft),
plusone-fourthoftheaveragecrownspread(ft),aformulagiving
no explanatory power with respect to the trait of inter-
agreaterweightingtotreeheightandcircumference thanspread.
est. Note that a low R2 merely says that two variables
OnehundredandsixtyspeciesintheBigTreedatabasewerealso
areunrelatedandsaysnothingaboutthedegreeofvari- representedin fullGLOPNET dataset,andwepairedtheheight
ance of either one. It is useful, however, when applied measurements from Big Tree data base with the corresponding
along with other criteria because it directly addresses leaftraitdatafromGLOPNET.AstheGLOPNETdatasetdoes
not contain bole circumference of crown radius data, these data
whether the central tendency of one trait varies in rela-
fromtheBigTreedatasetwerenotused.
tiontoanother.
TheWBEmodel,uponwhichMTErests,assumesanidealized
4. Low slope. Regression fits to bivariate plots should plant where stems, branches and petioles only fulfil support and
have a shallow slope which may also demonstrate that hydraulicsupplyroles,thatis,theyareconsiderednon-photosyn-
size has little to no explanatory power with respect to thetic, and thus this typically applies to woody species (West,
Brown&Enquist1999).Scalingpredictionsforherbaceousplants
the trait of interest. Low slopes will often be correlated
orplantswithphotosyntheticstemsmaystillfollowthepredicted
with low variance ratios (Criterion 1 and identical if
quarter power scaling relationships, provided their branching
using SMA regression) and low R2 values (Criterion 3) geometry meets model assumptions, but (all else being equal)
(Warton et al. 2006), but provide a further line of evi- would be expected to have different normalizations (y-intercepts)
denceforassessinginvariance. for various scaling relationships. Therefore, to allow for this
potentialdifference,weexaminedtraitmeansandcorrelationsfor
5. Isometric variation. This method is commonly used in
all species together, and within woody and herbaceous growth
the study of life-history invariants (Charnov 1993). If
forms separately. Given the anatomical and physiological differ-
twotraitsshowanisometricrelationship (i.e.aslopeof ences between angiosperms and gymnosperms, particularly with
1 on a log–log plot), then their ratio will be invariant respecttoleafformandhydraulicarchitecture,wealsoexamined
across the spectrum of variation in the two traits and differencesbetweenthesetwomajorcladesofseedplants.
Natural selection is a local-scale process, thus plants growing
may also be invariant (by criteria above) when
within a biome or habitat are typically subject to more similar
regressed against some third variable, typically body
selective pressures than plants across biomes or habitats. If LES
size (see Savage et al. 2006 for a discussion on this traitsareinvariantwithplantheightglobally,thiscanariseinone
topic).ThechoiceofSMAvs.OLSregressioniscritical oftwoways:(i)LEStraitsareinvariantwithheightatbothlocal
in assessing isometric relationships, as uncorrelated and global scales, (ii) LES traits vary systematically with height
withinsomeorallhabitatsand/orbiomes,yetshiftsintheeleva-
variables will have a slope of 1 under SMA regression,
tion of these traits between habitat or biomes and an increase in
soinpractice,itisimportanttoconsiderthebothslope
thetotalrangeofheightsampleddecreasetheexplanatorypower
and the R2 to make a substantive claim of isometric ofheightacrosstheselocal-scalegroupings.Toevaluatewhichof
variation. these two possibilities is operating within our data set, we also
grouped species according to the habitat and biome within the
Forsituationsinwhichinvarianceisasimplifyingmodel GLOPNETdataset.Biomeclassificationsfollow(Whittaker1975;
assumption, further insight can be gained from model- Wrightetal.2004)andincludethefollowingtypes:boreal,alpine,
based sensitivity analysis. For example, one can explore woodland, temperate forest, tropical forest and rain forest. We
determined habitat classifications from the original published
how changes in model parameters influence outcomes or
papersleadingto21distincthabitatclassifications(TableS1).One
predictions. If the model is highly sensitive, then even
of these, ‘high elevation grasslands’, had only five observations
small amounts of variation (or shallow slopes) could be and was not included in statistical analysis at the habitat level.
sufficient to drive change. If a model has low sensitivity, Data from two papers were from a mosaic of habitats across a
then steeper slopes might have little influence on model range of sites and were also not included in the habitat analysis
(Table S1). The Big Tree data set does not contain habitat or
predictions.
biome classifications, thus was not included in the analysis of
biomeorhabitatlevelpatterns.
All bivariate relationships were log-transformed (base 10), to
Materials andmethods
meet the assumption of homogeneityof variance, and fit with an
Data for our analyses come from two sources. The first is the ordinaryleast-squares(OLS)regressionslopes,withheightasthe
‘GLOPNET’ data set (GLObal Plant trait NETwork; Wright predictorvariable.InlinewithCriterion1,weexaminedtherela-
etal. 2004). A subset of the data base contains maximum height tive variance in plant height relative to the variance in the LES
measurements co-occurring with the leaf economic traits we traitsandleafarea.ToevaluateCriterion2,weexploredtheshape
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
Areleaftraits‘invariant’withplantsize? 5
anddispersionofeachLEStraitandleafarea.InlinewithCrite- standard deviations of the mean, and for the remaining
ria3and4,weusedthreecommonmetricstoinformourconsid- two traits, 93% of the observations were within two stan-
eration of whether traits were effectively invariant: (i) the slope,
darddeviations.
(ii) the coefficient of determination (R2), which estimates the
In contrast to the other leaf traits, the variance for leaf
strength of the linear relationship between variables, and (iii) the
P-value,whichtestsforanassociationbetweenXandYandindi- area is greater than that of plant height. This is likely
cateswhethertherelationshipunderconsiderationhasaslopethat related to the fact that leaf area is proportional to length
is different than zero. We further tested for a common slope squared while plant height is proportional to length to the
between woody and herbaceous groups. If a common slope was
firstpower.Ifweconsiderthelogofthesquarerootofleaf
found, a further test was performed to determine whether there
area, the variance is then less than that for plant height
hadbeenashiftinelevationbetweengroups(Wartonetal.2006).
Performingnumerousregressionspotentiallyincreasesthefam- andsimilartotheothertraitswehaveexamined(Table 3).
ily-wiseerrorrate orthe chanceofa type1 error.Tocorrectfor This would also likely be true if we considered leaves and
the large number of regressions, we used the Holm-Bonferroni trunksonthesamescale,thatis,volumeormass.
(Holm 1979) method to adjust P-values within each ‘family’,
InagreementwithCriterion3,thecoefficientofdetermi-
where our family groupings were (i) across angiosperms, gymno-
nation (R2) was consistently very low across the relation-
sperms, herbaceous and woody taxa (Table1); (ii) at the biome
level(Table2);and(iii)atthehabitatlevel(TableS2).Asreliance ships we examined, with a mean value of 0(cid:3)04 (Table 1).
on corrected P-values alone would bias our analysis towards a Considering both within and among growth forms and
findingofinvariantrelationships,whenconsideredintermsofsig- taxonomic groupings (Figs 2 and 3, Table 1), only 12 out
nificance of regressions, we report uncorrected P-values in
of 43 of the bivariate relationships had OLS slopes that
Tables1and2andTableS2andnotethoseP-valuesthatremain
were statistically different from zero (P < 0(cid:3)05), largely
significantfollowingtheHolm-Bonferronicorrection.
satisfying Criterion 4 (and following a Holm-Bonferroni
correction, this number dropped to just 8 out of 43;
Results
P < 0(cid:3)05). However, even for those 12 relationships, the
There were 648 woody plant species (trees or shrubs) and averageR2valuewasonly0(cid:3)105,andthusplantheighthas
52 herbaceous species in the combined data set. The only modest explanatory power for this suite of leaf func-
grasses wererepresented byonly15observationsandwere tional traits. The relationship with the highest R2 value
groupedwiththeherbaceousplantsforanalyses.Thetotal was that of leaf area which increased with plant height
number of combined height-trait measurements for each witha slopeof 0(cid:3)573forall plants (R2 = 0(cid:3)15) anda slope
relationship is given in the fourth column of Tables 1 and of0(cid:3)765forwoodyplants(R2 = 0(cid:3)25;Table 1).
2andTableS2.Samplesizesrangefromaminimumof19 Just as for the all-species analyses, in general, the
to a maximum of 679 for the growth form groupings biome-specificrelationshipsshowednotablylowR2values,
(Table 1); a minimum of 14 to a maximum of 624 for the averaging 0(cid:3)11 (Fig. 4, Fig. S2, Table 2). Fifteen out of 42
taxonomicgrouping(angiospermorgymnosperm);amini- relationships (36%) were statistically significant (dropping
mum of 8 to a maximum of 207 for the biome grouping to 8 with a Holm-Bonferroni correction), and among this
(Table 2); and a minimum of 8 to a maximum of 121 for 15, the average R2 value was 0(cid:3)2 (Table 2). The mean R2
the habitat grouping (Table S2). Some trait combinations across habitat groupings was slightly higher at 0(cid:3)17 (Table
contained insufficient data and are thus not reported. A S2). Twenty-eight out of 109 (26%) relationships at the
full list of species and their corresponding measurements habitatscaleweredifferentthanzero,andthemeanR2for
areincludedintheSupportingInformation,TableS1. significant (a = 0(cid:3)05) non-zero relationships was 0(cid:3)38. Fol-
In our data set, plant height varied from a minimum of lowing the Holm-Bonferroni correction at the habitat
0(cid:3)02 m in Oxytropis nigrescens to a maximum of 62(cid:3)8 m level, only 5 of 109 relationships differed from zero (Table
for Picea sitchensis or over 3(cid:3)5 orders of magnitude on a S1). In summary, adult plant height has relatively little
log scale. The overwhelming majority of extant land plant explanatory value with respect to interspecific differences
speciesfallwithinthisrange. inLEStraitsinmostbiomeorhabitattypes.
Before reporting coefficients of determination (R2), we For woody and herbaceous groups, six of the traits that
first look at relative variance in each relationship. As seen we have examined contained sufficient data to allow a test
in Table 3, the variance in (log-transformed) plant height for a common slope between groups (LMA, N , N ,
mass area
was always greater than the variance in (log-transformed) A , A and leaf size; Table 1). Of these, four traits
mass area
leafeconomictraits,rangingfrom2(cid:3)9to11(cid:3)4timesgreater shared a common slope across woody and herbaceous
acrossallplants.Theseresultsaregenerallyconsistentwith groups: N , N , A and A (P-value > 0(cid:3)05,
mass area mass area
Criterion 1, the suggested convention that the variance in Table 1). Among these, there was a significant difference
they-variableshouldbelessthanthevarianceinthex-var- in slope elevation between woody and herbaceous species
iable for a trait to be considered invariant (Savage et al. for N and A relationships (P-value > 0(cid:3)05). Simi-
area area
2006), with an order of magnitude more variance (11(cid:3)4) larly, nine of the traits allowed us to test whether the
representing a stronger case for invariance. Similarly, con- slopes were common between angiosperms and gymno-
sistent with Criterion 2, all traits we examined are unimo- sperm groups. Six of those tests showed no differences in
dal, and as seen in Fig. 1 and in Table 3, 95% of the slopes (P-value > 0(cid:3)05). Of those six, five had significant
observationsfor7outof9functionaltraitsfellwithintwo shiftsinelevationbetweengroups(P-value > 0(cid:3)05).
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
6 C.A.Priceet al.
hinangiospermandgymnosperms.Growth2PPR),-value(with-valuesremainingsig-(ndupper95%confidenceinterval,meanYwhethertherehasbeenashiftinelevationmn,heighttypicallyexplainslittlevariation SameslopeElevationshiftPPX(-value)?(-value)?mean (cid:3)0759NANA(cid:3)0815NANA(cid:3)0814NANA(cid:3)0878NANA(cid:3)0872NANA(cid:3)0725NANA(cid:3)0719NANA(cid:3)0719NANA(cid:3)0651NANA(cid:3)(cid:3)05940049NA(cid:3)(cid:3)079703550(cid:3)(cid:3)(cid:3)06420190539(cid:3)0783NANA(cid:3)0759NANA(cid:3)(cid:3)(cid:3)069504510000(cid:3)(cid:3)(cid:3)056701660588(cid:3)(cid:3)07630029NA(cid:3)(cid:3)(cid:3)082703030000(cid:1)(cid:3)(cid:3)04970049NA(cid:1)(cid:3)(cid:3)050403550(cid:1)(cid:3)(cid:3)(cid:3)05090190539(cid:1)(cid:3)(cid:3)(cid:3)029904510000(cid:1)(cid:3)(cid:3)(cid:3)029901660588(cid:1)(cid:3)(cid:3)02670029NA(cid:1)(cid:3)(cid:3)(cid:3)050003030000(cid:3)(cid:3)071108150(cid:3)(cid:3)(cid:3)075906610023(cid:3)(cid:3)07600005NA(cid:3)(cid:3)(cid:3)084607710157(cid:3)(cid:3)084608740(cid:3)(cid:3)062502020(cid:3)(cid:3)062709550(cid:3)(cid:3)06890011NA(cid:3)(cid:3)05660017NA(cid:3)(cid:3)130508150(cid:3)(cid:3)(cid:3)136106610023(cid:3)(cid:3)13530005NA
baceousgroupsandwitfficientofdeterminationercept,interceptlowerashareacommonslope,beseeninthefifthcolu UppCIYmean (cid:3)(cid:3)19951992(cid:3)(cid:3)02900256(cid:3)(cid:3)02830255(cid:1)(cid:3)(cid:1)(cid:3)09820946(cid:1)(cid:3)(cid:1)(cid:3)09320968(cid:3)(cid:3)19931902(cid:3)(cid:3)10120986(cid:3)(cid:3)06730967(cid:3)(cid:3)09781032(cid:3)(cid:3)19901975(cid:3)(cid:3)02420221(cid:3)(cid:3)02780240(cid:1)(cid:3)(cid:1)(cid:3)09950980(cid:1)(cid:3)(cid:1)(cid:3)09330978(cid:3)(cid:3)19201863(cid:3)(cid:3)10070980(cid:3)(cid:3)04620926(cid:3)(cid:3)11271096(cid:3)(cid:3)19231888(cid:3)(cid:3)04370361(cid:3)(cid:3)02900238(cid:3)(cid:3)22462148(cid:3)(cid:3)10130961(cid:3)(cid:3)20321720(cid:3)(cid:3)07930617(cid:3)(cid:3)19881959(cid:3)(cid:3)02890267(cid:3)(cid:3)02750232(cid:1)(cid:3)(cid:1)(cid:3)09850942(cid:1)(cid:3)(cid:1)(cid:3)09260987(cid:3)(cid:3)19931974(cid:3)(cid:3)10111005(cid:3)(cid:3)06421027(cid:3)(cid:3)09610972(cid:3)(cid:3)26832373(cid:3)(cid:3)05450152(cid:3)(cid:3)11420481
aterelationshipsweexaminedwithinandacrosswoodyandher–ncolumns215bythey-variable,x-variable,samplesize(),coeold),slope,upperandlower95%slopeconfidenceintervals,intuesresultingfromtestsforacommonslope,andifthegroupsmmonslope,testingforacommoninterceptisnotdone.Ascanfferentthanzeroarehighlighted PSlopeLowCIUppCIInterceptLowCI (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)003500060065196519350019(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)049100090033001602630237(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)098000000026002502550228·(cid:3)(cid:3)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)000001030052015510361090(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)044400200032007209861040(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)006400520106000319391885(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)057500100024004409790945·(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)000005730445070105550437·(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)000001630111021509260874(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)017600200009005019631936(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)051700090018003602140186(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)013400190045000602530228(cid:3)(cid:3)(cid:3)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)009400330155105411120003(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)084600050046005709821032(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)098000010062006318631805(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)075300060029004009770946·(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)000007650638089303420222(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)017500470021011410570988(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)007501390292001518191716(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)056100420184010103400244(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)017501050258004801850080(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)055300740327017921262005(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)018301260316006309230833(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)049003461379068816281223(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)008101400018029706870581(cid:3)(cid:3)(cid:3)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)030002519601933085100030(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)084800020020002502660242(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)009300210046000402490223·(cid:3)(cid:3)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)000001140062016510381090(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)069500100061004109791031(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)007900450005009619461899(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)003900060073098009490023·(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)000007180596084005320423·(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)000001050054015609120864(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:3)078500280230017524092136(cid:3)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)(cid:1)(cid:3)066200790281043900440456·(cid:1)(cid:3)(cid:1)(cid:3)(cid:1)(cid:3)(cid:3)(cid:3)000103090485013409000657
Ordinaryleast-squaresregressionresultsforthe43bivariTable1.formortaxonomicgrouparegiveninthefirstcolumnfollowedinnificantfollowingHolm-BonferronicorrectionunderlinedandinbPvalueandthemeanXvalue.Thefinaltwocolumnsarethe-val(seeMaterialsandmethods).NotethatifarelationshiplacksacoPinleaffunctionaltraits.-valuesforthoserelationshipsthataredi 2nRGroupingY-variableX-variable (cid:3)AllplantsLMAHeight6790008(cid:3)NHeight5710001Allplantsmass(cid:3)NHeight5660000Allplantsarea(cid:3)PHeight3050049Allplantsmass(cid:3)PAllplantsHeight3020002area(cid:3)AHeight3110011Allplantsmass(cid:3)AHeight3090001Allplantsarea(cid:3)AllplantsLeafareaHeight4440150(cid:3)AllplantsLeaflifespanHeight3830090(cid:3)WoodyLMAHeight5280003(cid:3)NHeight3780001Woodymass(cid:3)NWoodyHeight4270005area(cid:3)PHeight2370038Woodymass(cid:3)PHeight2420000Woodyarea(cid:3)AHeight2160000Woodymass(cid:3)AWoodyHeight2460000area(cid:3)WoodyLeafareaHeight4250247(cid:3)WoodyLeaflifespanHeight3320006(cid:3)HerbaceousLMAHeight490066(cid:3)NHeight490007Herbaceousmass(cid:3)NHeight480040Herbaceousarea(cid:3)AHeight310012Herbaceousmass(cid:3)AHerbaceousHeight310060area(cid:3)HerbaceousLeafareaHeight190028(cid:3)HerbaceousLeaflifespanHeight510061(cid:3)AngiospermLMAHeight6240000(cid:3)NAngiospermHeight5170000mass(cid:3)NHeight5150005Angiospermarea(cid:3)PHeight2880062Angiospermmass(cid:3)PAngiospermHeight2880001area(cid:3)AHeight2670012Angiospermmass(cid:3)AAngiospermHeight2680019area(cid:3)AngiospermLeafareaHeight4190244(cid:3)AngiospermLeaflifespanHeight3420046(cid:3)GymonospermLMAHeight550001(cid:3)NHeight540004Gymnospermmass(cid:3)NHeight510204Gymnospermarea
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
Areleaftraits‘invariant’withplantsize? 7
hift The amount of variance explained within and across
s each relationship increased going from global to biome to
ElevationP(-value)? (cid:3)0157000NANA ahnadbit0a(cid:3)1t6scaatlegl(oFbiagl.,4b)i.omTheeamndeahnabRit2atvaslcuaelessw,reersep0ec(cid:3)0ti1v,e0ly(cid:3)1.1
pe? Discussion
sloue)
eal 142517 How constant is constant enough to be considered invari-
mv 770511
SaP(- (cid:3)07(cid:3)08(cid:3)02(cid:3)09(cid:3)00(cid:3)00 antisworthyofmuchthought,consideringthatnoisyfield
parametersareourstockintradeandwillbeforever.Char-
932029
n 103225 nov(1993),LifeHistoryInvariants.
mea (cid:3)14(cid:3)14(cid:3)13(cid:3)13(cid:3)12(cid:3)13
X
Collectively, our results suggest that interspecific LES
traits vary little, if at all, as a function of plant height. As
270036
mean (cid:3)101(cid:3)057(cid:3)146(cid:3)086(cid:3)003(cid:3)153 seenin Figs 2and3, FigsS1andS2(Supportinginforma-
Y (cid:1)(cid:1) (cid:1) tion), and in Tables 1 and 2, and Table S2, the LES traits
we evaluated show little or no systematic variation
I 994925
pC 471754178194 withplantheightbasedongrowthform,taxonomicgroup,
Up (cid:1)(cid:3)0(cid:1)(cid:3)0(cid:3)1(cid:3)1(cid:3)0(cid:3)2 biome or habitat. This reinforces previous work by
expanding the suite of traits analysed and suggests that
CI 920856101852 height and leaf functional trait variability are indeed lar-
w 007475
o (cid:3)2(cid:3)1(cid:3)0(cid:3)0(cid:3)0(cid:3)1 gely orthogonal to one another (Diaz et al. 2004; Wright
L (cid:1)(cid:1) (cid:1)
et al. 2007; Lalibert(cid:2)e et al. 2012). Height and LES traits
pt may represent independent axes upon which natural selec-
e 630479
Interc (cid:1)(cid:3)128(cid:1)(cid:3)059(cid:3)115(cid:3)079(cid:3)004(cid:3)224 teivoenr,aoctusrwainthaliynsissomalesocoshmomwusntithiaest (tAhecrkeermlyay20b0e4).mHodoewst-
trends in some LES traits with plant height within some
I 473569
C 492321 biomesorhabitats(Table 2,TableS2,Fig. 3,Fig.S2).
p 725350
Up (cid:3)0(cid:3)0(cid:3)0(cid:3)0(cid:3)0(cid:1)(cid:3)0 This suggests that while somecommunities exhibit sepa-
rationinLEStraitsbasedonheight(Thomas1996;Falster
CI 597457355630 & Westoby 2005; Niinemets 2010), when looking across
w 320260
o (cid:3)0(cid:3)0(cid:3)0(cid:3)0(cid:3)0(cid:3)1 multiple communities, shifts in the location of data (eleva-
L (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
tion and horizontal position) effectively reduces the
313054 explanatorypowerofheight.Forexample,LMAincreases
pe 190123050652
o (cid:3)0(cid:3)0(cid:3)0(cid:3)0(cid:3)0(cid:3)0 systematicallywithheightin6ofthe14habitatsweexam-
Sl (cid:1)(cid:1)
ined (Fig. 3, Table S2). However, there are shifts in the
823512 mean LMA values between habitats, and an increase in
631224
P (cid:3)04(cid:3)09(cid:3)01(cid:3)07(cid:3)08(cid:3)00 the total height range such that when looking across an-
giosperms or gymnosperms, or across plants generally,
360159030201 height has little explanatory power with respect to LMA.
2R (cid:3)00(cid:3)00(cid:3)00(cid:3)00(cid:3)00(cid:3)01 This phenomenon is repeated in several of the relation-
ships we examined and is exemplified in Fig. 4, where we
744151
n 114424 see a decrease in the amount of variance explained by
height for each functional trait and across all traits when
e
bl goingfromhabitattoglobalscales.Thereisthusagreater
ria hthththththt likelihood of observing size-based selection on leaf func-
a gggggg
X-v HeiHeiHeiHeiHeiHei tionaltraitswithinlocalcommunities.Duetothelowsam-
ple sizes within some of these biomes and habitats
an (Table 2 and Table S2), we caution against over-interpre-
d) Y-variable PmassPareaAmassAareaLeafareaLeaflifesp ttparretoniovdnesenoinlfightlahtreegnseeirn,gp.amttoerrens.coSmupbrseehqeunesnivteadnaatlyasessetosfwtohueslde
e Looking at the variance structure also suggests that the
u
n
nti mmmmmm LES traits we examined display consistently low variance,
(co ng spersperspersperspersper with shallow slopes and low R2 values, when compared
Table1 Groupi GymnoGymnoGymnoGymnoGymnoGymno gwriethateprlathnatnhleoigg1h0t.leTafhteraliotgv1a0rivaanrciaenincealilncapsleasntbuhtetihghattoisf
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
8 C.A.Priceet al.
Table2. Ordinaryleast-squaresregressionresultsforthe42bivariaterelationshipsweexaminedwhengroupingspeciesbybiome.Biome
classificationsaregiveninthefirstcolumnfollowedincolumns2–14bythey-variable,x-variable,samplesize(n),coefficientofdetermina-
tion (R2), P-value (with P-values remaining significant following Holm-Bonferroni correction underlined and in bold), slope, upper and
lower95%slopeconfidenceintervals,intercept,interceptlowerandupper95%confidenceinterval,meanYvalueandthemeanXvalue.
P-valuesforthoserelationshipsthatweredifferentthanzeroareshowninbold
Y- X-
Biome variable variable n R2 P Slope LowCI UppCI Intercept LowCI UppCI Y X
mean mean
Temperate LMA Height 207 0(cid:3)162 0 0(cid:3)158 0(cid:3)109 0(cid:3)207 1(cid:3)835 1(cid:3)794 1(cid:3)877 1(cid:3)926 0(cid:3)576
forest
Temperate N Height 118 0(cid:3)107 0 (cid:1)0(cid:3)096 (cid:1)0(cid:3)147 (cid:1)0(cid:3)045 0(cid:3)272 0(cid:3)220 0(cid:3)324 0(cid:3)201 0(cid:3)738
mass
forest
Temperate N Height 118 0(cid:3)048 0(cid:3)017 0(cid:3)052 0(cid:3)010 0(cid:3)094 0(cid:3)181 0(cid:3)138 0(cid:3)224 0(cid:3)219 0(cid:3)738
area
forest
Temperate P Height 19 0(cid:3)005 0(cid:3)768 0(cid:3)025 (cid:1)0(cid:3)151 0(cid:3)201 (cid:1)1(cid:3)343 (cid:1)1(cid:3)462 (cid:1)1(cid:3)224 (cid:1)1(cid:3)328 0(cid:3)581
mass
forest
Temperate P Height 19 0(cid:3)195 0(cid:3)058 0(cid:3)213 (cid:1)0(cid:3)008 0(cid:3)434 (cid:1)1(cid:3)393 (cid:1)1(cid:3)543 (cid:1)1(cid:3)243 (cid:1)1(cid:3)269 0(cid:3)581
area
forest
Temperate A Height 117 0(cid:3)065 0(cid:3)005 (cid:1)0(cid:3)112 (cid:1)0(cid:3)189 (cid:1)0(cid:3)034 2(cid:3)000 1(cid:3)921 2(cid:3)079 1(cid:3)917 0(cid:3)744
mass
forest
Temperate A Height 117 0(cid:3)021 0(cid:3)115 0(cid:3)038 (cid:1)0(cid:3)010 0(cid:3)086 0(cid:3)901 0(cid:3)852 0(cid:3)949 0(cid:3)929 0(cid:3)744
area
forest
Temperate Leaflife Height 126 0(cid:3)13 0 0(cid:3)210 0(cid:3)113 0(cid:3)306 0(cid:3)871 0(cid:3)772 0(cid:3)970 1(cid:3)032 0(cid:3)770
forest span
Temperate Leafarea Height 205 0(cid:3)018 0(cid:3)054 0(cid:3)152 (cid:1)0(cid:3)003 0(cid:3)307 0(cid:3)920 0(cid:3)787 1(cid:3)053 1(cid:3)011 0(cid:3)598
forest
Tropicalforest LMA Height 19 0(cid:3)007 0(cid:3)727 (cid:1)0(cid:3)053 (cid:1)0(cid:3)366 0(cid:3)261 1(cid:3)853 1(cid:3)500 2(cid:3)205 1(cid:3)795 1(cid:3)101
Tropicalforest N Height 19 0(cid:3)424 0(cid:3)003 (cid:1)0(cid:3)372 (cid:1)0(cid:3)594 (cid:1)0(cid:3)150 0(cid:3)761 0(cid:3)511 1(cid:3)011 0(cid:3)351 1(cid:3)101
mass
Tropicalforest N Height 19 0(cid:3)263 0(cid:3)025 (cid:1)0(cid:3)350 (cid:1)0(cid:3)649 (cid:1)0(cid:3)050 0(cid:3)525 0(cid:3)189 0(cid:3)862 0(cid:3)140 1(cid:3)101
area
Tropicalforest P Height 10 0(cid:3)025 0(cid:3)661 (cid:1)0(cid:3)067 (cid:1)0(cid:3)405 0(cid:3)271 (cid:1)0(cid:3)722 (cid:1)1(cid:3)058 (cid:1)0(cid:3)386 (cid:1)0(cid:3)787 0(cid:3)977
mass
Tropicalforest P Height 10 0(cid:3)466 0(cid:3)03 (cid:1)0(cid:3)425 (cid:1)0(cid:3)795 (cid:1)0(cid:3)054 (cid:1)0(cid:3)648 (cid:1)1(cid:3)017 (cid:1)0(cid:3)280 (cid:1)1(cid:3)063 0(cid:3)977
area
Tropicalforest Leaflife Height 19 0 0(cid:3)944 0(cid:3)013 (cid:1)0(cid:3)372 0(cid:3)398 1(cid:3)032 0(cid:3)599 1(cid:3)464 1(cid:3)046 1(cid:3)101
span
Tropicalforest Leafarea Height 9 0(cid:3)041 0(cid:3)602 0(cid:3)225 (cid:1)0(cid:3)750 1(cid:3)200 1(cid:3)349 0(cid:3)127 2(cid:3)571 1(cid:3)628 1(cid:3)239
Tropicalrain LMA Height 95 0(cid:3)275 0 0(cid:3)239 0(cid:3)159 0(cid:3)319 1(cid:3)621 1(cid:3)528 1(cid:3)715 1(cid:3)887 1(cid:3)115
forest
Tropicalrain N Height 91 0(cid:3)025 0(cid:3)138 (cid:1)0(cid:3)058 (cid:1)0(cid:3)135 0(cid:3)019 0(cid:3)289 0(cid:3)199 0(cid:3)379 0(cid:3)224 1(cid:3)111
mass
forest
Tropicalrain N Height 90 0(cid:3)17 0 0(cid:3)173 0(cid:3)092 0(cid:3)253 (cid:1)0(cid:3)086 (cid:1)0(cid:3)180 0(cid:3)009 0(cid:3)106 1(cid:3)108
area
forest
Tropicalrain P Height 69 0(cid:3)007 0(cid:3)489 (cid:1)0(cid:3)041 (cid:1)0(cid:3)160 0(cid:3)077 (cid:1)0(cid:3)863 (cid:1)1(cid:3)009 (cid:1)0(cid:3)716 (cid:1)0(cid:3)912 1(cid:3)195
mass
forest
Tropicalrain P Height 69 0(cid:3)249 0 0(cid:3)266 0(cid:3)153 0(cid:3)379 (cid:1)1(cid:3)355 (cid:1)1(cid:3)494 (cid:1)1(cid:3)216 (cid:1)1(cid:3)037 1(cid:3)195
area
forest
Tropicalrain A Height 27 0(cid:3)08 0(cid:3)153 (cid:1)0(cid:3)187 (cid:1)0(cid:3)447 0(cid:3)074 2(cid:3)191 1(cid:3)926 2(cid:3)456 2(cid:3)019 0(cid:3)921
mass
forest
Tropicalrain A Height 26 0(cid:3)04 0(cid:3)327 0(cid:3)108 (cid:1)0(cid:3)115 0(cid:3)330 0(cid:3)856 0(cid:3)635 1(cid:3)078 0(cid:3)954 0(cid:3)903
area
forest
Tropicalrain Leaflife Height 27 0(cid:3)032 0(cid:3)375 0(cid:3)184 (cid:1)0(cid:3)236 0(cid:3)604 0(cid:3)862 0(cid:3)435 1(cid:3)289 1(cid:3)032 0(cid:3)921
forest span
Tropicalrain Leafarea Height 83 0(cid:3)152 0 (cid:1)0(cid:3)479 (cid:1)0(cid:3)729 (cid:1)0(cid:3)228 2(cid:3)277 1(cid:3)979 2(cid:3)575 1(cid:3)732 1(cid:3)139
forest
Boreal LMA Height 51 0(cid:3)001 0(cid:3)874 0(cid:3)006 (cid:1)0(cid:3)073 0(cid:3)086 2(cid:3)043 1(cid:3)972 2(cid:3)114 2(cid:3)040 (cid:1)0(cid:3)531
Boreal N Height 51 0(cid:3)004 0(cid:3)657 (cid:1)0(cid:3)016 (cid:1)0(cid:3)087 0(cid:3)056 0(cid:3)267 0(cid:3)205 0(cid:3)329 0(cid:3)275 (cid:1)0(cid:3)507
mass
Boreal N Height 50 0(cid:3)001 0(cid:3)795 0(cid:3)011 (cid:1)0(cid:3)072 0(cid:3)094 0(cid:3)301 0(cid:3)228 0(cid:3)374 0(cid:3)295 (cid:1)0(cid:3)511
area
Boreal P Height 8 0(cid:3)433 0(cid:3)076 0(cid:3)212 (cid:1)0(cid:3)030 0(cid:3)455 (cid:1)0(cid:3)684 (cid:1)0(cid:3)879 (cid:1)0(cid:3)488 (cid:1)0(cid:3)840 (cid:1)0(cid:3)734
mass
Boreal P Height 8 0(cid:3)433 0(cid:3)076 0(cid:3)261 (cid:1)0(cid:3)037 0(cid:3)560 (cid:1)0(cid:3)483 (cid:1)0(cid:3)724 (cid:1)0(cid:3)242 (cid:1)0(cid:3)675 (cid:1)0(cid:3)734
area
Boreal A Height 19 0(cid:3)065 0(cid:3)293 0(cid:3)152 (cid:1)0(cid:3)144 0(cid:3)448 2(cid:3)084 1(cid:3)865 2(cid:3)302 1(cid:3)990 (cid:1)0(cid:3)615
mass
Boreal A Height 19 0(cid:3)031 0(cid:3)473 0(cid:3)050 (cid:1)0(cid:3)094 0(cid:3)194 1(cid:3)060 0(cid:3)954 1(cid:3)166 1(cid:3)029 (cid:1)0(cid:3)615
area
Boreal Leaflife Height 53 0(cid:3)02 0(cid:3)307 0(cid:3)087 (cid:1)0(cid:3)082 0(cid:3)255 0(cid:3)804 0(cid:3)655 0(cid:3)953 0(cid:3)758 (cid:1)0(cid:3)530
span
Woodland LMA Height 151 0(cid:3)003 0(cid:3)534 (cid:1)0(cid:3)024 (cid:1)0(cid:3)099 0(cid:3)052 2(cid:3)108 2(cid:3)046 2(cid:3)169 2(cid:3)093 0(cid:3)622
Woodland N Height 145 0(cid:3)023 0(cid:3)066 0(cid:3)051 (cid:1)0(cid:3)004 0(cid:3)105 0(cid:3)215 0(cid:3)171 0(cid:3)260 0(cid:3)247 0(cid:3)629
mass
Woodland N Height 145 0(cid:3)004 0(cid:3)431 0(cid:3)023 (cid:1)0(cid:3)035 0(cid:3)081 0(cid:3)315 0(cid:3)267 0(cid:3)362 0(cid:3)329 0(cid:3)629
area
Woodland P Height 136 0(cid:3)032 0(cid:3)036 0(cid:3)100 0(cid:3)006 0(cid:3)194 (cid:1)1(cid:3)048 (cid:1)1(cid:3)125 (cid:1)0(cid:3)970 (cid:1)0(cid:3)984 0(cid:3)635
mass
Woodland P Height 136 0(cid:3)043 0(cid:3)016 0(cid:3)093 0(cid:3)018 0(cid:3)168 (cid:1)0(cid:3)979 (cid:1)1(cid:3)041 (cid:1)0(cid:3)916 (cid:1)0(cid:3)920 0(cid:3)635
area
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
Areleaftraits‘invariant’withplantsize? 9
Table2 (continued)
Y- X-
Biome variable variable n R2 P Slope LowCI UppCI Intercept LowCI UppCI Y X
mean mean
Woodland A Height 84 0(cid:3)023 0(cid:3)17 (cid:1)0(cid:3)111 (cid:1)0(cid:3)269 0(cid:3)048 1(cid:3)868 1(cid:3)772 1(cid:3)964 1(cid:3)814 0(cid:3)485
mass
Woodland A Height 84 0(cid:3)015 0(cid:3)264 0(cid:3)053 (cid:1)0(cid:3)041 0(cid:3)146 1(cid:3)023 0(cid:3)966 1(cid:3)079 1(cid:3)048 0(cid:3)485
area
Woodland Leaflife Height 86 0(cid:3)038 0(cid:3)072 0(cid:3)168 (cid:1)0(cid:3)015 0(cid:3)351 1(cid:3)069 0(cid:3)958 1(cid:3)179 1(cid:3)151 0(cid:3)487
span
Woodland Leafarea Height 148 0(cid:3)351 0 0(cid:3)988 0(cid:3)768 1(cid:3)208 (cid:1)0(cid:3)194 (cid:1)0(cid:3)373 (cid:1)0(cid:3)015 0(cid:3)422 0(cid:3)623
Table3. Observedvarianceforeachoftheeightleaffunctionaltraits,leafsizeandthesquarerootofleafsize,andplantheightforall
speciestogether(1strow),woodyspecies(3rdrow),herbaceousspecies(5throw),angiosperms(7throw),gymnosperms(9throw),atglo-
balscale(11throw),biomescale(13throw)andhabitatscale(15throw).Evenrowscontaintheratioofthevarianceinheighttothevari-
ance in each trait. For example, in row 2, column 1, we see that the ratio of the variance in height to the variance in LMA across all
speciesis6(cid:3)561,andthus,thereisconsiderablymorevarianceinheightthaninLMA.Notethatthevarianceinheightisgreaterthanthe
variance in all functional traits examined save leaf size or the square root of leaf size, for some groupings. The last row represents the
numberofobservationsforeachtraitthatfallwithintwostandarddeviationsoftheglobalmean.Notethatrows1:2and11:12areidenti-
cal,with11:12repeatedsimplytomakeiteasiertocomparetotheglobal,biomeandhabitatlevelvariances
Log Log Log Log Log Log Log Log Log Log sqrt Log
10 10
LMA LL N N P P A A leafsize (leafsize) height
mass area mass area mass area
Varianceallplants 0(cid:3)073 0(cid:3)168 0(cid:3)045 0(cid:3)048 0(cid:3)074 0(cid:3)071 0(cid:3)112 0(cid:3)042 0(cid:3)746 0(cid:3)094 0(cid:3)479
Heightvar/traitvar 6(cid:3)561 2(cid:3)849 10(cid:3)591 10(cid:3)036 6(cid:3)447 6(cid:3)711 4(cid:3)270 11(cid:3)363 0(cid:3)642 5(cid:3)084 NA
Variancewoody 0(cid:3)073 0(cid:3)153 0(cid:3)044 0(cid:3)047 0(cid:3)075 0(cid:3)071 0(cid:3)110 0(cid:3)043 0(cid:3)736 0(cid:3)096 0(cid:3)363
Heightvar/traitvar 4(cid:3)978 2(cid:3)369 8(cid:3)312 7(cid:3)783 4(cid:3)839 5(cid:3)126 3(cid:3)300 8(cid:3)526 0(cid:3)492 3(cid:3)778 NA
Varianceherbaceous 0(cid:3)064 0(cid:3)067 0(cid:3)051 0(cid:3)060 0(cid:3)004 0(cid:3)037 0(cid:3)066 0(cid:3)039 0(cid:3)383 0(cid:3)041 0(cid:3)207
Heightvar/traitvar 3(cid:3)245 3(cid:3)071 4(cid:3)081 3(cid:3)429 51(cid:3)753 5(cid:3)565 3(cid:3)132 5(cid:3)313 0(cid:3)539 5(cid:3)057 NA
Varianceangiosperm 0(cid:3)051 0(cid:3)134 0(cid:3)032 0(cid:3)036 0(cid:3)072 0(cid:3)056 0(cid:3)068 0(cid:3)032 0(cid:3)481 0(cid:3)705 0(cid:3)47
Heightvar/traitvar 9(cid:3)224 3(cid:3)514 14(cid:3)53 13(cid:3)16 6(cid:3)548 8(cid:3)458 6(cid:3)916 14(cid:3)69 0(cid:3)978 0(cid:3)667 NA
Variancegymnosperm 0(cid:3)02 0(cid:3)043 0(cid:3)005 0(cid:3)012 0(cid:3)018 0(cid:3)003 0(cid:3)022 0(cid:3)008 0(cid:3)124 0(cid:3)037 0(cid:3)057
Heightvar/traitvar 2(cid:3)901 1(cid:3)319 11(cid:3)02 4(cid:3)693 3(cid:3)103 16(cid:3)52 2(cid:3)546 6(cid:3)887 0(cid:3)456 1(cid:3)545 NA
Varianceglobal 0(cid:3)073 0(cid:3)168 0(cid:3)045 0(cid:3)048 0(cid:3)074 0(cid:3)071 0(cid:3)112 0(cid:3)042 0(cid:3)746 0(cid:3)094 0(cid:3)479
Heightvar/traitvar 6(cid:3)561 2(cid:3)849 10(cid:3)591 10(cid:3)036 6(cid:3)447 6(cid:3)711 4(cid:3)270 11(cid:3)363 0(cid:3)642 5(cid:3)084 NA
Meanbiomevar 0(cid:3)038 0(cid:3)136 0(cid:3)029 0(cid:3)027 0(cid:3)03 0(cid:3)031 0(cid:3)08 0(cid:3)033 0(cid:3)375 0(cid:3)261 0(cid:3)24
Heightvar/traitvar 6(cid:3)348 1(cid:3)763 8(cid:3)296 8(cid:3)788 8(cid:3)038 7(cid:3)683 3(cid:3)006 7(cid:3)357 0(cid:3)639 0(cid:3)918 NA
Meanhabitatvar 0(cid:3)037 0(cid:3)099 0(cid:3)019 0(cid:3)018 0(cid:3)016 0(cid:3)016 0(cid:3)059 0(cid:3)023 0(cid:3)377 0(cid:3)172 0(cid:3)213
Heightvar/traitvar 5(cid:3)806 2(cid:3)163 11(cid:3)19 11(cid:3)9 13(cid:3)51 13(cid:3)56 3(cid:3)599 9(cid:3)306 0(cid:3)565 1(cid:3)238 NA
%Within2SDmean 95(cid:3)29 97(cid:3)13 94(cid:3)57 95(cid:3)05 93(cid:3)11 95(cid:3)36 93(cid:3)25 96(cid:3)44 96(cid:3)17 98(cid:3)09 95(cid:3)57
individual leaf area, regardless of the spatial scale (global, LMA in gymnosperms is consistent with their long life
biome or habitat, Table 3). Seven out of nine of the traits spans, and an increase in structural and/or defence tissue
had greater than 95% of their observations within two likely explains the lower mass-based nutrient concentra-
standard deviations of the mean, and the remaining two tionsandphotosyntheticrates.
had greater than 93% (Table 3). Thus, based on Criteria Alsoconsistentwithpreviousevaluations(Fonsecaet al.
1–4, all LES traits exhibit little variation with plant height 2000; Wright et al. 2007), individual leaf size increased
and may be considered effectively invariant within some modestly with plant height, but the reasons for this trend
modelling frameworks, perhaps most appropriately at are not fully understood. Figure 3 shows that this trend is
globalscalesandwithinwoody/herbaceousorangiosperm/ not apparent in all habitats and is in fact reversed in wet
gymnospermgroupings. habitats such as tropical rain forest, upland pine forest
While there is little dependence of LES traits on plant andmeadowtundra.Theglobaltrendseemsmainlydueto
height within plant functional types or taxonomic group- a large number of small-statured angiosperm species with
ings (angiosperm or gymnosperm), we do see systematic small leaves (Fig. 2c), many of these occurring in the drier
shifts in data that are of interest. For example, six of habitats(Fig. 3c).Smallleaveshavethinnerboundarylay-
the nine traits showed no difference in slopes between ers,whichfacilitateconvectiveheatlossandthushelppre-
angiosperm and gymnosperms, and five of those had a vent overheating (Givnish 1978), and which also increase
significant shift in elevation of the data (Fig. 2, Table 1). stomatal control over transpiration rates (Jarvis &
For a given height, gymnosperms had higher LMA and McNaughton 1986). Heat loss and transpiration are, how-
P , but lower P , N , A and A . The high ever, also influenced by several other factors such as
area mass mass mass area
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology
10 C.A.Priceet al.
(a) 80 (b) 60 (c)60
60
40 40
y y y
c c c
n n n
ue 40 ue ue
q q q
e e e
Fr Fr 20 Fr 20
20
0 0 0
1 1·5 2 2·5 3 0 1 2 3 −2 0 2 4
Log LMA (g m–2) Log leaf lifespan (months) Log leaf area (cm2)
(d)100 (e) 60 (f) 60
80
40 40
cy 60 cy cy
n n n
e e e
u u u
q q q
e 40 e e
Fr Fr 20 Fr 20
20
0 0 0
−1 −0·5 0 0·5 1 −2 −1·5 −1 −0·5 0 0 1 2 3
Log N (%) Log P (%) Log A (nmol g−1 s−1)
mass mass mass
(g)150 (h) 60 (i) 60
100 40 40
y y y
c c c
n n n
e e e
u u u
q q q
e e e
Fr 50 Fr 20 Fr 20
0 0 0
−1 −0·5 0 0·5 1 −2 −1·5 −1 −0·5 0 0 0·5 1 1·5 2
Log N (g m−2) Log P (g m−2) Log A (µmol m2 s−1)
area area area
Fig.1.Panelsa–iarehistogramsofthelog10-transformeddataforeachoftheLEStraitsandleafsize.Theredstarrepresentsthemean
foreachdistribution,andeachshaded,lightgreenrectanglerepresentsplus/minustwostandarddeviationsfromthemean.Thepercentage
ofvaluesthatfallwithintwostandarddeviationsofthemeanforeachplotarereportedinthelastrowofTable3.Notethatalldistribu-
tionsaremodalwhichsatisfiesoursecondproposedcriteriaforevaluatinginvarianttraits.
microclimate, canopy structure and other leaf traits such greater vulnerability to hydraulic disruption due to lower
as their angle, reflectivity, clumping and being lobed or density of secondary veins (Scoffoni et al. 2011). As with
compound, indicating that alternative strategies are possi- all LES traits, leaf size is influenced by opposing effects of
bleinsomeenvironmentsandthattheassociationofsmall environmental factors and by integration among other
leaf size with arid habitats is not absolute. Reducing leaf plant traits (Milla & Reich 2011). In contrast to all invari-
temperature and transpiration is much less important in ant LES traits, the range of variation in leaf size is very
cool and/or moist environments and even less so where large, and environmental influences are strong enough to
such environments are also shaded, as in the understorey cause some global and within-habitat correlations with
ormid-storyofforests,wherethepremiumisonenhanced plant height. Understanding these drivers of leaf size vari-
light capture. Indeed, the global positive correlation ability is clearly an area in need of further inquiry and
betweenleafsize andplant heightisreversedinsuchhabi- synthesis.
tats,suchaswetforests(Fig. 3c).Anadditionalreasonfor The MTE model has been supported by some empirical
thisreversedtrendmaybethegreatersupportandhydrau- studies identifying allometric phenomena in plants that
lic costs of larger leaves (Givnish 1978; Niinemets, Ports- exhibit near ¼ scaling relationships (West, Brown &
muth&Tobias2006;Milla&Reich2007;Niinemetset al. Enquist1999;Enquist2002;Enquist,West&Brown2009;
2007; Niinemets, Portsmuth & Tobias 2007; Niklas et al. West, Enquist & Brown 2009). However, under what con-
2007; Price & Enquist 2007; Price & Weitz 2010) and their ditions ¼ power scaling is observed remains an area of
©2014TheAuthors.FunctionalEcology©2014BritishEcologicalSociety,FunctionalEcology