Trubs, but no trianas: filled and empty regions of angiosperm stem lengthdiametermechanics space

13 Pages·2015·1.16 MB·English

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Botanical Journal of the Linnean Society, 2015, 179, 361–373. With figures
Trubs, but no trianas: filled and empty regions of
angiosperm stem length-diameter-mechanics space
MATISS CASTORENA1, JULIETA A ROSELL2 and MARK E OLSON1*
1Instituto de Biología, Universidad Nacional Autónoma de México, Tercer Circuito s/n de Ciudad
Universitaria, México DF 04510, Mexico
2Departamento de Ecología de la Biodiversidad, Instituto de Ecología, Universidad Nacional
Autónoma de México, Tercer Circuito s/n de Ciudad Universitaria, México DF 04510, Mexico
Received 10 March 2015; revised 19 June 2015; accepted for publication 5 August 2015
Discreteplanthabitcategoriessuchas‘tree’,‘shrub’,and‘liana’beliecontinuousvariationinnature.Tostudythe
evolution of this continuous variation, we gathered data on stem length, diameter and tissue mechanical stiffness
across a highly morphologically diverse highland xerophytic scrub on a lava flow in central Mexico. With stem
allometric and mechanical data from 1216 segments from 50 species, we examined relationships between stem
length–diameter proportions and tissue mechanical stiffness using linear mixed-effects models. Rather than a
series of discrete clouds in stem length–diameter–tissue stiffness space, corresponding to traditional habit
categories, the plants of this xerophytic scrub formed a single continuous one. Within this cloud, self-supporting
plantshadstemsthatbecamepredictablylongerandtissuesthatbecamestifferforagivendiameterincrease,and
therewasnopaucityofintermediatesbetweentreesandshrubs(‘trubs’).Nonself-supportingplantshadasteeper
stem length–diameter slope and their tissues did not increase in stiffness with stem size. The area between self-
and non self-supporting plants was sparsely occupied as stem size increased. We predict that this ‘empty’ space
betweenlianasandtreesisdevelopmentallyaccessiblebutoflowfitness,meaningthatthereshouldbefew‘trianas’
in nature. © 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373.
ADDITIONAL KEYWORDS: adaptation – allometry – angiosperms – biomechanics – liana – mixed-effects
models – plant habits – shrub – tree.
INTRODUCTION 1993, 1994a,b, 1995a,b; Niklas & Buchman, 1994;
Niklas, Cobb & Marler, 2006; Rosell etal., 2012).
Studies covering hundreds of species show that dif-
Even liana stem length–diameter allometry scales
ferent plant habits have largely predictable stem
predictablyacrossspecies,althoughwithmuchlonger
length–diameter allometries. Tree height scales with
stems for a given diameter than in self-supporting
diameter over an ample range of life stages to the 2⁄3 plants(Olsonetal.,2014;Rosell&Olson,2014).Stem
power (McMahon, 1973; Rich etal., 1986; King, 1990,
length–diameter proportions across habits are often
1991, 1996; Farnsworth & Niklas, 1995; O’Brien
regarded as sufficiently predictable that palaeobota-
etal., 1995; Thomas, 1996; Sterck & Bongers, 1998;
nistsusethemtoestimatefossilplantheight(Niklas,
Muller-Landau etal., 2006; Poorter, Bongers &
1994c).Mappingthewaysthatstemlength–diameter
Bongers, 2006; Feldpausch etal., 2011; Olson &
relationships vary across species is useful because it
Rosell, 2013; Olson etal., 2013). The scaling power of
allows studying the ways that natural selection acts
stem length–diameter allometry appears to vary to
on the diversity of stem size and shape.
greater or lesser degrees across other self-supporting
Mapping stem length–diameter relationships can
habits, such as mosses, herbs, palms, pteridophytes,
be seen as part of a long tradition of studying organ-
pachycaul plants, and young or old trees (Niklas,
ismal shape and size, but the simultaneous study of
tissue mechanical properties has lagged behind. The
*Corresponding author. E-mail: [email protected] size-shape tradition, prominent early examples being
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373 361
362 M. CASTORENA ETAL.
works of Cuvier and Dubois in the second half of the succulents with completely parenchymatized (fibre-
19th century (Gayon, 2000), made shape and size the free) xylem (Carlquist, 1966), leaf succulents, and
central aspects for studying organismal form and small to large cacti (Fig.1). This span of anatomical
function(Alberchetal.,1979;Sweet,1980;Bookstein, modes is greater than that occurring across many
1989; Jungers, Falsetti & Wall, 1995; Klingenberg, much larger temperate areas (e.g. Tutin etal., 1993),
2010). However, all else being equal, any change in and this community is important to study as a rela-
organismal shape or size will also change the tivelysmallnaturalareathreatenedbyurbansprawl.
mechanical behaviour of the structure in question Thisdiversityisthereforeidealtomapquantitatively
(Thompson, 1924; McMahon, 1973; Bertram, 1989; how plant habits vary across L-D-E . This mapping
stem
Alfaro, Bolnick & Wainwright, 2004; Rosell etal., allowed us to examine relationships between stem
2012; Niklas, 2013). For example, given a cylinder of length–diameter proportions and tissue mechanics
1cm in diameter and another of 100cm, the thicker and the presence of unoccupied patches of L-D-E
stem
cylinder will be more resistant to bending than the space. For example, Scheffer etal. (2014) claimed to
thinner one, even if they are the same length and have identified an empty space between trees and
have identical mechanical properties of materials. shrubs. They asserted that heights intermediate
Allometryisthereforeideallypairedwithbiomechan- between trees and shrubs (8–10m) are rare, conclud-
ics to study morphological and functional diversity of ingthat‘trubs’areselectedagainstinnature(butsee
organismal structures. McGlone etal., 2015; Qian & Ricklefs, 2015; Scheffer
In woody plants, simultaneous study of allometry etal., 2015). Our data permitted us to examine this
and mechanics is ideal because small variation in issue with additional variables of great functional
combinationsofstemproportionsandtissuemechani- relevance.Ourapproachallowedustotestwhethernot
cal properties can have drastic effects on habit, pro- justtreesandshrubs,butalsoothertraditionalhabit
ducing a wide span from self-supporting trees and categories, have distinctive L-D-E combinations.
stem
shrubs to semi-self-supporting shrubs to non self- Traditional habit categories overlapped consider-
supporting lianas or vines (see Rowe & Speck, 2005; ably in our data. Rather than an area of sparse
Speck & Burgert, 2011). For example, lianas and occupation between trees and shrubs, we found a
vines have long stems for a given diameter with distinct empty space between self- and non self-
relatively low tissue stiffness. Trees and shrubs have supportingplantsatlargestemsizes.Wecommenton
stems that are moderately long for a given diameter thepossiblecausesandsignificanceofthesepatterns.
with relatively high tissue stiffness. Much of the We conclude by showing the capacity of our approach
diversity in plant habit can therefore plausibly be for mapping the limits in the stem morphological
seen as the interplay between stem length (L), stem diversification and indicate methodological avenues
diameter(D),andstemtissueYoung’smodulus(E ; for further research.
stem
we term this interplay hereafter as ‘L-D-E ’).
stem
Young’s modulus describes how resistant a given
MATERIALS AND METHODS
material is to bending; stems made of stiff materials
have high E values, whereas those of flexible ones Our study community, the Reserva Ecológica del
stem
have low values (Vogel, 2003; Gere & Goodno, 2009). Pedregal de San Ángel, is a xerophytic scrub on
Studies of individual species or small groups of highland lava fields at 2000m above sea level in the
species underscore the central importance of these southern part of the Valley of Mexico (19°19′12.68″N,
variables in summarizing plant habit diversity 99°11′26.99″W) with mostly thin, rocky soil, a mean
(Bertram, 1989; Isnard, Speck & Rowe, 2003; Rowe, annual precipitation of 835mm, and a mean annual
Isnard & Speck, 2004; Lahaye etal., 2005; Ménard, temperature of 15.5°C (Castillo-Argüero etal., 2004).
McKey & Rowe, 2009; Rosell etal., 2012), but almost To represent the habit diversity of our study commu-
nothing is known about the general patterns of how nity, we selected 50 species (Supporting Information
stem length, diameter, and tissue mechanics vary in Table S1), with vouchers deposited at Herbario
relation to one another in woody plants generally. Nacional de México (MEXU). Species sampling was
To begin to explore the ways that plant stems vary guided by three criteria. The first was to span all
acrossL-D-E ,weusedallometricandbiomechanical woody plant habits in our community. Maximizing
stem
data from 1216 stem segments from 50 species of habit diversity helped map the extent of L-D-E
stem
floweringplantsfromahabitallydiversecommunityin space occupation in our community and to test
central Mexico. We chose this community because it whether these traits recovered the traditional growth
includes a remarkable combination of plant habits form categories or whether these categories repre-
includingsmalllianas,vines,scramblers,shrubswith sented a continuum in this space. The second was to
low to high wood density, small to large forbs, trees, include the most common species, and the third was
broomstick succulents (Rosell & Olson, 2007), stem to maximize the phylogenetic span of our collections.
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
PLANT HABIT ALLOMETRIC-MECHANICAL SPACE 363
Figure1. See caption on next page.
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
364 M. CASTORENA ETAL.
Figure1. Stemformdiversity,focusingonstemlength,diameter,andmechanicsinthePedregaldeSanÁngel,central
Mexico. A, Buddleja cordata, classed as a tree, has slender, flexible terminal stem tissues, and wide, stiff stem basal
tissues. B, Bouvardia ternifolia, classed as a shrub, has one the of the highest tissue stiffnesses in the community. C,
Peperomia galioides, classed as a forb, has succulent stems, but has similar mechanical behaviour to self-supporting
woody plants. D, Opuntia tomentosa has wider stems and more flexible tissues for a given length as compared to
conventional trees. E, Pittocaulon (∼Senecio) praecox is classed as a shrub, but in contrast to B.ternifolia it has longer,
wider stems, and more flexible tissues. F, Echeveria gibbiflora has stubby and flexible stems in its main body and long,
slender inflorescences. G, Passiflora subpeltata, classed as non self-supporting, has narrower, longer stems, and more
flexibletissuesthananyself-supportingplantinthecommunity.H,Asclepiaslinariawasclassedasshrub.I,Plumbago
pulchella has a scrambler habit with arching non self-supporting branches.
Includingthecommonspeciesgivesasummaryofthe using a tape measure. To measure stem tissue
bulkoftheplantsinagivenarea,presumablyreflect- Young’s modulus (E ), we mechanically tested each
stem
ing the adaptive responses that result in high abun- segment in three-point bending in an Instron 3345
dance in a given environment. Maximizing the testing machine using a 5kN load cell and Series IX
phylogenetic span of a comparative study lends software (Instron Corporation, Canton, Massachu-
support to the idea that the patterns recovered are setts, USA). E is calculated from the initial rate of
stem
general ones. flexural displacement of the segment under loading.
Weclassifiedspeciesintwoways.First,weclassified HighE valuesrepresentstiffstemtissueswhereas
stem
each species as self- vs. non self-supporting (we use low values represent flexible ones. Each tested
the term ‘climber’ interchangeably with non self- segment had a 1:20 diameter-length ratio to avoid
supporting). Non self-supporting stems were those shear (Vincent, 1992; Gere & Goodno, 2009). We
that did not maintain their tips off the ground when measuredE usingthediameterofeachsegmentat
stem
thebaseofthesampledstemwashelderectatground its mid point and the formula for solid cylinders
level.Speciesnotmeetingthiscriterionwereclassified (Niklas, 1992).
as self-supporting. The second classification assigned For all analyses, we log transformed L, D, and
10
each of the self-supporting species to the classes tree, E . We plotted L, D, and E as a three-
stem stem
shrub, forb, and inflorescence following Calderón de dimensional graph (Fig. 2). To examine differences in
Rzedowski & Rzedowski (2005; Supporting Informa- L vs. D scaling between self- and non self-supporting
tion Table S1). When Calderón de Rzedowski & Rze- plants, we fit a linear model predicting L based on D,
dowskilistedhabitasarange,weclassifiedtheplant plus a categorical variable reflecting whether species
in the largest of the listed categories because our were self- or non self-supporting, and an interaction
sampling emphasized the largest plants (e.g. if the term between D and the self-/non self-supporting
range is listed from shrub to tree, we classed the variable.Asignificantinteractiontermindicatedthat
species as tree). We sampled the inflorescences of the self- and non self-supporting habits differed in
Agave salmiana Otto ex Salm-Dyck, Echeveria gibbi- their L vs. D scaling relationship. In our model,
flora DC., and Manfreda scabra (Ortega) McVaugh, segments of the same species were likely to be more
classing them as ‘inflorescences.’ Finally, five self- similar to one another than to segments from other
supportingspecieswerenotassignedahabitcategory species. To take this similarity into account, we
byCalderóndeRzedowski&Rzedowski,soweclassed included a ‘species’ random variable that reflected
these species by following their habit descriptions of species membership of segments in a mixed-effects
similarspeciesofthesamegenera.Accordingly,E.gib- model (Goldstein, 2003; Kutner etal., 2005; Zuur
biflora, Mammillaria magnimamma Haw., Reseda etal., 2009). Our mixed-effects model included D, the
luteola L., Valeriana sorbifolia Kunth, and Zinnia self-/nonself-supportingvariableandtheD·self-/non
peruviana (L.) L. were classed as forbs. self-supporting interaction as fixed terms. The
For each species, we collected on average eight to ‘species’ random variable allowed nesting segments
ten branches from three to four large, healthy indi- within species. We explored two alternative versions
viduals. We selected straight branches that were of our mixed model. In one of these, species were
<5cm in diameter due to the size limitations of our allowed to have random intercepts, i.e. species could
testing device, and then we cut an average of three have different mean L for a given D, but all species
straight segments per branch. We collected a total of had the same mean scaling exponent. In a second
451 branches and 1216 segments (Table1). For each version, species were allowed to have random inter-
segment, we measured the average basal diameter cepts as well as random slopes, i.e. species varied in
(D) using digital calipers and the distance between their L-D scaling exponent. We used log-likelihood
the base of the segment and the tip of the branch (L) ratio tests and theAkaike and Bayesian information
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
PLANT HABIT ALLOMETRIC-MECHANICAL SPACE 365
of criteria to compare the fit of these two alternative
s
ernt models(Zuuretal.,2009).Themodelthatbestfitthe
be
mm 6799451 data was that with random slopes (and thus random
Nuseg 121141062736375 intercepts; Supporting Information Table S2). The
final best-fitting model had the following form:
of L=D+self/non self+D·self/non self+Sr+e, where
beres Sr was the species random effect allowing species to
mci haverandominterceptsandslopes,andeistheerror
Nuspe 505451014194 term(Table2).Wehereafterabbreviatethismodelas
L∼D·self/non self.
m We analyzed in more detail the L vs. D scaling of
u
m 0703005 our self-supporting species by comparing trees,
axi 73457369367384 shrubs, forbs, and inflorescences, according to the
M 12912911125 habit classification of Calderón de Rzedowski &
a)
P Rzedowski (2005). To this end, following the same
M n
ulus( Media 3073264431572357454727872783 mfiditoadmaeelmtefiortdtieanlngdpprertdohciecetdisnuegrlef-ssftuoeprmpLorl∼etinDnggt·hshebalfab/sinteodncaotsneeglfso,trewiemes
d
o
m m expressed as L=D+GF+D·GF+Sr+e, where GF
s u (growth form) was a nominal variable with the levels
Young’ Minim 1.733125422276 tinreet,hsehrmuobd,efolrbb,yorthinrefleordeuscmenmcyeavnadriwabalsesrepwrietshenfoterdb
as the reference category. This model had a non-
m significant D·GF interaction (F =2.00, P=0.11),
u 3,1043
m meaningthattheGFcategoriesdidnotdifferintheir
axi 0082835 L-D scaling exponents, so we refit the model without
M 2254584
8855522 the interaction (Table 3) and then tested whether
intercepts differed significantly. We hereafter abbre-
n
a viate this model as L∼D·+GF. Again, a structure
(cm) Medi 8515880107836067 w(SiuthppaorrtainndgoImnfionrtmeracteiopntaTnadblseloSp2e).perspeciesfitbest
h
ngt m ToexaminerelationshippatternsbetweenEstemand
e u stemL-Dproportions,wecalculatedforeachsegment
l m
Stem Mini 510599511 athleendgitshta–ndciaemferotemrptrhoepobratsioenoifndeeaxch(Ls/eDgm)beyntditvoidtinhge
tip of the stem by its diameter. Given that self- and
m non self-supporting habits represent different combi-
u
m nationsofstemlength–diameterproportionstogether
ry Maxi 0.521.550.520.525.758.084.57 with tissue mechanical properties, L/D provided a
go 1 11 simplevisualizationofdifferentmechanicalstrategies
e
t when plotted against E . We followed the same
ca m) an model fitting procedure satesm for the model exploring
hhabit eter(c Medi 0.740.460.811.430.820.501.07 LE-stDemsbcaalsiendg.oAnccLo/rDdinagnldy,twheefistetlef-d/naonmsoedlefl-spurpepdoircttiinngg
ataforeac Stemdiam Minimum 0.070.100.070.180.120.070.50 hEesu.astpbWempiteo=rcutLaistn/eegDdgos+trphiseciesaclilfem/svnoaodirnneicalrsbteeloalef.st+eeTdsLht/iisnwDhmm·eostedhecleheflr/anntsooitnoceakmlstesshltfoeiff+ffnsoSeerrlsmf+s-
d
with increasing L/D. We hereafter abbreviate this
e
Table1.Descriptiv Habitcategory AllcategoriesNonself-supportingSelf-supportingTreeShrubForbInflorescence Gsmw(mLSi/FgiooutDnddhpieepfic·allaocGatrrtahsFetaniganEnt+otdgsrtoSeeimmeIxrLnsp∼+,f/iloLnoeDrr.wt/mee·DidrtaTGcht·ehEFispoisestnttelhmfa/eTminvnnadsootbf.ednoslrLerelaosml/epScDlte2fih.o)Epas.AnecsdFgtaremailsniib=npn(aoFge,lLtcl3ahy/,ai1,e0scD1srtw6arofi+=uestscG0nfitb.uoFot9eunrs1+aert-,
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
366 M. CASTORENA ETAL.
Figure2. Twoviewsofthestemlength-diameter-mechanicsspaceofthehighlandxerophyticscrubstudiedhere.A,This
viewshowsthediversityinstemlength–diameterproportionsacrossthecommunity.Thereisaclearpositiverelationship
betweenstemlengthanddiameteracrossself-supportingplants.Nonself-supportingplantshavemuchlongerstemsfor
agivendiameterthanself-supportingplants.B,Thisviewshowsthewidespanofstemtissuemechanicalpropertiesand
theirinterplaywithstemlength–diameterrelations.Inself-supportingplants,longer,thickerstemshavestiffertissues.
Mammillaria magnimamma occupies the corner corresponding to short, thick stems with low tissue stiffnesses. Non
self-supporting plants have long, slender stems with low tissue stiffness. Black arrow in both views shows the empty
region between large self- and non self-supporting stems (see Discussion section).
P=0.44)andanon-significantGFterm(F =2.11, Savolainen & Chase (2001), removing singleton
3,1016
P=0.10), meaning that the GF categories did not branches with the ‘cleanphy’ command. We then
differ in their scaling exponents and intercepts. tested for the presence of significant phylogenetic
That is, traditional habit categories did not differ signal in the residuals (Revell, 2010) of our three
in their E vs. L/D scaling relationships. We base models using a randomization test based on phyloge-
stem
our discussion of E ∼L/D scaling on the model netically independent contrasts and the descriptive
stem
E ∼L/D·self/non self. statisticsλ(Pagel,1999)andK(Blomberg,Garland&
stem
We calculated the coefficient of determination (R2) Ives, 2003). All analyses were performed in R (R
for our final mixed models using the method of Development Core Team, 2013) using the packages
Nakagawa&Schielzeth(2013;Table2).Theirmethod ‘rgl’ (Adler & Murdoch, 2013), ‘nlme’ (Pinheiro etal.,
usesamarginalcoefficientofdetermination(R2 )that 2013), ‘MuMIn’(Barton, 2013), ‘ape’(Paradis, Claude
m
represents the variance explained by the fixed com- & Strimmer, 2004), and ‘phytools’ (Revell, 2012).
ponent and a conditional coefficient of determination
(R2) that represents the variance explained by the
c RESULTS
fixed and the random component.
Additionally, we tested for phylogenetic signal in The ranges of L, D, and E for each habit category
stem
ourdata.Todoso,webuiltacommunityphylogenetic are given in Table 1 and for each species in Support-
tree using the APG backbone (APG III, 2009). We ing Information Table S1.Athree dimensional graph
then assigned branch lengths using the ‘bladj’ of L-D-E variation (Fig. 2) showed that habit cat-
stem
command of Phylocom v. 4.2 (Webb, Ackerly & egories formed a single continuum with two distinc-
Kembel, 2008) and divergence times of Wikström, tive trends. First, self-supporting stems, consisting of
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
PLANT HABIT ALLOMETRIC-MECHANICAL SPACE 367
Table 2. Linear fit of the fixed components of L∼D· trees, shrubs, forbs, and inflorescences, clearly had a
self/non self and E ∼L/D·self/non self models lower slope and L-D intercept as compared to non
stem
self-supportingones(Fig.2A).Second,self-supporting
L∼D·self/ Estem∼L/D· stems tended to lie in high Estem space, especially
non self self/non self largerstems,whereasnonself-supportingstemstend
to fall in low E space (Fig. 2B). These two trends
stem
n 1258 1216
were evident in the two mixed models: L∼D·self/
R2 0.58 0.17
m non self and E ∼L/D·self/non self (Fig. 3A and
R2 0.94 0.81 stem
c Fig. 4, respectively).
Equality of slopes F =9.32, F =11.40,
1,1205 1,1163 Non self-supporting plants tended to have longer
test P<0.005 P<0.001
stems for a given diameter than self-supporting
Non self-supporting
plants, with stems becoming markedly longer as
Intercept 2.76(2.42,3.11) 3.38(2.42,4.35)
diameter increased (Fig. 3A). Non self-supporting
Slope 1.72(1.41,2.04) −0.05(−0.47,0.37)
plants had a mean L-D scaling slope of 1.72 and
Self-supporting
self-supporting plants of 1.20. These slopes differed
Intercept 1.96(1.62,2.30) 1.93(0.91,2.95)
significantly as indicated by their mutually exclusive
Slope 1.20(0.86,1.54) 0.74(0.30,1.18)
confidence intervals (Table 2). Across GF categories,
Notes:RandomeffectsareshowninTableS3.Equalityof there were no significant differences in scaling expo-
slopes test determined whether interaction terms of the nents (common slope of 1.23), but we observed a
models were significant. Values in parentheses are 95% varying degree of overlap in the confidence intervals
confidence intervals. Abbreviations: n, sample size; R2, of intercepts (Table 3). Shrubs, trees, and forbs had
c
conditional determination coefficient; R2 , marginal deter- similar intercepts (ranging from 1.87 to 2.10). In
m
mination coefficient. contrast, inflorescences had the lowest intercept
(1.38)withrelativelylittleoverlapinconfidenceinter-
val with those of the other growth forms (Fig. 3B).
Self- and non self-supporting species had different
E vs. L/D scaling relationships (Fig. 4). In self-
Table 3. Linear fit of the fixed components of L∼D+GF stem
supporting plants, E tended to increase with
model stem
higher L/D, i.e. stem tissues tended to be stiffer
L∼D+GF inlargerstems(slope=0.74).Instrongcontrast,Estem
did not vary in non self-supporting species with L/D
n 1096 (slope did not differ significantly from zero; Table 2).
R2 0.65 Therefore,thenonself-supportingplantsrepresented
m
R2 0.95 a different mechanical-allometric organization as
c
Equality of slopes test F =2.00, P=0.11 compared to self-supporting plants.
3,1043
Equality of intercepts test F3,1043=5.21, P<0.005 Per-species random slopes and intercepts for our
Tree three models are given in Supporting Information
Intercept 2.03 (1.79, 2.27) Table S3. All models fitted the data well, with
Slope 1.23 (1.11, 1.35) R2 =0.94 for L∼D·self/non self, R2 =0.96 for
c c
Shrub L∼D+GF, and R2 =0.81 for E ∼L/D·self/non
c stem
Intercept 1.87 (1.65, 2.09)
self. Phylogenetic signal was not significant in the
Slope 1.23 (1.11, 1.35)
residuals of L∼D·self/non self as indicated by the
Forb
randomization test based on phylogenetic independ-
Intercept 2.10 (1.94, 2.26)
ent contrasts (P=0.862). This lack of signal was
Slope 1.23 (1.11, 1.35)
congruent with the small values of K (=0.269) and λ
Inflorescence
(=0.137).ThesameappliedforL∼D+GF(P=0.965)
Intercept 1.38 (0.97, 1.79)
whereK=0.236andλ=0.00007andforE ∼L/D·
Slope 1.23 (1.11, 1.35) stem
self/non self (P=0.619) where K=0.339 and
λ=0.00007.
Random effects are shown in Table S3. Equality of slopes
test determined whether interaction term of the model
was significant. Because this interaction was not signifi- DISCUSSION
cant, we compared the intercepts across GF categories
usingtheequalityofinterceptstest.Valuesinparentheses For the most part, traditional plant habit categories
are 95% confidence intervals. Abbreviations: n, sample overlapped considerably in our data. This overlap
size; R2, conditional determination coefficient; R2 , mar- means that it is possible to move between any two
c m
ginal determination coefficient. points via a series of intermediate forms. Within this
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
368 M. CASTORENA ETAL.
Figure 3. Self-/non self-supporting and traditional habit categories in L vs. D mixed models.A, Stem length predicted
bystemdiameterbetweenself-andnonself-supportingplants,showingthatnonself-supportingplantshadlongerstems
for a given diameter than self-supporting plants. This figure corresponds to the L∼D·self/non self model. Dashed red
lines represent non self-supporting species and solid black lines represent self-supporting species. B, Stem length
predictedbystemdiameterbetweentree,shrub,forb,andinflorescence,showingthathabitsdidnotdifferintheirscaling
exponents,butdiddifferintheirintercepts.Forbshadthelongeststemsforagivendiameterfollowedbytrees,shrubs,
and inflorescences. This figure corresponds to the L∼D+GF model. Solid green lines represent forbs and dashed blue
lines represent shrubs, followed by orange lines representing inflorescences and then by brown lines representing trees.
InAandB,thicklinesrepresentthefixedcomponentofthemodel,andthinlinesrepresentspecieswithrandomslopes
andintercepts.Figureaxesgivenon-transformedvalueswhereasmodellinesarelog transformed.Modelcoefficientsare
10
presented in Tables 2 and 3.
continuous cloud, our data seemed to indicate areas supporting region were decumbent and prostrate
that were more densely occupied than others, with plants, with stiffer tissues and shorter stems for a
some areas that corresponded to plausible morpholo- given diameter than tendril and twining climbers.
gies being apparently empty in our community. The self-supporting region included trees, shrubs,
forbs, and inflorescences, with stiffer tissues and
shorter stems for a given diameter compared to non
CONTINUOUS VS. CATEGORICAL DESCRIPTIONS OF self-supporting plants. The lower extreme of the self-
PLANT HABIT DIVERSITY supporting region was made up of succulent species
The different habit categories did not form distinct that would be classified as pachycaul using the crite-
clouds, but instead the entire range of stem forms riaofNiklasetal.(2006),thoughtheywereclassedby
formed a single continuous cloud, albeit an irregular Calderón de Rzedowski & Rzedowski (2005) as forbs.
one. This continuous cloud ranged from a non self- These plants had flexible tissues and short stems for
supporting region, made up of climbers and decum- a given diameter (see Mammillaria magnimamma
bent plants, to a self-supporting region, made up of highlighted in Fig. 2). In summary, the plants of our
a wide diversity of habits, including trees, shrubs, xerophytic community ranged from long-stemmed
forbs, pachycaul species, and even inflorescences (see climbers, through conventional trees and shrubs, to
Calderón de Rzedowski & Rzedowski, 2005; Niklas squatpachycaulspeciesinasinglegradedcontinuum
etal., 2006). The non self-supporting region included, across L-D-E space.
stem
at its farthest extreme from the self-supporting In this continuum, the categories that overlapped
region,climbingplantswithflexibletissues(lowE ) most conspicuously were traditional self-supporting
stem
and markedly long stems for a given diameter. ones.Thesetraditionalcategoriesdidnotdifferintheir
The non self-supporting plants closest to the self- E vs. L/D scaling relationships (see model fitting
stem
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
PLANT HABIT ALLOMETRIC-MECHANICAL SPACE 369
tipletrunks,smallindividualswithsingleormultiple
trunks all apparently form a single biological con-
tinuum, in which no relevant breakpoints separate
trees from shrubs or forbs.
Instead, our approach expressing L, D, and E as
stem
a continuum offers a more biologically real and ana-
lytically powerful means of describing plant habit
diversity. Our analyses showed that stem length,
diameter, and tissue mechanical properties are inter-
related in ways that are predictable and highly sig-
nificant biologically. For example, the E ∼L/D·
stem
self/non self model highlighted the tendency for self-
supporting plants with low E to have wide stem
stem
diameters for a given length. This tendency reached
an extreme in pachycaul species (Niklas etal., 2006),
which have minimally stiff stem tissue and maxi-
mally thick stems for their diameters. We showed
that across the continuum of self-supporting plants,
as E becomes stiffer, stems become predictably
stem
longer for a given diameter (see Rosell etal., 2012).
Replacing arbitrary habit categories for the continu-
Figure4. Self-/nonself-supportinginEstemvs.L/Dmixed ous variables L, D, and Estem thus gives access to
models. Stem Young’s modulus increased with stem pro- quantification of trait relationships of central evolu-
portions in self-supporting plants. In contrast, there was
tionary importance. The relationship between organ
notendencyforYoung’smodulustoincreasewithincreas-
size, proportions, and tissue mechanical properties
ing size in non self-supporting plants. This figure corre-
that we documented here is essential not just
spondstotheE ∼L/D·self/nonselfmodel.Dashedred
stem for the study of plant morphological evolution, but
linesrepresentnonself-supportingspeciesandsolidblack
of morphological evolution in general (Rosell etal.,
lines represent self-supporting species. Thick lines repre-
2012).
sent the fixed component of the model, and thin lines
Ourdataalsoprovideameansofaddressingrecent
represent species, with random slopes and intercepts.
debate regarding the lack of ‘trubs’in nature. ‘Trubs’
Figure axes give non-transformed values whereas model
are intermediate in height between trees and shrubs,
lines are log transformed. Model coefficients are pre-
10
in the 8–10m range or so, and some authors assert
sented in Table 2.
that they are rare in nature (Scheffer etal., 2014,
2015; McGlone etal., 2015; Qian & Ricklefs, 2015).
procedure in Materials and Methods). This extensive Our data, which focused on the functionally crucial
overlapmeansthatallofourself-supportingplantsfell relationship between allometry and mechanics, did
inthesamegeneralL-D-E space.Inotherwords,we not reveal any difference between terminal branches
stem
foundnosalientbiologicaldistinctionsbetweentrees, of trees and shrubs (Bertram, 1989). We therefore
shrubs,forbs,andinflorescencesintheircombinations foundnoreasontosuspectthatnaturalselectionacts
ofstemproportionsandtissuemechanicalstiffness.All against self-supporting plants of intermediate size.
this means that, although plant habit categories may We did, however, find evidence for a marked distinc-
be appropriate for rapid communication in floras or tion between self- and non self-supporting plants as
forestry,nobreakpointsseparatedtheself-supporting plants increased in size.
categoriesinourcommunity.Consequently,oneques-
tion is whether L, D, and E are appropiate for
stem
recovering biological distinctions across traditional THE SELF-/NON SELF-GAP: NO TRIANAS
planthabits(see,e.g.,Küchler,1988,orGschwantner Our results identified a distinct lack of intermediate
etal., 2009). In traditional classifications, trees are stem L-D relationships between self- and non self-
often defined as woody plants with single stems little supportingplantsatlongerstemsizes(seealsoRosell
branchedfromthebasethatare>10cmindiameterat & Olson, 2014). When predicting L by D and the
breast height. This definition makes a great deal of self-/non self- categorical variable, we found signifi-
senseforforesters,whowishtoknowifthereiswood cantly different slopes between self- and non self-
to be harvested at any given location. However, it supporting plants. At small sizes, self- and non
makes little sense in allometric-biomechanical terms, self-supporting stem proportions were similar, but
given that individuals with large single trunks, mul- with increasing size, L-D proportions diverged.
© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373
370 M. CASTORENA ETAL.
Narrow climbers were not much longer than their approachandforillustratingthebiologicalinferences
self-supporting counterparts, but thick climbers were that it can facilitate.
considerably longer than self-supporting stems of
similar diameters. Bearing out the distinctness of
self- vs. non self-supporting plants, their slope confi- CONCLUSIONS
dence intervals were different. Self- vs. non self-
Categoriessuchas‘shrub’or‘forb’serveasconvenient
distinctiveness was underscored by the E ∼L/D·
stem terms for rapid communication, but they often artifi-
self/non self model. This model suggested that self-
cially divide the continuous variation in nature.
and non self-supporting plants have markedly differ-
We show that much of the continuous functional
ent stem proportion-tissue mechanics combinations.
diversity in plant stem morphology can be expressed
E increased predictably with increasing stem pro-
stem by a simple stem length–diameter–tissue mechanics
portions in our self-supporting species, but remained
approach. The use of continuous variables avoids the
constant with size increase in non self-supporting
lossofinformationthatcategorizationcauses(Roth&
species. This means that, although our community
Mercer, 2000) and is biologically more accurate
L-D-E space was strictly continuous, the self-/non
stem because rather than shoehorning all species, even
self-categorizationdoesappeartoidentifybiologically
intermediate ones, into one category or another, their
distinct length–diameter–mechanics combinations.
attributes are simply depicted based on their L-D-
Our results imply that, at large sizes, selection
E values. Accordingly, our approach allowed us to
favours plants being either strictly self-supporting stem
identify an overlap between trees, shrubs, forbs, and
or non self-supporting. This either-or condition is
inflorescences in L-D-E space, not surprisingly
manifest in the empty space between self- and non stem
giventheirfunctionalsimilarity.Wewerealsoableto
self-supporting plants. Potentially explaining this
highlight a notably sparsely occupied area between
empty space is a scenario in which, at least at large
self- and non self-supporting plants, especially at
sizes, non self-supporting plants that ‘over-invest’ in
largersizes.Basedonourresults,wepredictthatthis
support tissue are selected against in favour of those
area is developmentally accessible, but that the vari-
with maximally long stems for a given diameter with
ants corresponding to it will have low fitness relative
maximally flexible tissues (see also Niklas, 1994b).
to either self-supporting plants of similar stem diam-
Similarly, self-supporting plants with stiff tissues but
eters or to maximally long climbers of similar diam-
overlyslenderstemsareprobablyvulnerabletobuck-
eters. Our approach therefore seems to offer a
lingandselectedagainst(Niklas,1994b).Ittherefore
promising means of studying plant habit diversity
seems likely that stems corresponding to the ‘empty’
with a small set of continuous variables within and
space in our data are developmentally possible but
between communities, and a useful tool for generat-
would have lower fitness than either conventionally
ing testable predictions regarding plant adaptation.
self-supportingormaximallylongnonself-supporting
morphologies (Olson, 2012). In other words, we found
plenty of ‘trubs’, but we found no ‘trianas’, interme-
diates between trees and lianas. ACKNOWLEDGEMENTS
This work was supported by Consejo Nacional de
Ciencia y Tecnología (132404 and 237061) and Pro-
SOME METHODOLOGICAL CONSIDERATIONS
grama deApoyo a Proyectos de Investigación e Inno-
Although our approach is a significant advance over
vación Tecnológica (UNAM, grant IA201415). We
traditional habit categories, as implemented it had
thank Antonio Lot-Helgueras for kind permission to
limitations to be overcome in subsequent studies.
work in the Reserva Ecológica del Pedregal de San
Although stems of all sizes and proportions could be
Ángel; Axel F. Maldonado-Romo for the use of his
includedinourapproach,wewerelimitedtoterminal
photographs for Figure 1; RebecaAguirre-Hernández
stems because of the size limitations of our mechani-
for statistical advice; Roselia Garduño-Torres for
cal testing procedure, which used whole stem seg-
assistance in the design of figures, and Leonardo O.
ments. As a result, the L-D-E values did not
stem Alvarado-Cárdenas for kind assistance.
represent the true extremes of length, diameter, and
likelyE whichwouldbeexpectedtoberepresented
stem
by main trunks. Another limitation of our approach
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© 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179, 361–373