Abstract Cephalocereus columna-trajani is a
giant columnar cactus endemic of the Tehuacan-
Cuicatlan Valley in Central Mexico. Stem tilting
and northward pseudocephalium azimuth in
C. columna-trajani have functional advantages in
terms of interception of direct solar radiation at
the northernmost portions of its range. Since the
success of both characters strongly depends on the
apparent position of the sun during the growing
season, in this paper we test the hypothesis that
the occurrence of such columnar morphology is
restricted geographically and imposes mechanical
restrictions that limit column height. Following a
latitudinal gradient along the Tehuacan-Cuicatlan
Valley, we selected five populations, recorded
tilting angle and pseudocephalium azimuth, and
carried out allometric and biomechanical analyses
of height–diameter relationships. Northern popu-
lations showed higher tilting angles. Pseudoceph-
alium azimuth significantly differed among
populations, and pseudocephalium orientation
was consistently North-Northwestern. Stem
allometry showed that the stems of the southern
populations increased in height at a far greater
rate with respect to diameter than the northern
populations. The southernmost population
showed the lowest safety factor. These results
support the hypothesis that stem tilting in
C. columna-trajani is functionally advantageous in
a restricted geographical range, and imposes
mechanical restrictions to column height.
Keywords Allometric scaling exponents ÆBiomechanics Æ Columnar cactus Æ Safety factor ÆTehuacan-Cuicatlan Valley
Introduction
The Cactaceae is a very diverse plant family that
displays a great variety of forms and sizes along
its geographical range in its native America
(Altesor and Ezcurra 2003). This diversity rep-
resents a notable catalog of morphological,
physiological, and ecological solutions to drought
and temperature extremes (Gibson and Nobel
1986; Nobel 1988; Nobel and Loik 1999). Many
physiological attributes such as the photosyn-
thetic pathway (i.e. Crassulacean acid metabo-
lism) or water use efficiency, and morphological
traits such as stem succulence, ribs, spines and
apical pubescence have been considered as
adaptations that allowed cacti to inhabit almost
all the arid and semi-arid environments (Gibson
P. L. Valverde (&) Æ F. Vite ÆM. A. Perez-Hernandez ÆJose Alejandro Zavala-HurtadoDepartamento de Biologıa, Universidad AutonomaMetropolitana-Iztapalapa, Apartado Postal 55-535,Mexico 09340 Distrito Federal, Mexicoe-mail: [email protected]
Plant Ecol (2007) 188:17–27
DOI 10.1007/s11258-006-9144-1
123
ORIGINAL PAPER
Stem tilting, pseudocephalium orientation, and stemallometry in Cephalocereus columna-trajani along a shortlatitudinal gradient
Pedro Luis Valverde Æ Fernando Vite ÆMarco Aurelio Perez-Hernandez ÆJose Alejandro Zavala-Hurtado
Received: 16 December 2005 / Accepted: 28 March 2006 / Published online: 21 April 2006� Springer Science+Business Media B. V. 2006
and Nobel 1986; Nobel 1988; Nobel and Loik
1999; Altesor and Ezcurra 2003). Although such
variation among cacti species has been matter of
several studies (e.g. Yeaton and Cody 1979;
Nobel 1978, 1980, 1981, 1982, 1988; Gibson and
Nobel 1986), the occurrence of variation among
populations along a species geographic range has
been poorly examined, particularly in ecologically
relevant traits (Niering et al. 1963; Felger and
Lowe 1967; Ehleringer et al. 1980; Nobel 1980,
1981). In spite of the recognition that intraspecific
variation is related to differences in biotic and
abiotic factors (Briggs and Walters 1969; Endler
1977; Linhart and Grant 1996), there are few
studies on cacti dealing with the analysis of trait
differences that could reflect adjustment to
important environmental factors (Ehleringer
et al. 1980; Nobel 1980, 1981).
Cephalocereus columna-trajani (Karwinski ex
Pfeiffer) Schumann is a giant columnar cactus
endemic of the Tehuacan-Cuicatlan Valley in
Central Mexico (Bravo-Hollis 1978; Fig. 1).
C. columna-trajani is one of the only two giant
columnar species in the Tehuacan-Cuicatlan
Valley that do not usually branch (Zavala-
Hurtado et al. 1998). The maximal height in this
species varies from 10 to 16 m. At north of its
distribution, a notable feature of C. columna-tra-
jani is the curved tilting of the upper part of the
stem, which shows a consistent north-northwest
orientation (Zavala-Hurtado et al. 1998). In the
concave side of the curved stem, which also is
facing approximately north, a hairy non-photo-
synthetic structure, called pseudocephalium
(Gibson and Nobel 1986), is found in sexual ma-
ture individuals. The pseudocephalium is a lateral
cluster of very pubescent, flower-bearing areoles
formed along the stem as the cactus blooms each
season (Gibson and Nobel 1986; Zavala-Hurtado
and Dıaz-Solıs 1995; Vite et al. 1996). The sexual
maturity and production of pseudocephalium in
individuals of C. columna-trajani begin when they
attain an average height of 3.35 m (Zavala-
Hurtado and Dıaz-Solıs 1995).
A previous simulation study of light intercep-
tion in C. columna-trajani at the north of its range
(Valle de Zapotitlan, Puebla: 18�20¢ N and
97�28¢ W) suggests that stem tilting and pseudo-
cephalium orientation permits the fine-tuning of
the columnar morphology to its thermal and
radiation environment (Zavala-Hurtado et al.
1998). That study revealed that the observed
morphology corresponds to tilted cacti with
northwards pseudocephalia (Zavala-Hurtado
et al. 1998). This morphology maximizes inter-
ception of direct solar radiation (i.e. PAR) in the
growing season, minimizes heating during periods
of more thermal or light related stresses, and
protects reproductive structures from overheating
and excessive evapotranspiration during the
bloom in the dry season (Zavala-Hurtado et al.
1998).
Under the hypothesis that stem tilting
and northwards pseudocephalium azimuth in
C. columna-trajani actually have functional and
adaptive advantages in terms of interception of
direct solar radiation at the northern populations,
it is not expected to be favored at the southern
populations. Since the success of the inclination is
Fig. 1 Individuals of Cephalocereus columna-trajani in (a)Las Ventas (northernmost population) and (b) Cuicatlan(southernmost population) at the Tehuacan-CuicatlanBiosphere Reserve. Note the differences in stem tiltingand stem allometry. The arrows show the pseudocephalium
18 Plant Ecol (2007) 188:17–27
123
strongly dependent on the apparent position of
the sun during the growing season, the occurrence
of such columnar morphology could be restricted
geographically and, thus, could be nonadaptive at
other latitudes. Given that the previous field
study in a northern population of C. columna-
trajani found that the observed morphology cor-
responds to a tilted cacti with northward
pseudocephalia, this study addresses the following
questions: (1) is there a latitudinal variation
among populations in stem tilting?, and (2) is
northward pseudocephalia orientation favored at
other latitudes? Moreover, given that gravita-
tional force, acting to bend or break a stem, in-
crease with stem angle from vertical (Geller and
Nobel 1987; Nobel 1988), we expected that stem
tilting in C. columna-trajani would impose
mechanical restrictions that limit the column
height (Zavala-Hurtado 1997). If so, across pop-
ulations, the type of allometric relationship be-
tween height and stem diameter will indicate the
amount of support required against buckling
pressures (Niklas and Buchman 1994; Claussen
and Maycock 1995), so that, less slender stems of
the more tilted cacti would reflect the constraints
of support (Geller and Nobel 1987). Thus, we also
asked if (3) the allometric relationship between
height and diameter, and (4) the safety factor
against mechanical failure differ among popula-
tions of C. columna-trajani varying in latitude.
Methods
Study site
The study was carried out in the Tehuacan-
Cuicatlan Biosphere Reserve, in the States of
Puebla and Oaxaca, in Central Mexico (17�20¢ to
18�53¢ N and 96�55¢ to 97�44¢ W; 500–2400 m
a.s.l.). This area is located in the Puebla-Oaxaca
semi-arid region (Vite et al. 1992). The climate is
mainly semi-arid with summer rains. The annual
mean precipitation ranges from 400 to 500 mm,
while temperature from 18 to 26�C (Zavala-
Hurtado and Hernandez-Cardenas 1998). The
vegetation is dominated by xerophytic scrub
(Rzedowski 1978). The study area corresponds to
the whole acknowledged area of distribution of
C. columna-trajani.
Sampling and measurements of plant traits
Following a latitudinal gradient along the
Tehuacan-Cuicatlan Valley, we selected five
populations of C. columna-trajani (Table 1). The
five populations occurred in plain or gentle sloped
terrains without major topographic obstructions.
Distances between populations ranged from 10 to
70 km. The populations located at the ends of this
gradient represent the north and south limits of
the natural distribution range of C. columna-
trajani, respectively (Table 1).
In each population, a sample of 61–84 mature
and undamaged individuals was drawn. Since
C. columna-trajani is a naturally unbranched
columnar cactus, undamaged individuals were
those that did not show evidence of transversal
damage or reiterated shoots above it (Zavala-
Hurtado and Dıaz-Solıs 1995). We recorded, on
each individual, plant height (m; H), basal stem
diameter (cm; D0), and maximum stem diameter
(cm; Dmax). Both stem diameters were calculated
by averaging two orthogonal measures obtained
with a Haglof giant caliper (diameter resolu-
tion = 0.1 cm; Haglof Sweden AB, Sweden). We
Table 1 Geographic location, environmental characteristics and sample size of five populations of Cephalocereus columna-trajani in the Tehuacan-Cuicatlan Biosphere Reserve, Central Mexico
Number and localityof each population(State)
Geographicalcoordinate
Altitude abovesea level(m)
Mean annualtemperature(�C)
Mean annualprecipitation(mm)
Sample size
nadults nyoungs
I. Las Ventas (Puebla) 18�21¢ N 97�27¢ W 1500 21 447 61 14II. Tetitlan (Puebla) 18�16¢ N 97�20¢ W 1200 22 446 81 14III. Tilapa (Puebla) 18�10¢ N 97�07¢ W 861 24 456 69 16IV. Santa Lucıa (Oaxaca) 18�05¢ N 97�21¢ W 1684 20 483 64 21V. Cuicatlan (Oaxaca) 17�48¢ N 97�02¢ W 1110 24 547 84 8
Plant Ecol (2007) 188:17–27 19
123
measured plant height with a Haglof Vertex III
Hypsometer (height resolution = 0.1 m; Haglof
Sweden AB, Sweden). In an additional sample of
15–20 young individuals between 1 and 3.5 m (i.e.
lacking pseudocephalium and stem tilting) for each
of the five populations we recorded the total height,
basal stem diameter and maximum stem diameter.
Stem tilting and pseudocephalium orientation
analyses
For the sample of mature individuals, the tilting
angle of the stem was recorded from digital pho-
tographs analyzed with image processing software
(Scion Image for Windows Release beta 3b, Scion
Corporation, 1998). Using a vertical reference, we
measured the angular deviations (�) from the
vertical of the upper shoot of the cactus. Similar
approach was used previously (Zavala-Hurtado
et al. 1998). Finally, the azimuth of the pseudo-
cephalium for each individual was measured in the
field using a Brunton compass. The azimuth data
were then corrected for the true north (i.e. geo-
graphic north) with a magnetic declination calcu-
lator (National Geophysical Data Centre),
available at the website < http://www.ngdc.noaa.
gov/seg/geomag/jsp/Declination.jsp>.
We used a Kruskal–Wallis one-way ANOVA
(Zar 1999) to test differences among populations
with respect to the tilting angle of the cactus
stems. Multiple comparisons for the tilting angle
of the cactus stems were done with Kruskal–
Wallis z-value tests with significance levels ad-
justed according to the Bonferroni procedure
(a ¼ 0:05=½kðk� 1Þ=2�, where k(k )1)/2 = num-
ber of non-redundant pair-wise comparisons;
Hollander and Wolfe 1973; Rice 1989). The
analyses of the pseudocephalium orientations
were evaluated by means of circular statistics
(Zar 1999) and carried out using the statistical
package ORIANA for Windows v.2.02a (Kovach
2004).
Allometric and biomechanical analyses of
height-diameter relationships
In order to explore whether the allometric rela-
tionships between C. columna-trajani height and
stem diameter differs across populations varying
in latitude, the allometry of height (H) with re-
spect to basal stem diameter (D0) and maximum
stem diameter (Dmax) for each population were
determined using a simple linear function
Y ¼ bþ aX (Niklas 1994). In allometric analysis,
the slope of the simple linear function (a) is called
the scaling exponent (Niklas 1994), which is the
quotient of change in height with respect to the
change in stem diameter (Niklas and Buchman
1994). There are two reasons to justify the use of a
simple linear model rather than a log-log trans-
formed model (i.e. logY ¼ logbþ alogX). First,
intraspecific data tend to be normally distributed
while interspecific data are generally log-nor-
mally distributed (Smith 1980; Harvey 1982;
LaBarbera 1989). Second, because the range of
variation among closely related groups, such as
populations, usually is smaller than among spe-
cies, the functional relation of intraspecific data is
well estimated by regression of untransformed
rather than log transformed variables (Niklas
1994).
Since neither plant height (H) nor both diame-
ters (D0 and Dmax) are independent variables,
scaling exponents of H with respect to D0 and Dmax
were computed by means of reduced major axis
regression analyses (RMA) (Niklas 1994, 2002a).
The RMA regression analyses were performed
with the software for reduced major axis regression
RMA for JAVA v. 1.19 (Bohonak and van der
Linde 2004). Although previous statistical analyses
revealed normal distribution of the residuals in
nine out of ten regression analyses (Shapiro-Wilks
test: 0:962 � w � 0:982;P � 0:06), the jackknife
estimates of the scaling exponents of the RMA
regression analyses (aRMA) and the associated
standard error and r2 values were obtained. In
order to evaluate whether scaling exponents (H
versus D0 and H versus Dmax) differed among
populations along the latitudinal gradient, we
determined the 95% confidence intervals based
on 1000 bootstrap samples. Both jackknife esti-
mates and 95% bootstrap confidence intervals
were calculated with the RMA software.
Following the Niklas and Buchman (1994) al-
lometric study of the giant columnar cactus,
Carnegiea gigantea (saguaro), we generated stem
critical buckling height (Hcrit) and safety factor
(SF) for each individual. Assuming that the
20 Plant Ecol (2007) 188:17–27
123
mechanical and physical characteristics to the
stem of saguaro are similar to C. columna-trajani,
the values of critical buckling height were calcu-
lated from the formula Hcrit ¼ 46:4133 ðDmaxÞ2=3,
which was derived from the critical buckling
height of the saguaro (Niklas and Buchman 1994).
Hcrit represent the theoretical height that a ver-
tical stem could achieve before it undergoes
elastic buckling (McMahon 1973; Niklas 1994).
The SF is a dimensionless measure that describes
the safety margin against elastic mechanical fail-
ure (Niklas and Buchman 1994; Molina-Freaner
et al. 1998). SF was calculated for each individual
as the quotient of Hcrit and actual height,
H. Among population differences in the SF were
analyzed with Kruskal–Wallis one-way ANOVA
(Zar 1999). Multiple comparisons among popu-
lation were evaluated by Kruskal–Wallis z-value
tests (Bonferroni adjusted P values < 0.05; see
above). Except for circular statistical analyses and
RMA regressions, all analyses were carried out
using the statistical software NCSS (Hintze 2001)
and/or JMP (SAS 1999).
Results
Stem tilting and pseudocephalium orientation
Significant differences among populations in
tilting angle of stem were detected (Kruskal–
Wallis one-way ANOVA: v2 = 98.028, df = 4,
P < 0.0001, Fig. 2). Tilting angle among individ-
uals varied from 0� to 25.2�. Multiple comparisons
tests (Bonferroni adjusted P values < 0.05)
revealed that the northern populations, I and II,
showed relatively high tilted angles
(mean – standard error; �xI ¼ 6:98� 0:36 and�xII ¼ 7:56� 0:32, respectively, Fig. 2), whereas
populations III, IV, and V had lower angles
(�xIII ¼ 4:75� 0:34; �xIV ¼ 3:89� 0:36 and �xV ¼4:04� 0:31, respectively, Fig. 2). Although popu-
lations mean tilting angles showed the pattern
described by Fig. 2, we found no significant cor-
relation between tiltilng angles and latitude
(Spearman rank correlation: rs = 0.8, n = 5,
P = 0.1041).
The pseudocephalium orientation showed a
significant mean direction in the five populations
(Table 2, Fig. 3). We detected significant differ-
ences in the mean angle among populations
based on Watson–Williams multi-sample F-test
Table 2 Summary of circular statistics for pseudocephalium orientation in five populations of Cephalocereus columna-trajani from the Tehuacan-Cuicatlan Biosphere Reserve
Population n �a r q sangular SE 95% CI L1 � L2
I 61 334.41� 0.81 < 0.001 37.41� 4.70� 324.38� 342.82�II 80* 302.70� 0.74 < 0.001 44.04� 4.88� 293.13� 312.26�III 69 326.81� 0.73 < 0.001 44.64� 5.29� 316.60� 337.35�IV 64 356.90� 0.85 < 0.001 33.00� 4.11� 348.85� 4.95�V 83* 308.58� 0.76 < 0.001 42.06� 4.57� 299.63� 317.54�
n = sample size, �a = angular mean, r = measure of concentration, q = Rayleigh test of circular uniformity, sangular = angularstandard deviation, SE = standard error of angular mean, 95% CI L1 � L2 = Lower and upper confidence limits of �a. Labelscorrespond to populations listed in Table 1.*One individual was eliminated of this analysis because it showed two oppositepseudocephalia
N S
Tilt
ing
angl
eof
the
stem
(˚)
bb
aa a
0
2
4
6
8
10
I II III IV V(18˚ 21’) (18˚ 16’) (18˚ 10’) (18˚ 05’) (17˚ 48’)
N S
Populations along North-South latitudinal gradient
th
bb
aa a
0
2
4
6
8
10
I II III IV V(18˚ 21’) (18˚ 16’) (18˚ 10’) (18˚ 05’) (17˚ 48’)
Fig. 2 Mean values (–1SE) of tilting angle of the stem (�)in five populations of Cephalocereus columna-trajanifollowing a North–South latitudinal gradient along theTehuacan-Cuicatlan Biosphere Reserve. Different lettersindicate significant differences among populations accord-ing to Kruskal–Wallis multiple comparisons z-value tests(Bonferroni adjusted P values < 0.05). Labels correspondto populations listed in Table 1. Latitudes are given inparenthesis
Plant Ecol (2007) 188:17–27 21
123
(F4,352 = 20.078, P < 0.0001). Paired comparisons
tests revealed that cacti from population IV
showed significant different pseudocephalium
orientation than cacti of all the other four pop-
ulations (Watson–Williams two sample F-test: F
values ranging from 12.718 to 66.506, P < 0.0001,
Table 2, Fig. 3). Populations II and V did not
show significant differences in pseudocephalium
orientation (F1,161 = 0.753, P = 0.387) but they
were significantly different from populations I
and III, which did not differ from each other
(F1,128 = 1.08, P = 0.301) (Table 2, Fig. 3). We
found no significant angular–linear correlation
between population mean direction and latitude,
expressed as UTM units (angular-linear correla-
tion coefficient: ral = 0.317, n = 5, P = 0.818).
Allometric and biomechanical analyses of
height-diameter relationships
The allometric scaling exponents (aRMA) for H
versus D0 and H versus Dmax were generally lower
20 20
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16 16
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12 12
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Population I Population II
Population III Population IV
Population V
20 20
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16 16
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90270˚
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Fig. 3 Circular frequencydistributions ofpseudocephaliumorientation of fivepopulations ofCephalocereus columna-trajani from theTehuacan-CuicatlanBiosphere Reserve.Angular mean ( �a) and95% confidence intervalsof �a are indicated for eachpopulation. Labelscorrespond to populationslisted in Table 1
22 Plant Ecol (2007) 188:17–27
123
in the northern than in the southern populations
(Table 3). Based on the 95% confidence intervals,
analyses for H versus D0 revealed that the stems of
the individuals from population I increased in
height at a lower rate with respect to basal diam-
eter than those of populations III, IV and V, which
did not differ from each other (Table 3). Similarly,
the allometric scaling exponent of population I for
H versus Dmax was statistically lower than the one
from populations IV and V (Table 3). We found
no differences in the aRMA for H versus Dmax
between populations IV and V. The scaling
exponents for H versus D0 and H versus Dmax of
the population III, which has a latitudinal midway
position, always showed intermediate values (Ta-
ble 3). We found significant negative correlations
between latitude and aRMA for H versus D0 and H
versus Dmax. Pearson correlation (r) analyses
indicated a high decrease of the aRMA values for H
versus D0 (r = )0.90, n = 5, P = 0.0364; Fig. 4a)
and H versus Dmax (r = )0.96, n = 5, P = 0.0107;
Fig. 4b) along the north-south latitudinal gradient.
We found significant differences in SF (i.e.
Hcrit/H) among populations (Kruskal–Wallis one-
way ANOVA: v2 = 97.41, df = 5, P < 0.0001). In
this case, multiple comparisons indicated that the
safety factor for population V was the lowest
(mean – standard error; 2.97 – 0.17). By contrast,
population I showed higher SF value
(4.81 – 10.19). The populations II and III showed
intermediate SF values, which did not differ
statistically from each other (3.87 – 0.17 and
4.04 – 0.18, respectively). The multiple compari-
sons test yielded ambiguous results about popu-
lation IV (4.38 – 0.18), which did not differ
statistically from populations I, II and III. We
found no significant correlation between popula-
tion mean SF values and latitude (Spearman rank
correlation: rs = 0.6, n = 5, P = 0.2848).
Discussion
The observed latitudinal variation among popu-
lations in stem tilting angle support our hypoth-
esis that the tilting strategy is not favored at
southern latitudes along the geographical range of
C. columna-trajani. Although we detected signif-
icant differences in the mean angle of pseudo-
cephalium orientation among populations, the
pseudocephalium mean direction showed a con-
sistent north-northwestern azimuth in all popu-
lations. The analyses of stem allometry show that
the stems of the southern populations increase
in height at a far greater rate with respect to
diameter than the northern populations. These
results coupled with the differences in safety
factor, support our hypothesis that stem tilting in
C. columna-trajani would impose mechanical
restrictions that limit the column height. In gen-
eral, our results suggest that the stem tilting
morphology in this giant columnar cactus species
Table 3 Reduced major axis regression analyses between height (H) and both basal (D0) and maximal diameter (Dmax) offive populations of Cephalocereus columna-trajani from the Tehuacan-Cuicatlan Biosphere Reserve, Central Mexico
Regression/Population n r2 aRMA–SE 95% bootstrapconfidence intervalsof aRMA
H versus D0
I 75 0.832 32.65–1.21 30.42 35.17II 95 0.794 38.42–1.76 35.29 42.11III 85 0.895 44.51–1.62 41.55 47.96IV 85 0.830 41.43–1.52 38.54 44.55V 92 0.781 48.59–3.35 42.84 55.27H versus Dmax
I 75 0.870 22.63–0.81 21.74 24.43II 95 0.858 26.16–1.03 24.41 28.44III 85 0.786 28.36–1.50 25.72 31.41IV 85 0.841 27.76–1.22 25.59 30.30V 92 0.709 32.61–2.43 28.51 36.94
Values for r2, aRMA and standard error (SE) are jackknife estimates. 95% bootstrap confidence intervals of aRMA are shown.n= sample size. Labels correspond to populations listed in Table 1
Plant Ecol (2007) 188:17–27 23
123
is functionally advantageous in a restricted geo-
graphical boundary. Additionally, we show that
the geographical variation in stem tilting affects
the column allometry in C. columna-trajani. As
far as we know, this is the first study finding var-
iation in stem tilting and allometry among popu-
lations of a giant columnar cactus over a small
latitudinal gradient.
The effect of latitude on how different archi-
tectures of trees utilize and compete for photo-
synthetically active radiation (PAR) has been
well documented (see Kuuluvainen 1992). For
instance, trees with broad extended crowns are
most efficient at low latitudes, while narrow ver-
tically extended crowns are most efficient at high
latitudes (Kuuluvainen 1992). It seems to be the
case for C. columna-trajani. Our results revealed
that the angle of stem tilting among populations
increase with latitude and the northern popula-
tions showed the highest tilted angles. Thus, tilt-
ing strategy appears to be more efficient in terms
of direct solar radiation interception at the
northern populations. In contrast, in the southern
populations the development of an erect stem
appears to be favored. The limited evidence re-
ported for cacti species, a study on the Chilean
barrel cactus Copiapoa cinerea (Ehleringer et al.
1980), supports our findings: two populations that
differed in latitude showed differences in the an-
gle of the cactus body. The population farthest
from the equator showed a higher angle than the
nearest population (Ehleringer et al. 1980). The
fact of finding significant differences among pop-
ulations on a quite small geographical scale,
where the latitudinal difference between northern
and southern population in only of 33’, highlights
the fundamental effect of the apparent position of
the sun during the growing season in the success
of the tilted form in C. columna-trajani.
Alternative factors as wind could be invocated
to explain inclination of stems of C. columna-
trajani, in a similar way to that known for trees
species (e.g. Yoshino 1973). For cacti, there is
only one case of such an explanation, but the
evidence is only based in the correspondence
between dominant wind direction and degree of
prostration of stems for Ferocactus fordii var.
fordiii (Ortrega-Rubio et al. 1995). There are at
least three further points against the wind expla-
nation. First, there are several giant columnar
cacti in the study area which do not show stem
tilting (Neobuxbaumia mezcalaensis, as an
example, is an even tallest unbranched columnar
cactus). Secondly, stem tilting has long been rec-
ognized and related to light interception and
temperature regulation in many other cacti spe-
cies (e.g. Nobel 1994; Gibson and Nobel 1986;
Nobel 1988), and even other succulent species
(e.g. Rundel et al. 1995). Finally, stem tilting has
been observed under laboratory unidirectional
light conditions for several species (Geller and
Nobel 1987).
The orientation of stems and reproductive
structures (flowers and fruits) among barrel and
columnar cacti species, towards the equator, is
well known (e.g. Johnson 1924; Rundel 1974;
a
b
Fig. 4 Relationships between the population allometricscaling exponents (aRMA) and a North–South latitudinalgradient (Universal Transverse Mercator, UTM units)along the Tehuacan-Cuicatlan Biosphere Reserve. aRMA
are the quotients of change in height with respect to thechange in stem diameter. (a) aRMA of H with respect to D0
and (b) aRMA of H with respect to Dmax. Bars indicate–1SE. Scaling exponents and its standard errors (SE) arejackknife estimates. Labels correspond to populationslisted in Table 1
24 Plant Ecol (2007) 188:17–27
123
Ehleringer et al. 1980; Nobel 1981; Geller and
Nobel 1987; Tinoco-Ojanguren and Molina-
Freaner 2000). This mechanism is considered to
be advantageous since improve light interception
during the growing season (Nobel 1981; Geller
and Nobel 1987) and ameliorate tissue tempera-
ture extremes (Smith et al. 1984; Geller and
Nobel 1987) in the north as well as south hemi-
spheres (Gibson and Nobel 1986; Nobel 1988). In
contrast, both stem tilting and pseudocephalium
orientation in C. columna-trajani are northward.
Since C. columna-trajani grows in an intertropical
zone, the orientation away from the equator
intercepts less direct solar radiation during the
summer, the hottest season (Zavala-Hurtado
et al. 1998). In this study, the pseudocephalium
was non-randomly oriented and its mean direc-
tion varied among populations. Such differences
appear to be explained by differences specific to
the local landscape since the pseudocephalium
mean direction showed a consistent north-north-
western azimuth in all populations. If we set
practical limits to north (0� – 22.5� [337.5�–22.5�])
and northwestern azimuth (315� – 22.5� [292.5�–
337.5�]), they included the pseudocephalium
mean direction of all populations (i.e. 292.5�–
22.5�, the north-northwestern azimuth). Similar
results about pseudocephalium orientation in C.
columna-trajani were reached by Zavala-Hurtado
and colleagues (1998) in a population at the north
of its distribution area (18�20¢ N and 97�28¢ W).
Our results point out that, regardless to geo-
graphic position of the population, the north-
northwestern orientation of pseudocephalium in
C. columna-trajani is favored along its geograph-
ical range.
The stems of most self-supporting plants face
the force of gravity (Waller 1986; Niklas 2002b).
In simple terms, they represent columns that
sustain a compressive loads at their free ends
(Niklas 1992; Hibbeler 1994), which must in any
case be able to support their own weight to avoid
mechanical failures such as collapsing, tearing or
buckling (Givnish 1995). In addition, plant stems
also are subjected to dynamic loads like wind and
other physical stresses. Cacti, however, cope with
another biomechanical challenge. Giant columnar
species, particularly, face the mechanical limita-
tion imposed by the stem succulence (Altesor and
Ezcurra 2003). The stems of large cacti support
great masses of water-storing tissues (i.e. paren-
chyma) by a limited amount of woody rods or a
hollow woody cylinder (Altesor et al. 1994;
Cornejo and Simpson 1997; Altesor and Ezcurra
2003). According to that, stem tilting in columnar
cacti is not expected (Nobel 1988). In fact, tilt
stems are uncommon, apparently because gravity
would exert a considerable bending moment
on their massive stems (Nobel 1988). Thus,
C. columna-trajani would be the only columnar
cactus that shows such behavior.
Stem tilting, although ecologically valuable,
seems to have some biomechanical costs. As we
formerly noted, tilt also increases the risk of stem
fracture (Zavala-Hurtado and Dıaz-Solıs 1995;
Zavala-Hurtado et al. 1998). In this sense, Niklas
(1988) stated that large deflection angles can
maximize light interception but they also maxi-
mize bending stresses. From a mechanical point
of view, stem tilting seems to be disadvantageous.
In the northern populations of C. columna-trajani,
where stems are tilted, the center of gravity is
displaced laterally such that the bending moments
increase (Mattheck 1995), as well as the risk of
mechanical failure. Frequently, individuals of
C. columna-trajani show evidences of mechanical
failure or stem breakage (Zavala-Hurtado and
Dıaz-Solıs 1995).
Our analyses of stem allometry and safety
factor revealed differences among populations
varying in latitude. The scaling exponents (i.e.
aRMA for H versus D0 and H versus Dmax) in-
crease toward southern latitude, implying thinner
stems with increasing height. These results indi-
cate that the stems of the southern populations
are taller and slenderer than those of the northern
populations. Thus, an increased risk of column
fracture on the populations that show more stem
tilting is reflected in a low rate of height incre-
ment to units of diameter. Indeed, Givnish (1995)
predicted that stems with higher margin of
biomechanical safety can resist greater stresses
but it also entails the cost of lesser stature. Al-
though we found no significant correlation be-
tween population mean SF and latitude, the SF of
the southernmost population (i.e. V) is signifi-
cantly lower than the other populations, which
agrees with our expectations. Therefore, in C.
Plant Ecol (2007) 188:17–27 25
123
columna-trajani there is a possible trade-off
involving the balance between the functional
benefits of tilting against the adaptive value of
maximizing stature (King 1990; Zavala-Hurtado
1997). Allometric differences among population
could be caused by other factors like intraspecific
competition. For instance, plants growing in
crowded conditions could be much thinner than
uncrowded plants of the same height (e.g. Weiner
and Fishman 1994). However it seems not to be
the case, as density of C. columna-trajani in the
southernmost population (i.e. V) is similar and
even smaller to that of the northern population II
(mean – standard deviation: 470 – 157 plants/ha
and 540 – 180 plants/ha, respectively).
The form and biomechanical properties of
stems play a major role in adapting plants for
different environmental conditions and influenc-
ing their ecological distribution (Givnish 1995).
Among cacti, these aspects are more than evident
since stems simultaneously function as support,
transport, storage and photosynthetic organ
(Cornejo and Simpson 1997; Niklas 2002a). Al-
though further analysis of radiation interception
remains to be explored, the fact of having found
significant differences among populations of
C. columna-trajani on a small geographical scale,
highlight the influence of fine tuned stem mor-
phology on how individual plants exploit the
above-ground resources within their environ-
ment.
Acknowledgments We thank Pedro Miranda for fieldassistance. This study was carried out with the support ofthe Universidad Autonoma Metropolitana-Iztapalapa(143.05.06). The comments of Dylan Schwilk and ananonymous reviewer greatly improved the manuscript.
References
Altesor A, Silva C, Ezcurra E (1994) Allometric neotenyand the evolution of succulence in cacti. Bot J LinnSoc 114:283–292
Altesor A, Ezcurra E (2003) Functional morphology andevolution of stem succulence in cacti. J Arid Environ53:557–567
Briggs DM, Walters SM (1969) Plant variation and evo-lution. McGraw Hill Book Company, New York
Bohonak AJ, van der Linde K (2004) RAM: softwarefor reduced major axis regression for JAVAv. 1.19. User’s guide
Bravo-Hollis H (1978) Las cactaceas de Mexico (Vol 1).Universidad Nacional Autonoma de Mexico, MexicoD. F.
Claussen JW, Maycock CR (1995) Stem allometry in aNorth Queensland tropical rainforest. Biotropica27:421–426
Cornejo DO, Simpson BB (1997) Analysis of form andfunction in North American columnar cacti (tribePachycereeae). Am J Bot 84:1482–1501
Ehleringer J, Mooney HA, Gulmon SL, Rundel P (1980)Orientation and its consequences for Copiapoa (Cact-aceae) in the Atacama Desert. Oecologia 46:63–67
Endler JA (1977) Geographic variation, speciation, andclines. Princeton University Press, Princeton
Felger S, Lowe CH (1967) Clinal variation in the surface–volume relationship of the columnar cactus Loph-ocereus schottii in Northwestern Mexico. Ecology48:530–536
Geller GN, Nobel PS (1987) Comparative cactus archi-tecture and PAR interception. Am J Botany 74:998–1005
Gibson AC, Nobel PS (1986) The cactus primer. HarvardUniversity Press, Cambridge
Givnish TJ (1995) Plant stems: biomechanical adaptationfor energy capture and influence on species distribu-tion. In: Gartner BL (eds) Stems: physiology andfunctional morphology. Academic Press, San Diego,pp 3–49
Harvey PH (1982) On rethinking allometry. J Theor Biol95:37–41
Hibbeler RC (1994) Mechanics of materials. MacMillan,New York
Hintze J (2001) NCSS (Number Cruncher StatisticalSoftware) 2001. NCSS Statistical Software, Kaysville
Hollander M and Wolfe DA (1973) Nonparametric sta-tistical methods. John Wiley and Sons, New York
Johnson DS (1924) The influence of insolation on thedistribution and on the developmental sequence ofthe flowers of the giant cactus of Arizona. Ecology5:70–82
King DA (1990) The adaptive significance of tree height.Am Nat 135:809–828
Kovach WL (2004) ORIANA for Windows v. 2.02a.Kovach Computing Services, Pentraeth Wales
Kuuluvainen T (1992) Tree architectures adapted to effi-cient light utilization: is there basis for latitudinalgradients? Oikos 65:275–284
LaBarbera M (1989) Analyzing body size as factor inecology and evolution. Ann Rev Ecol Syst 20:97–117
Linhart YB, Grant MC (1996) Evolutionary significance oflocal genetic differentiation in plants. Ann Rev EcolSyst 27:237–277
Mattheck C (1995) Biomechanical optimum in woodystems. In: Gartner BL (ed) Stems: physiology andfunctional morphology. Academic Press, San Diego,pp 75–90
McMahon T (1973) Size and shape in biology. Science179:1201–1204
Molina-Freaner F, Tinoco-Ojanguren C, Niklas KJ (1998)Stem biomechanics of three columnar cacti from theSonoran Desert. Am J Bot 85:1082–1090
26 Plant Ecol (2007) 188:17–27
123
Niering WA, Whittaker RH, Lowe CH (1963) The sa-guaro: a population in relation to environment. Sci-ence 142:15–23
Niklas KJ (1988) Biophysical limitations on plant form andevolution. In: Gottlieb LD, Jain SK (eds), Plant evo-lutionary biology. Chapman and Hall, Cambridge,pp 185–220
Niklas KJ (1992) Plant biomechanics: an engineering ap-proach to plant form and function. The University ofChicago Press, Chicago
Niklas KJ (1994) Plant allometry: the scaling of form andprocess. The University of Chicago Press, Chicago
Niklas KJ (2002a) On the allometry of biomass partition-ing and light harvesting for plants with leafless stems.J Theor Biol 217:47–52
Niklas KJ (2002b) Wind, size, and tree safety. J Arboricult28:84–93
Niklas KJ, Buchman SL (1994) The allometry of saguaroheight. Am J Bot 81:1161–1168
Nobel PS (1978) Surface temperatures of cacti-influencesof environmental and morphological factors. Ecology59:986–996
Nobel PS (1980) Morphology, surface temperatures, andnorthern limits of columnar cacti in the SonoranDesert. Ecology 61:1–7
Nobel PS (1981) Influences of photosynthetically activeradiation on cladode orientation, stem tilting, andheight of cacti. Ecology 62:982–990
Nobel PS (1982) Low temperatures tolerance and coldhardening of cacti. Ecology 63:1650–1656
Nobel PS (1988) Environmental biology of agave andcacti. Cambridge University Press, New York
Nobel PS (1994) Remarkable agaves and Cacti. OxfordUniversity Press, Oxford
Nobel PS, Loik ME (1999) Form and function of cacti. In:Robichaux RH (ed) Ecology of Sonoran Desert plantsand plants communities. The University of ArizonaPress, Tucson, pp 143–163
Ortega-Rubio A, Romero-Schmidt H, Arguelles-MendezC, Castellanos-Vera A (1995) Effect of wind on aFerocactus fordii var. fordii population on Piedra Is-land, Baja California Sur, Mexico. J Arid Environ31:15–19
Rice WR (1989) Analyzing tables of statistical tests.Evolution 43:223–225
Rundel PW (1974) Trichocereus in the Mediterraneanzone of Central Chile. Cactus Succulent J 46:86–88
Rundel PW, Cowling RM, Esler KJ, Mustart PM, vanJaarsveld E, Bezuidenhout H (1995) Winter growthphenology and leaf orientation in Pachypodiumnamaquanum (Apocynaceae) in the succulent karooof the Richtersveld, South Africa. Oecologia 101:472–477
Rzedowski J (1978) Vegetacion de Mexico. Limusa,Mexico D. F
SAS (1999) JMP�. Statistics and graphics guide, v. 3.1.SAS Institute Inc., North Carolina
Smith RJ (1980) Rethinking allometry. J Theor Biol 87:97–111
Smith SD, Didden-Zopfy B, Nobel PS (1984) High-tem-perature responses of North American cacti. Ecology65:643–651
Tinoco-Ojanguren C, Molina-Freaner F (2000) Flowerorientation in Pachycereus pringlei. Can J Bot78:1498–1494
Vite F, Zavala-Hurtado JA, Armella MA and Garcıa-Suarez MD (1992) Regionalizacion y caracterizacionmacroclimatica del Matorral Xerofilo. Superficies derespuesta a variables climaticas de once generos deplantas caracterısticos de este tipo de vegetacion.Carta escala 1:8,000,000. Atlas Nacional de Mexico.Instituto de Geografıa, Universidad Nacional Auto-noma de Mexico, Mexico, D. F.
Vite F, Portilla E, Zavala-Hurtado JA, Valverde PL andDıaz-Solıs A (1996) A natural hybrid population be-tween Neobuxbaumia tetetzo and Cephalocereuscolumna-trajani (Cactaceae). J Arid Environ 32:395–405
Waller DM (1986) The dynamic of growth and form. In:Crawley MJ (ed) Plant ecology. Blackwell ScientificPublications, Oxford, pp 291–320
Weiner J, Fishman L (1994) Competition and allometry inKochia scoparia. Ann Bot 73:263–271
Yeaton RI, Cody ML (1979) The distribution of cactialong environmental gradients in the Sonoran andMohave Deserts. J Ecol 67:529–541
Yoshino MM (1973) Wind-shaped trees in the subalpinezone in Japan. Artic Alpine Res 5:A115–A126
Zar JH (1999) Biostatistical analysis (4th edn). PrenticeHall, Upper Saddle River
Zavala-Hurtado JA (1997) Morfologıa funcional de Ce-phalocereus columna-trajani (Cactaceae) en una co-munidad semiarida del tropico mexicano. PhDDissertation. Facultad de Ciencias, Universidad Nac-ional Autonoma de Mexico, Mexico, D.F.
Zavala-Hurtado JA and Dıaz-Solıs A (1995) Repair,growth, age and reproduction in the giant columnarcactus Cephalocereus columna-trajani (Karwinski ex.Pfeiffer) Schumann (Cactaceae). J Arid Environ31:21–31
Zavala-Hurtado JA and Hernandez-Cardenas G (1998)Estudio de caracterizacion y diagnostico del areapropuesta como Reserva de la Biosfera Tehuacan-Cuicatlan. Instituto Nacional del Ecologıa—Univers-idad Autonoma Metropolitana-Iztapalapa, Report,Mexico, D. F.
Zavala-Hurtado JA, Vite F, Ezcurra E (1998) Stem tiltingand pseudocephalium orientation in Cephalocereuscolumna-trajani (Cactaceae): a functional interpreta-tion. Ecology 79:340–348
Plant Ecol (2007) 188:17–27 27
123
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