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: plvp@xanum.uam.mx

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

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270 20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270

20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270 20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270

20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270˚

˚

˚

˚

˚ ˚ ˚ ˚

˚ ˚ ˚ ˚

˚

˚

˚

˚

˚

˚

˚

˚

Population I Population II

Population III Population IV

Population V

20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270 20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270

20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270 20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90

180

270

20 20

20

20

16 16

16

16

12 12

12

12

8 8

8

8

4 4

4

4

0

90270˚

˚

˚

˚

˚ ˚ ˚ ˚

˚ ˚ ˚ ˚

˚

˚

˚

˚

˚

˚

˚

˚

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