Ecology, 79(1), 1998, pp. 340–348
q 1998 by the Ecological Society of America
STEM TILTING AND PSEUDOCEPHALIUM ORIENTATION IN
CEPHALOCEREUS COLUMNA-TRAJANI (CACTACEAE):
A FUNCTIONAL INTERPRETATION
JOSÉ ALEJANDRO ZAVALA-HURTADO,1 FERNANDO VITE,1
1
AND
EXEQUIEL EZCURRA2
Departamento de Biologı́a, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-535,
09340 México D.F., México
2Instituto de Ecologı́a, Universidad Nacional Autónoma de México, Apartado Postal 70-275,
04510 México D.F., México
Abstract. This paper analyzes the functional implications of stem tilting and pseudocephalium orientation in the giant columnar cactus Cephalocereus columna-trajani. This
species shows a consistent northern orientation of its pseudocephalium (a nonphotosynthetic
hairy structure where flowers are produced) and stem tilting in the same direction. Analysis
of pseudocephalium orientation was made on field data gathered from subpopulations of
C. columna-trajani from slopes with different exposures. Additionally, from morphometric
characteristics measured in the field, a model cactus was constructed with the purpose of
simulating radiation interception by different morphologies. Variations of this model cactus
allowed the simulation of irradiance on erect and tilted cacti, as well as on plants with
varying pseudocephalium orientation. Results of irradiance interception by different morphologies were related to actual data of growth rates, flowering period, and rainfall and
temperature patterns on the study zone. Sampled individuals of C. columna-trajani showed
a significant north-northwest pseudocephalium orientation (angular mean 5 3398 6 228).
Simulations showed that tilted cacti with pseudocephalia facing northwards increase yearly
interception of direct solar radiation by the whole plant compared to erect cacti with or
without a pseudocephalium (2 and 7% increase, respectively), and with tilted cacti with
the pseudocephalium facing away from the north (9–10% increase). Additionally, the observed morphology decreases radiation interception during the hottest and driest period of
the year. From our results, pseudocephalium orientation and stem tilting in C. columnatrajani appear to be morphological adaptations that allow the fine-tuning of a columnar
morphology to its thermal and radiation environment. However, the cost of tilting in this
giant columnar cactus is that branching (which increases photosynthetic area and reproductive output) appears to be almost impossible without serious risk of stem breakage.
Key words: adaptation; functional morphology; growth rate; irradiance; photosynthetically active
radiation (PAR); pseudocephalium; semiarid lands; thermal regulation; tilting; Zapotitlán, Mexico.
INTRODUCTION
Cephalocereus columna-trajani (Karwinski ex Pfeiffer) Schumann is a giant, usually unbranched, columnar
cactus, which forms dense populations on hills of the
semiarid region of Puebla and Oaxaca in intertropical
Mexico (Bravo-Hollis 1978). This spectacular plant
(Fig. 1), known locally as cardón, reaches a height of
10–12 m and characterizes a vegetation unit named
cardonal in the xerophytic scrub of the Valley of Zapotitlán (Zavala-Hurtado 1982).
An eye-catching feature of these populations is the
marked stem tilting of the upper shoot of the cactus,
which bends northwards with a similar orientation in
almost all plants. In the concave side of the bent stem,
and also facing approximately north, a pseudocephalium is found in all adult plants (Fig. 1; Greenwood
1964). The pseudocephalium is a cluster of densely
Manuscript received 12 September 1996; revised 7 January
1997; accepted 23 January 1997; final version received 7
March 1997.
pubescent, flower-bearing areoles that are formed along
the sides or at the top of a cactus stem, not including
the shoot apex (Gibson and Nobel 1986). C. columnatrajani individuals initiate the production of the pseudocephalium when they attain an average height of 3.35
m and become reproductive (Zavala-Hurtado and Dı́azSolı́s 1995). The developing flower buds are embedded,
and hence protected, in the previously formed pseudocephalium hairs.
The surface of the pseudocephalium is not photosynthetic. On the one hand, the woolly cover impedes
the arrival of light to the epidermis. On the other, the
tissue surface under the hairy mat of the pseudocephalium is suberose and does not contain chloroplasts.
Thus, this cactus species may lose a significant proportion (9–10%) of its potentially photosynthetic tissues with the development of the pseudocephalium.
Because of their stem-succulent nature and their extremely low surface–volume relationship, giant columnar cacti maintain a large proportion of nonphotosyn-
340
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FUNCTIONAL MORPHOLOGY OF CEPHALOCEREUS
341
umna-trajani in plain terrain, and in north, south, east,
and west slopes; (b) simulations of irradiance received
by a model cactus with the pseudocephalium at different azimuths, and with and without tilting of the
trunk, and (c) analysis of radiation interception curves
in terms of their relationship with growth rate, flowering, and rainfall and temperature curves.
METHODS
Study site
Field data were gathered from a cardonal in a hill
at the semiarid valley of Zapotitlán (188209 N, 978 289
W, 1550 m elevation), a local basin of the Tehuacán
Valley in the Pueblan-Oaxacan Region in the Mexican
State of Puebla (Vite et al. 1992). Climate in this zone
is semiarid with summer rains. Annual mean temperature is 188–228C and precipitation is ;400 mm/yr. The
soils are shallow, stony, and halomorphic (Byers 1967).
Semiarid conditions are imposed by the rain shadow
of the Sierra Madre Oriental, which intercepts humid
winds from the Gulf of Mexico. The vegetation has
been classified as a xerophytic scrub (matorral xerófilo;
Rzedowski 1978).
Orientation of the pseudocephalia in the field
FIG. 1. Individual plant of Cephalocereus columna-trajani in Zapotitlán, Mexico; the photograph was taken from
the western side of the plant. The stem is tilted towards the
north-northwest (as is the rest of the population visible in the
background). The arrow shows the pseudocephalium.
thetic parenchyma, which lives at the expense of the
relatively scarce chlorenchyma that is only found in
the epidermis of the stem. Thus, on a whole-plant basis
the compensation level for net photosynthesis is high
(Nobel 1988), and the functionality of the stem epidermis as a light-capturing structure is extremely important. In this context, the evolution of a morphological trait such as the pseudocephalium, which has
evolved at the cost of losing a significant amount of
the photosynthetic epidermis, needs to be explored in
terms of its functional morphology.
In this paper, we advance the hypothesis that pseudocephalium orientation and stem tilting in Cephalocereus columna-trajani actually have functional advantages in terms of radiation interception compared
with unbranched erect cacti with no pseudocephalium
and tilted cacti with pseudocephalium orientations different from the observed one. Additionally, we hypothesized that the northwestern orientation of the
pseudocephalium and stem tilting protect the flowers
from direct solar radiation. This hypothesis is explored
by means of: (a) a statistical description of the orientation of the pseudocephalium in Cephalocereus col-
Five samples of 50 individuals of C. columna-trajani
each were drawn from five different conditions: eastern, western, northern, and southern slopes and an
unobstructed plain. The azimuth of the pseudocephalium for each individual was measured using a Brunton
compass corrected for true north. Angular mean and
circular deviation of pseudocephalium azimuth for each
sample were calculated using circular statistics (Zar
1974).
Modeling plant morphology
The irradiance received by a Cephalocereus columna-trajani individual was estimated from that computed for a three-dimensional figure made up of 209
intercepting planes, or facets, each with specific dimensions, azimuth, tilting angle, and suppressed photosynthetic area due to the pseudocephalium. The data
for the construction of the geometric model cactus were
gathered from ten randomly selected adult individuals
with a mean height of 5.63 m (minimum 5 4.91 m;
maximum 5 6.82 m; SD 5 0.63 m) growing in an
unobstructed plain. We measured cactus heights to the
nearest centimeter using a 10-m extendible pole gauge.
Shoot diameter was measured to the nearest millimeter
using a caliper. Measurements were taken every meter
starting from the cactus base. Additionally, we recorded pseudocephalium length and width every 0.5 m using a measuring tape. Tilting angle of the cactus shoot
was measured for each of three 2 m high segments
from a vertical reference on printed photographs taken
from a sample of 35 randomly selected adult individuals growing in the same plain, with a mean height of
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JOSÉ ALEJANDRO ZAVALA-HURTADO ET AL.
Ecology, Vol. 79, No. 1
6.74 m (minimum 5 5.80 m; maximum 5 7.80 m; SD
5 0.52 m; we used a larger sample for this measurement in order to obtain accurate regression estimations
of tilting). With these data, a geometric model cactus
was constructed as described in the Appendix.
The simulations were run for six theoretical morphologies: (a) erect plants without a pseudocephalium
(tilting angle 5 08 and number of facets covered by
the pseudocephalium 5 0 for all segments); (b) erect
plants with north-northwestern pseudocephalia (tilting
angle 5 08 for all segments); (c) tilted plants with
north-northwestern pseudocephalia; (d) tilted, east-oriented pseudocephalia (azimuth of facets rotated 1118);
(e) tilted, west-oriented pseudocephalia (azimuth of
facets rotated 2698); and (f) tilted, south-oriented pseudocephalia (azimuth of facets rotated 21598). Model
cacti with no pseudocephalium have a photosynthetic
surface of 5.70 m2. In model cacti with a pseudocephalium the photosynthetic surface becomes reduced
in 9.4% (although the total surface area is the same).
geometric projection of the stem. For simplicity, we
referred our results to the unribbed projection. If the
results are referred to ribbed plants, then the intercepted
radiation per unit area is proportionally less, but the
relative differences between morphologies do not
change.
The simulation data were supplemented with climatic information and with data on growth and flower
production. Mean temperature and rainfall data (1990–
1991) were provided by the climatological station of
Zapotitlán Salinas (Servicio Meteorológico Nacional,
Mexico). Average number of flowers per individual per
month for 75 individuals of C. columna-trajani in
1990–1991 were drawn from our own unpublished
data. Finally, mean monthly growth rates for the same
two years were estimated from data of Zavala-Hurtado
and Dı́az-Solı́s (1995).
Simulation analyses
The five populations showed a significant mean direction (P , 0.001) according to a Raleigh test (Zar
1974). The mean azimuth and circular standard deviation of the pseudocephalium in plants from the unobstructed plain were 3398 6 21.88. This orientation
(hereafter called north-northwestern) was considered as
the typical natural orientation, and hence, the one to
be evaluated in terms of efficiency in light interception.
Two-sample tests using the method of Watson and
Williams (1956, cited in Zar 1974) revealed that there
were nonsignificant differences (P . 0.1) in pseudocephalium orientation between cacti from the northern
and southern slopes and the unobstructed plain. Cacti
from the eastern slope showed significantly different
(P , 0.001) pseudocephalium azimuth from cacti of
all the other four sites. The same occurred with cacti
from the western slope, which showed significantly different (P , 0.001) pseudocephalium azimuth from cacti of all the other sites, excepting the northern slope
(Fig. 2).
A computer program simulating direct solar radiation
(Ezcurra et al. 1991) was supplied with data describing
the azimuth, inclination, and area of the 209 intercepting planes, plus the latitude and the date to be
simulated. Using standard astronomical equations
(Meeus 1988), the program calculates the apparent position of the sun from sunrise to sunset at 10-min intervals and estimates the interception efficiency of each
individual plane at each time.
Based on the fact that the pathway of the solar beam
through the atmosphere becomes shorter as the sun
approaches the zenith, the proportion of direct solar
radiation that is dampened by the air mass was calculated as a function of the angular elevation of the
sun above the celestial horizon (Ross 1981). The estimations were done following Gates’ (1980) method,
which calculates direct solar radiation (in watts per
square meter) intercepted by a given body with a known
surface at a given hour of the day under a given air
transmittance (which ranges between 0.5 and 0.8 in
most desert areas). The simulations were run for three
different dates: the equinox, the summer solstice, and
the winter solstice, using an air transmittance value of
0.7 for each date. An extension of this program integrates the daily direct solar radiation (in joules per
square meter per day), allowing the estimation for a
whole year. Resulting figures of irradiance were multiplied by the photosynthetic area of the model cactus
in order to estimate total irradiance received by the
photosynthetic surface of the simulated plant.
As in most giant columnar cacti, the stem of C. columna-trajani is ribbed, and its total stem surface is
;5% larger than in the facet projection we used for
our simulations. The simulated radiation interception
per unit photosynthetic surface may be referred either
to the ‘‘true’’ (i.e., ribbed) surface, or to the unribbed
RESULTS
Orientation of the pseudocephalia in the field
Simulation analyses
In our model, an erect cactus with no pseudocephalium intercepts 11652 MJ/yr of direct solar radiation (Table 1). The presence of a pseudocephalium in
erect plants reduced light interception in values ranging
from 11.6% when the structure faced east, to 3.1% in
northern orientations. An erect cactus bearing a pseudocephalium with north-northwestern azimuth would
reduce its light interception by 5.1%, compared with
an erect cactus with no pseudocephalium.
Bending of the shoot in plants with a pseudocephalium dramatically increased light interception (Table 1). A tilted cactus with a north-facing pseudocephalium intercepts more (4.0%) light than an erect one
without a pseudocephalium. In tilted cacti, minimum
light interception would occur for a plant with a pseu-
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FUNCTIONAL MORPHOLOGY OF CEPHALOCEREUS
343
TABLE 1. Total annual direct solar radiation intercepted by
11 simulated plants differing in location of pseudocephalium and tilting (see Appendix for details of model cacti).
Percentages are relative to an erect cactus with no pseudocephalium.
Tilted
Erect
Type of simulated
pseudocephalium
None
North-northwest facing
North facing
East facing
South facing
West facing
Radiation
intercepted
(MJ/d)
11 652
11 062
11 285
10 303
10 324
10 303
Radiation
intercepted
%
(MJ/d)
100
94.9
96.9
88.4
88.6
88.4
11 853
12 113
10 825
10 615
10 825
%
101.7
104.0
92.9
91.1
92.9
FIG. 2. Frequency distributions of pseudocephalium azimuth of 50 individuals of Cephalocereus columna-trajani
from different slope aspects in the valley of Zapotitlán, Mexico. Angular means (f) and circular standard deviations of
pseudocephalium azimuth are shown for each slope.
docephalium facing south. The average observed cactus morphology (tilted, with a north-northwestern pseudocephalium) intercepts 1.7% more light than that received by an erect individual with no pseudocephalium.
Looking at the yearly pattern of light interception
(Fig. 3a), it can be seen that the average observed cactus morphology shows the highest light interception
during fall and winter when relatively low temperatures
prevail in the region (Fig. 3b). This estimated radiationinterception pattern contrasts with the theoretical patterns of erect cacti without a pseudocephalium, and
especially of south-tilted cacti, which would maximize
light interception during the relatively hot summer
months. Additionally, the less efficient east- and westtilted cacti would show lower interception values
throughout the year. It also can be seen that tilting
FIG. 3. (a) Simulated intercepted solar radiation by five
different model cacti (continuous line, erect cactus with no
pseudocephalium; long-dashed line, erect cactus with pseudocephalium facing north-northwest; dotted line, tilted cactus
with pseudocephalium facing north-northwest; dash-dot line,
tilted cactus with pseudocephalium facing east or west; and
dashed line, tilted cactus with pseudocephalium facing S).
(b) Average rainfall (solid line) and mean monthly temperature (dotted line) from the Zapotitlán Salinas climatological
station during 1990–1991. (c) Mean growth rate (solid line)
and mean number of flowers produced per individual (dotted
line) from a population of 75 Cephalocereus columna-trajani
individuals during 1990–1991.
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JOSÉ ALEJANDRO ZAVALA-HURTADO ET AL.
improves light interception from September to March
in cacti with north-northwestern azimuths in relation
to the interception pattern of cacti showing the same
orientation of the pseudocephalium but no shoot bending.
Maximization of light interception during fall in the
average cactus morphology (Fig. 3a) coincides with the
peak in growth rate of Cephalocereus columna-trajani
(Fig. 3c) and with the September rainfall period in the
study site (Fig. 3b) for the analyzed years. Flower
blooming presents a peak in March (Fig. 3c), during a
period of high incident radiation (Fig. 3a) and relatively
low temperatures, before the onset of the rainy season
(Fig. 3b).
The simulations of the daily patterns of light interception are presented only for the three most efficient
morphologies: (a) erect plants with no pseudocephalium; (b) erect plants with a north-northwestern pseudocephalium; and (c) north-northwestern tilted plants
with a pseudocephalium (Fig. 4). Simulations were performed for the equinox (Fig. 4a), the summer solstice
(Fig. 4b), and the winter solstice (Fig. 4c).
Although the three types of cacti showed similar
trends in their daily patterns of direct solar radiation
interception, some relevant differences must be highlighted: (a) erect cacti with no pseudocephalium
showed a symmetric pattern around noon; (b) cacti
bearing a north-northwestern pseudocephalium (both
erect and tilted) intercepted more radiation before noon
in the summer solstice and in the equinox, compared
to the radiation intercepted after midday; (c) tilted cacti
with pseudocephalium showed the highest direct solar
radiation interception of all morphologies during the
equinox (33.7 MJ/d) and the winter solstice (34.1
MJ/d), and present an intermediate value during the
summer solstice (29.5 MJ/d); (d) erect cacti with a
pseudocephalium showed the lowest radiation interception of all morphologies in the three simulations
(31.1 MJ/d on the equinox, 28.1 MJ/d on the summer
solstice, and 32.2 MJ/d in the winter solstice); (e) erect
cacti with no pseudocephalium showed intermediate
values of radiation interception in the equinox and winter solstice (32.5 and 32.3 MJ/d, respectively), and the
maximum value of all morphologies during the summer
solstice (31.8 MJ/d).
DISCUSSION
Orientation in the flowering structures of columnar
cacti is well known. For example, in Carnegiea gigantea it has long been reported that flowers are primarily produced on the east-southeast side of the top
of the plant (MacDougall and Spaulding 1910, cited in
Nobel 1981; Johnson 1924), i.e., exactly on the opposite side from that for C. columna-trajani. For this
northern species (C. gigantea), flower development
seems to be enhanced by high surface temperatures
achieved on the southern side of stem. Conversely, Trichocereus chilensis and T. litoralis, two species of co-
Ecology, Vol. 79, No. 1
FIG. 4. Simulated daily interception of direct solar radiation
(W/m2) for cactus models of different morphology (
, erect
cactus with no pseudocephalium; ········, erect cactus with pseudocephalium facing north-northwest; and – – –, tilted cactus with
north-northwest-facing pseudocephalium). Graphs show intercepted radiation during (a) autumn equinox (the same simulation
curve is obtained for 21 March, the spring equinox); (b) summer
solstice; and (c) winter solstice.
lumnar cacti from the southern hemisphere, produce
flowers mainly in the warmer, northern side of the stem
(Rundel 1974).
Stem tilting, however, has only been studied in barrel
cacti, a life form with relatively short stems. Nobel
(1988) argued that giant columnar cacti do not tilt because gravity would exert a considerable bending moment on their massive stems, causing their breakage.
Indeed, from the many giant columnar species in the
Tehuacán Valley, C. columna-trajani is the only one
that exhibits stem tilting, and is also one of the only
two species that do not usually branch. Additionally,
stem breakage is a very frequent cause of physical injury on these plants (Zavala-Hurtado and Dı́az-Solı́s
1995). Some barrel cactus species (e.g., Ferocactus
spp. in North America and Copiapoa spp. in South
America) expose their apical region (in which flowers
are produced) to the south and north, respectively (i.e.,
toward the equator) by means of a stem tilting. The
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FUNCTIONAL MORPHOLOGY OF CEPHALOCEREUS
northern azimuth and tilting in three species of Copiapoa were explained by Ehleringer et al. (1980) as a
mean of increasing apical temperatures by enhancing
meristematic activity during the winter and spring
months. The equatorwards tilting of barrel cacti does
not improve PAR interception and CO2 uptake for the
whole plant. On the contrary, the bending of the longitudinal stem axis towards the sun’s trajectories in fact
leads to less PAR annually incident on the stem (Nobel
1988). The functional advantages of tilting, hence, are
possibly more related to temperature control than to a
maximization of intercepted PAR.
The behavior of C. columna-trajani contrasts with
previous reports on this problem in various aspects.
First, C. columna-trajani is the only giant columnar
species known to show a conspicuous stem tilting. Second, the species tilts away from the equator, and not
towards it. Third, the flowers, which are embedded in
the pseudocephalium, are also oriented away from the
equator, in contrast with other columnar species that
produce their flowers on the warmer side of the columnar stem facing the equator. And fourth, this cactus
species is endemic to the intertropical zone, while all
the previous reports of nonrandom orientation in columnar or barrel cacti are for subtropical plants growing
either north of the Tropic of Cancer or south of the
Tropic of Capricorn.
The importance of photosynthetically active radiation (PAR) as a limiting factor for cacti has been previously documented (Nobel 1980, 1981, 1982, Geller
and Nobel 1986, 1987). PAR limitation occurs because
of the opacity, rigidity, and vertical orientation of the
photosynthetic surfaces of most cacti and of other CAM
plants such as cactoid Euphorbiaceae. The capture of
light in these desert succulents implies necessarily the
risk of overheating their photosynthetic tissues. Many
perennial desert plants, including succulent and nonsucculent evergreen species, present their chlorenchyma vertically oriented (e.g., Woodhouse et al. 1980,
Nobel 1982, 1986, Cano-Santana et al. 1992, Ezcurra
et al. 1991, 1992, Valverde et al. 1993). As a general
rule, a vertically oriented structure will intercept more
light in the morning and afternoon, and less light at
midday, when the sun is near the zenith. Thus, the
vertical orientation helps to solve the compromise between capturing light and avoiding overheating during
the warmer hours of the day. In the Tehuacán Valley,
opuntioid, barrel, and columnar cacti establish under
the shade of nurse plants, and their seedlings do not
survive a dry season if they are exposed to direct solar
radiation (Valiente-Banuet et al. 1991, Valiente-Banuet
and Ezcurra 1991). Adult plants manage to survive
direct exposure to the sun because of their vertical orientation. Felled individuals of C. columna-trajani, exposed horizontally to direct solar radiation, attain midday temperatures in their chlorenchyma above 558C,
while the normal erect plants are only slightly above
air temperature, and around 358C (J. A. Zavala-Hur-
345
tado, unpublished data). In Opuntia pilifera the horizontal exposure of the usually vertical cladodes increases their midday temperature from 358C to 478C
(Cano-Santana et al. 1992). Most cacti will show an
abrupt increase in chlorophyll fluorescence (an indicator of decreasing electron flow in Photosystem I during photosynthesis) between 508 and 568C. Furthermore, the electron transport involved in Photosystem
II starts to decrease in cacti when the photosynthetic
tissues reach temperatures between 408 and 508C (Nobel 1988). Thus, even if the plant survives high midday
temperatures, its photosynthetic system may lose much
of its functional capacity if the chlorenchyma reaches
temperatures above 458–508C. The columnar life form
allows cacti to avoid the potentially harmful effects of
high temperatures by maximizing PAR interception in
the early morning and late afternoon. The strategy,
however, has a cost, as PAR interception becomes suboptimal. For example, while horizontal cladodes of
Opuntia pilifera in Zapotitlán intercept in one day as
much as 41 mol photons/m2 of cladode area, vertical
cladodes facing east and west will intercept 23 mol
photons/m2, and vertical cladodes facing north and
south will intercept only 5 mol photons/m2 (Cano-Santana et al. 1992). In the case of C. columna-trajani, an
approximate conversion of our model’s predictions
from direct solar radiation into PAR indicates that the
plants in the field intercept ;12 mol photons·m22·d21.
Although this value is well above the compensation
level reported for cacti, which is ;3 mol photons·m22·d21, it is also below the daily PAR level that
results in maximum net uptake of CO2, which is ;30
mol photons·m22·d21 (Nobel 1988), and it is also well
below the maximum measured PAR interception for a
plane surface in the region (41 mol photons·m22·d21).
In this framework, tilting appears to be a morphological adaptation that allows the fine-tuning of a columnar morphology to its thermal and radiation environment. By tilting north-northwestwards with an angle
that is greater than the northern declination of the sun
during the summer solstice, the plant achieves a series
of changes in its radiation-interception pattern. It intercepts less radiation at midday and during the afternoon than a vertical columnar plant during the hotter
months of the year (Figs. 4 and 5). This is especially
important as it is frequently the case that summer rains
may arrive as late as July. The tilted stem intercepts
more light than an erect structure during the September
equinox, the time of the year when the summer rains
have commenced and the soils are moister, and also
when the plant shows greatest growth (Fig. 3). By tilting the stem, the nonphotosynthetic pseudocephalium
can develop without significantly losing PAR interception. In fact, tilting actually improves global PAR interception by ;2%, and it particularly improves PAR
interception during favorable seasons and during the
most favorable hours of the day. The spiny pseudocephalium, in turn, protects the flowers from potential
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Ecology, Vol. 79, No. 1
FIG. 5. Angle of incidence of direct solar radiation at midday for an erect unbranched columnar cactus compared with
an average C. columna-trajani, for the summer and winter solstices, and for the equinox. NW 5 northwest.
nectar robbers, and also keeps the night-blooming flowers shaded during the day. Finally, the simulation
shows that by shifting the pseudocephalium northnorthwest instead of directly north, the plant increases
light interception during the cooler hours of the morning (when the apparent position of the sun is in the
east), and decreases interception in the afternoon (when
the sun is in the west).
Thus, tilting has a direct bearing on the plant’s reproductive system, and ultimately on its fecundity, as
a mechanism that allows the protection of the flowers
(that bloom in the dry season) from excessive evaporative demand and from potential predators. Additionally, tilting does not hinder PAR interception, which is
fundamental for successful plant growth. In short, our
simulations suggest that tilting may have a positive
effect on plant reproduction (an important component
of fitness) without compromising plant growth (a second fundamental component of fitness). The obvious
cost of tilting in a giant columnar cactus such as our
study species is that branching becomes almost impossible without serious risk of stem breakage. Thus,
C. columna-trajani faces a trade-off compared with
other columnar species in the region, such as Neobuxbaumia tetetzo: while tilting may increase its capacity
to intercept PAR and at the same time to passively
regulate stem temperature, the species cannot benefit
from the increased PAR interception and CO2 uptake
(Geller and Nobel 1986, 1987), as well as the increased
reproductive potential (Yeaton et al. 1980) that derive
from stem branching.
This interpretation of the results of our model can
be tested with field data on the orientation of the pseu-
docephalia. In open plain habitats, the azimuth of the
pseudocephalium is north-northwest (angular mean 5
3398), but in plants growing on steep slopes, which
obstruct part of the incoming radiation, the angular
location of the pseudocephalium is shifted towards the
slope, i.e., both tilting and the development of the pseudocephalium shift in the direction where the plant receives less direct solar radiation and less PAR.
It is interesting to note that the geographic range of
this species is extremely restricted in terms of latitude.
C. columna-trajani is only found in the Tehuacán Valley between Zapotitlán and Zinacatepec, ranging from
978139 to 978309 W, and from 188189 to 188219 N (Bravo-Hollis 1978). That is, the species traverses the Tehuacán Valley occupying some 40 km from east to west,
but less than 10 km from north to south. The development of a tilting stem may be adaptive in this narrow
area, but could be nonadaptive at other latitudes, as the
success of the tilting strategy is strongly dependent on
the apparent position of the sun during the growing
season, and hence on the latitude of the site. The extreme degree of architectural specialization of this species may be at the same time the cause of its local
success and also of its geographic rareness.
The northern orientation of the flowers in C. columna-trajani and the tilting away from the equator, in
contrast with the equatorwards tilting and flower production in other cacti, deserve some attention. The difference between our study species and other reported
cactus species with stem directionality lies in the fact
that C. columna-trajani grows in a frost-free intertropical zone, where a vertically oriented columnar plant
receives light on both its southern and northern face at
January 1998
FUNCTIONAL MORPHOLOGY OF CEPHALOCEREUS
different times of the year (Peters 1993). By tilting
slightly to the north, this species intercepts less radiation during the hotter months of the year. Tilting thus
allows the passive regulation by the plant of its thermal
and radiation environment. Extratropical cacti, on the
other hand, are often limited both by low temperatures
in winter and high temperatures in summer. The apparent position of the sun for these plants is always
towards the equinox. Tilting towards the equator may
help to regulate radiation interception during the hot
summers, while still allowing the interception of significant amounts of radiation during the cold months
of the year. The interaction between the yearly radiation
pattern, the radiation interception by tilted stems, and
the growth season, remains to be studied in more detail
for these plants.
ACKNOWLEDGMENTS
We thank Amaury Dı́az-Solı́s, Pedro Luis Valverde, and
David Hodson for their field assistance. The criticisms of Stan
Szarek and an anonymous reviewer greatly improved a first
version of this paper. The contribution of J. A. Zavala-Hurtado to this investigation was part of his Ph.D. research. We
gratefully acknowledge the financial support of the National
Council of Science and Technology (CONACyT), Mexico.
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JOSÉ ALEJANDRO ZAVALA-HURTADO ET AL.
348
Ecology, Vol. 79, No. 1
APPENDIX
Characteristics of the model cactus and their variations,
b 5 [3.8798 3 exp(1.2777 H)] 2 7.0
(A.2)
used in this study for estimating the irradiance received by where b is the angle of deviation and H is the height of a
an actual or hypothetical Cephalocereus columna-trajani in- standardized plant 6 m high. This function allowed us in turn
dividual with similar characteristics.
to model the tilting angle of any specific stem segment.
Total heights and stem diameters were used for obtaining
For a plant with a total height of 600 cm, Eq. A.1 was used
the overall shape of a cactus by means of the following re- in the computation of diameters at every 50 cm from 0 to
gression equation:
550 m high, and at 595 cm high. With these data, each of the
D(H) 5 [0.03844 1 0.09673H/T 2 0.1080(H/T)2]T (A.1) 12 stem stretches was approximated as a truncated pyramid
composed by 16 equal trapezoidal sides, or facets. The calwhere D(H) 5 stem diameter (in centimeters) at any height culated diameters at each height were ascribed to the maxi(H) of the stem (in centimeters) and T 5 total height of an mum width of the bottom and the top of the truncated pyrindividual (in centimeters). This equation was obtained by amids. Finally, the plant apex was simulated by a 5 cm high
polynomial regression on field data from 10 plants growing truncated pyramid with 16 lateral sides and a 8.45 cm wide
in open plain areas (R2 5 0.75; F2,59 5 86.5; P , 0.00001).
flat top. Eq. A.2 was used to calculate the expected tilting
With the tilting angles measured for the plant segments, a angle of the stem axis for each of the 12 segments. Standard
data set was constructed for statistical analyses. As tilting of trigonometric equations were used for assigning an azimuth
the upper part of the plant may bend the lower part of the and a vertical angle to each truncated pyramid with respect
stem in the opposite direction, negative signs were assigned to the main axis of the stem. Spherical trigonometry was used
to the angles of sectors that were bent away from the azimuth to calculate the azimuth and the inclination of each facet with
of the pseudocephalium. The tilting angles for the midpoint respect to the local horizontal coordinates, knowing their azof these three categories were fitted to an arbitrary exponen- imuth and inclination with respect to the main axis of the
tial function (r 5 0.72 on a semilog scale; n 5 105; P , stem and the inclination and azimuth of each stem sector.
0.05), which allowed us to interpolate the mean angle of
Thus, the basic characteristics of the model plant (which
deviation from the basal point for any height of the stem. The are similar to the mean characteristics of actual plants in the
function obtained was
field) were as shown in Table A1.
TABLE A1. Morphometric characteristics of a model cactus used in the simulations analysis. Figures are based on average
measurements on 35 individuals of Cephalocereus columna-trajani in the field.
No. of
segment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Height class
Stem
Tilting angle
(cm)
diameter (cm)
(8 )
0–50
150–100
100–150
150–200
200–250
250–300
300–350
350–400
400–450
450–500
500–550
550–595
595–600
(crown)
23.06
27.45
30.94
33.52
35.21
36.00
35.88
34.87
32.96
30.14
26.43
21.82
16.89
8.45
22.68
21.71
20.58
0.74
2.28
4.05
6.11
8.47
11.17
14.23
17.68
21.33
21.53
Number
of facets
Facet area
(cm2)
16
16
16
16
16
16
16
16
16
16
16
16
16
1
246.60
284.94
314.49
335.28
347.30
350.58
345.10
330.86
307.86
276.10
235.54
170.14
16.04
56.81
Pseudocephalium
Segment area
(cm2)
No. of facets % covered
3945.60
4559.00
5031.87
5364.43
5556.84
5609.20
5521.52
5293.77
4925.84
4417.55
3768.67
2722.24
256.64
56.81
0
0
0
0
0
0.40
0.99
1.59
2.19
2.79
3.39
3.99
4.59
0
0.00
0.00
0.00
0.00
0.00
2.48
6.22
9.96
13.71
17.45
21.19
24.93
28.68
0.00