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Demographic analysis of a rare columnar cactus (Neobuxbaumia
macrocephala) in the Tehuacan Valley, Mexico
Ligia Esparza-Olguı
´n, Teresa Valverde*, Elena Vilchis-Anaya
Laboratorio Especializado de Ecologı
´a, Facultad de Ciencias, Universidad Nacional Auto
´noma de Me
´xico (UNAM),
Ciudad Universitaria, Me
´xico D.F. 04510, Mexico
Received 15 April 2001; received in revised form 15 May 2001; accepted 1 June 2001
Abstract
In this study we used population projection matrices to evaluate the conservation status of Neobuxbaumia macrocephala,a
columnar cactus endemic to a small region in the Tehuacan Valley, in central Mexico. Demographic data included 2-year obser-
vations on growth, fecundity and survival of individuals classified by size. Our results indicate that the population is comprised of
70% juveniles. Population growth rate was 0.979 and 0.994 for the 1997/1998 and the 1998/1999 periods, respectively. The slight
increase in lin 1998/1999 was a result of increased fecundity and seedling survival. The highest elasticity values correspond to the
survival of large/old individuals. Numerical simulations were performed by changing the value of particular matrix entries and
directly evaluating their effect on l. Population growth rate reached values above unity only when either fecundity or seedling
survival probability were increased 10-fold. Given these limitations for population growth, along with its limited distribution range
and low population densities, we propose N. macrocephala to be classified as a rare species and to promote its conservation by
favoring management practices aimed to increase germination and seedling establishment success. #2001 Elsevier Science Ltd. All
rights reserved.
Keywords: Population dynamics; Columnar cacti; Population projection matrices; Tehuacan Valley; Rare species
1. Introduction
Currently, the Cactaceae is one of several plant
families with a very high proportion of species included
in the IUCN (International Union for the Conservation
of Nature) red list of endangered taxa (Hunt, 1992;
Herna
´ndez and Godı
´nez, 1994; Nobel, 1994). This may
be explained by the fact that many cacti are specific to
particular kinds of habitats and/or they tend to support
relatively small populations, which accounts for the
high level of endemism found in this family (Herna
´ndez
and Godı
´nez, 1994). These features appear to be intrin-
sic to the biology of this group and may be determined
in part by their low relative growth rates and their low
survival probability during the early phases of estab-
lishment (Steenbergh and Lowe, 1969; Valiente-Banuet
and Ezcurra, 1991; Valiente-Banuet et al., 1991a, 1991b;
Nobel, 1994). Additionally, in recent years habitat
destruction and illegal trade have severely threatened
the persistence of many cacti species which, given their
biological features, appear to be particularly vulnerable
to disturbance.
Mexico is one of the most diverse countries with
respect to cacti. Of the nearly 2000 cacti species cur-
rently recognized by taxonomists, 850 are found in
Mexico, 84% of which are endemic (Bravo-Hollis and
Sa
´nchez-Mejorada, 1978, 1991; Arias-Montes, 1993).
Although efforts are being made by academic and gov-
ernment organizations to protect some of these species,
many of them are vulnerable because conservation and
management plans are almost non-existent given the
lack of information regarding their population biology.
In addition, the social problems involved in the nature
preservation politics of third-world rural areas are par-
ticularly complex, which makes conservation practices
even more difficult. Population studies are urgently
needed in order to provide the tools necessary to evalu-
ate the current status of existent populations, detect
vulnerable stages in the species’ life cycle and project the
populations’ fate under different ecological scenarios. This
study addresses these issues through the demographic
0006-3207/01/$ - see front matter #2001 Elsevier Science Ltd. All rights reserved.
PII: S0006-3207(01)00146-X
Biological Conservation 103 (2002) 349–359
www.elsevier.com/locate/biocon
* Corresponding author. Fax: +525-622-4828.
E-mail address: mtvv@hp.fciencias.unam.mx (T. Valverde).
analysis of a rare columnar cactus, Neobuxbaumia mac-
rocephala (Weber) Dawson, whose distribution range is
restricted to a small valley in the Tehuaca
´n area in cen-
tral Mexico.
The study of plant demography has grown tre-
mendously in the past couple of decades. A wealth of
demographic information has been generated since the
use of transition matrices was adapted to the complex
life cycles characteristic of plant populations (Lefko-
vitch, 1965; Caswell, 1989). The introduction of matrix
analysis, along with sensitivity and elasticity analyses,
has given the possibility to address important aspects of
the biology of populations including evolutionary, eco-
logical and conservation issues. Much of the demo-
graphic information that has been generated is now
being used for all kinds of purposes, from management
plans (Olmstead and Alvarez-Buylla, 1995) to life his-
tory analysis and conservation policies (Crouse et al.,
1987; Silvertown et al., 1993, 1996).
The search for demographic patterns in nature is still
a central issue in plant ecology (Horvitz and Schemske
1995). Some attempts have been made to systematize
the available knowledge on plant demography and
interesting trends have arisen (Silvertown et al., 1993).
However, little is known regarding the demography of
long-lived plant species given the complications
involved in dealing with large, slow-growing individuals
in which population changes may occur in the scale of
decades. In the case of columnar cacti, the knowledge
on both life histories and population dynamics is rather
limited (but see Steenberg and Lowe, 1969, 1977, 1983;
Zavala-Hurtado and Dı
´az-Solı
´s, 1995; Godı
´nez-Alvarez
et al., 1999), which represents a drawback when trying
to evaluate the conservation status of rare species that
might be facing significant threats to their persistence.
Thus, the contribution of this paper is to: (1) increase
our understanding of demographic patterns in nature,
in particular within a plant group for which little is known
regarding population dynamics; (2) contribute to the
knowledge of the life-histories of long-lived cacti species;
and (3) offer insight into the species’ demographic fea-
tures that determine its rarity, which in turn will allow
us to evaluate the potential impact of different conserva-
tion strategies upon the species long-term persistence.
2. Methods
2.1. Study area
The demographic analysis of N. macrocephala was
carried out in the Valley of Zapotitlan Salinas, in the
Mexican state of Puebla (18200N, 97280W). This
small valley forms a sub-system within the larger
Tehuacan Valley, which is well known for its high cacti
diversity (Herna
´ndez and Godı
´nez, 1994; Zavala-Hur-
tado and Dı
´az-Solı
´s, 1995; Valiente-Banuet et al., 1997).
The Valley of Zapotitlan Salinas has a sub-arid climate
with mean annual temperature oscillating between 18
and 22C (minimum annual temperature=11C, occur-
ring in January; maximum annual temperature=34C,
occurring in June), and total annual rainfall of ca. 400
mm; nearly 85% of the total annual precipitation falls
during the summer rainy season between June and Sep-
tember. The soils in this area are calcareous, shallow
and rocky and support a xerophitic vegetation domi-
nated by columnar cacti (e.g. N. macrocephala,N.
tetetzo,Cephalocereus columna-trajani), globular cacti
(i.e. Mammillaria sp., Echinocactus sp, Ferocactus sp.)
and other elements such as Agave macroacantha,Yucca
periculosa,Lippia graveolens,Hechtia podantha,Cerci-
dium praecox,Beucarnea gracilis,Acacia spp. and
Mimosa spp.
2.2. The species
Neobuxbaumia macrocephala is a branching columnar
cactus that may reach between 7 and 15 m in height.
The number of branches in an adult plant may vary
from one to 10. Plants bear a reddish cephalium at the
tip of each branch from which purple-red flowers
emerge during the end of the dry season (May–June).
Flowers are pollinated by bats (Valiente-Banuet et al.,
1997). Fruits ripen during June and July and are con-
sumed by bat and bird species that presumably act as
seed dispersers.
N. macrocephala has a narrowly restricted distribution
that comprises only a small area within the Tehuacan
Valley in central Mexico (the Tehuacan Valley itself is
roughly 8050 km). Within this region the species may
be found on calcareous soils in xerophitic shrublands
and tropical dry forests at an altitude of 1600–2300 m
above sea level (Bravo-Hollis and Sa
´nchez-Mejorada,
1991; Arias-Montes et al., 1997). Within its distribution
N. macrocephala is consistently found at relatively low
densities (ca. 130–200 plants/ha) compared with other
columnar cacti from the same area (e.g. Neobuxbaumia
tetetzo: 1500–2000 plants/ha—Valiente-Banuet and
Ezcurra, 1991).
2.3. Field methods
All N. macrocephala plants found within four 20020
m permanent transects were located, numbered and
tagged in June 1997. Length-wise and cross-wise coor-
dinates within each transect were recorded for each
plant for relocation purposes. The total stem length of
each plant was measured with the aid of a measuring
tape, or with a leveling rod (for plants taller than 2 m).
When a plant had several branches, the length of each
branch was measured separately and then added up
together to give a measure of total stem length.
350 L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359
Plants were tagged with the aid of metal plaques
attached to the stem through a metal wire (n= 206
juvenile and adult plants). The purpose of these tags
was to identify each individual (or each branch) with a
number, and to mark the spot from which individual (or
branch) length would be re-measured a year after. Thus,
in June 1997 two measures were taken per plant (or per
branch): total stem length, and the length from the tags
to the stem tips. Subsequently, in June 1998 and June
1999 only the length from the tag to the tip was re-
measured to obtain total length increments. In this way
we were able to measure yearly individual growth for a
2-year period.
During the fruiting season of 1997, 1998 and 1999 we
recorded the number of fruits produced per plant. This
was done with the aid of a mirror attached to the tip of
a leveling rod, which was maneuvered until the number
of fruits (or fruit marks) could be counted with bino-
culars in the mirror’s image from the ground. Addi-
tionally, a fruit sample was collected in 1997 (n= 50) to
obtain an estimate of the mean number of seeds per
fruit. These data were used to calculate a component of
plant fecundity, as detailed later.
Seed germination and seedling establishment experi-
ments were carried out in the field in order to obtain
estimates of survival and transition probabilities during
these life-cycle phases. These estimates had to be
experimentally obtained because no seeds or seedlings
were found in the field that could be followed directly to
determine their fate. Seeds were introduced to the field
at the beginning of the rainy season, in June 1997 and
June 1998, in small open boxes (15105 cm) made of
plastic mesh and half-filled with soil. Eight boxes, each
with 100 seeds, were placed on the ground, four in
completely open conditions (full sunlight), and four
under the cover of Lippia graveolens shrubs, which
appears to be the nurse plant for N. macrocephala seed-
lings and juveniles.
In N. macrocephala seed germination takes place
within the first week after sowing, given enough moist-
ure is provided. If moisture conditions are maintained,
most seeds germinate within 2 weeks. In 1997 germina-
tion was recorded monthly in our field experiment; the
first record was taken 1 month after seed sowing, and
only in this first observation did we observe germinated
seeds. In 1998 germination was recorded daily for the
first 8 days, and then monthly until no further germi-
nation was observed. The data resulting from these
observations, along with the information on seed pro-
duction, was used to calculate plant reproductive suc-
cess, which was incorporated as a fecundity measure
(F=no. of seedlings/plant=no. of seeds per plantseed
germination probability) in subsequent matrix analyses.
In this case fecundity was given in seedling units because
it was assumed that this species does not form a long-
term seed bank in the soil. Since seeds are produced
during the rainy season and are readily viable after dis-
persal, it is reasonable to suppose that dispersed seeds
either germinate or die within a relatively short time
after dispersal, as appears to be the case for other
columnar cacti (Godı
´nez and Valiente-Banuet 1998;
Godı
´nez et al., 1999). Thus, the seed stage was not
included in the population projection matrix.
Seedling establishment experiments were carried out in
1997 and 1998. Seedlings were obtained by germinating 1-
month-old seeds in a greenhouse at Mexico City in June
1997 and June 1998. Seeds were placed in Petri dishes
with an agar (2%) substrate. Seed germination reached
an average of 85% within the first 8 days; no further
germination was recorded after this date. One week
after germination seedlings were transplanted to small
plastic containers with soil and agrolite and left in the
greenhouse for 6 weeks. During this period they were
watered every 2 weeks. In 1997, seedlings were introduced
to the field in September; eight groups of 30 seedlings
each were planted in small areas (3030 cm) marked on
the ground with wooden sticks. Four of these groups
were placed in open conditions and four under the cover
of Lippia graveolens shrubs. In 1998 the same procedure
was followed and approximately the same dates were
used, with the exception that this time only 25 seedlings
were planted per group. Both in 1997 and 1998 seedling
survival was monitored monthly for 1 year.
2.4. Data analysis
2.4.1. Germination and seedling establishment
Within each season we obtained a mean germination
percentage in each of the two conditions analyzed (i.e.
open and shaded); these percentages (arcsin trans-
formed for linearity) were compared through a Student
t-test. We built seedling survivorship curves (log l
x
) for
each of the periods analyzed (1997–1998 and 1998–
1999); within each period, curves obtained in different
conditions were compared through the Peto and Peto
analysis (Pyke and Thompson, 1986) to test the sig-
nificance of the effect of the nurse plant on establish-
ment probability.
2.4.2. Matrix analysis
We subdivided the population into 10 size classes
according to plant total stem length. Each size class had
a minimum of 10 individuals from which to calculate
matrix transitions (Table 1). We estimated transition
probabilities among size classes by calculating the rela-
tive frequencies of each observed transition (including
death) from 1 year to the next. Since no deaths were
observed in the largest size class, the probability of
dying in this class was estimated as the inverse of the
length of the class, in years (Enright and Ogden, 1979),
estimated from an age-based analysis of plant growth
rate (Vilchis-Anaya 2000), as detailed in Section 3.
L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359 351
Fecundities were estimated as the mean number of
seedlings produced per adult individual in each size
class. We first calculated the number of seeds produced
per plant (obtained from its number of fruits times the
mean number of seeds per fruit) and multiplied it by the
germination probability (given by the results of the ger-
mination experiments averaged between treatments). As
previously noted, fecundities were given in seedling
units because our observations suggest that seeds do not
remain viable in the soil for long periods of time.
Seedling establishment probabilities (i.e. the transition
from the first to the second class) were calculated from
the seedling establishment experiments described earlier,
by counting the number of seedlings alive after 1 year of
planting with respect to the initial number of seed-
lings introduced in the two experimental conditions
considered.
The matrix limit properties (i.e. the dominant eigen-
value and the right and left eigenvectors, which corre-
spond to population growth rate, the stable stage
distribution and the stage-specific reproductive values,
respectively) were obtained by iteration using an Excel
worksheet especially designed for that purpose. The
95% confidence intervals for lwere calculated through
the analytic method proposed by Alvarez-Buylla and
Slatkin (1994; Valverde and Silvertown 1998).
From the right and left matrix eigenvectors we calcu-
lated the sensitivity of lto changes in each matrix entry
(Caswell, 1989); from these values we built elasticity
matrices for both study periods (1997/1998 and 1998/
1999). Elasticity evaluates the relative sensitivity of lto
relative changes in each matrix entry. Since all the elas-
ticities in a matrix add up to unity, each elasticity value
may also be interpreted as the contribution of each
matrix entry to the population’s finite rate of increase
(de Kroon et al., 1986; Caswell, 1989). Thus, elasticities
are a useful tool from a conservation point of view
because they allow us to identify the most vulnerable
phases of the species’ life cycle (de Kroon et al., 1986;
Silvertown et al., 1996; Mills et al., 1999). Additionally,
since elasticity values corresponding to different demo-
graphic processes (i.e. growth, persistence or stasis, and
fecundity) may be added up to represent proportions,
the relative contribution of each of these processes to
population growth rate may be evaluated (Silvertown et
al., 1993).
2.4.3. Matrix simulations
We used the population projection matrix obtained
for the period 1997/1998 to carry out numerical simu-
lations to evaluate the potential impact of specific
changes in particular matrix entries on population
growth rate (l). We evaluated (1) the effect of changes in
juvenile and adult mortality by increasing or decreasing
the original mortality values in percentages from 5 to
30%; (2) the effect of modifying the fecundity values by
multiplying or dividing the original values by different
numbers ranging between 2 and 10; and (3) the impact
of changes in seedling establishment success by increas-
ing or decreasing that particular matrix entry in pro-
portions ranging from 2 to 10 times. We chose to test
the effect of these particular matrix modifications
because we observed that those are the main sources of
the variation in demographic behavior between years,
and because they may throw light onto the potential
success of particular conservation practices.
Additionally, we carried out simulations by modifying
the value of the survival and persistence probability of
size-class 9 individuals, since this matrix entry was esti-
mated from growth rate analysis as the inverse of the
number of years spent by individuals in this category.
The simulations performed allowed us to evaluate the
extent to which the potential errors in our estimate
altered the results of our demographic analysis, in par-
ticular the lvalue.
3. Results
3.1. Seed germination and seedling establishment
Seed germination in greenhouse conditions reached
an average of 85%; however, in the field it was much
lower. During the summer of 1997 only one out of 400
seeds was observed germinating in each treatment, i.e. the
open and the shaded microsites, corresponding to 0.25%
germination, and thus the t-test did not detect sig-
nificant differences between treatments (t=2.138,
d.f.=2, P=0.166). In the summer of 1998 germination
percentage was significantly higher in the shaded
(4.75%) than in the open microsites (0.0%; t=4.526,
d.f.=2, P=0.032). These germination percentages were
interpreted as germination probabilities (averaged
between treatments) and were incorporated in the
Table 1
Size categories used to describe the demography of Neobuxbaumia
macrocephala
a
Category Total length (cm) Life-cycle stage
0 0–1 Seedlings
1 1.1–5 Juveniles
2 5.1–15
3 15.1–45
4 45.1–135
5 135.1–300
6 300.1–550 Adults
7 550.1–850
8 850.1–1050
9 >1050
a
Total stem length refers to the sum of the length of all stems in a
plant.
352 L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359
matrix model as part of the fecundity values. The aver-
age germination probability obtained in summer 1997
was used to build the 1997/1998 matrix, while the one
obtained in summer 1998 was applied to the 1998/1999
matrix.
With regards to the seedling survival experiments, a
significantly higher mortality was observed in the
exposed microsites than in the shaded ones for both
study periods (for 1997/1998: LR=9.056, d.f.=1,
P<0.05; for 1998/1999: LR= 4.63, d.f.= 1, P<0.05;
Fig. 1). In the exposed treatment, 100% mortality was
reached by the 5th month in 1997/1998, while in 1998/
1999 total mortality was attained within the 1st month
after seedling transplant. In the shaded treatments some
seedlings were still alive 1 year after their introduction
to the field: 2.6 and 7.4% of seedlings reached the age of
1 year in 1997/1998 and 1998/1999 respectively (Fig. 1).
Seedling survival probability was averaged between
treatments for each study period and was incorporated
in the matrix model as the transition probability from
the first to the second size category.
3.2. Matrix analysis
Mortality of N. macrocephala individuals was found
to be closely associated with size (Table 2); for both
study periods the highest probability of dying was
found among the seedling category, whereas all adult
categories showed no mortality at all. To build the
population projection matrices some adult mortality
must be incorporated in the largest size category in
order to have a defined matrix with real positive eigen-
values and to reflect the fact that old/large plants even-
tually die. The mortality of individuals in category 9
was estimated by calculating the time that an individual
may spend in this category, i.e. the approximate time
that elapses from the moment in which a plant reaches a
total stem length of 1050 cm to the moment in which it
reaches 2240 cm, which was the largest total stem length
measured. According to a study on N. macrocephala
growth rates, this time was estimated to be around 25
years (Vilchis-Anaya, 2000). Thus, mortality of category
9 individuals was estimated as the inverse of this value
(i.e. 1/25=0.04). Therefore, to calculate the persistence
probability of individuals in category 9, we took into
account both the probability of decreasing in size
towards category 8 (i.e. retrogression), and the mortal-
ity value. These persistence probabilities turned out to
be 0.869 for 1997–1998 and 0.883 for 1998–1999; the
difference between years was given by a small difference
in the retrogression probability. As detailed later,
numerical simulations were carried out by modifying
this matrix entry in order to evaluate the extent to which
the observed lvalue may depend on these estimates.
Table 2 shows the transition matrices obtained in this
study for the 1997/1998 and the 1998/1999 periods.
Along with the matrices we present the population finite
rate of increase (l) and the right and left eigenvectors of
the matrices, which correspond to the stable size struc-
ture (w) and the size-specific reproductive values (v).
The matrices for both periods are similar to some
Fig. 1. Survivorship curves (log l
x
) for the seedlings introduced to the
field in shaded and exposed microsites in (a) summer 1997 and (b)
summer 1998.
Fig. 2. Relative frequency (%) of individuals in each size category
according to the observed population structure (in summer 1997 and
summer 1998) and the calculated stable size distribution for (a) the
1997–1998 and (b) the 1998–1999 matrices. Category 0 is not shown in
these graphs because no seedlings were observed in the field; thus, the
stable size distribution vectors were standardized accordingly.
L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359 353
extent, with the exception of seedling establishment and
fecundity, which were higher in the second compared
with the first period. In both cases we observed, in gen-
eral, higher fecundity values with increasing plant size.
Only a small number of plants decreased in size from 1
year to the next; these were in category 7 in 1997/1998
and in category 2 in 1998/1999. These types of transi-
tions correspond to either the loss of branches, or the
loss of plant tips due to injury by peasants and/or cattle.
Both matrices are characterized by higher values corre-
sponding to stasis or persistence in the same plant cate-
gory compared to values corresponding to growth.
The lvalue of the two matrices was slightly below
unity (Table 2), although the 95% confidence intervals
(calculated through the analytical method proposed by
Alvarez-Buylla and Slatkin, 1994) do not allow us to
consider them as significantly different from one: the
low and high limits of lfor 1997/1998 were 0.860–1.098,
and for 1998/1999 they were 0.879–1.109. The slight
increase in lduring the second study period was asso-
ciated with an increase in both fecundity and seedling
establishment probability compared with the values
recorded during the first period.
The population’s size structure observed in 1997 and
1998 was characterized by a relatively high frequency of
plants in the first four categories, with an increasing
number of individuals towards category 4 (Fig. 2).
Individuals in categories 6–9 (i.e. adults) represent
approximately 30% of the population, with a decreasing
number of individuals towards the largest categories.
These population structures differ significantly from
those expected at equilibrium, i.e. vector win Table 2
(for 1997/1998: G=68.811, d.f.=9, P<0.05; for 1998/
1999: G=190.457, d.f.=9, P<0.05). Stable population
structures for both periods were characterized by a high
proportion of individuals in the first and the last cate-
gories (Fig. 2), particularly for the matrix corresponding
to 1997/1998. Note that Fig. 2 does not include the
seedling category since no seedlings were observed in
the field during the study period due to their small size
and their low survival probability; thus the transitions
corresponding to this category had to be estimated through
Table 2
Population projection matrices corresponding to (a) 1997–1998 and (b) 1998–1999
a
Category n
t+1
Category (n
t
)
0 123456789wv
(a) l=0.9790.119
0 4.130 11.456 10.238 31.73 0.896 0.000
1 0.013 0.435 0.022 0.003
2 0.217 0.677 0.016 0.009
3 0.097 0.865 0.013 0.029
4 0.108 0.875 0.013 0.035
5 0.025 0.900 0.004 0.152
6 0.050 0.850 0.077 0.002 0.240
7 0.150 0.615 0.001 0.200
8 0.308 0.700 0.091 0.009 0.173
9 0.300 0.869 0.024 0.158
n300 23 31 37 40 20 20 13 10 12
q
x
0.987 0.348 0.226 0.027 0.100 0.050 0 0 0 0.040
(b) l=0.9940.115
0 7.364 35.615 33.425 76.77 0.775 0.000
1 0.023 0.857 0.038 0.141 0.002
2 0.071 0.654 0.030 0.004
3 0.115 0.829 0.021 0.010
4 0.086 0.872 0.015 0.019
5 0.026 0.842 0.003 0.090
6 0.053 0.895 0.001 0.259
7 0.105 0.909 0.002 0.239
8 0.091 0.917 0.077 0.008 0.205
9 0.083 0.883 0.006 0.173
n300 14 26 35 39 19 19 11 12 13
q
x
0.977 0.072 0.193 0.085 0.102 0.105 0 0 0 0.040
a
Only non-zero entries are included to facilitate reading. Above each matrix the population growth rate ( 95% confidence intervals) is given.
w=stable-size structure; v=size-specific reproductive value; n=number of individuals in each size category; q
x
= mortality. The mortality reported
for plants in category 9 was estimated for both matrices.
354 L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359
experimental analyses. Therefore, the stable population
structures represented in Fig. 2 were standardized after
eliminating the seedling category in order to compare
them with the observed population structure. Table 2
shows that the stable population structure including the
seedling category comprises almost 90% seedlings and
2.4% category 9 adults for the 1997/1998 matrix, and
78% seedlings and 0.6% category 9 adults for the
matrix corresponding to 1998/1999.
The vector describing the size-specific reproductive
values for both study periods (i.e. vector vin Table 2)
shows very low values for the seedling and juvenile
categories, with the exception of category 5, which pre-
sents a relatively high reproductive value compared with
the other non-reproductive categories. Within the
adults, despite the increasing fecundity towards larger
sizes, the reproductive value decreases with increasing
size, which must be related to the gradual approach to
the end of life.
The elasticity matrices show that the demographic
events that contribute the most to population growth
rate are the persistence (i.e. stasis) of category 8 and 9
individuals (Table 3). The elasticities of stasis entries
were consistently higher that those representing plant
growth. In both periods the lowest elasticity values cor-
responded to fecundity entries. The elasticity of the
matrix entry corresponding to seedling establishment
was low in both the 1997/1998 and the 1998/1999 peri-
ods. The results of adding up the elasticity values asso-
ciated to each of the different demographic processes
are presented in Fig. 3. Note that in this case we con-
sidered the transitions corresponding to a decrease in
size as part of the stasis component. In both periods
stasis contributed with 88–90% of total elasticity, fol-
lowed by growth (9–10%) and fecundity (1–2%).
3.3. Matrix simulations
Although the lvalues obtained in this study were not
significantly different from unity according to their 95%
confidence intervals, we considered it interesting to
simulate the absolute effect on lof potential changes in
the values of particular matrix entries to analyze the
type of demographic behavior that would result in
higher or lower lvalues. This is precisely the aim of
sensitivity and elasticity analyses; however, these ana-
lyses do not consider the actual range of potential var-
iations in matrix entries; thus, by directly manipulating
matrix values simulating different ecological scenarios,
we could explore the way in which particular changes
would affect population dynamics. Although the mag-
nitude of the resulting changes in lmight not be mean-
ingful in an absolute sense (because they occur mostly
within the confidence intervals for l), this approach
allows us to detect those conservation strategies that
would render relatively better results.
Although mortality was found to be fairly constant
during our study period, we used our matrix model (for
1997/1998) to simulate changes in mortality because this
is one of the most important demographic components
Table 3
Elasticity matrices for the Neobuxbaumia macrocephala population studied
a
Category n
t1
Category (n
to
)
0123456 7 89
(a)
0 5.2E-05 6.1E-05 0.001 0.005
1 0.005 0.004
2 0.006 0.012
3 0.006 0.043
4 0.006 0.051
5 0.006 0.070
6 0.006 0.057 0.002
7 0.008 0.015
8 0.006 0.142 0.050
9 0.056 0.440
(b)
1 0.008 0.053 0.000
2 0.008 0.016
3 0.008 0.040
4 0.008 0.056
5 0.008 0.043
6 0.008 0.070
7 0.008 0.079
8 0.007 0.327 0.021
9 0.025 0.201
a
(a) 1997–1998 and (b) 1998–1999. The five highest values in each matrix are bold. Only non-zero entries are represented to facilitate reading.
L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359 355
that may vary as a result of changes in land use, for
instance. We modeled the effect of changes on juvenile
and adult mortality independently because we con-
sidered that survival probabilities of both groups are
quite distinct and that the mortality factors that affect
each of them might be different. When increasing juve-
nile mortality up to 30%, lvaries from 0.979 to 0.974
(Fig. 4a), which represents a very slight change. How-
ever, when adult mortality was increased 30% the effect
on lwas more dramatic (i.e. varying from 0.979 to
0.931—Fig. 4a).
The results concerning the effect of potential varia-
tions in the fecundity entries (F=seed pro-
ductionseedling germination probabilities) showed
interesting trends. When fecundities were given values
10 times lower than the original ones the effect on lwas
only slight (i.e. varying from 0.979 to 0.974—Fig. 4b).
However, when fecundity values were increased up to 10
times their original value, we obtained a labove unity
(i.e. 1.002—Fig. 4b). Note that these simulations were
carried out with the 1997/1998 matrix, which showed
lower fecundities compared with the 1998/1999 matrix.
When simulations of potential increases in fecundity
entries were carried out with the 1998/1999 fecundity
values, only a 3-fold increase was necessary to obtain a
l=1 value (results not shown).
With respect to potential changes in seedling estab-
lishment probability, we found that a 10-fold decrease
in this matrix entry produced a change in lfrom 0.979
to 0.976. However, an equivalent increase in the same
matrix entry resulted in a change in lfrom 0.979 to
1.002 (Fig. 4b). Thus, the only potential changes that
resulted in lvalues above unity were those correspond-
ing to fecundity and seedling establishment. Yet, it is
likely that these values do not vary independently but
are affected in the same way by weather conditions, for
instance. Thus, during favorable years both seed germi-
nation (which is a component of fecundity values) and
seedling establishment may vary in a correlated way.
We carried out simulations that included changes in
both fecundity and seedling establishment values simul-
taneously, and found that only a 3-fold increase in these
matrix entries was necessary to obtain a lvalue above
unity (i.e. 1.02).
As noted earlier, the matrix entry corresponding to
the survival and persistence of size-category 9 indivi-
duals was estimated by assuming that plants spend 25
years in this size category. However, the time lapse
spent in this category may vary and an error in this
estimate may have an effect on l. To address this issue
we carried out simulations assuming that individuals
may spend from 20 years to 50 years in size-category 9,
thus the value of the relevant matrix entry varied from
0.859 to 0.889, respectively (Table 4). As a result, l
changed from 0.974 to 0.991. Thus, ldid not reach a
value above unity even when the estimated time spent in
size-category 9 was doubled (i.e. from 25 to 50 years).
Population growth rate reached a positive value
(l=1.0001) only when the survival probability of the
largest adults was 0.905, which would mean a persistence
Fig. 3. Relative contribution of the different demographic processes
(i.e. fecundity, stasis and growth) to the value of laccording to the
elasticity matrices obtained for (a) the 1997–1998 and (b) the 1998–
1999 periods.
Fig. 4. Variation in population growth rate (l) that results from
modifications in matrix entries corresponding to (a) juvenile and adult
mortality (increase in mortality by the given percentages); and (b)
fecundity and seedling establishment probability. The latter graph
displays only one curve, since the results for both simulation yielded
completely overlapping trends. The projection matrix for 1997–1998
was used to perform these simulations.
356 L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359
time of 250 years for adult 9 individuals in their own
category.
4. Discussion
It has been estimated that N. macrocephala indivi-
duals may reach a maximum age of approximately 200
years, and the age at first reproduction may be close to
90 years (Vilchis-Anaya, 2000). It is clear that in the
case of this and other such long-lived species a 2-year
demographic data set is rather limited to address its
long-term population dynamics, since population chan-
ges occur in the scale of decades. Thus, the evaluation of
extinction risks for these species becomes a particularly
complicated task (Alvarez-Buylla et al., 1996; Schwartz
et al., 1999, 2000). However, until long-term studies are
performed we must do our best to use the available
information to understand the population processes of
rare taxa, like N. macrocephala. In this sense, the use of
matrix simulations may throw light onto this and other
aspects of the biology of rare species.
The results of this study showed a population growth
rate slightly below unity in both years. Yet, lconfidence
intervals do not allow us to distinguish it from a
numerically stable population. For a long-lived species
it is expected that lwould be very close to unity for
most years. Additionally, it has been recognized that in
plant populations from semi-arid regions recruitment is
favored during rainy years, thus increasing population
numbers, while the rest of the time the lack of recruit-
ment gives the impression of a slowly decreasing popu-
lation. In fact, other columnar cacti populations appear
to be performing well despite wide fluctuations in
population numbers and periods of poor seed produc-
tion and seedling recruitment. Such is the case for Neo-
buxbaumia tetetzo in the Tehuacan Valley (Godı
´nez-
Alvarez et al., 1999) and Carnegia gigantea in the
Sonoran desert (Steenbergh and Lowe, 1969, 1977, 1983;
Pierson and Turner, 1998). Thus, the case of N. macro-
cephala might be somewhat similar and the population
might be maintaining itself through occasional high
recruitment events followed by several years in which
almost no recruitment might be taking place, which in
fact may be suggested by the observed size-frequency
distribution (Fig. 2).
Although our results do not point in the direction of a
clearly declining population, we can think of a number
of factors that might threaten the long-term persistence
of this and other highly restricted, slow-growing, long-
lived species. Many of these factors arise from both the
dynamics of its natural environment and from human
activities. In the first category we may consider the low
water availability and high solar radiation, which char-
acterize semi-arid regions and impose serious limitations
to population growth, mainly because they induce high
seedling mortality and constrain the establishment of
new individuals. With regards to the human-induced
environmental threats, perhaps one of the most sig-
nificant is the increasing pressure on land-use transfor-
mation, especially in the region where N. macrocephala
lives, which is a relatively densely populated and very
poor rural area in central Mexico. As agriculture is tre-
mendously unproductive in this region due to its high
aridity, steep slopes and poor soils, peasants must rely
mainly on goats to make their living. These animals do
not need much tending and are capable of moving
around on uneven terrain and feeding on almost any
plant species; these features make them a convenient,
yet precarious, productive activity in the region.
The widespread presence of goats on semi-arid lands
in Mexico affects populations of columnar cacti by: (1)
reducing recruitment probability by directly killing
recently established seedlings; (2) limiting seedling
establishment success by reducing the shade provided by
nurse plants; and (3) causing mortality among adult
plants, since peasants frequently sever cactus stems for
thirsty goats, thus producing injuries that may result in
infections and eventual plant death. The increased adult
mortality and the absence of seedling establishment are
slowly creating a sparse landscape in which the lack of
vegetation combined with strong summer showers are
resulting in significant soil erosion.
In N. macrocephala, seed germination and seedling
recruitment appear to be strong population bottlenecks,
even when compared with other columnar cacti
(Valiente-Banuet et al., 1991a; Godı
´nez-Alvarez and
Valiente-Banuet, 1998). These features may constitute
important limitations to population growth. Yet, elasti-
city values of seed germination (an element of fecundity
entries) and seedling establishment are low, which coin-
cides with what has been found for other columnar cacti
(Silvertown et al., 1993; Godı
´nez-Alvarez et al., 1999).
In general, many long-lived species with lvalues close
to unity show this kind of elasticity pattern in which the
population dynamics appears to depend mainly on
juvenile and adult survival rather than on seed produc-
tion and seedling establishment (Enright and Odgen,
Table 4
Results of the simulations performed by changing the estimated dura-
tion of size-class 9, from 20 to 50 years
Duration of size-class
(years)
Value of
matrix entry
le
ija
20 0.859 0.974 0.437
25
b
0.869 0.979 0.440
30 0.876 0.983 0.442
50 0.889 0.991 0.445
a
e
ij
refers to the elasticity value of the matrix entry corresponding
to the persistence probability of size-class 9 individuals.
b
The conditions of the original projection matrix.
L. Esparza-Olguı
´n et al. / Biological Conservation 103 (2002) 349–359 357
1979; Oyama, 1993; Silvertown et al., 1993; Alvarez-
Buylla et al., 1996).
The result of the elasticity matrices appears to suggest
that potential changes in matrix entries representing
fecundity or seedling survival may have a negligible
effect on population growth rate. However, our matrix
simulations showed that lvalues were larger than unity
when either seedling establishment or fecundity (or
both) were significantly increased. On the other hand,
introducing changes in other matrix entries with rela-
tively higher elasticity values did not result in positive
population growth rates. Note however, that the mag-
nitude of the changes that may occur in both fecundity
and seedling establishment is much larger than that of
other matrix entries. Although the variations in l
resulting from matrix simulations are only slight and are
within the confidence intervals of the original lvalue,
the comparison of the different simulation results offer a
relative evaluation of the way in which the population
may respond to changes in alternative demographic
pathways.
The results presented here suggest that the interpreta-
tion of elasticity values for conservation purposes must
be cautious since they may provide a limited tool for
decision making (de Kroon et al., 2000). In addition to
elasticity analysis, the use of numerical simulations
using population matrix models may provide a deeper
insight into the actual limitations for population growth
(Crouse et al., 1987; Olmstead and Alvarez-Buylla,
1995; Schwartz et al., 1999, 2000). Using this metho-
dology we were able to show that N. macrocephala is
limited by restrictions in seed germination and seedling
establishment. Thus, if it is eventually necessary to imple-
ment management practices aimed to the conservation of
the N. macrocephala populations, they must concentrate
on these particular aspects of the species life cycle.
The definition of a rare species differs among classifi-
cation systems. The IUCN classification emphasizes
that rare taxa show small population numbers and are
generally restricted to remote habitats; although they
are not at present endangered or vulnerable, they are at
risk given their population characteristics (Hunter,
1996). According to the CITES classification, rare spe-
cies have small total numbers of individuals, often due
to limited geographical ranges or low population den-
sities; these populations do not face any immediate
danger but are candidates to become endangered (Pri-
mack, 1993). Both descriptions fit N. macrocephala,
which shows a small distribution range, low population
densities (ca. 130–200 plants/ha) and intrinsic limita-
tions for population growth given by low seedling
recruitment. Therefore, we suggest that N. macrocephala
should be formally classified as a rare species, since at
the moment it does not hold any conservation protec-
tion status (Hunt 1992). If long-term demographic data
eventually reveals that populations are in fact declining,
then it would be adequate to classify it as a vulnerable
species. In any case, an appropriate management plan
should favor the recruitment of new individuals to the
population, either by actively introducing seedlings and
juveniles or by increasing the survival probabilities of
naturally established ones. In this context, the wide-
spread presence of goats in the region should be some-
how regulated in order to give both the human
communities and the native vegetation a chance to
coexist.
Acknowledgements
We are grateful to CONABIO (project No. R129) for
economic support during the development of the pre-
sent study. The first author was given a grant by Fun-
dacio
´n UNAM to carry out this project. We wish to
thank Pedro Eloy Mendoza, Mariana Herna
´ndez,
Marco Antonio Romero, Sandra Quijas, Marcela
Ruedas, Cinthya Contreras, Ariel Arias and Jero
´nimo
Reyes for valuable help in the field. The comments
of two anonymous reviewers greatly improved the
manuscript.
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