Demography of an endangered endemic rupicolous cactus

Alejandro Flores Martınez • Gladys Isabel Manzanero Medina •

Jordan Golubov • Carlos Montana • Marıa C. Mandujano

Received: 2 September 2009 / Accepted: 12 February 2010 / Published online: 27 February 2010

� Springer Science+Business Media B.V. 2010

Abstract We compared the demography of two

populations of Mammillaria huitzilopochtli, an ende-

mic and threatened rupicolous cacti species with a

narrow distribution in the semiarid Tehuacan-Cui-

catlan region of central Mexico. Censuses were

conducted over a 5-year period in two populations:

a disturbed site (S1) and a well-preserved site (S2).

Five annual size-based matrices and a mean transition

matrix of each population were constructed to

estimate demographic trends. Prospective time-

invariant analyses were performed to calculate pop-

ulation growth rate and elasticities, whereas prospec-

tive stochastic analyses were performed to assess

quasi-extinction probabilities and how simulated

changes in recruitment, stasis and growth affected

the population growth rate. Retrospective perturba-

tion analyses (life table response experiments,

LTREs) were used to explore the contributions of

demographic processes, plant sizes, and temporal

variability (years) to the observed variations in

population growth rate. The species showed decreas-

ing population growth rates for almost all years and

sites, S1 showed lower population growth rates than

S2. Quasi-extinction probabilities were 1 after

9 years for S1 and 17 years for S2. Elasticity values

were highest for matrix entries corresponding to

plants remaining in the same category (stasis)

followed by growth and fecundity. LTREs showed

that fecundity had negative contributions to popula-

tion growth rates for all years in S1 population, while

it had positive contributions in 4 out of 5 years in

population S2. Prospective stochastic analyses

showed that increasing recruitment by 50% could

give population growth rates [1 in S2 while none of

the simulations give this value in S1. Increasing

survival also raises population growth rates but

always below one. These results indicate that

A. F. Martınez � G. I. M. Medina

Centro Interdisciplinario de Investigacion para el

Desarrollo Integral Regional, Unidad Oaxaca, Instituto

Politecnico Nacional (CIIDIR IPN Oaxaca), Hornos 1003,

C.P. 71230 Santa Cruz Xoxocotlan, Oaxaca, Mexico

e-mail: alexfmtz62@gmail.com

G. I. M. Medina

e-mail: gmanzane@ipn.mx

J. Golubov

Lab. Ecologıa, Sistematica y Fisiologıa Vegetal, Depto. El

Hombre y Su Ambiente, Universidad Autonoma

Metropolitana Xochimilco (UAM Xochimilco),

Calzada del Hueso 1100, Col. Villa Quietud,

04960 Coyoacan, DF, Mexico

e-mail: gfjordan@correo.xoc.uam.mx

C. Montana

Instituto de Ecologıa, A. C., Carretera Antigua a Coatepec

Km 2.5, Apartado Postal 63, C.P. 91000 Xalapa,

Veracruz, Mexico

e-mail: carlos.montana@inecol.edu.mx

M. C. Mandujano (&)

Depto. Ecologıa de la Biodiversidad, Instituto de

Ecologıa, Universidad Nacional Autonoma de Mexico

(UNAM), Apdo Postal 70-275, 04510 Mexico, DF,

Mexico

e-mail: mcmandu@miranda.ecologia.unam.mx

123

Plant Ecol (2010) 210:53–66

DOI 10.1007/s11258-010-9737-6

populations under the influence of human disturbance

will eventually be lost. According to the models the

most promising management strategy to conserve this

species is to increase recruitment rates and to give

special care to reproductive adults.

Keywords Cactaceae � Demography �Elasticity � LTREs � Mammillaria huitzilopochtli �Matrix model � Perturbation analysis

The Cactaceae family, endemic to the New World, is

made up of around 2000 species (Anderson 2001). In

the Americas, Mexico has one of the highest diversity

of cacti, both at the generic (63 genera) and specific

levels (&670 species; Bravo Hollis 1978; Guzman

et al. 2003). Species diversity comprises approxi-

mately 37% of total cacti species of which nearly

84% are endemic to Mexico (Arias et al. 2005).

Currently, this group includes a particularly high

number of threatened species (Anderson et al. 1994;

Arias et al. 2005). Their threatened status is mostly

due to the fact that cacti are vulnerable to distur-

bance, have high habitat specificity which limits their

ability to recover after natural or anthropogenic

disturbance, low individual and population growth

rates, high mortality during juvenile phases, and low

recruitment rates (Schmalzel et al. 1995; Contreras

and Valverde 2002; Esparza-Olguın et al. 2002;

2005; Alvarez et al. 2004; Mandujano et al. 2007b).

In arid environments, extreme temperatures, unpre-

dictable precipitation (Valiente-Banuet and Ezcurra

1991), and the pressure of herbivores (Cody 1993)

lead to new seedlings of succulents establishing only

rarely. Successful seedling establishment usually

occurs under the canopy of nurse plants or inanimate

objects, which both mitigate such harsh conditions

and protect seedlings from herbivores. However, the

relative importance of factors in controlling seedling

establishment varies among species (e.g. Mandujano

et al. 1998, 2002; Esparza-Olguın et al. 2002, 2005;

Navarro and Guitian 2003; Valverde et al. 2004;

Carrillo-Angeles et al. 2005; Valverde and Zavala-

Hurtado 2006, Munguıa-Rosas and Sosa 2008).

The population structure and dynamics of peren-

nial plants is the result of the demographic processes

of reproduction, establishment, growth, and survival

over many generations, but most population models

in cacti employ the simplifying assumption that the

environment is constant and analyze a single popu-

lation for few time intervals (Valverde et al. 2004;

Valverde and Zavala-Hurtado 2006; Mandujano et al.

2007b). Most ecosystems, however, can be hetero-

geneous in both time and space showing strong

variation in their environmental conditions among

years (Mandujano et al. 2001, 2007a; Esparza-Olguın

et al. 2005). Recognizing the importance of this

heterogeneity on population behavior has resulted in

an increase in the number of studies that contrast the

population structure and dynamics between habitats

and time intervals (e.g. van Groenendael and Slim

1988; Svensson et al. 1993; Navarro and Guitian

2003; Esparza-Olguın et al. 2005; Mandujano et al.

2007a).

Traditionally, the population dynamics of plant

species have used transition matrix models (van

Groenendael and Slim 1988; Silvertown et al. 1993;

Svensson et al. 1993; Menges 2000; Caswell 2001,

Ramula 2008). These models constitute a powerful

analytical tool since they allow the projection of the

potential fate of a population under different theo-

retical scenarios, as well as the evaluation of the

relative contributions of the demographic processes

occurring in different life cycle stages (de Kroon

et al. 1986; Silvertown et al. 1993). The use of

stochastic matrix models, which allow the inclusion

of the spatial and temporal environmental variability

into the analysis of the long-term population dynam-

ics (Caswell 2001; Mandujano et al. 2001; Pico and

Riba 2002; Valverde et al. 2004; Boyce et al. 2006),

has recently demonstrated that the effect of stochas-

ticity on the long-term fate of populations may

depend on an interaction between life history traits

and sensitivity to environmental variance. In this

context, stochastic demographic analyses may con-

tribute to our understanding of the causes of rarity, at

least in the aspect concerned with limitation in

population numbers and rates of seedling recruitment.

Many cacti populations have been subjected to

intense perturbations, such as habitat fragmentation,

illegal collection and trade, and land use change

toward farming and cattle ranching. Consequently,

several species are now facing marked population

declines that need urgent attention (Anderson et al.

1994; Carrillo-Angeles et al. 2005; Mandujano et al.

2007b). This need for information is in striking

contrast to the few number of species that have been

studied from a demographic point of view (Godınez-

54 Plant Ecol (2010) 210:53–66

123

Alvarez et al. 1999, 2003; Esparza-Olguın et al. 2002,

2005; Valverde et al. 2004; Clark-Tapia et al. 2005;

Mandujano et al. 2001, 2007a, b; Valverde and

Zavala-Hurtado 2006; Jimenez-Sierra et al. 2007),

even though demographic information is needed for

adequate conservation measures (Schemske et al.

1994). In addition, most studies have been done over

short time periods contributing information of limited

value to understand the long-term trends of popula-

tion parameters.

In this study we analyzed the population dynamics

of Mammillaria huitzilopochtli Hunt, a globose

cactus endemic to a small region of central Mexico,

listed as endangered under Mexican legislation on the

grounds of its limited distribution and illegal collec-

tion of specimens (Rabinowitz et al. 1986; Garcıa-

Mendoza et al. 1994; SEMARNAT 2002; Arias et al.

2005). Populations of this rupicolous species inhabit

cliffs in which gravity prevents soil accumulation,

and humidity is limited due to rapid runoff.

Over a 5-year period we studied two out of the

seven remaining populations. The two populations

differ in the degree of anthropogenic disturbance

(well-preserved and disturbed) in Oaxaca, Mexico.

We set up matrix population models, perturbation

analyses, and simulations (Caswell 2001) to address

three questions. (1) Are the populations declining?

(2) What are the most sensitive life history compo-

nents for population growth through time (years) for

each population? and (3) When incorporating sto-

chasticity, what are the potential long-term conse-

quences of the observed short-term demographic

behavior for each population?

Materials and methods

Study species and sites

Mammillaria huitzilopochtli D. R. Hunt is a globose

at first and later cylindrical rupicolous cactus with a

single stem and dark green coloration. Flowering

occurs between September and November, and the

red colored flowers (12–17 mm long) are arranged in

a crown near the tip of the stem. The clavate 15–

25 mm long fruits mature from April to July, and

have reddish to brown red coloration once ripe

(Anderson 2001). The species is found in the

Oaxacan portion of the Tehuacan-Cuicatlan

Biosphere Reserve, Mexico, a floristic region recog-

nized as a center of endemism and diversity of cacti

and other species (Villasenor et al. 1990). The species

grows in xerophilous scrub and dry tropical forest,

and populations are fragmented into small local

populations that are relatively far from each other.

Only seven populations are known to actually exist

(Peters and Martorell 2000), and they are established

on a total surface of 1058 ha, with a density ranging

from 450 to 6300 ind/ha. This study was carried out

from 1999 to 2004 (5 years of demographic data) in

the Cuicatlan Valley (17�480 N, 96�580 W) where

mean annual rainfall is 553 mm, most of which falls

between June and September, and a mean annual is

temperature of 25.5�C. In 1999 when we started this

study, three populations were reported to exist, one of

which (Distrito de Etla) when revisited had already

been destroyed by urban development. The two

remaining populations were the ones reported in

herbarium specimens at the time (Voucher specimens

in Mexico City, Mexico MEXU 474935, 518191,

790174, 202345, 387911). The two populations were

living under contrasting disturbance conditions (Flo-

res-Martınez and Manzanero 2005). The first site

(disturbed site, hereafter S1, 17�480 4100 N,

96�570 5000 W) is in an area fragmented by housing,

road construction, and sand-mine operations. The

second site (conserved site, hereafter S2,

17�5401900 N, 96�570 5600 W) is 18 km north of S1

and still has large portions of native vegetation cover.

The sites also differed in plant density (900 ind/ha in

S1 and 3850 ind/ha in S2). The species is very

patchily distributed in its distributional range; so

extrapolations of total number of individuals are

always overestimates. Both sites have Neobuxbaumia

tetetzo (F.A.C. Weber) Backeb. as the dominant

species with associates Escontria chiotilla (F.A.C.

Weber) Rose, Pachycereus weberi (J.M. Coulter)

Backeb., Myrtillocactus geometrizans (Mart.) Con-

sole, Hechtia sp., Turnera difusa Willd, Plumeria

rubra L., and Bursera morelensis Ramırez. Individ-

uals of M. huitzilopochtli can be found on both sides

of gorges running through the area, with no relation

of the number of individuals or their density with the

cardinal orientation of the slope. Since the beginning

of our study, individuals found in the vicinity of our

permanent plot at S1 were killed by the construction

of a secondary road leading out of the town of

Cuicatlan. We found no differences in rainfall

Plant Ecol (2010) 210:53–66 55

123

regimes (t = 2.117, df = 10, P [ 0.05) during the

study period or in soil characteristics between sites

(Flores-Martınez 2008). To characterize disturbance,

we used the method proposed by Martorell and Peters

(2005) that uses 14 different metrics that incorporate

human activities, livestock raising, and land degra-

dation into a weighted relative disturbance index

(DI = 0.1334 GOAT - 0.1631 CATT ? 0.1334

BROW ? 0.0799 LTRA - 0.1257 COMP ? 0.1931

FUEL - 0.0231 LTRA ? 0.0758 TRAS ? 0.1389

PROX ? 0.1371 CORE ? 0.0929 LUSE ? 0.1133

EROS ? 0.1837 ISLA ? 0.1009 TOMS) that varies

from 0 to 100 (0 being less disturbed).

Population dynamics

Transition matrix construction

All individuals within each population (N = 197 in

S1 and N = 476 in S2) were labeled, mapped, and

surveyed annually in the month of July from 1999 to

2004 (5 years of demographic data), and fruits were

counted during summer. Each individual was mea-

sured (height) with the aid of a caliper to the nearest

0.01 mm as height more accurately described the

growth of the single shoot apical meristem than other

morphological measurements.

In order to examine population dynamics five

annual size-transition matrices were constructed for

each population studied (S1 and S2). Populations

were structured into five classes, which were a

combination of size (cm) and stage: seedlings C1,

juveniles C2 (0.1–2 cm), young adults C3 (2.1–

4 cm), mature adults C4 (4.1–6 cm), and old adults

C5 ([6.1 cm) included the last size class that actually

changed shape due to gravity.

The seed category was not considered in matrix

construction because seeds rapidly lose viability in

periods greater than 1 year (Flores-Martınez et al.

2008). Entries for fecundity, located in the first row of

the matrix (elements a1j), represented the average

contribution of the individuals in each size category to

the seedling class. Since no establishment of seedlings

was found during the study period, fecundities (entries

a1j) were assessed by multiplying the number of fruits

per plant in each size category (from the yearly census)

times mean seed production (43 seeds per fruit) times

the mean proportion of seed germination (0.89)

divided by the number of individuals found in each

size class. Seed germination was estimated through

laboratory experiments with seeds\1-year-old kept at

room temperature and germinated in humid filter paper

(Flores-Martınez et al. 2008). Owing to the difficulty

of estimating seed mortality and evidence of high fruit

consumption in the field, the value of fecundity was

multiplied by 0.1% to get final fecundities (a1j), a value

that reflects the rare establishment of individuals in the

Cactaceae and also makes the life cycle adequate for

analysis (Mandujano et al. 2001; Contreras and

Valverde 2002). In order to determine seedling

survival under field conditions, seedlings were germi-

nated in controlled conditions, acclimatized by water-

ing spaced into 2 week periods, and transplanted to

field conditions during September 2002 at each site. As

previous experiments showed no seedling survival

under direct solar radiation we used the two most

common nurse plants (see Flores-Martınez 2008).

Seedlings were followed for 8 months, and the values

of final survival (0.15 for S1 and 0.125 for S2) were

used for analysis (entry a21).

For each habitat we constructed two kinds of

transition matrices: (1) annual matrices, based on the

data for each year, and (2) mean matrices, con-

structed by averaging the class-specific individual

number values for the five matrices at each site. The

matrix population model was: nt ? 1 = A nt, where

A is the transition matrix and nt is a vector which

includes the numbers of individuals in the stage

classes in time t (Caswell 2001). The program

MATLAB-PC ver 7.0 (The MathWorks Inc, MA,

USA) was used for all matrix analyses. Confidence

intervals for the finite rate of population growth (k)

were estimated using the series approximations

proposed by Caswell (2001): V(k) =P

i,j

Pkl

Cov(aij, ajk)(qk/q aij)(qk/q akl). Because transition

probabilities represent estimates of the binomial

parameter, p, the variance was calculated as

V(aij) = aij (1 - aij)/n the SE of k was then the

square root of V(k), and 95% confidence intervals

were k ± 2SE(k) (Caswell 2001). Annual projection

matrices were used to characterize the population

dynamics, determine changes in k between years and

sites, and assess changes in mortality rates and

reproductive values between years (Mandujano et al.

2001). Mean matrices were also used to determine

differences in population growth rates, compare vital

rates between sites, and to represent the life cycle

diagram.

56 Plant Ecol (2010) 210:53–66

123

The contribution of the vital rates toward popula-

tion growth was assessed through the construction of

sensitivity and elasticity matrices, a prospective

approach that helped us determine how k would be

affected by changes in survivorship, growth, and

fecundity (de Kroon et al. 1986; Mandujano et al.

2001; Boyce et al. 2006).

Life table response experiments (LTREs)

Life table response experiments (LTREs, Horvitz

et al. 1997; Caswell 2001) were used to estimate the

contribution of year, plant size, and site to the

variation of k in one analysis, and of year, site, and

demographic process to the variation of k the

elasticities of k in a second analysis. These analyses

provided a means of exploring the contribution of any

given entry from the transition matrix to the observed

value of k (Horvitz et al. 1997; Tickin and Nantel

2004; Mandujano et al. 2007a). LTREs have n

treatments (in this case n = 10, two levels of site

and five levels of year), yielding population projec-

tion matrices A(m) and rates of increase k(m) for

m = 1,…,n. The main effects of each factor and the

interactions among factors in two-way cross-classi-

fied treatments can be decomposed. A(m) = A(ij) was

the transition matrix resulting from the ith level of

time (years, with five levels, 2000–2001, 2001–2002,

2002–2003, 2003–2004, and 2004–2005) and the jth

level of site (S1 or S2), and k(ij) its eigenvalue. A(r)

was the reference population projection matrix (mean

matrix, overall S1 and S2 by year combinations) with

corresponding rate of increase k(r). The effect of a

treatment m on k was then decomposed into contri-

butions from each of the matrix entries (Caswell

2001).

Numerical simulations

We used numerical simulations to find out how

changes in demographic parameters would impact

population growth rates. In these models the popu-

lation growth rate depends on different conditions

(annual matrices that have a certain probability of

occurrence), in such a way that a temporal sequence

of annual projection matrices is generated by a

stochastic process (Caswell 2001). To estimate ks (the

stochastic growth rate) we used the popbio package

(Stubben and Miiligan 2007) for both sites (consid-

ering the five transition matrices with equal proba-

bility). We also estimated quasi-extinction

probabilities (50,000 simulations) for both popula-

tions over a 50-year period, when a final mean

population size of 30 individuals was reached. Given

the difficulty and estimation of fecundity, the C1 size

class was excluded from final population densities in

calculating quasi-extinction probabilities (Morris and

Doak 2002).

We simulated changes in particular matrix entries

in the annual projection matrix by changing the

relevant entries in the matrices and directly evaluated

their effect on k. Perturbations were done on three

processes because of the following reasons: (1) the

values of fecundity were changed because seed

germination and seedling establishment (a component

of fecundity) were only estimated and not seen during

the study period within the permanent plots, (2)

growth was identified as having and important effect

on k (according to the values of elasticity), and (3)

survival because this demographic process had the

highest values of elasticity, and the effect of illegal

collection and trade is directly linked to this demo-

graphic process. We therefore modified the following

entries: fecundity (matrix entry a1j) growth of the C3

size class (entry a43) and survival of C3, C4, and C5

(matrix entries a33, a44, and a55, respectively). For all

numerical simulations, we changed the relevant

values in the annual matrices and obtained the

stochastic growth rates (ks) after 50,000 simulations

assuming equal probability of occurrence for each

matrix (Morris and Doak 2002).

Owing to the difficulty of estimating fecundity

under natural conditions, we simulated changes (50,

20, 10, and 1% of total seedling survival) in seedling

survival of the mean matrix in order to explore the

influence of successful reproduction on rate of

population growth. The reductions in the estimates

of fecundity were based on the observed seedling

survival rates under field conditions. This analysis

would indicate the effect of different fecundity

probabilities in each population on the population

growth rate. In addition, growth of size class C3 was

increased by 10 and 20%, and stasis in size classes

C3, C4, and C5 was increased by 10 and 20% (to

simulate the protection of adult individuals).

Plant Ecol (2010) 210:53–66 57

123

Results

We found that both sites showed some degree of

human disturbance (DI), but DI differed between

sites. The value of DI for the most disturbed site (S1

site) was 52.05, and 14.71 for the S2 site mainly

related to land degradation and human activities. This

disturbance was also reflected in plant density: mean

density was 90 ind/ha in S1 and 385 ind/ha in S2.

Population dynamics

We found that reproductive individuals do not

produce fruits in successive years. In S2, most

individuals produced fruits in one of the studied

years, while others produced fruits during two or

three consecutive years. No individuals, however,

produced fruits in all five studied years. On the

contrary, reproductive individuals at S1 only pro-

duced fruits once over the study period. The

percentage of plants bearing fruits was highly vari-

able between years in S2 (7.71, 9.83, 25.74, 9.7, and

17.81 each year from 1999 to 2004, respectively) and

in S1 plants showed a decreasing fruit production in

four of the five studied years (4.23, 3.78, 0.8, 0, and

5.28 from 1999 to 2004, respectively). Individuals of

the largest size class had lower fruit and seed

production than smaller sized reproductive classes

(4 years in S1, and for 3 years in S2). Even though

mean number of seeds per fruit did not differ between

populations (S1 = 42 ± 23 and S2 = 40 ± 11;

t = 0.17, df = 38, P = 0.864), there were differ-

ences in the number of fruits per plant which resulted

in a contrasting total mean seed production by

individual (5.85 ± 2.12 SE seeds/ind for S1 and

23.37 ± 5.24 SE seeds/ind for S2, P \ 0.01). The

germination rate of seeds less than 1-year-old was

95% ± 2.332 SE in S2 and 89% ± 0.808 SE in S1,

and the mean seedling survival after 8 months in field

conditions was 12.5% ± 1.847 SE in S1 and

15% ± 2.771 SE in S2 (Fig. 1, transition from

seedling to C2). The mean life cycle shows that both

populations begin reproduction at size class C2

(Fig. 1a, b), and stasis increased with size class

except in size class C2 for S1, which showed

important contributions of growth to size class C5

(Table 1). Retrogression from class C3 was observed

at both sites, but at S1 regression to smaller size

0.150 0.4876 0.245 0.181

0.0034 0.0068 0.0082

0.095 0.09080.0322

0.0058

bλ = 0.8117 ± 0.1122

0.002

0.3848 0.569 0.5484 0.6964

C2 C3 C4 C5C1

aλ = 0.7733 ± 0.1220

0.125 0.2226 0.2414 0.1126

0.0008 0.0013 0.0018

0.1338 0.04780.043

0.0214

0.0144

0.0001

0.5288 0.5042 0.5646 0.6464

C2 C3 C4 C5C1

Fig. 1 Life cycle diagram

of Mammillariahuitzilopochtli from two

sites a = S1 and b = S2 in

central Mexico. The values

correspond to the mean

matrix (1999–2000, 2000–

2001, 2001–2002, 2002–

2003, and 2003–2004). The

numbers in the center of

each circle indicate size

class (C1–C5) and stasis.

The average fecundity

(number of seedlings

individual-1 year-1) is

indicated by the lower

hatched arrow connecting

reproductive classes to size

class 1. The solid arrows

connecting circles represent

probabilities of growth and

retrogression between size

classes. Finite rate of

population growth (k ± SE)

of each site is provided at

the top of each life cycle

diagram

58 Plant Ecol (2010) 210:53–66

123

Table 1 Transition matrices by site and year for Mammillaria huitzilopochtli populations

S1 1999–2000 k = 0.8096± 0.1535

S2 1999–2000 k = 0.7356± 0.1534

C1 C2 C3 C4 C5 ni C1 C2 C3 C4 C5 ni

C1 0 0.0004 0.0005 0.005 0.002 0.0079 C1 0 0 0.004 0.005 0.009 0.017

C2 0.125 0.281 0 0 0 57 C2 0.150 0.236 0 0 0 110

C3 0 0.351 0.538 0.054 0 78 C3 0 0.591 0.318 0.010 0 217

C4 0 0 0.321 0.568 0.040 37 C4 0 0 0.429 0.375 0 104

C5 0 0 0.013 0.216 0.760 25 C5 0 0 0 0.375 0.733 45

mi 0.875 0.368 0.128 0.162 0.200 mi 0.850 0.173 0.244 0.240 0.267

S1 2000–2001 k = 0.6973

± 0.1554

S2 2000–2001 k = 0.8832

± 0.1032C1 C2 C3 C4 C5 ni C1 C2 C3 C4 C5 ni

C1 0 0 0.003 0.001 0 0.004 C1 0 0 0.002 0.005 0.006 0.013

C2 0.125 0.563 0.156 0 0 16 C2 0.150 0.731 0.096 0 0 26

C3 0 0.063 0.578 0.447 0.107 64 C3 0 0.154 0.756 0.235 0 135

C4 0 0 0.031 0.340 0.143 47 C4 0 0 0.037 0.561 0.243 132

C5 0 0 0 0.043 0.536 28 C5 0 0 0 0.038 0.595 74

mi 0.875 0.375 0.234 0.170 0.214 mi 0.850 0.115 0.111 0.167 0.162

S1 2001–2002 k = 0.6556± 0.5367

S2 2001–2002 k = 0.8366± 0.1241

C1 C2 C3 C4 C5 ni C1 C2 C3 C4 C5 ni

C1 0 0 0.0006 0 0.002 0.0026 C1 0 0 0.008 0.013 0.015 0.037

C2 0.125 0.500 0 0 0 20 C2 0.150 0.563 0.029 0 0 32

C3 0 0.300 0.435 0.043 0 62 C3 0 0.344 0.652 0.062 0 138

C4 0 0 0.355 0.565 0 23 C4 0 0 0.174 0.691 0.082 97

C5 0 0 0 0.130 0.647 17 C5 0 0 0.007 0.144 0.653 49

mi 0.875 0.200 0.210 0.261 0.353 mi 0.850 0.094 0.138 0.103 0.265

S1 2002–2003 k = 0.7338

± 0.2328

S2 2002–2003 k = 0.8729

± 0.1014C1 C2 C3 C4 C5 ni C1 C2 C3 C4 C5 ni

C1 0 0 0 0 0.003 0.003 C1 0 0 0.001 0.004 0.002 0.007

C2 0.125 0.500 0 0 0 10 C2 0.150 0.227 0.009 0 0 22

C3 0 0.200 0.441 0 0 34 C3 0 0.682 0.519 0.042 0 108

C4 0 0 0.324 0.600 0 35 C4 0 0 0.398 0.547 0 95

C5 0 0 0.059 0.143 0.733 15 C5 0 0 0.009 0.295 0.872 47

mi 0.875 0.300 0.176 0.257 0.267 mi 0.850 0.091 0.065 0.116 0.128

S1 2003–2004 k = 0.8742± 0.2154

S2 2003–2004 k = 0.7809± 0.1422

C1 C2 C3 C4 C5 ni C1 C2 C3 C4 C5 ni

C1 0 0 0 0.0006 0.002 0.0026 C1 0 0 0.002 0.007 0.009 0.018

C2 0.125 0.800 0.059 0 0 5 C2 0.150 0.167 0.027 0 0 6

C3 0 0.200 0.529 0.125 0 17 C3 0 0.667 0.600 0.126 0 75

C4 0 0 0.176 0.750 0.056 32 C4 0 0 0.187 0.568 0.129 95

C5 0 0 0 0.031 0.556 18 C5 0 0 0.013 0.053 0.629 70

mi 0.875 0 0.235 0.094 0.389 mi 0.850 0.167 0.173 0.253 0.243

S1 = population disturbed site; S2 = population conserved site; C1 = seedlings \0.1 cm; C2 = juvenile of 0.1–2 cm; C3 = young adults of 2.1–4 cm; C4 = mature adults of 4.1–6 cm; and C5 = old adults of[6 cm, mi = mortality. In the first row, seedlings per class are given. Values in the

main diagonal indicate the probability of stasis, values below the diagonal are transitions corresponding to growth, and values above the diagonal

indicate regression. Instantaneous rates of growth (k ± SE) are given next to each site 9 year combination. ni is the number of individuals in each sizeclass

Plant Ecol (2010) 210:53–66 59

123

classes could be found between noncontiguous cat-

egories. Mortalities based on the total number of

individuals of the mean matrix were higher in S1 that

in S2 (35.9 and 30.3%, respectively) being variable

between years and sites (mi, Table 1). In both

populations the highest levels of mortality were

predominantly in size class C5, followed by C2 in S1

and C4 in S2 (Table 1).

Growth rates showed declining populations except

in S1 for 2001–2002 (k = 0.6556 ± 0.5367) and

2003–2004 (k = 0.8742 ± 0.2154, Table 1). How-

ever, the confidence intervals make the value of k at

equilibrium uncertain. The mean matrix showed

values of k below unity for both populations

(Fig. 1) suggesting that over the long term, popula-

tions are prone to be in further peril. We found

significant differences between the mean observed

and projected stable size distributions in both popu-

lations (Fig. 2, G-test; P \ 0.01). Differences were

mainly found by an excess of observed individuals in

size class C2 and C3 and a more than expected

number of individuals in the last two size classes.

Size classes C1 for both populations and C4 for S1

did not differ from projected stable size distributions.

Elasticity analysis

The elasticity analysis on mean annual matrices

showed that the elasticity of stasis was similar for

both sites (S1 = 73.7% and S2 = 75.4%), growth

elasticities were 14.11% and 12.52% for S1 and S2,

respectively, and the elasticity of fecundity was

higher in S2 (13.09%) than in S1 (11.8%). On a

yearly basis, the highest elasticity values corre-

sponded to stasis in some years and to growth in

others suggesting that the populations respond to

precipitation by an increase in the relative importance

of growth (Table 1). In addition, the elasticity of

retrogression was higher at S1 (13.09%) than at S2

(11.8%). In terms of stasis, the highest values were

associated to size category C5 followed by C4 in S1

and by C3 in S2.

Life table response experiments (LTREs)

The LTREs showed different results between popu-

lations. In terms of size classes, S2 showed consistent

positive contributions from three out of four size

classes toward k, while in S1 all but size class C4

contributed negatively to k (Fig. 3a). When consid-

ering the effect of year (Fig. 3b), the contribution of

C1 was negligible for all years probably due the fact

that entries were estimated; however, contributions

were either consistently negative for size classes C3

or larger (1999–2000 and 2001–2002), and the

contributions for the other years are highly variable

between years. When subdividing the contributions

by demographic process, fecundity was consistently

negative for S1 and positive (except during 2000–

2001) for S2 (Fig. 4). Stasis contributed negatively in

3 out of 5 years in S1 and 1 out of 5 in S2 (Fig. 4).

For growth, contributions in S1 and S2 tended to have

the same pattern except during 2001–2002, which

showed positive contributions in S1 and negative in

S2, negative contributions were very high in one year

(2000–2001, Fig. 4).

Numerical simulations

Mean matrix population growth rate in S1 was below

unity regardless of increases in fecundity, growth or

stasis (Fig. 5). The same decline was found for S2,

except that increases in fecundity above 50% gave

values above unity (Fig. 5). The stochastic growth

Fig. 2 Differences between the observed distribution (hatchedbars) and projected stable size (solid bars) of Mammillariahuitzilopochtli in S1 (black/solid hatch) and S2 = (white/coarse hatch) habitats. Data were from the mean matrix for

each site from 1999 to 2004. Size classes 1–5 correspond to the

following (cm): \0.1 (C1, seedlings); 0.1–2 (C2, juveniles),

2.1–4 (C3, young adults), 4.1–6 (C4, mature adults), and [6

(C5, old adults). Asterisks indicate significant differences

between the observed and projected stable size distributions

(P \ 0.05)

60 Plant Ecol (2010) 210:53–66

123

rates suggested that both populations are decreas-

ing (S1, ks = 0.7711 ± 0.0004 95% CI, S2, ks =

0.8094 ± 0.0005 95% CI). The quasi-extinction

probability after 6 years was above 0.5 and reached

1 after 9 years for S1, while the population at S2 had

a quasi-extinction probability above 0.5 after

12 years and reached 1 after 17 years.

Discussion

The projected stable size distribution was signifi-

cantly different from the observed distribution for

both populations as found in other demographic

studies (Rosas and Mandujano 2002; Esparza-Olguın

et al. 2002; Pico and Riba 2002, Godınez-Alvarez

et al. 2003). Interestingly, the reported pattern is

similar: an overrepresentation of the largest size

classes and seedling or juveniles in the stable

structure, suggesting a lack of adults and seedlings

in the observed structure. On the one hand for M.

huitzilopochtli two reasons could determine the

pattern (1) the recent removal of adult individuals

by looting or disturbance and (2) the limiting

conditions imposed by habitat (water runoff, slope,

and bare rock habitat) that contribute to adult

mortality. The main cause of mortality in the largest

size class was associated to dropping of individuals

from the cliffs when their weight can no longer be

supported by the substrate and root system, a size

constraint that is also imposed by habitat conditions.

Garcıa et al. (2002) also found small numbers of large

individuals in four rupicolous species of the Pyre-

nees, even though the causes of mortality were not

explored. On the other hand, because seedling

recruitment was not seen during the study period,

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Con

trib

utio

ns

C1 C2 C3 C4 C5

Size class

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

C1 C2 C3 C4 C5C

ontr

ibut

ions

Size class

a

b

C2

Fig. 3 Contribution by asize class (C1–C5) from

analyzing the life table

response experiments

(LTREs) by population

(S1 = white bars and

S2 = black bars), and b by

size class and year (1999–

2000 black, 2000–2001

white, 2001–2002 gray,

2002–2003 hatched, and

2003–2004 dotted), in order

from left to right. Positive

values are associated to

increases in the values

of k, while negative values

are responsible for a

decrease in k

Plant Ecol (2010) 210:53–66 61

123

differences observed for size class C2 were probably

due to the fact that our model includes the rate of

recruitment as an estimation, calculated from the

number of seeds (under natural conditions), seed

germination (in controlled conditions), and seedling

survival (under natural conditions). The estimated

probabilities of seedling recruitment and survival for

M. huitzilopochtli are very high (i.e., [0.1) in

comparison to other demographic studies (i.e.,

\0.01, Mandujano et al. 2001, 2007a; Esparza-

Olguın et al. 2002; Clark-Tapia et al. 2005; Valverde

and Zavala-Hurtado 2006; Jimenez-Sierra et al.

2007). The method used to estimate recruitment and

seedling survival has been previously used as a

surrogate of fecundity (see Valverde et al. 2004;

Clark-Tapia et al. 2005; Esparza-Olguın et al. 2005);

however, the approach tends to overestimate recruit-

ment. Although the lack of realistic information on

this life cycle transition is a drawback of our data set,

the use of simulations allows an evaluation of their

contributions. In this study, we strongly reduced the

fertility schedule estimated from greenhouse exper-

iments and included a value of fecundity multiplied

by 0.1% as means of adding the realism of field

observations (Mandujano et al. 2001; Contreras and

Valverde 2002).

The simulations and LTREs reinforce the com-

bined importance of seedlings for population growth.

In the Cactaceae, seedling establishment has been

shown to be one of the main bottlenecks to popula-

tion growth due to the harsh environmental condi-

tions found in arid and semiarid environments

(Shreve 1931; Franco and Nobel 1989; Valiente-

F

L

G

-0.002 -0.001 0 0.001 0.002 0.003

1999-2000

2000-2001

2001-2002

2002-2003

2003-2004

-0.2 -0.1 0 0.1 0.2 0.3

1999-2000

2000-2001

2001-2002

2002-2003

2003-2004

1999-2000

-0.2 -0.15 -0.1 -0.05 0 0.05

1999-2000

2000-2001

2001-2002

2002-2003

2003-2004

Yea

r

Contributions

Fig. 4 Contributions by demographic process (F = fecundity,

L = stasis and G = growth) from the life table response

experiment (LTRE) for each population (S1 = white bars,

S2 = black bars) and year (2000–2004). Positive contributions

are associated to increases in the value of k and negative values

to decreases in k

Fig. 5 Stochastic log growth rates (log ks) under different

management scenarios in two populations of Mammillariahuitzilopochtli (S1, black circles and S2, empty circles) in

central Mexico. The matrices used corresponded to five annual

transitions per population (1999–2000, 2000–2001, 2001–

2002, 2002–2003, and 2003–2004), where each matrix had

the same probability of being chosen. Observed value with no

modification from the annual matrices (see Table 1),

SS = fecundity, GC3 = changes in growth for category C3,

S = changes in survival for individuals in size class C4 or C5.

The solid line represents equilibrium conditions (k = 1)

62 Plant Ecol (2010) 210:53–66

123

Banuet and Ezcurra 1991; Mandujano et al. 2001,

2007a). Almost all demographic studies obtain seed

germination and seedling recruitment from experi-

mental trails (e.g., Esparza-Olguın et al. 2002; Clark-

Tapia et al. 2005; Jimenez-Sierra et al. 2007). Added

to this difficulty is the fact that the habitat where

M. huitzilopochtli is found contributes to the absence

of seedlings and increases mortality of adults. In

other rupicolous species seedling establishment is

also rare because the natural conditions of these

microhabitats, cracks and cervices of limestone rock

without soil, hard runoff, and high rates of insolation,

strongly reduce the probability of germination and

subsequent survival (Kephart and Paladino1997; Pico

and Riba 2002; Navarro and Guitian 2003; but see

Munguıa-Rosas and Sosa 2008). In some cases

seedling establishment was increased by as much as

35% through hand sowing (Garcıa 2003), a response

also found in M. huitzilopochtli, where hand sowing

in natural conditions increased seedling survival by as

much as 15%.

Our results suggest that given the poor situation of

M. huitzilopochtli and the difficulties for increasing

survival in adult plants, reproduction (recruitment) is

the most practical solution to avoid extinction and

recover a more stable scenario for conservation. The

elasticity values of fecundity were low in all cases,

which is common for perennial plants (Silvertown

et al. 1993; Rosas and Mandujano 2002). Individual

fruit production has no apparent relation to environ-

mental factors (precipitation was similar between the

two studied populations), a phenomenon observed

also in other perennial plants and even in other

rupicolous species (Garcıa et al. 2002; Pico and Riba

2002; Garcıa 2003). Variation in flower and fruit

production for cacti species especially for those

inhabiting arid environments has been considered a

bet hedging strategy for the persistence of the

population, as reproductive success can be deferred

to adequate environmental conditions (Bowers 2000)

or pollinator availability. The elasticities were asso-

ciated to survivorship as found for most Cactaceae

(Rosas and Mandujano 2002; Godınez-Alvarez et al.

2003) but varied in each studied year. The variation

in elasticities is a common result in desert perennial

species (Golubov et al. 1999; Esparza-Olguın et al.

2005; Jimenez-Sierra et al. 2007), which are able to

respond to prevailing environmental conditions.

The best estimates of k suggest declining popula-

tions but the wide confidence intervals make this

conclusion very uncertain, both populations are

declining with one population tending to increase in

some years. The stochastic growth rate suggests a

dramatic story in which both populations are likely to

go extinct in the near future under current conditions.

The values of k did not correlate with high or low

seed production even though seeds do not generate a

seed bank (Flores-Martınez et al. 2008). Apparently,

perennial species can buffer environmental variation

through the rate of population growth, changing the

relative sensitivities of different demographic pro-

cesses through time (Mandujano et al. 2001, 2007a;

Esparza-Olguın et al. 2002, 2005; Pico and Riba

2002).

The LTREs showed that contributions of C1

toward k were small compared to other demographic

processes, and a constant negative contribution of

fecundity toward k in all years. However, the

percentage of plants producing seeds in S2 was

always above 6% while plants in S1 had a continuous

decrease in the number of fruits (\5% for all studied

years) a pattern that was followed by all reproductive

categories. It is possible that human disturbance may

be influencing some aspects of reproduction. Being

self-incompatible, with no clonal propagation,

M. huitzilopochtli depends entirely on sexual repro-

duction (fruit and seeds) and seedling establishment,

two attributes that were more affected at S1, which

had higher disturbance. In rare and threatened species

of cacti, population decreases have been found to be

related to reduced investment in reproduction (Espa-

rza-Olguın et al. 2005; Mandujano et al. 2007b),

which in turn is negatively effected by disturbance

(Jimenez-Sierra et al. 2007; Mandujano et al. 2007a).

The high elasticity values of stasis observed in both

populations suggest that they rely on the survival of

remaining adults, and therefore, population numbers

would decline as these adults disappear. Instead, the

S2 population had the highest elasticity values

associated to growth or stasis depending on the year

indicating a paramount importance of both demo-

graphic processes on the rate or population growth.

Under relatively benign conditions, changes in

growth rates affect k more intensely than under

disturbance regimes. If in addition to disturbance

individuals are collected (at a rate of 10% or more for

Plant Ecol (2010) 210:53–66 63

123

the largest size classes) in the disturbed site, popu-

lations will decrease over time.

Our results suggest that human disturbance may be

affecting population dynamics. Previous studies

applying the same disturbance technique have shown

that disturbance affects population density of Mam-

millaria pectinifera (Martorell and Peters 2005). Both

populations of M. huitzilopochtli under current con-

ditions may be lost over time, especially if distur-

bance is not stopped and a means of increasing

seedling survival is found. The whole species can

only be found in seven sites some of which have

\450 individuals (Peters and Martorell 2000) jeop-

ardizing the success of any recovery plan. The

demographic parameters of this species suggest that

its ability for population growth is severely limited by

a lack of reproduction, which was shown to have

important effects in reproductive populations.

Additionally, the high habitat specificity and small

distribution range of the species are attributes that

further make this species vulnerable to extinction. Few

studies have addressed endangered species in rupico-

lous habitats (Pico and Riba 2002; Garcıa et al. 2002;

Garcıa 2003); so there is little information on their

population dynamics. Specifically for the Cactaceae,

Martorell and Patino (2006) have suggested that some

of the species of the Series Supertextae included in the

Mammillaria (like M. huitzilopochtli and M. cruci-

gera) that are susceptible to chronic disturbance were

once more widely distributed (Martorell and Peters

2005) and are currently restricted to remnant popula-

tions (e.g., Pico and Riba 2002). Poor recruitment, the

continuously decreasing fruit and seed production and

high mortality over time could be driving the decline

of M. huitzilopochtli populations. The results of this

study suggest three things: (1) This species is currently

undergoing declining populations. Over longer time

periods, we would expect the decline or extinction of

those populations having small population sizes, no

fecundity and under disturbed habitats; (2) Habitat

conditions are highly restrictive for this species,

limiting seedling survival, establishment of individu-

als and increasing mortality of adults; and (3) Even

though disturbance cannot be considered to have an

effect on population dynamics it does seems to have

some effect on reproduction and stasis, making the

population rate of increase highly dependent on

survival of individuals rather than other demographic

processes. Several species of the Cactaceae are

rupicolous, a habitat that is resource limited, unstable,

and patchy that adds to their vulnerability and

conservation status; so the population dynamics of

these species is restricted by demographic behavior,

highly specific habitat requirements in addition to

illegal collection and land use change.

Acknowledgments This research is part of the doctoral studies

of AFM at the Universidad Autonoma Metropolitana-

Xochimilco (UAM-X) of Mexico under the advice of MMS,

JG. We are grateful to the Cassiano Conzatti Botanical Garden of

CIIDIR IPN Oaxaca for providing the facilities to carry out the

experiments. Permit to collect fruits (SGPA/DGVS/00615) was

granted by SEMARNAT, Mexico. This research was supported

by two CGPI–IPN projects (No. 20070431, 20080718) to AFM,

project BBV BIOCON 04-084 CONACyT CB-2006-1 #62390

and CONACyT CB-2007-01 #83790 to JG, project 0350

SEMARNAT-CONACyT and PASPA-DGAPA-UNAM

to MCM. We thank I. Rodriguez for field assistance, and

Jeronimo Reyes for locating of populations of M. huitzilopochtli.This article was written during a sabbatical leave by JG and

MCM at NMSU with B. Milligan who provided logistic support

and helped implementing the popbio package.

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