Demography and management of two clonal oaks: Quercus eduardii and Q. potosina (Fagaceae) in central México

Forest Ecology and Management 251 (2007) 129–141 www.elsevier.com/locate/foreco

Demography and management of two clonal oaks: Quercus eduardii and Q. potosina (Fagaceae) in central Me´xico Cecilia Alfonso-Corrado a, Ricardo Clark-Tapia b, Ana Mendoza a,* a

Departamento de Ecologı´a Funcional, Instituto de Ecologı´a, Universidad Nacional Auto´noma de Me´xico, Apartado Postal 70-275, Delegacio´n Coyoaca´n, 04510 Me´xico, D.F., Mexico b Departamento de Ecologı´a de la Biodiversidad, Instituto de Ecologı´a, Universidad Nacional Auto´noma de Me´xico, Estacio´n Regional del Noroeste, Apartado Postal 1354, 83000 Hermosillo, Sonora, Mexico Received 7 September 2006; accepted 7 November 2006

Abstract Quercus eduardii and Q. potosina are the most abundant tree species of the temperate forests of Sierra Frı´a, Aguascalientes, Mexico, in an area ranging between 2200 and 2600 m above see level. During the last century these clonal oaks were intensively exploited to obtain charcoal and firewood for local use; in addition, sections of the forest were transformed into grasslands for livestock. The effects of disturbance on the population dynamics of these species are poorly known. Therefore, a demographic study was carried out in order to: (a) evaluate the effects of disturbance on the population growth rate of these species; (b) assess the effects of inter-annual environmental variability on the long term population dynamics; (c) evaluate the relative importance of sexual reproduction and clonal propagation on population growth rate; (d) simulate the impact of different levels of tree harvesting on the population dynamics of these species, and (e) recommend a harvesting intensity, based on the information obtained above. Annual, mean and periodic matrices as well as stochastic simulations were used. These size-classified population matrix models also were employed to devise a schedule that maximizes the percentage of individual plants that can be harvested without affecting their population growth rates. For this reason specific entries of the matrices were modified to simulate different harvesting intensities. The study was carried out in two disturbed and two undisturbed sites during a 4-years period. Two plots were established inside each site; one plot was excluded from livestock and the other was left intact. Annual population growth rates were above or equal to unity in all sites, species and years, whereas mean, periodic and stochastic simulation matrix models showed no significant differences between species, years, sites or from unity, suggesting that logging and grazing did not have a negative effect on the population growth rate of these species. Both species produced clonal offspring during the 4 years of the study, but reproduced sexually only once, suggesting a masting reproduction. Elasticity analyses showed that the contribution of clonal propagation is more important than fecundity to the population growth rate of both species. Mean annual and periodic matrix models showed that extractions as low as 5% cause a population decline, while with stochastic simulations extractions of up to 5% are possible for both species; however, the environmental stochasticity will drive populations to local extinctions. # 2007 Published by Elsevier B.V. Keywords: Quercus; Clonal growth; Management; Matrix and periodic analyses; Stochastic simulations

1. Introduction Oak species are numerous and widely distributed mainly in temperate zones of the Northern Hemisphere (Nixon, 1998; Rogers and Johnson, 1998). Of the approximately 500 oak species described, nearly 135–200 are found in Mexico (Rzedowski, 1981; Nixon, 1998) and of these, 85–115 are endemic (Gonza´lez-Rivera, 1993; Nixon, 1998), mostly in the

* Corresponding author. Tel.: +52 5556229012; fax: +52 5556161976. E-mail address: [email protected] (A. Mendoza). 0378-1127/$ – see front matter # 2007 Published by Elsevier B.V. doi:10.1016/j.foreco.2006.11.004

centre and south of Mexico (Nixon, 1998). Pine and oak trees characterize the temperate forests in Mexico (Rzedowski, 1981; Challenger, 1998); oak forests cover 9  106 ha of its territory, mainly in the mountainous areas (Masera et al., 1997; Challenger, 1998). Oak forests have provided a wide variety of ecological and economic services to human populations over the centuries (Challenger, 1998; Nixon, 1998). However, human activities have partially or severely disturbed many areas; consequently, the distribution areas of oak species have been reduced considerably, regeneration of populations of many species has been affected (Rzedowski, 1981; Herna´ndez-Reyna and

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Ramı´rez-Garcı´a, 1995; Reyes and Gama-Castro, 1995; Bonfil, 1998, 2006), and diseases have increased (Reyes and GamaCastro, 1995; Pen˜a-Ramı´rez and Bonfil, 2003). Traditional uses of oak forests for wood and charcoal, agriculture and livestock (Challenger, 1998) are often in conflict with increasing demands for recreation, landscape and habitat preservation. Few studies have been carried out on the population biology of Mexican oak species (Bonfil, 1998, 2006; Bonfil and Sobero´n, 1999; Tlapa-Almonte, 2005). Accordingly, management and conservation policies of most species are scarce or non-existent (Zavala-Cha´vez, 1990; Bonfil, 1998). Hence, an evaluation of their current status is urgent, particularly in areas where human activities have caused a deterioration of the habitat and a reduction of oak forests (Rzedowski, 1981; Reyes and GamaCastro, 1995; Bonfil, 1998). Matrix models have proven to be powerful tools to evaluate the demographic conditions of particular species (Leslie, 1945; Lefkovitch, 1965). They have been widely used to project the population growth of species with complex lifecycles and under different ecological scenarios (Caswell, 2001). Matrix models disregard temporal and spatial variations in environmental conditions, because they assume that vital rates do not change (Caswell, 2001). However, fluctuations in the environment do cause changes in vital rates and therefore, produce changes in population growth rates (Nakaoka, 1997; Golubov et al., 1999; Zuidema, 2000; Mandujano et al., 2001; Pico´ et al., 2002; Kwit et al., 2004; Valverde et al., 2004). Periodic and stochastic population matrix models consider the occurrence of such fluctuations in the environment (Cohen, 1987 in Caswell, 2001; Nakaoka, 1996; Tuljapurkar, 1997). These models are very useful for assessing the relative contribution of clonal growth and sexual reproduction on the population dynamics of species, as in the case of Opuntia rastrera (Cactaceae) studied by Mandujano et al. (2001); exploring population viability of endangered species, as in the cases of Taxus floridana (Kwit et al., 2004), and Mammillaria magnimamma (Valverde et al., 2004); simulating different disturbance conditions (Valverde et al., 2004); and recommending management (Zuidema, 2000; Ticktin et al., 2002; Herna´ndez-Apolinar et al., 2006) and conservation strategies (Kwit et al., 2004). Quercus eduardii and Q. potosina are two clonal oak species endemic to the mountains of central and northern Mexico (de la Cerda, 1999), and the most abundant tree species in Sierra Frı´a, Aguascalientes, Mexico (SEDESO, 1993; de la Cerda, 1999). These species were heavily exploited to obtain charcoal and firewood for local use during the period between 1920 and 1950 (Minnich et al., 1994). In addition, more than 37% of the original oak forest was fragmented due to tree fell (Pe´rez et al., 1995). Also, some sections of the forest were transformed for agricultural (1.66%) and grazing (6.17%) activities, therefore reducing the population size of these species (SEDESO, 1993; Minnich et al., 1994). Nonetheless, accurate estimates of the rates of loss, the size of oak trees harvested, and the amount of resprouting of stems cut are lacking. According to local residents, they felled whole trees in the past, but at the present time they cut branches or collect dead wood to cover their

requirements. However, it is likely that illegal extraction is being carried out in Sierra Frı´a, as occurs in other temperate forests of Mexico. To provide guidelines on the adequate management and conservation strategies of Q. eduardii and Q. potosina, the population dynamics of these species were studied over a 4years period. During the 4 years of the study both species produced clonal offspring yearly, but produced acorns only once. Field observations carried out by Minnich et al. (1994) suggested that Q. eduardii and Q. potosina regenerated efficiently mainly by clonal growth. Regeneration in the area was also supported by the analysis of a series of aerial photographs taken from 1942 to 1993 that showed minor fragmentation in the area (Minnich et al., 1994). Thus, it is likely that these species regenerated through the growth of existing clonal offspring and the resprouting of stems cut that rapidly re-established the forest canopy. However, the role of sexual reproduction and clonal propagation on the population dynamics of these species is unknown. In order to consider the occurrence of spatial and temporal variations, we used both time-variant and time-invariant models. The aims of this study were: (a) to determine the effects of disturbance (logging and grazing) on the population growth rate of these species; (b) to assess the effects of annual environmental variability on the long term population dynamics; (c) to determine the role of sexual reproduction and clonal propagation on the population dynamics of these species; (d) to simulate the impact of different tree harvesting levels on the population dynamics of these species, and (e) to recommend a harvesting intensity, based on the information obtained above. 2. Materials and methods 2.1. Study area This study was conducted in Sierra Frı´a, Aguascalientes, Mexico (218520 45000 –238310 1700 N and 1028220 4400 – 0 00 102850 53 W). Mean annual temperature is 14.5 8C, and mean annual rainfall is 651.4 mm. Vegetation in the area are oak, oakjuniper or oak-pine forests at altitudes from 1900 to 2700 m (SEDESO, 1993; Minnich et al., 1994). Quercus-Juniperus forests are mainly dominated by Q. potosina, Q. eduardii, Q. grisea, Q. sideroxyla and Juniperus deppeana. 2.2. Study species Q. eduardii is a red oak (Lobatae) and Q. potosina is a white oak (Quercus). Both species coexist in Sierra Frı´a, Aguascalientes (SEDESO, 1993; de la Cerda, 1999); they have similar trunk heights, ranging between 5 and 10 m, although some trees of Q. eduardii are 12 m in height. Regeneration of these species occurs by sexual reproduction (acorn production), and clonal growth (root suckers). Flowering occurs in May in both species (de la Cerda, 1999) and fructification between August and September in Q. potosina and between October and November in Q. eduardii.

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2.3. Field work In December 1997, two study sites with replicate were selected according to the degree of disturbance. In one site, grazing and logging activities have been practiced for more than 60 years (disturbed site), while in the other these activities have not been practiced during the last 40–60 years (undisturbed site). Replicates were selected following the criterion of disturbance chosen for each site; to avoid pseudoreplicates these were located at the same altitude with similar slopes and were separated from each other at least 1 km. In order to assess the impact of grazing by wildlife and domestic animals on the population dynamics of these species, two permanent plots of 972 m2 were established for each treatment; one plot was wire-fenced (excluded), whereas the other plot was left intact (not excluded). All individual plants within the plots were mapped and numbered with plastic tags. The height of small individual plants (225

Seedling 0–5 5.01–25 25.01–50 50.01–150 >150 –

Stasis was estimated as the proportion of individual plants that remained in the same stage class; progression as the proportion of individual plants that moved to later stage classes and retrogression as the proportion of individual plants that moved to smaller stage classes from time t to t + 1. Whenever progression probabilities were not observed, we estimated the time required by an average individual plant at stage x to reach stage x + 1, assuming that the distribution of individual plants at any stage class was uniform; in other words, any individual plant at stage x had the same probability of moving to the stage x + 1. The inverse of this quantity multiplied by the probability of stasis represented the expected progression probability in 1 year, while the expected probability of stasis in 1 year was obtained by subtracting from the probability of stasis the estimated progression probability (Mendoza, 1994). In order to estimate transition probabilities from acorn to seedling, 5000 acorns per species were collected during 2001, when sexual reproduction occurred in both species. Acorns were sown in the field and watered every 2 weeks. Acorn germination and seedling survival were recorded 4 and 12 months after sowing, respectively. Transition probabilities were then estimated as the proportion of acorns that germinated from the total number of acorns sown. To estimate fecundity, we counted the number of acorns produced by each reproductive tree. The mean number of acorns produced in each stage class was multiplied by the probability of acorn germination (transition from acorn to seedling) and the probability of seedling survival (number of seedlings surviving 1 year after acorns germinated). Therefore, fecundity was the number of seedlings produced per individual plant in each stage class. Paternity of individual plants produced by clonal growth was difficult to assess in the field; clonal offspring were scattered in the area and there were no visible connections between parent trees and their ramets. In fact, the origin (sexual or clonal) of each individual plant in the population is unknown, unless molecular analyses are carried out. Therefore, in order to estimate clonal propagation in each stage class, we divided the number of clonal offspring produced in 1 year by the total number of individual plants in each stage class, assuming that any individual plant, except seedlings, had the same probability of producing a new clonal offspring. Matrix and elasticity analyses were carried out using the program developed by Cochran and Ellner (1992), and 95% confidence intervals for l were calculated using the analytic ´ lvarez-Buylla and Slatkin (1993, 1994). methods proposed by A

2.7. Time-variant matrix models A periodic matrix model was used to evaluate the effect of environmental changes on demographic rates. This method was used in order to consider the effect of inter-annual variation on vital rates (Caswell, 2001) of both species. Population growth rate over a cycle of m phases (annual matrices), was given by a periodic product: nðtþmÞ ¼ ½BðmÞ ; . . . ; Bð2Þ Bð1Þ nðtÞ

(5)

nðtþmÞ ¼ AðhÞ nðtÞ

(6)

where B(m), . . ., B(1) was a set of matrices corresponding to the annual population projection matrices or phases of the environmental cycle B. The periodic matrix product A(h) projected the population growth through the whole environmental cycle. The subscript of A indicated that the projection started at phase h. Since the complete cycle had m phases, there were h = m possible series of periodic matrix products A. The matrix A(h) depended on the order in which the matrices B(m), . . ., B(1) were multiplied. We constructed periodic matrix models of Q. eduardii and Q. potosina in each site (2 sites  2 conditions  4 years  2 species = 32). With 4 years worth of data, the assumption was that the entire environmental cycle for the two species of oaks was m = 4 and h = 1, 2, 3 and 4 (four annual matrices per site): Bð1Þ ¼ Bð19971998Þ ; Bð3Þ ¼ Bð19992000Þ ;

Bð2Þ ¼ Bð19981999Þ ; Bð4Þ ¼ Bð20002001Þ

(7)

Thus, the population growth rate for the entire cycle of 4 years was given by: Að19971998Þ ¼ ½Bð20002001Þ Bð19992000Þ Bð19981999Þ Bð19971998Þ  (8) Að19981999Þ ¼ ½Bð19971998Þ Bð20002001Þ Bð19992000Þ Bð19981999Þ  (9) Að19992000Þ ¼ ½Bð19981999Þ Bð19971998Þ Bð20002001Þ Bð19992000Þ  (10) Að20002001Þ ¼ ½Bð19992000Þ Bð19981999Þ Bð19971998Þ Bð20002001Þ  (11) This arrangement was used because the beginning of the cycle was unknown. Once we had four periodic matrix products for each species, site and condition, we obtained the long-term population growth rate for the entire period in which the environmental cycle occurred. This was given by the dominant root of the product of the periodic matrices (l(h)), which was used to give an annual l by converting it to r (the intrinsic rate of population increase) as follows: r¼

ln l m

(12)

where m scales it to the time step considered (1 year) and then taking its antilogarithm (Golubov et al., 1999).

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Fig. 1. Observed stage distribution (OSD) and stable stage distribution (SSD) for (a) Q. eduardii and (b) Q. potosina in the disturbed excluded (DE), disturbed nonexcluded (DN), undisturbed excluded (UE) and, undisturbed non-excluded sites (UN). Data were obtained from mean transition matrices at each site for a 4-years study period. Values of the log-likelihood ratio tests (G) and their associated level of significance (P) are shown for each site.

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According to Caswell and Trevisan (1994), the sensitivity of l to changes in periodic matrix entries in a given period h was given by ðhÞ

T ðhÞ

SB ¼ ½Bðh1Þ Bðh2Þ ; . . . ; Bð1Þ BðmÞ Bðm1Þ ; . . . ; Bðhþ1Þ  SA

(13) ðhÞ where SB

was the sensitivity matrix of the periodic matrix B(h), ðhÞ h = 1, 2, . . ., m phases of the entire cycle and SA was the (h) sensitivity matrix of the annual matrix A , both calculated during the period h. The superscript T in the formula denoted the matrix transpose. ðhÞ The elasticity matrix EB of the periodic matrix B(h) in the period h was calculated as: 1 ðhÞ ðhÞ EB ¼ BðhÞ SB l

(14)

where  indicated a matrix product, element by element. Elasticities of each of the periodic matrices summed to one, and l may be decomposed into contributions made by each of the periodic matrix elements. All matrices modeling were performed using MATLAB version 5.2 (The MathWorks, 1998). Confidence intervals were estimated by means of the analytic methods proposed by Pico´ et al. (2002). If rainy and dry years do not occur in a cyclic pattern over time, periodic matrix models may lead to unrealistic

projections of population growth. Therefore, stochastic matrix models were used to explore the consequences of a fluctuating environment on the population growth rate (Caswell, 2001). According to the rainfall data in Sierra Frı´a from Comisio´n Nacional del Agua (CNA), Aguascalientes, there has been an equal number of rainy (>650 mm year1) and dry years (< 650 mm year1) for the last 40 years (1961–2001). No pattern was found as to whether a certain number of dry years were preceded by a rainy year or vice versa. Thus, the probability of a rainy (2000–2001) or a dry (1997–1998, 1998–1999 and 1999– 2000) year was 0.25 for each year. These probabilities were used to simulate a stochastic process, where a population projection matrix A was chosen at random from one of the four annual matrices in each site and for each species (4 years  2 sites  2 conditions  2 species). The stochastic matrix model used was nðtþ1Þ ¼ AðtÞ Aðt1Þ ; . . . ; Að0Þ nðtÞ

(15)

where n(t) was a vector of stage classes, and A(t), . . ., A(0) were a series of annual projection matrices. We carried out 10,000 stochastic simulations for each site and species using a series of four annual transition matrices corresponding to each year. The first 3000 iterations were eliminated to decrease the initial transient behavior (Caswell, 2001). For each population, we estimated the stochastic population growth rate (ln l(s)) by averaging the 7000 remaining iteration estimates (Caswell,

Fig. 2. Annual population growth rates and their confidence intervals (l  C.I.) for populations of Q. eduardii and Q. potosina in (a) disturbed excluded (DE), (b) disturbed non-excluded (DN), (c) undisturbed excluded (UE), and (d) undisturbed non-excluded (UN) sites, during a 4-years study period. Note that the minimum value for the y-axis is 0.8. The horizontal line shows the point where populations are in demographic equilibrium (l = 1).

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2001) as follows: PT1 ln l ¼

ðln lt Þ T 1

t¼0

(16)

where T in this formula was the number of time intervals on which the estimate was based. All matrix modeling and confidence intervals were estimated following Caswell (2001). 2.8. Harvest simulations Since local people use oaks for domestic necessities, tree harvest simulations were carried out in order to estimate the amount of individual plants that can be removed without causing a population decline. In each census, we randomly removed 5, 15, 30 and 50% of individual plants with basal areas larger than 50 cm2. Individual plants removed in every census were eliminated completely from the database and were not included in subsequent harvests. Transition probabilities and fecundities were estimated for each percentage of harvested individual plants, and the corresponding annual (4 tree harvest simulations  4 years  2 sites  2 conditions  2 species), mean (4 tree harvest simulations  4 mean annual matrices  2 species), and periodic matrices (4 tree harvest simulations  4 years  2 sites  2 conditions  2 species) were constructed. To determine the annual population growth rate (l(4)) of the periodic matrices, we projected each matrix product for the entire 4-years period in which the environmental cycle occurred. Likewise, stochastic matrix models were used for each tree harvest simulation with probabilities of 0.25 of rainy (2000– 2001) and dry (1997–1998, 1998–1999 and 1999–2000) years. In order to obtain the population growth rate for each harvest simulation of each species in each site and condition, every series of annual matrices (4 harvest simulations  4 years  2 conditions  2 sites  2 species) was used to make 10,000 stochastic simulations. As stated before, the first 3000 iterations were eliminated and the stochastic population growth rates were estimated by averaging the 7000 remaining iteration estimates.

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where l was almost equal to one (0.9706  0.029) in 1999– 2000. For Q. eduardii l was significantly above unity in the DE and the DN sites in 1997–1998, in all sites in 1998–1999, and in the UN site in 2000–2001, whereas for Q. potosina l was significantly above unity in the UE and UN sites in 1998–1999 and in the DE site in 1999–2000. In all other sites and years, population growth rates were equal to one. Regarding differences in population growth rates between species, we found that l was significantly higher in Q. eduardii than in Q. potosina during 1998–1999 in the DE and UE sites, whereas l was significantly lower in Q. eduardii than in Q. potosina during 1999–2000 in the DE site (Fig. 2). In all other sites and years l did not differ between species. Population growth rates for both species differed significantly between years in all sites, except in the DN site, where no significant differences were found (Fig. 2). Population growth rates obtained from the mean transition, periodic and stochastic matrices did not show significant differences among sites, species and from unity (Fig. 3).

3. Results 3.1. Stable stage distribution of mean matrices Comparisons between the observed and stable stage distributions of Q. eduardii and Q. potosina in all conditions (Fig. 1a and b) showed that the highest density was found in size class 2 (0–5 cms2). Log-likelihood ratio tests (Zar, 1984) showed no significant differences between stage distributions in both species. 3.2. Time-invariant and time-variant matrix models As shown in Fig. 2 population growth rates for Quercus eduardii and Q. potosina were above or equal to unity in all sites, species and years, except for Q. eduardii in the DE site,

Fig. 3. Population growth rates and their confidence intervals (l  C.I.) for Q. eduardii and Q. potosina obtained from mean, periodic and stochastic matrices in the disturbed excluded (DE), disturbed non-excluded (DN), undisturbed excluded (UE), and undisturbed non-excluded (UN) sites. Note that the minimum value for the y-axis is 0.8. The horizontal line shows the point where populations are in demographic equilibrium (l = 1).

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Fig. 4. Elasticities of fecundity (F), clonality (CL), stasis (S), growth (P) and retrogression (R) obtained from mean transition and mean periodic matrices for (a–b) Q. eduardii and (c–d) Q. potosina in the disturbed excluded (DE), disturbed non-excluded (DN), undisturbed excluded (UE) and undisturbed non-excluded (UN) sites.

3.3. Elasticities of mean annual transition and periodic matrices Results obtained from mean annual and periodic matrices showed that stasis made the greatest contribution to l in both species, ranging between 86 and 93% in all conditions (Fig. 4a– d). Clonal growth and progression were the second parameters in importance; however, elasticity values are between 0.014 and 0.10. This is lower by one order of magnitude when compared to stasis. Elasticity of clonal growth was higher than fecundity and the latter and retrogression made the smallest contributions to l. Elasticities for stasis obtained with the mean annual and periodic matrices showed a similar pattern for both species and sites (Fig. 4a–d). However, elasticities for other parameters showed differences if these were obtained with the mean annual or the periodic matrices for both species. Fecundity had a very small contribution to l with the mean matrices, but its contribution disappeared completely with the periodic matrices for both species. Contrary, while elasticity for clonal growth and progression had similar contributions to l with the mean annual matrices, the former increased and the latter decreased with the periodic matrices (Fig. 4a–d). Elasticities for clonal growth obtained with the mean annual and periodic matrices showed the lowest values in the UE site

for both species (Fig. 4a–d). Elasticities for progression showed the highest values in the DE and UE sites for both species, but for Q. eduardii, these values were obtained with the periodic matrices and for Q. potosina were obtained with the mean annual matrices. Elasticity for retrogression had similar values in all sites either with the mean or the periodic matrices for Q. eduardii, but for Q. potosina elasticity values increased with the periodic matrix, having the highest values in the DN and UN sites. Stage-specific elasticities of mean transition matrices showed that plants in stage class 2 of Q. eduardii contributed to l between 20 and 68%, and of Q. potosina between 22 and 57% (Fig. 5). The lowest elasticities were those of stage class 2 in the UE site for both species, while the highest were found in the other stage classes of Q. eduardii, except in stage class 5. Stage classes 3, 4 and 7 of Q. eduardii and 4 and 5 of Q. potosina had the highest contribution to l in the UE sites. 3.4. Tree harvest simulations Tree harvest simulations obtained with the mean (Fig. 6a, d), periodic (Fig. 6b, e) and stochastic (Fig. 6c, f) matrices caused a reduction in population growth rates, which was more severe as harvest intensity increased. In all conditions, harvest

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Fig. 5. Stage-specific elasticities obtained from mean annual transition matrices for Q. eduardii and Q. potosina in the disturbed excluded (DE), disturbed non-excluded (DN), undisturbed excluded (UE) and undisturbed nonexcluded (UN) sites.

simulations using the mean and periodic matrices showed that harvesting less than 5% of adult individual plants of Q. eduardii (Fig. 6a–c) and Q. potosina (Fig. 6d–f) caused l to drop below the point where populations are in a numerical equilibrium. However, using the stochastic matrices our results showed that the maximum harvest intensity should not exceed 5%, otherwise l decreases more rapidly. Harvesting effects were more severe in Q. eduardii than in Q. potosina in all conditions. 4. Discussion The finite rate of population growth (l) obtained from individual annual projection matrices clearly shows that populations of Quercus eduardii and Q. potosina are in or above the numerical equilibrium in this area. The absence of significant differences between the observed and the stable stage distributions also confirms that populations of these species in the area are in a demographic equilibrium. Population growth rates close to unity have been reported for other species of the Family Fagaceae (Batista et al., 1998;

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Bonfil, 1998, 2006; Davelos and Jarosz, 2004; Tlapa-Almonte, 2005), and several long-lived managed plant species (West, 1995; Bernal, 1998; Zuidema, 2000; Guedje et al., 2003; Herna´ndez-Apolinar et al., 2006). Undoubtedly Q. eduardii and Q. potosina can cope with the environment in a very efficient way. Neither variations in time (4-years study), space (disturbed versus undisturbed), or condition (excluded versus not excluded), affected the population growth rates of these species. On the contrary, population growth rates were equal to one in 21 of the 32 matrices and greater than one in 10 of the 32 matrices, meaning that not only these species maintain their populations in a demographic equilibrium, but still grow despite logging, grazing or weather conditions. Population growth rates higher than one were not restricted to a particular site, condition or time. An equal number of l’s >1 were found in the disturbed (three in the excluded and two in the non-excluded) and undisturbed sites (two in the excluded and three in the nonexcluded sites). Even in the disturbed excluded site in 1999– 2000, this value (0.9706) with its upper confidence interval was very close to unity (0.9996) for Q. eduardii. It has been reported that plant species living in unstable habitats such as deserts (Mandujano et al., 2001), or areas where hurricanes occur (Ticktin et al., 2002), show plasticity in their vital rates. It appears that these species can buffer either climatic fluctuations or disturbances caused by human activities possibly by adjusting their vital rates. Our results point toward this direction since population growth rates of Q. eduardii and Q. potosina resulted unaffected in a year-to-year, periodic or stochastic environmental variability in any site and condition. The lack of significant differences between the observed and stable stage distributions of both species supports this idea, but also suggests that the rate of disturbance (either by logging or grazing) has been low and constant, so that populations of these species remained unaffected by these practices. It also suggests that the rates of growth and survival observed during the study period have prevailed in the past without major alterations (Mendoza, 1994), probably due to the low levels of disturbance. However, we cannot conclude that this pattern will be kept invariable in other sites of Sierra Frı´a. The capacity to propagate clonally undoubtedly allowed these species to maintain their populations in or above the demographic equilibrium. It has been suggested that clonal propagation is an effective mechanism to keep population growth rates above or equal to unity, regardless of weather conditions or disturbances caused by human activities (Mandujano et al., 2001; Clark-Tapia et al., 2005). Besides having population growth rates above or equal to unity, stage distributions of Q. eduardii and Q. potosina showed a large amount of individual plants in size class 2. This was mainly due to regeneration produced by clonal propagation rather than seedling recruitment. Q. eduardii and Q. potosina produced on average 35 and 32 ramets year1, respectively. Clonal growth through root suckering is widespread in several species of Quercus (Mu¨ller, 1951; Zavala-Cha´vez and Garcı´a-Moya, 1997; Malanson and Trabaud, 1988; Papatheodorou et al., 1998; Cierjacks and Hensen, 2004), is common in xerophytic or

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Fig. 6. Population growth rates and their confidence intervals (l  C.I.) for (a–c) Q. eduardii and (d–f) Q. potosina under different simulating tree harvest intensities. Data were obtained with (a, d) mean transition, (b, e) periodic and (c, f) stochastic matrix models for each site. Note that the minimum value for the y-axis differs among mean (0.7), periodic (0.5) and stochastic (0.2) matrices.

xerophytic-mesophitic oaks, which can regenerate successfully in dry or semi-dry habitats because their large root system facilitates tolerance to fire and drought that are frequent in these habitats (Mu¨ller, 1951; Larsen and Johnson, 1998). It is also advantageous in sites where grazing, fire and logging are the most common factors of disturbance (Malanson and Trabaud, 1988; Rao et al., 1990; Cierjacks and Hensen, 2004).

It is not known for how long the parent tree subsidizes its offspring, but this mechanism must allow ramets to recover from grazing and trampling. Reallocation of resources from the parent to the offspring is common in clonal plants, and is particularly advantageous for ramets that remain physiologically integrated (Pitelka and Ashmun, 1985). It is possible that trees of Q. eduardii and Q. potosina reallocate resources to a

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damaged ramet ameliorating the survival of plants in stage class 2 and this must be one reason why plants in this stage had the greatest contribution to l. In addition, this mechanism allows a ramet to persist in the shade for long periods of time. According to Minnich et al. (1994), populations of Q. eduardii and Q. potosina underwent severe disturbances (logging) in Sierra Frı´a during the first half of the 20th century and have survived mainly due to regeneration by clonal propagation through root suckering. The fact that elasticity of clonal propagation is greater than that of fecundity also supports its importance in the regeneration of both oak species. In other plants clonal propagation also showed a higher contribution to l than did fecundity (Mandujano et al., 2001; Clark-Tapia et al., 2005). In contrast, seedling establishment was uncommon in populations of Q. eduardii and Q. potosina because these species do not reproduce every year. During the 4-years study period (1997–2001) these species produced acorns in one out of 4 years. It is worth mentioning that although we observed acorn production in 1996 (1 year before we started this study) in both species, this event was not recorded for either species. These results suggest that reproduction occurs under certain environmental conditions. As has been reported weather conditions cause fluctuations in acorn production (Healy et al., 1999; Kelly and Sork, 2002); among these are late spring frost (Goodrum et al., 1971), and temperature, humidity, and wind at the time of pollination (Sork et al., 1993; Koeing et al., 1994). It is likely then, that mast seeding (Kelly, 1994; Healy et al., 1999) characterizes reproduction of Q. eduardii and Q. potosina, which seems to be related to the amount of rainfall during the previous year. From 1997 to 2000, a period of precipitations lower than 650 mm year1, these species did not produce acorns. However, in 1996, 1 year previous to the beginning of this study, and in 2001 these species produced acorns. These years were preceded by precipitations close to the average (>650 mm year1) for this area. Nonetheless, to prove this hypothesis, reproduction and its correlation with precipitation should be recorded in longer periods of time. In other oak species seedling recruitment is affected by factors such as masting (Zavala-Cha´vez and Garcı´a-Moya, 1997; Healy et al., 1999), acorn and seedling predation (Thadani and Ashton, 1995; Bonfil and Sobero´n, 1999; Go´mez et al., 2003), and unfavorable microsites for seedling establishment (Negi et al., 1996, Larsen and Johnson, 1998; Bonfil and Sobero´n, 1999; Vetaas, 2000). Although elasticity values show that clonal propagation is more important than sexual reproduction in terms of recruitment of these species, populations of Q. eduardii and Q. potosina also regenerate by means of sexual reproduction. A genetic study carried out with populations of Q. eduardii and Q. potosina in the same plots of this study in Sierra Frı´a, using random polymorphic amplified DNA (RAPDs) molecular marker, showed that almost 50% of the sampled individual plants of both species had a sexual origin (Alfonso-Corrado et al., 2004). These results suggest that seedling recruitment occurs sporadically in populations of both species, when a good crop is produced followed by specific environmental conditions such as winter rains. Under these conditions acorns and seedlings have high

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probabilities of germination and survival, as is shown by the germination experiment carried out to determine transition probabilities from seed to seedling. Acorn germination of Q. eduardii and Q. potosina reached values of 75 and 55%, respectively, and the probability of seedling survival after 1 year was 6.5% for Q. eduardii and 4.6% for Q. potosina. According to our results any change in stasis will have great impact on population growth rates of Q. eduardii and Q. potosina. Therefore, harvesting adult individuals will cause a population decline, even if a harvest intensity of less than 5% is considered, which is equivalent to approximately 90 and 210 plants/ha for Q. eduardii and for Q. potosina, respectively. Removal of adult trees will not only cause a population decline of both species but will also arrest clonal propagation and sexual reproduction. Clonality, although one order of magnitude smaller than stasis was the second parameter in importance, and although fecundity had a low contribution to the population growth rate of these species, seed production enhances genetic diversity. Therefore, variations in these demographic parameters as a result of intensive extractions will definitively place these populations at risk, as must have occurred during the period between 1920 and 1950, where these species were heavily exploited (Minnich et al., 1994). While this study shows that Q. eduardii and Q. potosina respond quite well to changes in the environment or human disturbances, these species should be used only for local consumption in this area. Our tree harvest simulations using deterministic and time-varying matrix models do not recommend extractions of adult trees of Q. eduardii and Q. potosina in this area. Our results showed that harvesting up to 5% of adult individuals keep l on a demographic equilibrium when stochastic matrices were used. However, l decreased below unity when mean transition and periodic matrices were used. It is extremely risky then, to recommend an annual harvest intensity of up to 5% for these species in the area. The sole environmental stochasticity would probably cause such a decrease in the population growth rate of this species that they will be placed at jeopardy of local extinction in a short period of time. Management programs for commercial purposes would not be economically viable even considering harvest intensities of up to 5%, this would render a small amount of useful material (3.7–4.3 m3 and 3.6–8.0 m3 per hectare of Q. potosina and Q. eduardii, respectively); hence, production costs would be greater than the profits. The demographic study of Q. eduardii and Q. potosina carried out in Sierra Fria showed that populations of both species have recovered successfully from the serious disturbance occurred during the first half of last century. Additionally, this study showed that logging and grazing probably have been moderate or even low during the last decade in this area; population growth rates in or above the demographic equilibrium in all sites and conditions supports this idea. Moreover, the population growth rates of these species did not show any pattern among sites and conditions that could suggest that the history of disturbance or the exclusion could affect the populations of these species. Several factors have contributed to the successful persistence of these

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species in Sierra Frı´a, among these are: (i) the capacity of these species to produce clonal offspring on a regular basis; (ii) the possible physiological integration between the parent tree and its offspring; (iii) successful seedling establishment whenever acorns are produced; (iv) their ability to cope with unfavorable environmental conditions, and (v) the recent policies of environmental protection of Sierra Frı´a. Finally, results obtained with our tree harvest simulations do not recommend any extraction of adult individuals in this area. Mean annual and periodic matrix models showed that extractions as low as 5% cause a population decline, while with stochastic simulations showed that extractions of up to 5% are possible for both species; however, the environmental stochasticity will drive populations to local extinctions. Therefore, we recommend that local inhabitants continue the sustainable management that has been carried out with these species in the area (cutting of branches or collection of dead wood). This approach will keep populations in or above the numerical equilibrium; otherwise, as Minnich et al. (1994) have suggested, it would take 50–60 years to recover populations of these species if logging is practiced as it was during the first half of the 20th century. Acknowledgments The authors are especially grateful to Miguel Franco and to the late Carlos Va´zquez-Yanes for their comments and opinions during the development of this research, and to two anonymous reviewers for their valuable observations and suggestions that greatly improved the quality of the manuscript. He´ctor Godı´nez, Consuelo Bonfil, Arturo Flores and Eduardo Morales made useful comments to the manuscript. We thank Salvador Sa´nchez-Colo´n for all the technical and logistic support, Gabriel G. Adame and the Instituto del Medio Ambiente del Estado de Aguascalientes (IMAE) for field assistance and support and Susana Valencia and Margarita de la Cerda for identifying these species. Financial support was provided by CONABIO (L210). References Alfonso-Corrado, C., Esteban-Jime´nez, R., Clark-Tapia, R., Pin˜ero, D., Campos, J.E., Mendoza, A., 2004. Clonal and genetic structure of two Mexican oaks: Quercus eduardii and Quercus potosina (Fagaceae). Evol. Ecol. 18 (585), 599. ´ lvarez-Buylla, E.R., Slatkin, M., 1993. Finding confidence limits on populaA tion growth rates: Monte Carlo test of a simple analytic method. Oikos 68, 273–282. ´ lvarez-Buylla, E.R., Slatkin, M., 1994. Finding confidence limits on populaA tion growth rates: three real examples revised. Ecology 75, 255–260. Batista, W.B., Platt, W.J., Macchiavelli, R.E., 1998. Demography of a shadetolerant tree (Fagus grandifolia) in a hurricane disturbed forest. Ecology 79, 38–53. Bernal, R., 1998. Demography of the vegetable ivory palm Phytelephas seemannii in Colombia, and the impact of seed harvesting. J. Appl. Ecol. 35, 64–74. Bonfil, C., 1998. Dina´mica poblacional y regeneracio´n de Quercus rugosa: implicaciones para la restauracio´n de bosques de encinos. Tesis Doctoral. Instituto de Ecologı´a. Universidad Nacional Auto´noma de Me´xico, Me´xico, p. 107.

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