Population Projection Matrices Research Articles

Modeling the effect of fire on the demography ofDicerandra frutescensssp.frutescens(Lamiaceae), an endangered plant endemic to Florida scrub

AbstractManaging populations, either for conservation, harvesting, or control, requires a mechanistic or semi‐mechanistic understanding of population dynamics. Here, we investigate how time‐since‐fire affects demographic transitions in an endangered plant,Dicerandra frutescensssp.frutescens(Lamiaceae), which is specialized to gaps created by fire. We used a hierarchical Bayesian model to estimate transition probabilities (i.e., the elements of population projection matrices) as a function of time‐since‐fire and random effects, from 13 years of data on marked individuals in five populations. Using a standard Bayesian criterion to compare models, we find that death becomes increasingly probable and progression increasingly improbable with time‐since‐fire. The magnitude of some of the time‐since‐fire effects is substantial: death is 3–5 times more likely for flowering plants >6 years versus 3–6 years post‐fire, 3‐step progression is almost 7 times less likely, and large flowering plants are more than 6 times more likely to stop flowering. These insights inspire new hypotheses about the underlying cause of decline with time‐since‐fire, and how it can be managed. Our approach can be used by others who wish to model the effect of an exogenous factor on demography, while rigorously accounting for uncertainty and variability.

Life histories of female red squirrels and their contributions to population growth and lifetime fitness

The potential importance of life history traits to population growth rates has been well explored theoretically but has rarely been documented in wild mammals. In this study we used 18 consecutive years of data from a population of North American red squirrels (Tamiasciurus hudsonicus) in the southwest Yukon, Canada, to examine variation in female life history traits and their consequences for population growth rate. Red squirrels in this population experienced severe juvenile mortality, but survivorship beyond age 2 followed a Type I relationship where the annual survival probability decreased with age. Maximum lifespan was 8 y. Some females initiated breeding as yearlings, but most delayed first breeding until 2 y of age or in some cases even later. Annual reproduction generally involved the production of a single litter averaging 3.1 offspring (range: 1 to 7); however, some females attempted a second litter within a single breeding season, either following reproductive failure or, in rare circumstances, after a successful first breeding attempt. Life table characteristics for the 11 cohorts born between 1987 and 1997 indicated a population growth rate close to zero (r = 0.009). Elasticity analysis as well as individual population projection matrices and lifetime reproductive success data indicated that early survival and not age at first reproduction was most strongly associated with a female's contribution to population growth. Lifespan accounted for 83.9% of the variation in population growth rate and was positively correlated with age at first reproduction, such that females who bred as yearlings suffered decreased longevity. Collectively, these results emphasize the importance of female survival and not reproductive output to population growth and lifetime fitness in this system.

Analysis of the Population Dynamics of an Endangered Lizard (Xenosaurus Grandis) through the Use of Projection Matrices

We conducted a demographic analysis from 2000 to 2004 of a population of the crevice-dwelling lizard, Xenosaurus grandis, in Veracruz, México. We used population projection matrices to model its population dynamics. Three of the four annual matrices projected an actively growing population, whereas the matrix corresponding to 2003–2004 projected a declining population, apparently associated with a higher-than-average environmental temperature during this period. Observed population structure differed from that expected at equilibrium, according to the four matrices. Highest reproductive values corresponded to adult categories. The transition of newborns and juveniles to larger categories, as well as adult stasis, were the vital rates that made the largest contribution to population growth rate (λ). Growth from one size class to the next was the demographic process that contributed the most to λ, and all size classes had similar elasticities in all years. Stochastic simulations integrating interannual demographic variability projected population growth rates above unity, even under an ecological scenario that consisted of 50% of unfavorable years. Despite this trend toward positive population growth, this X. grandis population faces an imminent threat due to the growing industrial development in the region in which it is endemic. Thus, we suggest this population as a primary target for conservation efforts, as well as a change in the conservation category of this species from “special protection” to “threatened.”

Robustness: Predicting the effects of life history perturbations on stage-structured population dynamics

Matrix-based models lie at the core of many applications across the physical, engineering and life sciences. In ecology, matrix models arise naturally via population projection matrices (PPM). The eigendata of PPMs provide detailed quantitative and qualitative information on the dynamic behaviour of model populations, especially their asymptotic rates of growth or decline. A fundamental task in modern ecology is to assess the effect that perturbations to life-cycle transition rates of individuals have on such eigendata. The prevailing assessment tools in ecological applications of PPMs are direct matrix simulations of eigendata and linearised extrapolations to the typically non-linear relationship between perturbation magnitude and the resulting matrix eigenvalues. In recent years, mathematical systems theory has developed an analytical framework, called ‘Robustness Analysis and Robust Control’, encompassing also algorithms and numerical tools. This framework provides a systematic and precise approach to studying perturbations and uncertainty in systems represented by matrices. Here we lay down the foundations and concepts for a ‘robustness’ inspired approach to predictive analyses in population ecology. We treat a number of application-specific perturbation problems and show how they can be formulated and analysed using these robustness methodologies.

Population dynamics and clonal growth of Spartocytisus supranubius (Fabaceae), a dominant shrub in the alpine zone of Tenerife, Canary Islands

Major demographic processes in Spartocytisus supranubius, an endemic shrub dominant in the alpine zone of Tenerife, Canary Islands, were studied by a combination of dendrochronological and demographical techniques. Dendrochronological data were used to estimate growth rates of adult shrubs, frequency of fragmentation of shrubs by clonal growth, mortality, and seedling establishment. Isozymes were used to identify the extent of clonal growth in the species. The data collected were used to construct population projection matrices and to identify the role of generative reproduction vs. clonal growth in the life cycle of the species. Both isozymes and morphological analysis showed that the shrub is capable of clonal growth, but its contribution to the variation in the growth rate is much smaller than that of generative reproduction. The current population dynamics of the shrub seem to be strongly affected by rabbit grazing of seedlings, which controls effective establishment of young shrubs. Analysis of data from enclosures shows that rabbit removal would lead to rapid population growth of the species. Transition matrices showed that Spartocytisus supranubius populations currently are likely decreasing; this contrasts with the rapid increase over the past 40 years shown by historical aerial photographs. The stage structure of the shrub is far from equilibrium, indicating that the dynamics are driven by rare establishment events; dendrochronological analysis identified a peak in regeneration around 1980; this can be attributes to a combination of cessation of management in the caldera and to a series of wet years in that period.

Gonochorism vs. hermaphroditism: relationship between life history and fitness in three species of Ophryotrocha (Polychaeta: Dorvilleidae) with different forms of sexuality

1. The relationships between life history, fitness and sexuality, together with their ecological and evolutionary significance, has been analysed comparing the main life-history traits and demography in three closely related species belonging to the genus Ophryotrocha. The species are: the gonochoristic O. labronica, the simultaneous hermaphrodite O. diadema and the protandrous hermaphrodite O. puerilis. 2. Survivorship and reproductive data were collected weekly and were used to construct life tables and population projection matrices for each species and compare life-history characteristics. Elasticity, life-table response and decomposition analyses were performed to examine the relative contribution of fecundity and survivorship to differences in lamda between species. 3. The gonochoristic and hermaphroditic species differ in all the main life-history parameters and also in demographic characteristics. In particular the value of lamda, used commonly to express fitness, is markedly higher in the gonochoristic species while in terms of fitness simultaneous and sequential hermaphroditism are very similar. In the genus Ophryotrocha gonochorism currently represents the most widespread condition, being characteristic of the majority of the known species in the genus. 4. Given the demographic advantage ensured by gonochorism, it remains be understood why some species have retained simultaneous hermaphroditism and one has evolved a sequential type hermaphroditism; the most probable hypothesis is correlated with the density of the species in natural habitats.

Demography of Bursera glabrifolia, a tropical tree used for folk woodcrafting in Southern Mexico: An evaluation of its management plan

Tropical dry forest in Mesoamerica has long been disturbed by the extraction of different forest products by local inhabitants. Bursera glabrifolia (white “copalillo”) is a dry tropical forest tree extensively used in several communities of the State of Oaxaca, Mexico, for the elaboration of folk-art woodcarvings called “alebrijes”. Historically, the extraction of B. glabrifolia had not been regulated; however, in October 2002, the first management plan for this species was implemented in San Juan Bautista Jayacatlán, based on abundance, distribution and dasonomic data. However, no demographic information is available on which to base a sounder management plan that would guarantee the ecological sustainability of this extractive activity. Thus, we studied the population dynamics of this species over a 2-year period in Jayacatlán, where no tree extraction had taken place since 1998. We used stem expansion rates and observations on survival and fecundity to build size-based population projection matrices. The projected population growth rate values ( λ) were 1.14 and 1.04 for the 2001–2002 and the 2002–2003 periods, respectively. These values suggest that the B. glabrifolia population at Jayacatlán shows a growing trend. Several harvesting scenarios were simulated to theoretically assess the impact on population dynamics of harvesting whole trees and, in particular, to ascertain whether the extraction regime recommended by the management plan (8 trees/ha/yr) is sustainable. For this purpose, we used an average population matrix where specific entries were modified to simulate different extraction levels. The results suggest that the harvesting regimes established in the management plan for B. glabrifolia are sustainable. However, resource managers should not exceed the amounts recommended by the management plan and should avoid extrapolating our results to other regions of the country where no demographic studies have been carried out. The need for long-term demographic studies and their incorporation in ‘adaptive management plans’ is discussed.

Modeling vital rates improves estimation of population projection matrices

AbstractPopulation projection matrices are commonly used by ecologists and managers to analyze the dynamics of stage‐structured populations. Building projection matrices from data requires estimating transition rates among stages, a task that often entails estimating many parameters with few data. Consequently, large sampling variability in the estimated transition rates increases the uncertainty in the estimated matrix and quantities derived from it, such as the population multiplication rate and sensitivities of matrix elements. Here, we propose a strategy to avoid overparameterized matrix models. This strategy involves fitting models to the vital rates that determine matrix elements, evaluating both these models and ones that estimate matrix elements individually with model selection via information criteria, and averaging competing models with multimodel averaging. We illustrate this idea with data from a population of Silene acaulis (Caryophyllaceae), and conduct a simulation to investigate the statistical properties of the matrices estimated in this way. The simulation shows that compared with estimating matrix elements individually, building population projection matrices by fitting and averaging models of vital‐rate estimates can reduce the statistical error in the population projection matrix and quantities derived from it.

Population viability analysis and fire return intervals for an endemic Florida scrub mint

We use population viability analysis of an endangered Florida scrub mint, Dicerandra frutescens, to specify the optimal fire return intervals for its long-term persistence and for its specific habitat. We derived 83 population projection matrices from 13 years of demographic data from eight populations, 59 matrices from scrub populations and 24 from firelane or yard edges. Seed dormancy and germination transitions were inferred based on experimental data and verified by comparing modeled vs. observed population trajectories. Finite rates of increase in scrub sites were highest shortly after fire and declined steeply through 10 years postfire. The break-even value of λ = 1 was passed quickly, in about six years, suggesting that populations >6 years postfire were already facing decline. The decline is probably related to the rapid growth of competing shrubs in the habitat of D. frutescens. In long-unburned sites, finite rates of increase were nearly always <1 and declined the most in the long-unburned site with no foot trails or treefall gaps. Finite rates of increase in firelane populations also declined with years since fire or last disking. The yard edge population showed λ values both >1 and <1, with no temporal trend. Stochastic simulations in scrub sites suggested an optimal regular fire return interval of about 6–12 years. Regular fires at this interval were more favorable than stochastic fire regimes, but stochasticity reduced extinction percentages at longer fire return intervals. Stochastic fire return intervals implied a wider optimal fire return interval of 6–21 years. We suggest that prescribed fire in Florida scrub on yellow sand has occurred (and needs to occur) more frequently than previously recommended.

INTEGRATING DIRECT EFFECTS AND TRAIT-MEDIATED INDIRECT EFFECTS USING A PROJECTION MATRIX MODEL

In systems where indirect effects are mediated by traits (e.g., behavior) rather than density, direct and indirect effects may be measured in different biological currencies, making it difficult to quantify their relative contributions to a net interaction. For instance, the hydroid Hydractinia symbiolongicarpus, which colonizes shells occupied by the hermit crab Pagurus longicarpus, affects its host directly by reducing its fecundity and indirectly by modifying the behavior of its predators. In this study, I construct population projection matrices for P. longicarpus, which were housed with different assemblages of hydroids and predators. By defining direct and indirect effects as combinations of log-transformed λ's from these matrices, I translate direct effects on fecundity and indirect effects on survival into a common currency (population growth rate), allowing me to assess the relative strength of these effects. In the presence of a fish predator, strong positive indirect effects countered negative direct effects, producing a net mutualism. In the presence of a crab predator, indirect effects were equivalent in size and magnitude to direct effects, resulting in a net parasitism. These results provide insight into the mechanisms underlying context-dependency and help to explain the geographical and temporal variation observed in outcomes of symbiotic interactions.

EFFECTS OF TAG LOSS ON DIRECT ESTIMATES OF POPULATION GROWTH RATE

The temporal symmetry approach of R. Pradel can be used with capture– recapture data to produce retrospective estimates of a population's growth rate, λi, and the relative contributions to λi from different components of the population. Direct estimation of λi provides an alternative to using population projection matrices to estimate asymptotic λ and is seeing increased use. However, the robustness of direct estimates of λi to violations of several key assumptions has not yet been investigated. Here, we consider tag loss as a possible source of bias for scenarios in which the rate of tag loss is (1) the same for all marked animals in the population and (2) a function of tag age. We computed analytic approximations of the expected values for each of the parameter estimators involved in direct estimation and used those values to calculate bias and precision for each parameter estimator. Estimates of λi were robust to homogeneous rates of tag loss. When tag loss rates varied by tag age, bias occurred for some of the sampling situations evaluated, especially those with low capture probability, a high rate of tag loss, or both. For situations with low rates of tag loss and high capture probability, bias was low and often negligible. Estimates of contributions of demographic components to λi were not robust to tag loss. Tag loss reduced the precision of all estimates because tag loss results in fewer marked animals remaining available for estimation. Clearly tag loss should be prevented if possible, and should be considered in analyses of λi, but tag loss does not necessarily preclude unbiased estimation of λi.

Intrinsically dynamic population models

Intrinsically dynamic models (IDMs) depict populations whose cumulative growth rate over a number of intervals equals the product of the long term growth rates (that is the dominant roots or dominant eigenvalues) associated with each of those intervals. Here the focus is on the birth trajectory produced by a sequence of population projection (Leslie) matrices. The elements of a Leslie matrix are represented as straightforward functions of the roots of the matrix, and new relationships are presented linking the roots of a matrix to its Net Reproduction Rate and stable mean age of childbearing. Incorporating mortality changes in the rates of reproduction yields an IDM when the subordinate roots are held constant over time. In IDMs, the birth trajectory generated by any specified sequence of Leslie matrices can be found analytically. In the Leslie model with 15 year age groups, the constant subordinate root assumption leads to reasonable changes in the age pattern of fertility, and equations (27) and (30) provide the population size and structure that result from changing levels of net reproduction. IDMs generalize the fixed rate stable population model. They can characterize any observed population, and can provide new insights into dynamic demographic behavior, including the momentum associated with gradual or irregular paths to zero growth.

Population dynamics of benthic shallow-water foraminifera: effects of a simulated marine snow event

In this microcosm experiment, we determined the population dynamics of benthic foraminifera from the northern Adriatic Sea (from 32 m water depth) and how they were affected by an artificial marine snow event (AMS). The study focussed on the performance of individuals in 2 dif- ferent size fractions: one commonly used in micropaleontological studies (with foraminifera >63 µm) and 1 with smaller individuals (38-63 µm). Microcosms were incubated for 2 or 4 wk, and under AMS or control conditions. For each, the numbers of live (Rose Bengal-stained) individuals of different spe- cies in both size fractions were counted. From this, demographic parameters (fecundity, survival, growth) of specimens in different size classes were assessed. With these data, population projection matrices were constructed for the 4 most abundant taxa (Bolivina spp., Stainforthia fusiformis, Non- ionella turgida and Hopkinsina pacifica) and all foraminifera together. From the limit properties of these matrices, asymptotic population growth rates (λ) were derived. The results indicate that num- bers of larger benthic foraminifera decline more strongly because of AMS than those of the smaller individuals, and that growth is seriously inhibited. AMS, however, enhanced fecundity. Under AMS conditions (i.e. temporary anoxia and, concomitantly, extra food), the foraminifera seem to shift to an alternative life-history pathway of rapid reproduction and limited growth. After the first 2 wk, values of demographic parameters increase under AMS conditions, resulting in quickly recovering popula- tions. In our view, these demographic characteristics are beneficial for the observed species in peri- odically stressful and disturbed ecosystems, and could explain the increasing success of these species in the progressively eutrophicated northern Adriatic Sea.

METHODOLOGICAL INSIGHT: Linking management changes to population dynamic responses: the transfer function of a projection matrix perturbation

Summary An important task in applied population ecology is to understand how changes to individual life‐history parameters, such as survival, growth and fecundity, affect population dynamics. Parameter changes, or perturbations, may be caused by deliberate attempts to manage populations (e.g. in pest control, harvesting or conservation) or they may be side‐effects of pollution, genetic modification and climate change. For organisms with complicated life cycles, links between individual life histories and population dynamics are made using population projection matrix (PPM) modelling. Changes to individual, or groups of, life‐history transition rates within a PPM have a nonlinear impact on the resulting eigenvalues. Conventional sensitivity analysis calculates the derivative of the perturbation‐eigenvalue curve to provide tangential linear extrapolation. Until now, only the simulation of perturbed PPMs has captured nonlinear perturbation effects. Here we describe the transfer function of a matrix perturbation. The transfer function captures analytically the true relationship between perturbation magnitude and PPM eigenvalues. This analytical link extends easily to multi‐transition and multiple perturbations, promotes an understanding of matrix properties, and provides a simple method to predict the perturbation required to achieve a desired population rate of increase. We use the transfer function approach to analyse a PPM for the desert tortoise Gopherus agasizzii Cooper, in the context of conservation management decisions. Synthesis and applications. The transfer function offers a novel and powerful framework for the analysis of population projection matrices (PPMs), giving precise predictive power and analytical understanding of population‐level responses to life‐history perturbations, for example in the design of conservation, pest control and population harvesting strategies, prediction of population effects of pollution in ecotoxicology, and in ecological risk assessment. A useful focus is to set a target for the desired rate of increase (or decline) of a population, and use the transfer function to determine how best to achieve this rate.

Population Dynamics of Pterocereus gaumeri, a Rare and Endemic Columnar Cactus of Mexico

ABSTRACTWe conducted a demographic examination of Pterocereus gaumeri, a rare and endemic columnar cactus of the Yucatan peninsula, Mexico. Growth, survival, and fecundity of individuals were recorded in two populations from 1997 to 1999. Size‐based population projection matrices were constructed to document the population dynamics. Seed germination and seedling establishment experiments were conducted in the field to estimate the rate of seed and seedling survival. Our results show that P. gaumeri did not reproduce by asexual means or vegetative growth and thus relies wholly on sexual reproduction for population growth. Low reproductive success, seed predation, and low seedling survival appear to be important factors that contribute to the rarity of this species. The population growth rate (X) varied between 0.9545 and 1.0316. According to the matrix elasticity values, population dynamics of this species depend mainly on adult survival, with low values in fecundity and survival for the lowest size categories. Our results did not indicate that the population size of P. gaumeri was decreasing; however, increasing pressure on land use transformation is one of the most important factors that may threaten the persistence of this species.RESUMENSe presenta un estudio demográfico de Pterocereus gaumeri, un cactus raro, y endémico columnar de la Peninsula de Yucatán, México. Desde 1997 a 1999, se registró el crecimiento, la sobrevivencia y la fecundidad de individuos en dos poblaciones. Se construyeron marrices de proyección basadas en tamano poblacional para documentar la dinámica de las poblaciones. Se realizaron experimentos de germinación de semillas y establecimiento de plántulas en condiciones naturales, para estimar la tasa de sobrevivencia de semillas y plántulas. Nuestros resultados sugieren que P. gaumeri no se reproduce asexualmente o por crecimiento vegetative, por lo tan to el crecimiento poblacional depende completamente de la reproducción sexual. El bajo éxito reproductivo, la depredación de semillas y la baja tasa de sobrevivencia parecen ser factores importantes que contribuyen a la rareza de esta especie. La tasa de crecimiento poblacional (λ) varia entre 0.9545 y 1.0316. De acuerdo con los valores de las matriz de elasticidad, la dinámica poblacional de esta especie depende principalmente de la sobrevivencia de los adultos, con valores bajos en fecundidad y sobrevivencia de las categorias de tamanos menores. Nuestros resultados no indican que el tamano poblacional de P. gaumeri esté decreciendo, sin embargo, el incremento de presion por el cambio de uso de la tierra es uno de los factores más significativos que puede amenazar la continuidad de esta especie.

Seedling establishment and life history trade‐offs in alpine plants

Seedling establishment is central to population maintenance for nonclonal plant species. Plants with low recruitment rates are expected to have high survival rates, and life history theory indicates there should be a single curve for the trade-off between recruitment and mortality that applies to most or all plant species. Alpine perennials are thought to have extraordinarily low recruitment rates because of the harsh environment, but the importance of recruitment in the life history of these plants is unknown. Two alpine cushion plant species, Minuartia obtusiloba and Paronychia pulvinata, were used to (1) determine the role of recruitment in population maintenance and (2) determine whether the fecundity/mortality trade-off for these alpine plants falls on or off of the curve for other perennial plant species. Using size-based population projection matrices, we determined that the life history of Minuartia and Paronychia emphasizes recruitment less than that of any other nonclonal species in a literature survey. Estimated maximum life spans of these two species are 200 and 324 yr, respectively, and a regression with other perennial species from the literature indicated that the relationship between fecundity and mortality in these alpine species is consistent with the predicted trade-off curve for perennial species from other environments.

A COMPARATIVE DEMOGRAPHY OF PLANTS BASED UPON ELASTICITIES OF VITAL RATES

Elasticities of matrix elements from population projection matrices are com- monly used to analyze the relative contributions of different life history transitions (birth, survival, growth) to the finite rate of increase (l). Hitherto, comparative demography based on matrix models has relied upon decomposing elasticity matrices into blocks, each con- taining matrix elements deemed to represent recruitment, stasis, or progression to larger size classes. Elasticities across an entire matrix always sum to unity, and different popu- lations and species can be compared on the basis of the relative proportions of these three variables. This method has been widely used, but it contains a weakness in that the value of matrix elements is a function of more than one vital rate. For example, transitions representing progression to larger size classes involve a survival rate as well as a growth rate. Ideally, then, demographic comparisons between populations should be made using elasticities of vital rates themselves, rather than elasticities of matrix elements that are compounds of those rates. Here, we employ the complete set of general equations for the elasticity of vital rates in an entirely new analysis of matrices for 102 species of perennial plants. The results show a surprising similarity to an earlier analysis based upon matrix element elasticity and provide important confirmation of general patterns of correlation between plant life history and demography. In addition, we show that individual vital rate elasticities cannot, on their own, predict variation in life history. Therefore, all three de- mographic processes (survival, growth, and reproduction) are necessary to account for life history variation. The new analysis provides a firmer foundation for comparative demog-

Convexity and Elasticity of the Growth Rate in Size-Classified Population Models

This paper investigates both the convexity and elasticity of the growth rate of size-classsified population models. For an irreducible population projection matrix, we discuss the convexity properties of its Perron eigenvalue under perturbation of the vital rates, extending work of Kirkland and Neumann on Leslie matrices. We also provide nonnegative attainable lower bounds on the derivatives of the elasticity of the Perron eigenvalue under perturbation of the vital rates, sharpening, in the context of population projection matrices, the main result of Kirkland, Neumann, Ormes, and Xu.

Population dynamics of Mammillaria magnimamma Haworth. (Cactaceae) in a lava-field in central Mexico

One of the habitats occupied by Mammillaria magnimamma is a 2000-year old lava-field, in Mexico City. The great ecological interest on this lava-field and the little knowledge there is regarding cacti population ecology have compelled us to analyse the demography of this species to evaluate its present conservation status at this site. We studied two populations of this species within the lava-field: one in a disturbed site (i.e., recently burned) and another one in a well preserved site. For each population we built two size-based population projection matrices (1996/97 and 1997/98). Demographic data were gathered directly from observations of plant fates from one year to the next. Additionally, seed germination and seedling establishment experiments were carried out in the field to estimate fecundity values and seedling survival probabilities. The four matrices built were used to perform numerical analyses simulating yearly stochastic demographic variation to project the overall population's long-term behaviour under these changing conditions. Three of the four matrices showed λ values slightly below unity. In these cases elasticity values were highest for matrix entries corresponding to plants remaining in their same category. The matrix that showed a λ value above unity (well preserved site, 1997/98) had higher elasticity values for entries referring to seedling survival and growth. The numerical simulations of demographic stochasticity showed that the population appears to be growing at a slow rate. According to the simulation results, the variation in overall population size over time may be accounted for by yearly variation in seed germination and seedling survival. Population persistence probability might decrease significantly if fire frequency increases.

Population Dynamics of Pterocereus gaumeri, a Rare and Endemic Columnar Cactus of Mexico1

We conducted a demographic examination of Pterocereus gaumeri, a rare and endemic columnar cactus of the Yucatan peninsula, Mexico. Growth, survival, and fecundity of individuals were recorded in two populations from 1997 to 1999. Size-based population projection matrices were constructed to document the population dynamics. Seed germination and seedling establishment experiments were conducted in the field to estimate the rate of seed and seedling survival. Our results show that P. gaumeri did not reproduce by asexual means or vegetative growth and thus relies wholly on sexual reproduction for population growth. Low reproductive success, seed predation, and low seedling survival appear to be important factors that contribute to the rarity of this species. The population growth rate (λ) varied between 0.9545 and 1.0316. According to the matrix elasticity values, population dynamics of this species depend mainly on adult survival, with low values in fecundity and survival for the lowest size categories. Our results did not indicate that the population size of P. gaumeri was decreasing; however, increasing pressure on land use transformation is one of the most important factors that may threaten the persistence of this species.