Matrix Projection Models Research Articles

Sex in an uncertain world: environmental stochasticity helps restore competitive balance between sexually and asexually reproducing populations

Like many organisms, individuals of the freshwater ostracod species Eucypris virens exhibit either obligate sexual or asexual reproductive modes. Both types of individual routinely co-occur, including in the same temporary freshwater pond (their natural habitat in which they undergo seasonal diapause). Given the well-known two-fold cost of sex, this begs the question of how sexually reproducing individuals are able to coexist with their asexual counterparts in spite of such overwhelming costs. Environmental stochasticity in the form of 'false dawn' inundations (where the first hydration is ephemeral and causes loss of early hatching individuals) may provide an advantage to the sexual subpopulation, which shows greater variation in hatching times following inundation. We explore the potential role of environmental stochasticity in this system using life-history data analysis, climate data, and matrix projection models. In the absence of environmental stochasticity, the population growth rate is significantly lower in sexual subpopulations. Climate data reveal that 'false dawn' inundations are common. Using matrix projection modelling with and without environmental stochasticity, we demonstrate that this phenomenon can restore appreciable balance to the system, in terms of population growth rates. This provides support for the role of environmental stochasticity in helping to explain the maintenance of sex and the occurrence of geographical parthenogenesis.

The role of wildfire, prescribed fire, and mountain pine beetle infestations on the population dynamics of black-backed woodpeckers in the black hills, South Dakota.

Wildfire and mountain pine beetle infestations are naturally occurring disturbances in western North American forests. Black-backed woodpeckers (Picoides arcticus) are emblematic of the role these disturbances play in creating wildlife habitat, since they are strongly associated with recently-killed forests. However, management practices aimed at reducing the economic impact of natural disturbances can result in habitat loss for this species. Although black-backed woodpeckers occupy habitats created by wildfire, prescribed fire, and mountain pine beetle infestations, the relative value of these habitats remains unknown. We studied habitat-specific adult and juvenile survival probabilities and reproductive rates between April 2008 and August 2012 in the Black Hills, South Dakota. We estimated habitat-specific adult and juvenile survival probability with Bayesian multi-state models and habitat-specific reproductive success with Bayesian nest survival models. We calculated asymptotic population growth rates from estimated demographic rates with matrix projection models. Adult and juvenile survival and nest success were highest in habitat created by summer wildfire, intermediate in MPB infestations, and lowest in habitat created by fall prescribed fire. Mean posterior distributions of population growth rates indicated growing populations in habitat created by summer wildfire and declining populations in fall prescribed fire and mountain pine beetle infestations. Our finding that population growth rates were positive only in habitat created by summer wildfire underscores the need to maintain early post-wildfire habitat across the landscape. The lower growth rates in fall prescribed fire and MPB infestations may be attributed to differences in predator communities and food resources relative to summer wildfire.

Advancing population ecology with integral projection models: a practical guide

Summary Integral projection models (IPMs) use information on how an individual's state influences its vital rates – survival, growth and reproduction – to make population projections. IPMs are constructed from regression models predicting vital rates from state variables (e.g. size or age) and covariates (e.g. environment). By combining regressions of vital rates, an IPM provides mechanistic insight into emergent ecological patterns such as population dynamics, species geographic distributions or life‐history strategies. Here, we review important resources for building IPMs and provide a comprehensive guide, with extensive R code, for their construction. IPMs can be applied to any stage‐structured population; here, we illustrate IPMs for a series of plant life histories of increasing complexity and biological realism, highlighting the utility of various regression methods for capturing biological patterns. We also present case studies illustrating how IPMs can be used to predict species' geographic distributions and life‐history strategies. IPMs can represent a wide range of life histories at any desired level of biological detail. Much of the strength of IPMs lies in the strength of regression models. Many subtleties arise when scaling from vital rate regressions to population‐level patterns, so we provide a set of diagnostics and guidelines to ensure that models are biologically plausible. Moreover, IPMs can exploit a large existing suite of analytical tools developed for matrix projection models.

Estimating Allee Dynamics before They Can Be Observed: Polar Bears as a Case Study

Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.

Scaling Integral Projection Models for Analyzing Size Demography

Historically, matrix projection models (MPMs) have been employed to study population dynamics with regard to size, age or structure. To work with continuous traits, in the past decade, integral projection models (IPMs) have been proposed. Following the path for MPMs, currently, IPMs are handled first with a fitting stage, then with a projection stage. Model fitting has, so far, been done only with individual-level transition data. These data are used in the fitting stage to estimate the demographic functions (survival, growth, fecundity) that comprise the kernel of the IPM specification. The estimated kernel is then iterated from an initial trait distribution to obtain what is interpreted as steady state population behavior. Such projection results in inference that does not align with observed temporal distributions. This might be expected; a model for population level projection should be fitted with population level transitions.

Are the Economically Optimal Harvesting Strategies of Uneven-Aged Pinus nigra Stands Always Sustainable and Stabilizing?

Traditional uneven-aged forest management seeks a balance between equilibrium stand structure and economic profitability, which often leads to harvesting strategies concentrated in the larger diameter classes. The sustainability (i.e., population persistence over time) and influence of such economically optimal strategies on the equilibrium position of a stand (given by the stable diameter distribution) have not been sufficiently investigated in prior forest literature. This article therefore proposes a discrete optimal control model to analyze the sustainability and stability of the economically optimal harvesting strategies of uneven-aged Pinus nigra stands. For this model, we rely on an objective function that integrates financial data of harvesting operations with a projection matrix model that can describe the population dynamics. The model solution reveals the optimal management schedules for a wide variety of scenarios. To measure the distance between the stable diameter distribution and the economically optimal harvesting strategy distribution, the model uses Keyfitz’s delta, which returns high values for all the scenarios and, thus, suggests that those economically optimal harvesting strategies have an unstabilizing influence on the equilibrium positions. Moreover, the economically optimal harvesting strategies were unsustainable for all the scenarios.

Climate, social factors and research disturbance influence population dynamics in a declining sociable weaver metapopulation

Population trends are determined by gains through reproduction and immigration, and losses through mortality and emigration. These demographic quantities and resulting population dynamics are affected by different external and internal drivers. We examined how these demographic quantities were affected by weather, research-induced disturbance, local density, colony site and year in a metapopulation of 17 sociable weaver (Philetairus socius) colonies over 17 years of study (4 years for reproduction). Most colonies declined, but at different rates. The four demographic quantities were related to different drivers. Survival strongly varied among years and colonies and was positively related to rainfall and negatively related to extreme temperature (together explaining 30% of variation) and disturbance (measured as number of captures conducted at a colony; 7%). There was a trend for a positive relationship between reproduction and rainfall (50%). Movement was mainly related to local density: individuals were more likely to emigrate from small to large colonies and from colonies that were either well below or above their long-term mean. They were more likely to immigrate into colonies that were nearby, and below their mean size. We then quantified the effects of these relationships on metapopulation dynamics using a multi-site matrix projection model. Rainfall was potentially a strong driver of metapopulation dynamics. In addition, field-work disturbance might have contributed to the decline of this metapopulation but could not explain its full magnitude. Hence, through a combination of analytical methods we were able to obtain information on the main drivers affecting dynamics in a declining metapopulation.

The Implications of Habitat Management on the Population Viability of the Endangered Ohlone Tiger Beetle (Cicindela ohlone) Metapopulation

Despite their role in providing ecosystem services, insects remain overlooked in conservation planning, and insect management approaches often lack a rigorous scientific basis. The endangered Ohlone tiger beetle (Cicindela ohlone) occurs in a 24-km2 area in Santa Cruz County, California. The once larger metapopulation now consists of subpopulations inhabiting five patches of coastal prairie where it depends on bare ground for mating, foraging, and oviposition. Human activities have eliminated natural disturbances and spread invasive grasses, reducing C. ohlone's bare-ground habitat. Management actions to restore critical beetle habitat consist of cattle and horse grazing, maintaining slow bicycle speeds on occupied public trails, and artificial creation of bare-ground plots. Recreational biking trails help maintain bare ground, but can cause beetle mortality if left unregulated. We tracked C. ohlone survivorship and estimated fecundity for three years. We then constructed a stage-structured population projection matrix model to estimate population viability among the five patches, and to evaluate the success of management interventions. We demonstrate that habitat creation, regulation of bicycle speed, and migration between patches increase C. ohlone survival and population viability. Our results can be directly applied to management actions for conservation outcomes that will reduce species extinction risk and promote recolonization of extirpated patches.

Simulating the effects of global climate change on Atlantic croaker population dynamics in the mid-Atlantic Region

Projecting global climate change (GCC) effects on fish populations has primarily focused on temperature, while non-temperature effects are rarely simulated. In this study, we used a non-linear matrix population projection model of Atlantic croaker (Micropogonias undulatus) in the mid-Atlantic Bight to illustrate how global climate change effects, in addition to temperature, can be incorporated into population projections. The model was a multiple time step, stage-within-age matrix projection model with two nursery regions (Virginia and North Carolina estuaries) for young-of-the-year (YOY, egg to age-1) life stage development and a single ocean spatial box for adults. Late juvenile mortality was density-dependent and calibrated to generate a spawner-recruit relationship similar to observed values. Model simulations were for 160 years. Global climate change effects were estimated for 2020, 2050, and 2080, which resulted in three new sets of parameter values of the matrix model. The first 40 years of the 160 years were baseline, followed by 40 years of 2020 parameter values, 40 years of 2050 values, and 40 years of 2080 values. Changes in the parameters of the matrix model were based on changes in annual and seasonal temperatures generated by global circulation models, as well as presumed changes in precipitation causing increased hypoxia, increased variability in salinity, rising sea level, and changes in ocean circulation causing increased northward and offshore transport. Global climate change resulted in increased croaker abundance with lower inter-annual variability. Sensitivity analysis with each GCC effect imposed singly showed that the increase in croaker abundance under GCC was due to the complex suite of positive and negative responses across multiple life stages. The major positive response was due to warmer temperatures, and the major negative effects were due to increased variability in salinity, increased offshore transport, and sea level rise. A second sensitivity analysis showed that important, but highly uncertain, effects produced smoothly increasing population responses with increasing magnitude. We discuss how effects other than temperature can be important to projecting population responses to GCC, and the strengths and weaknesses of our analysis. Our analysis demonstrates how a variety of GCC-related effects can be incorporated into traditional population models; what is needed is sufficient empirical information to quantify the effects in terms of growth, mortality, movement, and reproduction.

Using a deterministic population model to evaluate population stability and the effects of fruit harvesting and livestock on baobab (Adansonia digitata L.) populations in five land-use types

The subsistence and commercial use of baobab (Adansonia digitata) fruit is important to many thousands of marginalized people in the arid tropics of Africa, yet sustainable harvest levels have not previously been studied. Size-class distributions of baobab populations tend to be stable, suggesting high tolerance to fruit harvesting. However, environmental conditions have changed substantially over the last 100years. Increasing livestock numbers, land modification and climate change are new threats which may affect tolerance to fruit harvesting. To investigate this, a deterministic stage-based population projection matrix model was developed using (a) long term baobab monitoring data from 2 sites, (b) radiocarbon age calculations, (c) extensive field surveys of population structure and fruit (and seed) production, and (d) experimental field trials on seed banks and seedling and sapling survival in relation to the presence of livestock. Projected population growth (λ) was then evaluated for five land-use types (nature reserves, rocky outcrops, plains, fields, and villages) under three levels of livestock (none, moderate and high stocking rates). Response to fruit harvest intensity was tested for each scenario by decreasing seed availability by 10% from 100%. High livestock numbers resulted in baobab population declines, with λ<1 in all land-use types. Under moderate and zero livestock numbers, baobab populations in plains, rocky outcrops, villages and fields were able to tolerate between 33% and 90% fruit harvest rates. In nature reserves there was already high predation on immature fruit by baboons, another cause of population decline, with the model showing no tolerance whatsoever to fruit harvesting. These results show that fruit harvesting can be sustainable in production landscapes under moderate livestock levels. However the future is uncertain, as a predicted lowering of rainfall due to climate change is a further concern, with likely negative impacts on fruit yields and recruitment and consequently population projections. Thus active planting and protection of seedlings should take place to mitigate current and future negative impacts facing baobab populations.

Inference for Size Demography From Point Pattern Data Using Integral Projection Models

Population dynamics with regard to evolution of traits has typically been studied using matrix projection models (MPMs). Recently, to work with continuous traits, integral projection models (IPMs) have been proposed. Imitating the path with MPMs, IPMs are handled first with a fitting stage, then with a projection stage. Fitting these models has so far been done only with individual-level transition data. These data are used to estimate the demographic functions (survival, growth, fecundity) that comprise the kernel of the IPM specification. Then, the estimated kernel is iterated from an initial trait distribution to project steady state population behavior under this kernel. When trait distributions are observed over time, such an approach does not align projected distributions with these observed temporal benchmarks. The contribution here, focusing on size distributions, is to address this issue. Our concern is that the above approach introduces an inherent mismatch in scales. The redistribution kernel in the IPM proposes a mechanistic description of population level redistribution. A kernel of the same functional form, fitted to data at the individual level, would provide a mechanistic model for individual-level processes. Resulting parameter estimates and the associated estimated kernel are at the wrong scale and do not allow population-level interpretation. Our approach views the observed size distribution at a given time as a point pattern over a bounded interval. We build a three-stage hierarchical model to infer about the dynamic intensities used to explain the observed point patterns. This model is driven by a latent deterministic IPM and we introduce uncertainty by having the operating IPM vary around this deterministic specification. Further uncertainty arises in the realization of the point pattern given the operating IPM. Fitted within a Bayesian framework, such modeling enables full inference about all features of the model. Such dynamic modeling, optimized by fitting data observed over time, is better suited to projection. Exact Bayesian model fitting is very computationally challenging; we offer approximate strategies to facilitate computation. We illustrate with simulated data examples as well as well as a set of annual tree growth data from Duke Forest in North Carolina. A further example shows the benefit of our approach, in terms of projection, compared with the foregoing individual level fitting.

The effect of habitat degradation on the long term survival of the Critically Endangered Madagascar spider tortoise (Pyxis arachnoides)

Pyxis arachnoides inhabits the dry, coastal forests of southwest Madagascar; a biologically unique ecoregion severely threatened by unsustainable small scale agricultural practices. Using remotely sensed data we established vegetation loss remains unabated within our study area at 1.2% year−1; consistent with ecoregion wide vegetation loss between 1990 and 2000. We monitored tortoise population density on four occasions over 8years and developed a stage class projection matrix to model the finite growth rate, matrix sensitivities and elasticities of the population. Monitoring revealed an actual mean population decline of 10.8% between 2003 and 2011. Our projection matrix model suggested the finite rate of growth to be λ=0.986, indicative of 1.4% year−1 decline for the duration of the existence of the population, with adult survival as the most sensitive parameter to overall survival of the population. Projection modeling suggests that the population would possibly become functionally non viable in approximately 170years. As our study was heavily reliant on the use of surrogate data, more information is needed on pre-adult survival and wild reproductive rates. Our study site currently represents a population of exceptional density, therefore, other less dense populations, subjected to the further stresses of poaching will likely become functionally non viable much sooner. This study highlights the utility of population projection matrices in determining the vulnerability of chelonians; a globally threatened taxon. In the case of the spider tortoise, well coordinated development programs and tighter protected area management are required to address the poverty induced drivers forcing this species closer to extinction.

Popdemo: an R package for population demography using projection matrix analysis

Summary1. Effective population management requires accurate predictions of future population dynamics and how they may be manipulated to achieve management goals.2. The R package popdemo provides software tools for novel analytical methods that aim to enhance the predictive power of basic population projection matrix models. These include indices of transient population dynamics and transfer function analyses.3. We use a case study to demonstrate the use and importance of these methods for population management and briefly discuss their potential application outside population ecology.

Paleodemographic analysis of a fossil porcupine (Hystrix refossa Gervais, 1852) population from the Upper Pleistocene site of Geula Cave (Mount Carmel, Israel)

For decades zooarchaeological studies mainly focused on teeth age profiles to derive central hypotheses concerning human subsistence during the Pleistocene. Behavior was often related to hunting and/or scavenging strategies according to two models: attritional versus catastrophic. However, few studies have estimated basic demographic parameters using standard methods of population ecology, which are necessary for a more confident interpretation of animal paleopopulation structures. Thanks to a remarkably rich fossil bone assemblage from the Upper Pleistocene cave of Geula (Mount Carmel, Israel), in this paper we perform a paleodemographic analysis of Hystrix refossa, Gervais 1852 (Mammalia, Rodentia). We first consider phylogenetic and morphometric dental criteria for the comparison of Pleistocene porcupine species, followed by an examination of taphonomic conditions of the bone assemblage. We focus strongly on the age structure of the fossil population, presenting a new methodological approach that combines life tables and Leslie matrix models – one of the best-known methods in population ecology for assessing population growth and age distribution. We detail demographic parameters derived from cross-sectional life tables and past trends in the porcupine population at Geula Cave using simple matrix projection model. Finally, we were able to perform an elasticity analysis to identify which demographic component was potentially the most critical for influencing growth. We show that the population of H. refossa did not decline or shrink but was stable. Our results permit us to characterize Geula Cave as a natural shelter for porcupines, with limited evidence to scavenging and hunting by either hyenas or humans.

Temporally variable dispersal and demography can accelerate the spread of invading species

We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines state-structured local demography (specified by an integral or matrix projection model) with general dispersal distributions that may depend on the state of the individual or its parent. It allows very general patterns of stationary temporal variation in both local demography and in the frequency and distribution of dispersal distances. We show that expressions for the asymptotic spread rate and its sensitivity to parameters, which have been derived previously for less general models, continue to hold. Using these results we show that random temporal variability in dispersal can accelerate population spread. Demographic variability can further accelerate spread if it is positively correlated with dispersal variability, for example if high-fecundity years are also years in which juveniles tend to settle further away from their parents. A simple model for the growth and spread of patches of an invasive plant (perennial pepperweed, Lepidium latifolium) illustrates these effects and shows that they can have substantial impacts on the predicted speed of an invasion wave. Temporal variability in dispersal has received very little attention in both the theoretical and empirical literature on invasive species spread. Our results suggest that this needs to change.

Population Responses to Perturbations: The Importance of Trait-Based Analysis Illustrated through a Microcosm Experiment

Environmental change continually perturbs populations from a stable state, leading to transient dynamics that can last multiple generations. Several long-term studies have reported changes in trait distributions along with demographic response to environmental change. Here we conducted an experimental study on soil mites and investigated the interaction between demography and an individual trait over a period of nonstationary dynamics. By following individual fates and body sizes at each life-history stage, we investigated how body size and population density influenced demographic rates. By comparing the ability of two alternative approaches, a matrix projection model and an integral projection model, we investigated whether consideration of trait-based demography enhances our ability to predict transient dynamics. By utilizing a prospective perturbation analysis, we addressed which stage-specific demographic or trait-transition rate had the greatest influence on population dynamics. Both body size and population density had important effects on most rates; however, these effects differed substantially among life-history stages. Considering the observed trait-demography relationships resulted in better predictions of a population's response to perturbations, which highlights the role of phenotypic plasticity in transient dynamics. Although the perturbation analyses provided comparable predictions of stage-specific elasticities between the matrix and integral projection models, the order of importance of the life-history stages differed between the two analyses. In conclusion, we demonstrate how a trait-based demographic approach provides further insight into transient population dynamics.

From metamorphosis to maturity in complex life cycles: equal performance of different juvenile life history pathways

Performance in one stage of a complex life cycle may affect performance in the subsequent stage. Animals that start a new stage at a smaller size than conspecifics may either always remain smaller or they may be able to "catch up" through plasticity, usually elevated growth rates. We study how size at and date of metamorphosis affected subsequent performance in the terrestrial juvenile stage and lifetime fitness of spadefoot toads (Pelobates fuscus). We analyzed capture-recapture data of > 3000 individuals sampled during nine years with mark-recapture models to estimate first-year juvenile survival probabilities and age-specific first-time breeding probabilities of toads, followed by model selection to assess whether these probabilities were correlated with size at and date of metamorphosis. Males attained maturity after two years, whereas females reached maturity 2-4 years after metamorphosis. Age at maturity was weakly correlated with metamorphic traits. In both sexes, first-year juvenile survival depended positively on date of metamorphosis and, in males, also negatively on size at metamorphosis. In males, toads that metamorphosed early at a small size had the highest probability to reach maturity. However, because very few toadlets metamorphosed early, the vast majority of male metamorphs had a very similar probability to reach maturity. A matrix projection model constructed for females showed that different juvenile life history pathways resulted in similar lifetime fitness. We found that the effects of date of and size at metamorphosis on different juvenile traits cancelled each other out such that toads that were small or large at metamorphosis had equal performance. Because the costs and benefits of juvenile life history pathways may also depend on population fluctuations, ample phenotypic variation in life history traits may be maintained.

Effect of maternal and grandmaternal care on population dynamics and human life-history evolution: A matrix projection model

We present a matrix population model for a single-sex human population comprising non-orphan daughters (whose mothers are alive) and orphan daughters (whose mothers are dead). Orphans suffer higher mortality than non-orphans, which simulates the need for daughters to receive maternal care in order to survive. The way that maternal care affects population dynamics and life-history evolution is then analysed for demographic regimes that encompass large ranges of daughter survival, mother survival and fertility. We provide stable age-distributions of orphans and non-orphans for each regime and perform sensitivity analyses on daughter survival, adult survival and fertility. The results show that natural selection will favour (i) faster daughter independence from maternal care, (ii) higher adult survival at all ages, and (iii) early reproduction to the detriment of late reproduction. We then build scenarios concerning the coevolution of daughter survival and maternal care with adult survival and fertility. We also incorporate grandmaternal care into the model. We show that (i) the acute altriciality of human babies, (ii) the increased maternal care resulting from emergence of complex sociality and (iii) the role played by grandmothers in caring for granddaughters may have led to the emergence of specific human life-history traits: a short reproductive period characterised by a reproductive senescence and menopause, as well as an extended lifespan characterised by a post-reproductive life.

The population dynamics and productivity of Acacia pennatula in the pasturelands of the Nature Reserve Mesas de Moropotente, Estelí, Nicaragua

Acacia pennatula trees are the most conspicuous woody species in the pasturelands of the Nature Reserve Mesas de Moropotente, Esteli, Nicaragua. Cattle ranchers keep A. pennatula because it produces fence posts, forage (pods) and firewood. A population projection matrix model was developed to: (1) estimate the sustainable harvest (H) of fence posts at different tree population densities, (2) explore the range of recruitment (R), and survival and growth of both saplings and small poles compatible with current population density, and (3) determine how much carbon is stored in the soil-pasture-tree system. Acacia pennatula trees take 40 years to reach H size (D30 ≥ 30 cm). Estimated sustainable H from current tree population density is 1.8l7 trees ha−1 year−1, yielding 2.8 large and 11.2 regular size fence posts ha−1 year−1. This annual output easily satisfies the needs of a typical 100 ha cattle ranch in the study area. Current population density is congruent with very low R (<100 saplings ha−1 year−1), very low survival rates (<0.30%) and/or retarded D30 growth of saplings and small poles. Total carbon in tree biomass was only 37 Mg ha−1. Cattle ranchers have learned to harness the invasive nature of the species to obtain valuable tree products for farm use or sale.

The effects of dataset length and mast seeding on the demography ofFrasera speciosa, a long-lived monocarpic plant

Frasera speciosa (Gentianaceae) is a long-lived monocarpic plant with mast seeding, a type of plant whose demography is rarely studied. Using a 35-year dataset from an ongoing study, we described the population dynamics of F. speciosa using matrix projection models, addressed how many years of data are needed to estimate population growth and elasticity values consistently, and examined the effects of mast seeding on demographic parameter estimates. Our results indicated that our population is likely stable, with the annual population growth rate near one (λ = 0.969, λs = 0.967 with 95% CI = 0.923–1.013). Mean generation time was 40 years and the mean estimated lifespan was 6.86 years with a high variance of 181.8 years for individuals starting in the seedling stage, consistent with observations of very long-lived individuals in the field. Elasticity values were highest for the transitions representing stasis and lowest for reproduction. For dataset length, 15 years of data yielded lambda estimates that were within 1% of the long-term estimate, but 20 years of data were needed to yield lambdas with confidence intervals that consistently overlap one. Although mast seeding is generally defined using the inter-annual variation in seed production per unit area, stochastic lambdas were not correlated with this measure of reproduction but instead correlated with per capita dormant seed production and per capita recruit production. Mean survival rate was also positively correlated with stochastic lambda estimates, despite the necessary increase in mortality in years with high reproduction. Our results indicated that the demography of F. speciosa is similar to that of other long-lived monocarps without mast seeding, that long datasets may be needed to capture the variation in demographic rates even for stable populations, and that life history stages with low elasticity values can still be very important to population growth.