Accounting for stochasticity in demographic compensation along the elevational range of an alpine plant

Demographic compensation arises when vital rates change in opposite directions across populations, buffering the variation in population growth rates, and is a mechanism often invoked to explain the stability of species geographic ranges. However, studies on demographic compensation have disregarded the effects of temporal variation in vital rates and their temporal correlations, despite theoretical evidence that stochastic dynamics can affect population persistence in temporally varying environments. We carried out a seven‐year‐long demographic study on the perennial plant Arabis alpina (L.) across six populations encompassing most of its elevational range. We discovered demographic compensation in the form of negative correlations between the means of plant vital rates, but also between their temporal coefficients of variation, correlations and elasticities. Even if their contribution to demographic compensation was small, this highlights a previously overlooked, but potentially important, role of stochastic processes in stabilising population dynamics at range margins.     

Demographic strategies of plant invaders in temporally varying environments

Plant populations may have evolved different demographic strategies to cope with temporal environmental variation. According to the demographic buffering hypothesis, vital rates that are most critical to population persistence are buffered against environmental variation and vary little over time, whereas the demographic lability hypothesis suggests that populations may track and benefit from environmental variation. While the hypotheses of demographic strategies have been widely tested in plant and animal species, they have not been explicitly examined for invasive plants, or in relation to different modelling methods (deterministic vs. stochastic). Here, we tested the demographic buffering and lability hypotheses for 23 populations of eight invasive plant species in relation to life form (woody vs. herbaceous species) and population growth rate using deterministic and stochastic modelling methods, and absolute and relative scales. We found that conclusions of demographic strategies depended on scale, with an absolute scale resulting in stronger negative correlations between the variability and importance of vital rates (i.e., buffering) than a relative scale. Conclusions of demographic strategies were also affected by life form that interacted with method. The populations of woody invaders exhibited buffering regardless of the method used, while for the populations of herbaceous species, deterministic calculations suggested buffering and stochastic calculations suggested lability. Overall, our findings emphasise the role of life form and methodological issues that need to be considered when exploring demographic strategies in fluctuating environments.     

Population Dynamics of the Endangered, Long-Lived Perennial Species, Ligularia sibirica

Ligularia sibirica is a relict wetland perennial plant species of the Czech and Slovak Republic. Explaining variation in population growth rate and identifying the causes of that variation is important for effective protection of such an endangered species. Matrix models based on four years of data of 11 populations were used to identify the pattern of variation in the demographic vital rates of this species, and to examine the causes of the variation such as population size and habitat type. Further, the matrix model was used to determine the population growth rate, longevity and risk of extinction of each population and to identify the specific vital rates that most affect population growth rate. The results showed that population growth rates were significantly different between years and populations. Temporal variation was mostly due to variable survival of adult individuals, while spatial variation was mainly driven by fertility of one small currently expanding population. Further, most studied populations of L. sibirica are performing well and only those growing in nitrogen-rich habitats have a high extinction risk. The results also indicate that all populations have low adult mortality, long-lived individuals (61.3?years on average) and some populations also show features of remnant populations (i.e., the persistence of populations in severe conditions in spite of no reproduction). Our results imply that detailed demographic data are needed to understand the long-term prospects of these populations. These data may serve as an early warning system for this species long before an obvious decline occurs in the populations.     

Density-dependent parameters and demographic equilibrium in open populations

Populations near their equilibrium are expected to show density-dependence through a negative feedback on at least one demographic parameter, e.g. survival and/or productivity. Nevertheless, it is not always clear which vital rate is affected the most, and even less whether this dependence holds in open populations in which immigration and emigration are also important. We assessed the relative importance of population density in the variation of local survival, recruitment, proportion of transients (emigrants) and productivity through the analysis of detailed life-histories of 4286  seabirds from a colony that reached an apparent demographic equilibrium after a period of exponential increase. We provide evidence that the role of population density and resource availability changes according to the demographic parameter considered. Estimates indicated that transients increased from 5% to 20% over the study period, suggesting an average turnover of about 1400 individuals per year. The parameters most influenced by population density alone were local survival and probability of transience. Recruitment was negatively associated with population density during the increasing phase but unexpected high values were also recorded at high population levels. These high values were explained by a combination of population size and food availability. Mean productivity varied with food availability, independently from population variations. The population density alone explained up to a third of the yearly variation of the vital rates considered, suggesting that open populations are equally influenced by stochastic and density-independent events (such as environmental perturbations) than by intrinsic (i.e. density-dependent) factors.     

Less favourable climates constrain demographic strategies in plants

Correlative species distribution models are based on the observed relationship between species’ occurrence and macroclimate or other environmental variables. In climates predicted less favourable populations are expected to decline, and in favourable climates they are expected to persist. However, little comparative empirical support exists for a relationship between predicted climate suitability and population performance. We found that the performance of 93 populations of 34 plant species worldwide – as measured by in situ population growth rate, its temporal variation and extinction risk – was not correlated with climate suitability. However, correlations of demographic processes underpinning population performance with climate suitability indicated both resistance and vulnerability pathways of population responses to climate: in less suitable climates, plants experienced greater retrogression (resistance pathway) and greater variability in some demographic rates (vulnerability pathway). While a range of demographic strategies occur within species’ climatic niches, demographic strategies are more constrained in climates predicted to be less suitable.     

Connecting geographical distributions with population processes

The geographical distribution of a species is determined by a large number of complex processes operating over spatial scales spanning 10 orders of magnitude. Patterns in population processes have been described at numerous scales. We show that two patterns, measured at different scales, jointly allow us to infer heretofore unknown patterns in the distribution of demographic patterns across the geographical range of a species. The resulting model describes three fundamentally different modes of geographical variation in vital rates of populations. One mode is characterized by a positive nonlinear relationship between the maximum rate of population growth and the intensity of intraspecific competition across a geographical range. That is, populations that grow rapidly are also those where individuals experience the greatest per capita negative effect of the presence of other individuals. The second mode of behaviour is described by a negative nonlinear relationship between maximum growth rate and density dependence. Under this scenario, populations with low capacity to grow rapidly have highest intensities of intraspecific competitive effects. A third mode of behaviour is characterized by a weak positive relationship between growth rate and intraspecific competition, with very little geographical variation in maximum growth rate. A survey of studies relating temporal means and variances in population abundance for a variety of species indicate that the second mode of geographical variation in population dynamics across species ranges is the most common, though a few species appear to be characterized by the third mode.     

Local environment and density-dependent feedbacks determine population growth in a forest herb

Linking spatial variation in environmental factors to variation in demographic rates is essential for a mechanistic understanding of the dynamics of populations. However, we still know relatively little about such links, partly because feedbacks via intraspecific density make them difficult to observe in natural populations. We conducted a detailed field study and investigated simultaneous effects of environmental factors and the intraspecific density of individuals on the demography of the herb Lathyrus vernus. In regression models of vital rates we identified effects associated with spring shade on survival and growth, while density was negatively correlated with these vital rates. Density was also negatively correlated with average individual size in the study plots, which is consistent with self-thinning. In addition, average plant sizes were larger than predicted by density in plots that were less shaded by the tree canopy, indicating an environmentally determined carrying capacity. A size-structured integral projection model based on the vital rate regressions revealed that the identified effects of shade and density were strong enough to produce differences in stable population sizes similar to those observed in the field. The results illustrate how the local environment can determine dynamics of populations and that intraspecific density may have to be more carefully considered in studies of plant demography and population viability analyses of threatened species. We conclude that demographic approaches incorporating information about both density and key environmental factors are powerful tools for understanding the processes that interact to determine population dynamics and abundances.     

Recruitment rates exhibit high elasticity and high temporal variation in populations of a short-lived perennial herb

Empirical studies for different life histories have shown an inverse relationship between elasticity (i.e. the proportional contribution to population growth rate) and temporal variation in vital rates. It is accepted that this relationship indicates the effect of selective pressures in reducing variation in those life‐history traits with a major impact on fitness. In this paper, we sought to determine whether changes in environmental conditions affect the relationship between elasticity of vital rates and their temporal variation, and whether vital rates with simultaneously large elasticity and temporal variation might represent a characteristic life‐history strategy. We used demographic data on 13 populations of the short‐lived Hypericum cumulicola over 5–6 years, in three time‐since‐fire classes. For each population of each time‐since‐fire, we computed the mean matrix over years and its respective elasticity matrix, and the coefficients of variation in matrix entries over study years as an estimate of temporal variability. We found that mean elasticity negatively significantly correlated with temporal variation in vital rates in populations (overall eight out of 13) included in each time‐since‐fire. However, seedling recruitment exhibited both high elasticity and high temporal variation in almost all study populations. These results indicated that (1) the general relationship between elasticity and temporal variation in vital rates was not modified by environmental changes due to time‐since‐fire, and (2) high elasticity and high temporal variation in seedling recruitment in H. cumulicola is a particular trait of the species' life history. After seed survival in the soil seed bank, seedling recruitment represents the most important life‐history trait influencing H. cumulicola population growth rate (and fitness). The high temporal variability in seedling recruitment suggests that this trait is determined by environmental cues, leading to an increase in population size and subsequent replenishment of the seed bank in favorable years.     

Evaluating the demographic buffering hypothesis with vital rates estimated for Weddell seals from 30 years of mark-recapture data

1. Life-history theory predicts that those vital rates that make larger contributions to population growth rate ought to be more strongly buffered against environmental variability than are those that are less important. Despite the importance of the theory for predicting demographic responses to changes in the environment, it is not yet known how pervasive demographic buffering is in animal populations because the validity of most existing studies has been called into question because of methodological deficiencies. 2. We tested for demographic buffering in the southern-most breeding mammal population in the world using data collected from 5558 known-age female Weddell seals over 30 years. We first estimated all vital rates simultaneously with mark-recapture analysis and then estimated process variance and covariance in those rates using a hierarchical Bayesian approach. We next calculated the population growth rate's sensitivity to changes in each of the vital rates and tested for evidence of demographic buffering by comparing properly scaled values of sensitivity and process variance in vital rates. 3. We found evidence of positive process covariance between vital rates, which indicates that all vital rates are affected in the same direction by changes in annual environment. Despite the positive correlations, we found strong evidence that demographic buffering occurred through reductions in variation in the vital rates to which population growth rate was most sensitive. Process variation in vital rates was inversely related to sensitivity measures such that variation was greatest in breeding probabilities, intermediate for survival rates of young animals and lowest for survival rates of older animals. 4. Our work contributes to a small but growing set of studies that have used rigorous methods on long-term, detailed data to investigate demographic responses to environmental variation. The information from these studies improves our understanding of life-history evolution in stochastic environments and provides useful information for predicting population responses to future environmental change. Our results for an Antarctic apex predator also provide useful baselines from a marine ecosystem when its top- and middle-trophic levels were not substantially impacted by human activity.     

The generality of management recommendations across populations of an invasive perennial herb

Demographic models are widely used to produce management recommendations for different species. For invasive plants, current management recommendations to control local population growth are often based on data from a limited number of populations per species, and the assumption of stable population structure (asymptotic dynamics). However, spatial variation in population dynamics and deviation from a stable structure may affect these recommendations, calling into question their generality across populations of an invasive species. Here, I focused on intraspecific variation in population dynamics and investigated management recommendations generated by demographic models across 37 populations of a short-lived, invasive perennial herb (Lupinus polyphyllus). Models that relied on the proportional perturbations of vital rates (asymptotic elasticities) indicated an essential role for plant survival in long-term population dynamics. The rank order of elasticities for different vital rates (survival, growth, retrogression, fecundity) varied little among the 37 study populations regardless of population status (increasing or declining asymptotically). Summed elasticities for fecundity increased, while summed elasticities for survival decreased with increasing long-term population growth rate. Transient dynamics differed from asymptotic dynamics, but were qualitatively similar among populations, that is, depending on the initial size structure, populations tended to either increase or decline in density more rapidly than predicted by asymptotic growth rate. These findings indicate that although populations are likely to exhibit transient dynamics, management recommendations based on asymptotic elasticities for vital rates might be to some extent generalised across established populations of a given short-lived invasive plant species.     

Interaction of climate,demography and genetics: a ten-year study of <Emphasis Type="Italic">Brassica insularis</Emphasis>, a narrow endemic Mediterranean species

Long-term demographic surveys, needed to obtain accurate information on population dynamics and efficiently manage rare species, are still very scarce. Matrix population models are useful tools to identify key demographic transitions and thus help setting up conservation actions. Furthermore, the combination of ecological, demographic and genetic data is likely to improve the identification of the threats acting upon populations and help conservation decisions. In this paper we illustrate the power of this approach on Brassica insularis, a Mediterranean endemic plant species, rare and endangered in Corsica (France). In four populations of this species, a long-term demographic survey (2000–2009), genetic analyses (in 2000 and 2009) and survey of ecological variables (climatic variables, competition and herbivory) were performed. By using both deterministic and stochastic matrix model analyses, we assessed the viability of each population and tested for both spatial and temporal variations in demographic vital rates. Populations exhibited differing demographic behaviours and environmental stochasticity occurred in populations. Significant correlations between climatic variables and vital rates were detected. Stochastic simulations suggested that three out of the four populations studied might present a high risk of extinction on the short-term and should actively be managed, or at least surveyed. It could be, however, that two of these populations are experiencing density-dependent regulation, rather than being declining. Microsatellite diversity was slightly reduced in a single population and similar in the three others, consistently with expectations based on population census size and geographic area, as well as with diversity at the S-locus observed in 2000. The combination of all data led to specific recommendations for managing each population. We discuss the implications for conservation of such a general approach.     

Sensitivity of the population growth rate to demographic variability within and between phases of the disturbance cycle

For species in disturbance-prone ecosystems, vital rates (survival, growth and reproduction) often vary both between and within phases of the cycle of disturbance and recovery; some of this variation is imposed by the environment, but some may represent adaptation of the life history to disturbance. Anthropogenic changes may amplify or impede these patterns of variation, and may have positive or negative effects on population growth. Using stochastic population projection matrix models, we develop stochastic elasticities (proportional derivatives of the long-run population growth rate) to gauge the population effects of three types of change in demographic variability (changes in within- and between-disturbance-phase variability and phase-specific changes). Computing these elasticities for five species of disturbance-influenced perennial plants, we pinpoint demographic rates that may reveal adaptation to disturbance, and we demonstrate that species may differ in their responses to different types of changes in demographic variability driven by climate change.     

Buffering and plasticity in vital rates of oldfield rodents

1. Under the hypothesis of environmental buffering, populations are expected to minimize the variance of the most influential vital rates; however, this may not be a universal principle. Species with a life span <1 year may be less likely to exhibit buffering because of temporal or seasonal variability in vital rate sensitivities. Further, plasticity in vital rates may be adaptive for species in a variable environment with reliable cues. 2. We tested for environmental buffering and plasticity in vital rates using stage-structured matrix models from long-term data sets in four species of grassland rodents. We used periodic matrices to estimate stochastic elasticity for each vital rate and then tested for correlations with a standardized coefficient of variation for each rate. 3. We calculated stochastic elasticities for individual months to test for an association between increased reproduction and the influence of reproduction, relative to survival, on the population growth rate. 4. All species showed some evidence of buffering. The elasticity of vital rates of Peromyscus leucopus (Rafinesque, 1818), Sigmodon hispidus Say & Ord, 1825 and Microtus ochrogaster (Wagner, 1842) was negatively related to vital rate CV. Elasticity and vital rate CV were negatively related in Peromyscus maniculatus (Wagner, 1845), but the relationship was not statistically significant. Peromyscus leucopus and M. ochrogaster showed plasticity in vital rates; reproduction was higher following months where elasticity for reproduction exceeded that of survival. 5. Our results suggest that buffering is common in species with fast life histories; however, some populations that exhibit buffering are capable of responding to short-term variability in environmental conditions through reproductive plasticity.     

The effects of climate change and land‐use change on demographic rates and population viability

Understanding the processes that lead to species extinctions is vital for lessening pressures on biodiversity. While species diversity, presence and abundance are most commonly used to measure the effects of human pressures, demographic responses give a more proximal indication of how pressures affect population viability and contribute to extinction risk. We reviewed how demographic rates are affected by the major anthropogenic pressures, changed landscape condition caused by human land use, and climate change. We synthesized the results of 147 empirical studies to compare the relative effect size of climate and landscape condition on birth, death, immigration and emigration rates in plant and animal populations. While changed landscape condition is recognized as the major driver of species declines and losses worldwide, we found that, on average, climate variables had equally strong effects on demographic rates in plant and animal populations. This is significant given that the pressures of climate change will continue to intensify in coming decades. The effects of climate change on some populations may be underestimated because changes in climate conditions during critical windows of species life cycles may have disproportionate effects on demographic rates. The combined pressures of land‐use change and climate change may result in species declines and extinctions occurring faster than otherwise predicted, particularly if their effects are multiplicative.     

Stochastic LTRE analysis of the effects of herbivory on the population dynamics of a perennial grassland herb

Herbivores can have strong deleterious effects on vital rates (growth, reproduction, and survival) and thus negatively impact the population dynamics of plant species. In practice, however, these effects might be strongly correlated, for example as a result of tradeoffs between vital rates. To get better insights into the effects of herbivory on the population dynamics of the long‐lived grassland plant Primula veris population projection matrices were constructed from demographic data collected between 1999 and 2008 (nine annual transitions). Data were collected in two large grassland populations, each of which was subjected to two treatments (grazing by cattle versus a mowing treatment), yielding a total of 36 matrices. We applied a lower‐level vital rate life table response experiment (LTRE) using the small noise approximation (SNA) of the stochastic population growth rate to disentangle the contributions of changes in mean vital rates, variability in vital rates, correlations between vital rates and vital rate elasticities to the difference in the stochastic growth rate. Stochastic growth rates (a= log λ_S) were significantly lower in grazed than in mown plots (a= 0.0185 and 0.1019, respectively). SNA LTRE analysis showed that contributions of mean vital rates by far made the largest contribution to the observed difference in a between grazed and control plots. In particular, changes in sexual reproduction rates made the largest contributions to lower the stochastic growth rate in grazed plots: both adult flowering probabilities and flower and seed production were importantly lower in grazed populations, but these negative effects were largely buffered by increased establishment and seedling survival rates. Among the stochastic terms of the SNA decomposition, contributions of covariance and correlations between vital rates had the largest impact, whereas contributions of elasticities were smaller. The strongest correlation driver was the association between adult survival and seedling establishment, suggesting that environmental conditions favouring adult survival also are beneficial for seedling establishment. Overall, our results show that herbivory had a strong negative effect on the long‐term population growth rate of P. veris that was primarily mediated by differences in fecundity (flower and seed production) and germination.     

Range position and climate sensitivity: The structure of among‐population demographic responses to climatic variation

Species’ distributions will respond to climate change based on the relationship between local demographic processes and climate and how this relationship varies based on range position. A rarely tested demographic prediction is that populations at the extremes of a species’ climate envelope (e.g., populations in areas with the highest mean annual temperature) will be most sensitive to local shifts in climate (i.e., warming). We tested this prediction using a dynamic species distribution model linking demographic rates to variation in temperature and precipitation for wood frogs (Lithobates sylvaticus) in North America. Using long‐term monitoring data from 746 populations in 27 study areas, we determined how climatic variation affected population growth rates and how these relationships varied with respect to long‐term climate. Some models supported the predicted pattern, with negative effects of extreme summer temperatures in hotter areas and positive effects on recruitment for summer water availability in drier areas. We also found evidence of interacting temperature and precipitation influencing population size, such as extreme heat having less of a negative effect in wetter areas. Other results were contrary to predictions, such as positive effects of summer water availability in wetter parts of the range and positive responses to winter warming especially in milder areas. In general, we found wood frogs were more sensitive to changes in temperature or temperature interacting with precipitation than to changes in precipitation alone. Our results suggest that sensitivity to changes in climate cannot be predicted simply by knowing locations within the species’ climate envelope. Many climate processes did not affect population growth rates in the predicted direction based on range position. Processes such as species‐interactions, local adaptation, and interactions with the physical landscape likely affect the responses we observed. Our work highlights the need to measure demographic responses to changing climate.     

Population dynamics of the rare plant Kosteletzkya pentacarpos (Malvaceae): a nine-year study

Rare plant species have extremely narrow distributions that can be reduced to a single or few populations. The rare long-lived plant Kosteletzkya pentacarpos is one such species because only two extant localities are known in the western Mediterranean. In this study, we analyse the population dynamics over nine years of the only population known in north-east Spain, which is located at the Llobregat delta (Barcelona). We collected basic demographic data to build a transition matrix model. We computed population growth rates λ and their confidence intervals for each year of study. We conducted elasticity and variance decomposition analyses to determine the relative importance of vital rates to overall population dynamics. On average, the K. pentacarpos population exhibited an increasing dynamics. Survivorship of adult plants contributed the most to each λ, whereas temporal variance in fecundity and juvenile fate explained the observed variation in λ. Despite the increasing dynamics of K. pentacarpos , important reductions in fecundity resulting from biotic agents and recruitment owing to habitat limitations are constraints for population growth. We conclude that the knowledge generated in this long-term study should be used to create new K. pentacarpos populations at the Llobregat delta in order to minimize the risk of extinction following catastrophic events that are nearly impossible to predict.  © 2007 The Linnean Society of London, Botanical Journal of the Linnean Society , 2007, 153 , 455–462.     

Demographic response of plant populations to habitat fragmentation and temporal environmental variability

Many plant species currently exist in fragmented populations of different sizes, while they also experience unpredictable climatic fluctuation over time. However, we still understand little about how plant demography responds to such spatial and temporal environmental variability. We studied population dynamics of an understory perennial herb Trillium camschatcense in the Tokachi plain of Hokkaido, Japan, where a significant effect of forest fragmentation on seedling recruitment was previously reported. Four populations across a range of fragment sizes were studied for 6 years, and the data were analyzed using matrix population models. Per capita fecundity (the number of recruits per plant) varied greatly among populations, but the variation in population growth rates (λ) was mainly driven by the variation in stasis and growth rates, suggesting that the general trend of reduced fecundity in fragmented populations may not be readily translated into subsequent dynamics. Temporal variation in λ among years was more than 2 times larger than spatial variation among populations, and this result was likely attributable to the contrasting response of correlation structures among demographic rates. The among-population variation in λ was dampened by negative covariation between matrix elements possibly due to density-dependent regulation as well as an inherent constraint that some elements are not independent, whereas positive covariation between matrix elements resulted in large temporal variation in λ. Our results show that population dynamics responded differently to habitat fragmentation and temporal variability of the environment, emphasizing the need to discriminate these spatial and temporal variations in demographic models. Although no populations were projected to be declining in stochastic simulations, correlation between current habitat size and plant density implies historical λ is positively related to habitat size.     

Genetic architecture for normal and novel host-plant use in two local populations of the herbivorous ladybird beetle, Epilachna pustulosa

Trade-offs in host-plant use are thought to promote the evolution of host specificity. However, usually either positive or no genetic correlations have been found. Whereas factors enhancing variation in overall viability have been claimed to mask negative genetic correlations, alternative hypotheses emphasize the sequential changes in genetic correlation in the course of host-range evolution. In this study, the genetic architectures of performances on different hosts were compared in two populations of the herbivorous ladybird beetle, Epilachna pustulosa, using three host plants, one being normal for both, one novel for only one population, and the other novel for both populations. The genetic correlations between larval periods on normal hosts were significantly positive whereas those between normal and novel hosts were not different from zero. There was no evidence for reduced genetic variation on the normal host-plants. These results suggest that the host-range is not restricted by the antagonistic genetic associations among exploitation abilities on different plant species, but rather that selection of different host-plants may improve the coordination between genes responsible for the use of different plants.     

Buffering of life histories against environmental stochasticity: accounting for a spurious correlation between the variabilities of vital rates and their contributions to fitness

Life-history theory predicts vital rates that on average make large contributions to the annual multiplication rate of a lineage should be highly buffered against environmental variability. This prediction has been tested by looking for a negative correlation between the sensitivities (or elasticities) of the elements in a projection matrix and their variances (or coefficients of variation). Here, we show by constructing random matrices that a spurious negative correlation exists between the sensitivities and variances, and between the elasticities and coefficients of variation, of matrix elements. This spurious correlation arises in part because size transition probabilities, which are bounded by 0 and 1, have a limit to their variability that often does not apply to matrix elements representing reproduction. We advocate an alternative analysis based on the underlying vital rates (not the matrix elements) that accounts for the inherent limit to the variability of zero-to-one vital rates, corrects for sampling variation, and tests for a declining upper limit to variability as a vital rate's fitness contribution increases. Applying this analysis to demographic data from five populations of the alpine cushion plant Silene acaulis, we provide evidence of stronger buffering in the vital rates that most influence fitness.