Climate change and grassland management interactively influence the population dynamics of Bromus erectus (Poaceae)

Climate and land management are important environmental drivers that affect the structure of terrestrial plant communities worldwide. Demographic studies allow a mechanistic understanding of the pathways in which environmental factors change population size. Climate and land management might interactively influence vital rates and growth rates of populations, however, demographic studies have not heretofore considered both factors in combination. We used the Global Change Experimental Facility as a platform to study the effect of climate (ambient climate conditions vs. future climate conditions) and land management (sheep grazing vs. mowing) on the demography of the common grass, Bromus erectus growing in semi-natural grassland communities. Using an integral projection model, we found positive population growth rates for B. erectus under all treatment combinations, and an interactive effect of climate and land management. Under ambient climate conditions, population growth of B. erectus was higher in mowed than grazed grassland plots, while population growth rates were similar across both management types under future climatic conditions. This interaction was primarily due to between-treatment changes in seedling recruitment, a vital rate to which the population growth rate is particularly sensitive. The interaction found in this study highlights the importance of considering multiple environmental drivers in demographic studies, to better predict future plant population dynamics and ultimately changes in community structure.     

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.     

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.     

Effects of sample size on estimates of population growth rates calculated with matrix models

Background

Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (λ) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of λ–Jensen''s Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of λ due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of λ.

Methodology/Principal Findings

Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating λ for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of λ with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography.

Conclusions/Significance

We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.     

Linking environmental and demographic data to predict future population viability of a perennial herb

Recent advances in stochastic demography provide tools to examine the importance of random and periodic variation in vital rates for population dynamics. In this study, we explore with simulations the effect of disturbance regime on population dynamics and viability. We collected 7 years of demographic data in three populations of the perennial herb Primula farinosa, and used these data to examine how variation in vital rates affected population viability parameters (stochastic growth rate, λ_S), and how vital rates were related to weather conditions. Elasticity analysis indicated that the stochastic growth rate was very sensitive to changes in regeneration, quantified as the production, survival, and germination of seeds. In one of the study years, all seedlings and mature plants in the demography plots died. This extinction coincided with the driest summer during the study period. Simulations suggested that a future increase in the frequency of high-mortality years due to climate change would result in reduced population growth rate, and an increased importance of survival in the seed bank for population viability. The results illustrate how the limited demographic data typically available for many natural systems can be used in simulation models to assess how environmental change will affect population viability.     

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.     

Plant performance in central and northern peripheral populations of the widespread Plantago coronopus

Peripheral populations have long been predicted to show lower vital rates, higher demographic fluctuations, and lower densities than central populations. However, recent research has questioned the existence of clear patterns across species’ ranges. To test these hypotheses, we monitored five central and six northern peripheral populations of the widespread herb Plantago coronopus along the European Atlantic coast during 5 yr. We estimated population density, and calculated mean values and temporal variability of four vital rates (survival, individual growth, fecundity and recruitment) in hundreds of plants in permanent plots. Central populations showed higher fecundity, whereas peripheral populations had higher recruitment per reproductive plant, indicating a higher overall reproductive success in the periphery. Central populations showed a marginally significant tendency for higher growth, and there were no differences between range positions in survival. Fecundity and growth were affected by intraspecific competition, and recruitment was affected by precipitation, highlighting the importance of local environmental conditions for population performance. Central and peripheral populations showed no significant differences in temporal variability of vital rates. Finally, density was significantly higher in peripheral than in central populations, in discrepancy with the abundant‐centre model. Density was correlated to seedling recruitment, which would counterbalance in peripheral populations the lower fecundity and the tendency for lower growth of established plants. Such compensations among vital rates might be particularly common in widespread plants, and advise against simplistic assumptions of population performance across ranges. The whole species’ life cycle should be considered, since different arrangements of vital rates are expected to maximize fitness in local environments. Our results show also the importance of discerning between geographical periphery and ecological marginality. In a context of climate‐induced range shifts, these considerations are crucial for the reliability of niche‐models and the management of plant peripheral populations.     

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.     

Demography in an increasingly variable world

Recent advances in stochastic demography provide unique insights into the probable effects of increasing environmental variability on population dynamics, and these insights can be substantially different compared with those from deterministic models. Stochastic variation in structured population models influences estimates of population growth rate, persistence and resilience, which ultimately can alter community composition, species interactions, distributions and harvesting. Here, we discuss how understanding these demographic consequences of environmental variation will have applications for anticipating changes in populations resulting from anthropogenic activities that affect the variance in vital rates. We also highlight new tools for anticipating the consequences of the magnitude and temporal patterning of environmental variability.     

Stage-structured ontogeny in resource populations generates non-additive stabilizing and de-stabilizing forces in populations and communities

Demographic heterogeneity influences how populations respond to density dependent intraspecific competition and trophic interactions. Distinct stages across an organism's development, or ontogeny, are an important example of demographic heterogeneity. In consumer populations, ontogenetic stage structure has been shown to produce categorical differences in population dynamics, community dynamics and even species coexistence compared to models lacking explicit ontogeny. The study of consumer–resource interactions must also consider the ontogenetic stage structure of the resource itself, particularly plants, given their fundamental role at the basis of terrestrial food webs. We incorporate distinct ontogenetic stages of plants into an adaptable multi-stage consumer–resource modeling framework that facilitates studying how stage specific consumers shape trophic dynamics at low trophic levels. We describe the role of density dependent demographic rates in mediating the dynamics of stage-structured plant populations. We then investigate how these demographic rates interact with consumer pressure to influence stability and coexistence in multiple stage-specific consumer–resource interactions. Results detail how density dependent effects across distinct ontogenetic stages in plant development produce non-additivity in the drivers of dynamic stability both in single populations and in consumer–resource settings, challenging the ubiquity of certain traditional ecological dynamic paradigms. We also find categorical differences in the population variability induced by herbivores consuming separate plant stages. Consumer–resource models, such as plant–herbivore interactions, often average out demographic heterogeneity in populations. Here, we show that explicitly including plant demographic heterogeneity through ontogeny yields distinct dynamic expectations for both plants and herbivores compared to traditional consumer–resource formulations. Our results indicate that efforts to understand the demographic effect of herbivores on plant populations may need to also consider the effects of plant demographics on herbivores and the reciprocal relationship between them.     

Assessing seasonal demographic covariation to understand environmental‐change impacts on a hibernating mammal

Natural populations are exposed to seasonal variation in environmental factors that simultaneously affect several demographic rates (survival, development and reproduction). The resulting covariation in these rates determines population dynamics, but accounting for its numerous biotic and abiotic drivers is a significant challenge. Here, we use a factor‐analytic approach to capture partially unobserved drivers of seasonal population dynamics. We use 40 years of individual‐based demography from yellow‐bellied marmots (Marmota flaviventer) to fit and project population models that account for seasonal demographic covariation using a latent variable. We show that this latent variable, by producing positive covariation among winter demographic rates, depicts a measure of environmental quality. Simultaneously, negative responses of winter survival and reproductive‐status change to declining environmental quality result in a higher risk of population quasi‐extinction, regardless of summer demography where recruitment takes place. We demonstrate how complex environmental processes can be summarized to understand population persistence in seasonal environments.     

Patterns and causes of demographic variation in a harvested moose population: evidence for the effects of climate and density-dependent drivers

1.?Better understanding of the mechanisms affecting demographic variation in ungulate populations is needed to support sustainable management of harvested populations. While studies of moose Alces alces L. populations have previously explored temporal variation in demographic processes, managers responsible for populations that span large heterogeneous landscapes would benefit from an understanding of how demography varies across biogeographical gradients in climate and other population drivers. Evidence of thresholds in population response to manageable and un-manageable drivers could aid resource managers in identifying limits to the magnitude of sustainable change. 2.?Generalized additive models (GAMs) were used to evaluate the relative importance of population density, habitat abundance, summer and winter climatic conditions, primary production, and harvest intensity in explaining spatial variation in moose vital rates in Ontario, Canada. Tree regression was used to test for thresholds in the magnitudes of environmental predictor variables that significantly affected population vital rates. 3.?Moose population growth rate was negatively related to moose density and positively related to the abundance of mixed deciduous habitat abundant in forage. Calf recruitment was negatively related to a later start of the growing season and calf harvest. The ratio of bulls to cows was related to male harvest and hunter access, and thresholds were evident in predictor variables for all vital rate models. 4.?Findings indicate that the contributions of density-dependent and independent factors can vary depending on the scale of population process. The importance of density dependence and habitat supply to low-density ungulate populations was evident, and management strategies for ungulates may be improved by explicitly linking forest management and harvest. Findings emphasize the importance of considering summer climatic influences to ungulate populations, as recruitment in moose was more sensitive to the timing of vegetation green-up than winter severity. The efficacy of management decisions for harvested ungulates may require regional shifts in targets where populations span bioclimatic gradients. The use of GAMs in combination with recursive partitioning was demonstrated to be an informative analytical framework that captured nonlinear relationships common in natural processes and thresholds that are relevant to population management in diverse systems.     

Temperature-driven regime shifts in the dynamics of size-structured populations

Global warming impacts virtually all biota and ecosystems. Many of these impacts are mediated through direct effects of temperature on individual vital rates. Yet how this translates from the individual to the population level is still poorly understood, hampering the assessment of global warming impacts on population structure and dynamics. Here, we study the effects of temperature on intraspecific competition and cannibalism and the population dynamical consequences in a size-structured fish population. We use a physiologically structured consumer-resource model in which we explicitly model the temperature dependencies of the consumer vital rates and the resource population growth rate. Our model predicts that increased temperature decreases resource density despite higher resource growth rates, reflecting stronger intraspecific competition among consumers. At a critical temperature, the consumer population dynamics destabilize and shift from a stable equilibrium to competition-driven generation cycles that are dominated by recruits. As a consequence, maximum age decreases and the proportion of younger and smaller-sized fish increases. These model predictions support the hypothesis of decreasing mean body sizes due to increased temperatures. We conclude that in size-structured fish populations, global warming may increase competition, favor smaller size classes, and induce regime shifts that destabilize population and community dynamics.     

Pattern of variation in avian population growth rates

A central question in population ecology is to understand why population growth rates differ over time. Here, we describe how the long-term growth of populations is not only influenced by parameters affecting the expected dynamics, for example form of density dependence and specific population growth rate, but is also affected by environmental and demographic stochasticity. Using long-term studies of fluctuations of bird populations, we show an interaction between the stochastic and the deterministic components of the population dynamics: high specific growth rates at small densities r(1) are typically positively correlated with the environmental variance sigma(e)(2). Furthermore, theta, a single parameter describing the form of the density regulation in the theta-logistic density-regulation model, is negatively correlated with r(1). These patterns are in turn correlated with interspecific differences in life-history characteristics. Higher specific growth rates, larger stochastic effects on the population dynamics and stronger density regulation at small densities are found in species with large clutch sizes or high adult mortality rates than in long-lived species. Unfortunately, large uncertainties in parameter estimates, as well as strong stochastic effects on the population dynamics, will often make even short-term population projections unreliable. We illustrate that the concept of population prediction interval can be useful in evaluating the consequences of these uncertainties in the population projections for the choice of management actions.     

Alternative spatial sampling in studies of plant demography: consequences for estimates of population growth rate

Ecologists commonly use matrix models to study the population dynamics of plants. Most studies of plant demography use plot-based methods to collect data, in part, because mapped individuals are easier to relocate in subsequent surveys and survey methods can be standardized among sites. However, there is tremendous variation among studies, both in terms of plot arrangement and the total area sampled. In addition, there has been little discussion of how alternative sampling arrangements influence estimates of population growth rates (λ) calculated with matrix models. We surveyed the literature to determine what sampling designs are most used in studies of plant demography using matrix models. We then used simulations of three common sampling techniques—using a single randomly placed plot, multiple randomly placed plots, and systematically distributed plots—to evaluate how these alternative strategies influenced the precision of estimates of λ. These simulations were based on long-term demographic data collected on 13 populations of the Amazonian understory herb Heliconia acuminate (Heliconiaceae). We found that the method used to collect data did not affect the bias or precision of estimates in our system—a surprising result, since the advantage in efficiency that is gained from systematic sampling is a well-known result from sampling theory. Because the statistical advantage of systematic sampling is most evident when there is spatial structure in demographic vital rates, we attribute this result to the lack of spatially structured vital rates in our focal populations. Given the likelihood of spatial autocorrelation in most ecological systems, we advocate sampling with a systematic grid of plots in each study site, as well as that researchers ensure that enough area is sampled—both within and across sites—to encompass the range of spatial variation in plant survival, growth, and reproduction.     

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.     

Does probability of occurrence relate to population dynamics?

Hutchinson defined species' realized niche as the set of environmental conditions in which populations can persist in the presence of competitors. In terms of demography, the realized niche corresponds to the environments where the intrinsic growth rate (r) of populations is positive. Observed species occurrences should reflect the realized niche when additional processes like dispersal and local extinction lags do not have overwhelming effects. Despite the foundational nature of these ideas, quantitative assessments of the relationship between range‐wide demographic performance and occurrence probability have not been made. This assessment is needed both to improve our conceptual understanding of species' niches and ranges and to develop reliable mechanistic models of species geographic distributions that incorporate demography and species interactions. The objective of this study is to analyse how demographic parameters (intrinsic growth rate r and carrying capacity K ) and population density (N ) relate to occurrence probability (P_occ ). We hypothesized that these relationships vary with species' competitive ability. Demographic parameters, density, and occurrence probability were estimated for 108 tree species from four temperate forest inventory surveys (Québec, western USA, France and Switzerland). We used published information of shade tolerance as indicators of light competition strategy, assuming that high tolerance denotes high competitive capacity in stable forest environments. Interestingly, relationships between demographic parameters and occurrence probability did not vary substantially across degrees of shade tolerance and regions. Although they were influenced by the uncertainty in the estimation of the demographic parameters, we found that r was generally negatively correlated with P_occ, while N, and for most regions K, was generally positively correlated with P_occ. Thus, in temperate forest trees the regions of highest occurrence probability are those with high densities but slow intrinsic population growth rates. The uncertain relationships between demography and occurrence probability suggests caution when linking species distribution and demographic models.     

Intraspecific interactions affect the spatial pattern of a dominant shrub in a semiarid shrubland: A prospective approach

Dispersal, physical conditions and biotic interactions contribute to determine the spatial distribution of individuals in plant populations. Much of what we know has been learned from studies that retrospectively posit mechanisms presumed to have generated the observed spatial patterns. Here we present a prospective approach. We start by measuring spatial demographic effects and evaluate if they can generate observed spatial patterns. We evaluated the influence of interactions among conspecifics on vital rates, demography and spatial distribution of Croton aff. wagneri, a dominant shrub in dry Andean ecosystems. Recruitment, survival and growth varied in relation with distance to conspecifics neighbours and with their summed cover. We built a spatial individual-based model and simulated its population dynamics in 30 × 30 m plots for a 30-year period. We compared the predicted spatial pattern from these demographic models with that observed among plants in 16 independent plots with the same area. Simulated populations mimicked observed spatial patterns, although in plots at high elevations the simulated populations did not reproduce the observed inhibition at small scales. Observed and simulated patterns indicated differences between elevations in maximum aggregation and location of the distances with higher aggregation. We discuss how consideration of critical seed and juvenile stages and interspecific interactions could further improve our understanding of spatial pattern and recommend that these factors be considered in future models.     

Partitioning the sources of demographic variation reveals density‐dependent nest predation in an island bird population

Ecological factors often shape demography through multiple mechanisms, making it difficult to identify the sources of demographic variation. In particular, conspecific density can influence both the strength of competition and the predation rate, but density‐dependent competition has received more attention, particularly among terrestrial vertebrates and in island populations. A better understanding of how both competition and predation contribute to density‐dependent variation in fecundity can be gained by partitioning the effects of density on offspring number from its effects on reproductive failure, while also evaluating how biotic and abiotic factors jointly shape demography. We examined the effects of population density and precipitation on fecundity, nest survival, and adult survival in an insular population of orange‐crowned warblers (Oreothlypis celata) that breeds at high densities and exhibits a suite of traits suggesting strong intraspecific competition. Breeding density had a negative influence on fecundity, but it acted by increasing the probability of reproductive failure through nest predation, rather than through competition, which was predicted to reduce the number of offspring produced by successful individuals. Our results demonstrate that density‐dependent nest predation can underlie the relationship between population density and fecundity even in a high‐density, insular population where intraspecific competition should be strong.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。