Local stability of a population with density-dependent fertility

The local stability of an equilibrium population configuration is investigated. The population is governed by a density-dependent, age-structured, nonlinear renewal equation. Local stability is shown to depend essentially on the rate of change of the net reproduction rate as a function of the population size. Examples illustrating the results and the characteristics promoting stability are discussed.     

Local forest environment largely affects below-ground growth, clonal diversity and fine-scale spatial genetic structure in the temperate deciduous forest herb Paris quadrifolia

Paris quadrifolia (herb Paris) is a long-lived, clonal woodland herb that shows strong differences in local population size and shoot density along an environmental gradient of soil and light conditions. This environmentally based structuring may be mediated by differences in clonal growth and seedling recruitment through sexual reproduction. To study the interrelationship between environmental conditions and spatial patterns of clonal growth, the spatial genetic structure of four P. quadrifolia populations growing in strongly contrasting sites was determined. In the first place, plant excavations were performed in order to (i) determine differences in below-ground growth of genets, (ii) investigate connectedness of ramets and (iii) determine total genet size. Although no differences in internode length were found among sites, clones in moist sites were much smaller (genets usually consisted of 1-3 interconnected shoots, most of them flowering) than genets in dry sites, which consisted of up to 15 interconnected shoots, the majority of which were vegetative. Further, amplified fragment length polymorphism (AFLP) markers were used. Clonal diversity was higher in populations located in moist and productive ash-poplar forests compared to those found in drier and less productive mixed forest sites (G/N: 0.27 and 0.14 and Simpson's D: 0.84 and 0.75, respectively). Patterns of spatial population genetic structure under dry conditions revealed several large clones dominating the entire population, whereas in moist sites many small genets were observed. Nevertheless, strong spatial genetic structure of the genet population was observed. Our results clearly demonstrate that patterns of clonal diversity and growth form of P. quadrifolia differ among environments. Limited seedling recruitment and large clone sizes due to higher connectedness of ramets explain the low clonal diversity in dry sites. In moist sites, higher levels of clonal diversity and small clone sizes indicate repeated seedling recruitment, whereas strong spatial genetic structure suggests limited seed dispersal within populations.     

Natural selection and density-dependent population growth

Natural selection was studied in the context of density-dependent population growth using a single locus, continuous time model for the rates of change of population size and allele frequency. The maximization principle of density-dependent selection was applied to a class of fitness expressions with explicit recruitment and mortality terms. Three general results were obtained: First, at low population densities, the genetic basis of selection is the difference between the mean recruitment rate and the mean mortality rate. Second, at densities much higher than the equilibrium population size, selection is expected to act to minimize the mean mortality rate. Third, as the population approaches its equilibrium density, selection is predicted to maximize the ratio of the mean recruitment rate to the mean mortality rate.     

Contrasting effects of different landscape characteristics on population growth of a perennial forest herb

Anthropogenic changes in landscape structure, such as habitat loss, habitat subdivision and edge increase, can strongly affect the performance of plants, leading to population declines and extinctions. Many studies to date have focused on single characteristics of landscape structure or single life‐cycle phases, but they poorly discern the different pathways through which landscape change influences plant population dynamics via different vital rates. In this study, we evaluated the effect of two structural characteristics (habitat quantity and edge length) on vital rates and population growth rates of a perennial forest plant (Primula vulgaris) in a historically managed landscape. Areas with higher amounts of forest habitat had higher population growth rates due to higher recruitment, survival and growth of seedlings, while increased forest edge length was positively associated with population growth rates primarily due to a higher survival of reproductive individuals. Effects were stronger during the first of the two transition intervals studied. The results demonstrate that changes in different landscape structural characteristics may result in opposing effects acting via different vital rates, and highlight the need for integrative analyses to evaluate the effects of rapid landscape transformation on the current and long term plant population dynamics.     

An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment

The evolution of population dynamics in a stochastic environment is analysed under a general form of density-dependence with genetic variation in r and K, the intrinsic rate of increase and carrying capacity in the average environment, and in σ_e², the environmental variance of population growth rate. The continuous-time model assumes a large population size and a stationary distribution of environments with no autocorrelation. For a given population density, N, and genotype frequency, p, the expected selection gradient is always towards an increased population growth rate, and the expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Long-term evolution maximizes the expected value of the density-dependence function, averaged over the stationary distribution of N. In the θ-logistic model, where density dependence of population growth is a function of N^θ, long-term evolution maximizes E[N^θ]=[1−σ_e²/(2r)]K^θ. While σ_e² is always selected to decrease, r and K are always selected to increase, implying a genetic trade-off among them. By contrast, given the other parameters, θ has an intermediate optimum between 1.781 and 2 corresponding to the limits of high or low stochasticity.     

Age-specific, density-dependent and environment-based mortality of a short-lived perennial herb

Density-independent and density-dependent processes affect plant mortality. Although less well understood, age-specific mortality can also play an important role in plant mortality. The goal of this study was to analyse several factors accounting for mortality in the Mediterranean short-lived perennial herb Lobularia maritima. We followed three cohorts of plants (from emergence to death) during 4 years in field conditions. We collected data on plant mortality of the effect of biotic agents (moth larvae and mycoplasma-like organisms, MLOs) and environmental variables. We also estimated density-dependent relationships affecting the fate of seedlings and adults. Results show that cohorts differed in their survival curves and ageing significantly increased mortality risk. Seedling mortality was density-dependent whereas adult mortality was not affected by density. MLO infection led to higher plant mortality whereas moth larvae attack did not affect plant mortality. In general, seedlings and adult plants experienced the highest mortality events in summer. We found, however, weak relationships between weather records and plant mortality. Age and size structures were not correlated. Overall, this study provides a comprehensive review of age-specific, density-dependent and density-independent factors that account for mortality of L. maritima plants throughout their life cycle in field conditions, highlighting the fact that age is an important factor in determining plant population dynamics.     

Succession stage variation in population size in an early-successional herb in a peri-urban forest

Urban and peri-urban forests incur high anthropogenic pressures (e.g. recreational activities, artificialization, and eutrophication). Plant species from early-successional, transient, forest habitats, often characterized by a short life span and a persistent seed bank in the soil may differ from late-successional species in key-factors for population persistence. This study investigated variation in population size and seedling recruitment for different forest succession stages and three consecutive years in Centaurium erythraea, an early-successional biennial herb, occurring in a peri-urban forest of Brussels urban zone (Belgium). Forest succession stage had a significant impact on C. erythraea population size and on its temporal fluctuation. Populations in closing vegetation (evolving to late-succession stages) showed small population sizes and a low number of recruits compared to populations from stable early-succession vegetation and clearcuts. The number of recruits was the highest after clearcutting, which can be related to the expression of the soil seed bank. Populations showed year-to-year variation in size (flowering individuals and recruits), even in stable (over three years) early-succession forest vegetation. In the absence of disturbance changing succession stage, population size is expected to depend on seed set of the previous years and subsequent seedling recruitment, which can be affected by environmental stochasticity. Opening gaps in the herbaceous vegetation may stimulate seedling recruitment, also in unoccupied patches where “cryptic” seed populations are present in the soil. Forest path and road verges, despite their potential negative impact on forests, can constitute refuge habitats for early-successional forest plant species. Their management should involve the preservation of these species.     

Influence of canopy opening on the environment and herb layer in a northern hardwoods forest

Single- (33–37 m²) and multi-tree (51–151 m²) gaps were created in an Allegheny Plateau northern hard-woods forest to investigate environmental and herb layer response to canopy opening. After gap creation, noon light on clear summer days was brightest north of opening center. At other times of the day, and when skies were overcast, there was no difference in the light quantity beneath opened and closed canopy. Nor was the distribution of soil moisture or of soil or air temperature greatly affected by gap creation. Species establishment tended to be higher near opening centers; otherwise, there was no pronounced effect of canopy opening on plant cover or species richness during the first four years after gap creation. Biotic responses were not significantly correlated with any environmental factor.     

Stochastic population growth in spatially heterogeneous environments: the density-dependent case

Journal of Mathematical Biology - This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for...     

Intraspecific and phylogenetic density-dependent seedling recruitment in a subtropical evergreen forest

Recent evidence suggests that plant performance can be influenced by the phylogenetic diversity of neighboring plants. However, no study to date has examined the effect of such phylogenetic density dependence on the transition from seed to seedling. Using 6 years of data on seedling recruitment and seed rain of 13 species from 130 stations (one 0.5 m² seed trap and three adjacent 1 m² seedling plots) in a subtropical evergreen forest, we asked: (1) Does negative density dependence act across seed to seedling stages? (2) Is there evidence for phylogenetic density dependence during the seed to seedling transition? (3) Does the strength of density dependence vary among years? Generalized linear mixed-effects models were used to model seed to seedling transition as a function of conspecific seed and seedling densities, heterospecific seed and seedling densities, and mean phylogenetic distance of heterospecific seeds and seedling. Conspecific seed density had a significant negative effect on seedling transition rates for 12 of 13 focal species. In contrast, conspecific seedling density had a positive effect for 7 species, suggesting species-specific habitat preferences. Few species were significantly affected by the density or phylogenetic relatedness of heterospecific seeds and seedlings. Only conspecific seed density effects varied among years for most focal species. Overall, our results reveal that conspecific seed and seedling densities play a more important role than the density or relatedness of heterospecific seeds and seedlings during the seed to seedling stage, suggesting that species-specific seed predators, along with habitat preferences, may contribute to diversity maintenance in this forest.     

Dietary niche and population dynamic feedbacks in a novel habitat

Population dynamics and resource use are often intricately connected via density‐dependent intraspecific competition. However, experimental studies of concurrent change in population and resource use dynamics are scarce. In particular, the impact of factors such as genetic diversity, which can affect both population dynamics and competition, remains unexplored. Using stable isotope analysis and periodic population censuses, we quantified both diet and population dynamics in wheat‐adapted Tribolium castaneum (flour beetle) populations provided with an additional novel resource (corn). Populations were initiated with different levels of genetic variation for traits relevant to population growth and resource use (e.g. fecundity and survival).We found that high population size decreased subsequent corn use, and high corn use in turn lowered population size. Surprisingly, we did not detect a significant effect of founding genetic variation on resource niche expansion, although genetic variation increased overall population size and stability. In contrast, dietary niche expansion decreased both population size and stability. Finally, larval and adult niche dynamics were uncorrelated, suggesting that various life stages perceive or respond differentially to intraspecific competition and resource availability. Our experiments indicate that population performance in a novel habitat depends on stage‐specific interactions between resource use, standing genetic variation, and population size.     

On a conjecture concerning population growth in random environment

Discrete stochastic models are constructed and their limit diffusion processes are derived to shed light on a controversial conjecture regarding the effects of environmental variance on the asymptotic behavior of a population subject to logistic growth in random environment.Work supported in part by the National Group for Mathematical Information Sciences (GNIM) of the National Council for Research     

Interspecific competition among macroparasites in a density-dependent host population

 We analyze the dynamics of a community of macroparasite species that share the same host. Our work extends an earlier framework for a host species that would grow exponentially in the absence of parasitism, to one where an uninfected host population is regulated by factors other than parasites. The model consists of one differential equation for each parasite species and a single density-dependent nonlinear equation for the host. We assume that each parasite species has a negative binomial distribution within the host and there is zero covariance between the species (exploitation competition). New threshold conditions on model parameters for the coexistence and competitive exclusion of parasite species are derived via invadibility and stability analysis of corresponding equilibria. The main finding is that the community of parasite species coexisting at the stable equilibrium is obtained by ranking the species according t! o th e minimum host density H ^* above which a parasite species can grow when rare: the lower H ^* , the higher the competitive ability. We also show that ranking according to the basic reproduction number Q ₀ does not in general coincide with ranking according to H ^* . The second result is that the type of interaction between host and parasites is crucial in determining the competitive success of a parasite species, because frequency-dependent transmission of free-living stages enhances the invading ability of a parasite species while density-dependent transmission makes a parasite very sensitive to other competing species. Finally, we show that density dependence in the host population entails a simplification of the portrait of possible outcomes with respect to previous studies, because all the cases resulting in the exponential growth of host and parasite populations are eliminated.. Received: 24 June 1996 / Revised version: 28 April 1998     

Pollination and reproduction of a self-incompatible forest herb in hedgerow corridors and forest patches

Habitat-corridors are assumed to counteract the negative impacts of habitat loss and fragmentation, but their efficiency in doing so depends on the maintenance of ecological processes in corridor conditions. For plants dispersing in linear habitats, one of these critical processes is the maintenance of adequate pollen transfer to insure seed production within the corridor. This study focuses on a common, self-incompatible forest herb, Trillium grandiflorum, to assess plant–pollinator interactions and the influence of spatial processes on plant reproduction in hedgerow corridors compared to forests. First, using pollen supplementation experiments over 2 years, we quantified the extent of pollen limitation in both habitats, testing the prediction of greater limitation in small hedgerow populations than in forests. While pollen limitation of fruit and seed set was common, its magnitude did not differ between habitats. Variations among sites, however, suggested an influence of landscape context on pollination services. Second, we examined the effect of isolation on plant reproduction by monitoring fruit and seed production, as well as pollinator activity and assemblage, in small flower arrays transplanted in hedgerows at increasing distances from forest and from each other. We detected no difference in the proportion of flowers setting fruit or in pollinator activity with isolation, but we observed some differences in pollinator assemblages. Seed set, on the other hand, declined significantly with increasing isolation in the second year of the study, but not in the first year, suggesting altered pollen transfer with distance. Overall, plants in hedgerow corridors and forests benefited from similar pollination services. In this system, plant–pollinator interactions and reproduction seem to be influenced more by variations in resource distribution over years and landscapes than by local habitat conditions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Soil nitrogen availability intensifies negative density-dependent effects in a subtropical forest

负密度制约在维持森林群落物种多样性方面起重要作用。然而,在不同的非生物条件下密度制约效应的强度和方向有可能发生改变。理论预测密度制约效应随土壤可利用氮浓度上升而增强,但仍有待实验结果的验证。本研究基于黑石顶常绿阔叶林群落长达10年的幼苗动态调查数据,以18个常见树种的新生幼苗为研究对象,分析邻体密度制约作用如何在不同环境梯度下变化。通过收集上述目标种中的5个树种的野外幼苗进行根系损伤观察实验,研究在不同可利用氮环境中,土壤病原菌驱动的负密度制约效应是否存在差异。幼苗动态分析结果表明,负密度制约作用的强度随土壤可利用氮浓度的上升而增强。同种幼苗密度在土壤可利用氮浓度低的生境中表现为中性或正密度依赖效应,在土壤可利用氮浓度高的生境中则表现为负密度制约效应。根系损伤观察实验中,在土壤可利用氮浓度高的情况下,5个目标物种中有3个物种表现出更强的负密度制约作用,与幼苗动态分析的结果一致。此外,物种丰富度在土壤可利用氮浓度高的环境中比在浓度低的环境中更高。上述结果表明,在土壤可利用氮浓度高的环境中,更强的土壤病害加剧了负密度制约作用。我们的研究结果强调了负密度制约研究中考虑背景环境的重要性。     

Incorporating environmental change over succession in an integral projection model of population dynamics of a forest herb

Despite seemingly obvious effects of environmental drivers, mechanisms behind long‐term changes in plant population sizes over time are often poorly known. We investigated how soil potassium concentration and seed predation are likely to change over time as a result of succession from deciduous forest to spruce forest, and how this affects population trajectories of Actaea spicata. Observations and addition experiments showed that high soil potassium concentration increased individual growth rates. Among‐site comparisons showed that soil potassium concentration was lower where proportion spruce was higher. Incorporation of a gradual increase in spruce over time in an integral projection model where individual growth depended on potassium suggested a net decrease in A. spicata population sizes over forest succession. This result suggests that small changes in factors with small effects on individual performance can influence patterns of species occupancy along successional gradients. We incorporated also density independent and density dependent effects of pre‐dispersal seed predation over succession into the same model. Seed predation influenced the tree composition at which A. spicata population growth was positive. However, significant effects of A. spicata population size on seed predation intensity did not translate into important feedback effects on population growth trajectories over succession. Our results illustrate how demographic models can be used to gain understanding of the mechanisms behind effects of environmental change on species abundances and distributions by the simultaneous inclusion of changing abiotic and biotic factors.     

Demographic,mechanistic and density-dependent determinants of population growth rate: a case study in an avian predator

Identifying the determinants of population growth rate is a central topic in population ecology. Three approaches (demographic, mechanistic and density-dependent) used historically to describe the determinants of population growth rate are here compared and combined for an avian predator, the barn owl (Tyto alba). The owl population remained approximately stable (r approximately 0) throughout the period from 1979 to 1991. There was no evidence of density dependence as assessed by goodness of fit to logistic population growth. The finite (lambda) and instantaneous (r) population growth rates were significantly positively related to food (field vole) availability. The demographic rates, annual adult mortality, juvenile mortality and annual fecundity were reported to be correlated with vole abundance. The best fit (R(2) = 0.82) numerical response of the owl population described a positive effect of food (field voles) and a negative additive effect of owl abundance on r. The numerical response of the barn owl population to food availability was estimated from both census and demographic data, with very similar results. Our analysis shows how the demographic and mechanistic determinants of population growth rate are linked; food availability determines demographic rates, and demographic rates determine population growth rate. The effects of food availability on population growth rate are modified by predator abundance.