Extinction conditions for isolated populations with Allee effect

One of the main ecological phenomenons is the Allee effect [1], [2] and [3], in which a positive benefit from the presence of conspecifics arises. In this work we describe the dynamical behavior of a population with Allee effect in a finite domain that is surrounded by a completely hostile environment. Using spectral methods to rewrite the local density of habitants we are able to determine the critical patch size and the bifurcation diagram, hence characterizing the stability of possible solutions, for different ways to introduce the Allee effect in the reaction-diffusion equations.     

Persistence,extinction, and critical patch number for island populations

Sufficient conditions are derived for persistence and extinction of a population inhabiting several islands. Discrete reaction-diffusion population models are analyzed which describe growth and diffusion of a population on a group of islands or a patch environment. A critical patch number is defined as the number of islands below which the population goes extinct on that group of islands. It is shown that population persistence on one island leads to population persistence for the entire archipelago. Both single-species and multi-species models are discussed.     

Extinction of populations by inbreeding depression under stochastic environments

Inbreeding depression may induce rapid extinction due to positive feedbacks between inbreeding depression and reduction of population size, which is often referred to as extinction vortex by inbreeding depression. The present analysis has demonstrated that the extinction vortex is likely to happen with realistic parameter values of genomic mutation rate of lethals or semilethals, equilibrium population size, intrinsic rate of natural increase, and rate of population decline caused by nongenetic extrinsic factors. Simulation models incorporating stochastic fluctuations of population size further indicated that extinction by inbreeding depression is facilitated by environmental fluctuations in population size. The results suggest that there is a positive interaction between genetic stochasticity and environmental stochasticity for extinction of populations by inbreeding depression. Received: May 10, 1999 / Accepted: November 5, 1999     

Extinction in relation to demographic and environmental stochasticity in age-structured models

The demographic variance of an age-structured population is defined. This parameter is further split into components generated by demographic stochasticity in each vital rate. The applicability of these parameters are investigated by checking how an age-structured population process can be approximated by a diffusion with only three parameters. These are the deterministic growth rate computed from the expected projection matrix and the environmental and demographic variances. We also consider age-structured populations where the fecundity at any stage is either zero or one, and there is neither environmental stochasticity nor dependence between individual fecundity and survival. In this case the demographic variance is uniquely determined by the vital rates defining the projection matrix. The demographic variance for a long-lived bird species, the wandering albatross in the southwestern part of the Indian Ocean, is estimated. We also compute estimates of the age-specific contributions to the total demographic variance from survival, fecundity and the covariance between survival and fecundity.     

Extinction Risk: Predicting and Redressing the Threat

Predicting and redressing the threat of species extinction is not a success story. The science of estimating extinction rates and risk prediction is approached in a manner that is difficult to apply in the field, and yet current integrated ecosystem management programmes in many parts of the world, which are trying to place the conservation of species into sustainable community projects, need predictive tools for planning land use programmes. Such programmes involve US$100s of millions of multilateral and bilateral aid; many predicated on a site's biodiversity importance, the risks of extinction, sustainable extraction, production forms of land use, community livelihoods, water, and many others factors, but increasingly on ensuring that after the pump-priming funds are finished the programmes are both environmentally and economically sustainable (Swingland 2002, 2003, 2004; Swingland et al. 2003). [Swingland I.R. 2002. In: Swingland I.R., Bettelheim E.C., Grace J., Prance G.T. and Saunders L.S. (eds), Carbon Biodiversity, Conservation and Income: An Analysis of a Free Market Approach to Land-use Change and Forestry in Developing and Developed Countries. Philosophical Transactions Royal Society London A: Mathematical, Physical and Engineering Sciences, London; Swingland I.R. (ed.) 2003. Capturing Biodiversity and Conserving Biodiversity: The Market Approach. Earthscan, London; Swingland I.R. (ed.) 2004. CO² e biodiversità. Un approccio integrato a favore del clima e del patrimonio naturale. Edizioni Ambiente, Milano, Italy, 296 pp.; Swingland I.R., Bettelheim E.C. and Niles J.O. 2003. In: Swingland I.R. (ed.), Capturing Biodiversity and Conserving Biodiversity: The Market Approach. Earthscan, London] This involves predictions of ‘what if?’ what if laws are changed to prevent over utilisation and prevent ‘The Tragedy of the Commons’ where land ownership is vested in the state and people degrade the environment, and instead institute private land ownership. In places like China and much of the Far East, biodiversity is over-exploited as nearly all their species are used for food, medicine and construction purposes, and private land ownership in rural areas is rudimentary or absent. Since most species extinction is anthropocentric, research on species extinction needs to be more accessible and focussed on global problems.     

Biodiversity enhancement induced by environmental noise

Recent research in ecology has concentrated on the effect of environmental changes on ecosystem structure and function. In most cases the focus has been on how ecosystems respond to changes in the mean values of environmental parameters, while the impact of changes in the variance has seldom been studied. However, changes in environmental variability may be important. For example, recent climate change predictions indicate that, in addition to trends in the mean values of climate variables, an increase in interannual variability is expected to occur in the near future. How will this increase in the variance of environmental parameters affect the dynamics of terrestrial and aquatic ecosystems? Environmental fluctuations are usually believed to play a "destructive role" in ecosystem dynamics and to act as a source of disturbance, which perturbs the state of a system. However, noise is also known for its "constructive role", i.e., for the ability to create new ordered states in dynamical systems. Here we show that environmental noise may also enhance biodiversity. To this end we develop a conceptual model to show how random environmental fluctuations may favor biodiversity. Noise-induced biodiversity is observed for moderate levels of noise intensity, while it disappears with stronger environmental fluctuations, consistently with the notion underlying the "intermediate disturbance hypothesis".     

Incorporating environmental stochasticity within a biological population model

The birth and death transition rates for a population are modelled as functions of both the population size and the environmental condition. An assortment of important theoretical results and techniques that can be utilized to analyze such a population’s behaviour is covered. Consequently, these results and techniques are used to study two examples. Firstly, we study a population with a stable equilibrium state, whose per capita birth and death rates are linearly related to the environmental condition. (The environmental condition in turn is modelled as an Ornstein–Uhlenbeck process.) Secondly, we study a population affected by two interdependent environmental factors.     

Approximate reduction of multiregional models with environmental stochasticity

In this work we extend previous results regarding the use of approximate aggregation techniques to simplify the study of discrete time models for populations that live in an environment that changes randomly with time. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. We present the reduction of a stochastic multiregional model in which the population, structured by age and spatial location, lives in a random environment and in which migration is fast with respect to demography. However, the technique works in much more general settings as, for example, those of stage-structured populations living in a multipatch environment. By manipulating the original system and appropriately defining the global variables we obtain a simpler system. The paper concentrates on establishing relationships between the original and the reduced systems for a given separation of time scales between the two processes. In particular, we relate the original state variables and the global variables and, in the case the pattern of temporal variation is Markovian, we relate the presence of strong stochastic ergodicity for the original and reduced systems. Moreover, we relate different measures of asymptotic population growth for these systems.     

Predicting extinction risks for plants: environmental stochasticity can save declining populations

An emerging generalization from theoretical and empirical studies on conservation biology is that high levels of environmental stochasticity increase the likelihood of population extinction. However, coexistence theory has illustrated that there are circumstances under which environmental stochasticity can increase the chance of population persistence. These theoretical studies have shown that the sign of the effect of environmental stochasticity on population persistence is determined by interactions between life history and environmental stochasticity. These interactions mean that the stochastic and deterministic rates of population growth might differ fundamentally. Although difficult to demonstrate in real systems, observed life histories and variance in the vital rates of populations suggest that this phenomenon is likely to be common, and is therefore of much relevance to conservation biologists.     

Effect of environmental fluctuations on invasion fronts

We determine the density profile and velocity of invasion fronts in one-dimensional infinite habitats in the presence of environmental fluctuations. The population dynamics is reformulated in terms of a stochastic reaction-diffusion equation and is reduced to a deterministic equation that incorporates the systematic contributions of the noise. We obtain analytical expressions for the front profile and velocity by constructing a variational principle. The effect of the noise differs, depending on whether it affects the density-independent growth rate, the intraspecific competition term or the Allee threshold. Fluctuations in the density-independent growth rate increase the invasion velocity and the population density of the invaded area. Fluctuations in the competition term also change the population density of the invaded area, but modify the invasion velocity only for certain initial conditions. Fluctuations in the Allee threshold can induce pulled or pushed invasion fronts as well as invasion failure. We compare our analytical results with numerical solutions of the stochastic partial differential equations and show that our procedure proves useful in dealing with reaction-diffusion equations with multiplicative noise.     

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications.     

Extinction risk, coloured noise and the scaling of variance

The impact of temporally correlated fluctuating environments (coloured noise) on the extinction risk of populations has become a main focus in theoretical population ecology. In this study we particularly focus on the extinction risk in strongly correlated environments. Here, we found that, in contrast to moderate auto-correlation, the extinction risk was highly dependent on the process of noise generation, in particular on the method of variance scaling. Such scaling is commonly applied to avoid variance-driven biases when comparing the extinction risk under white and coloured noise. We show that for strong auto-correlation often-used scaling techniques lead to a high variability in the variances of the resulting time series and thus to deviations in the subsequent extinction risk. Therefore, we present an alternative scaling method that always delivers the target variance, even in the case of strong auto-correlation. In contrast to earlier techniques, our very intuitive method is not bound to auto-regressive processes but can be applied to all types of coloured noises. We strongly recommend our method to generate time series when the target of interest is the effect of noise colour on extinction risk not obscured by any variance effects.     

Phenological spread in plants: A result of adaptations to environmental stochasticity?

Summary Plant species co-inhabiting a given geographical region often have distinetly different times of flowering. It is shown that such phenological spread, duc to short-term stochastic variation in weather variables, relaxes competition for empty sites to be colonized by diaspores. For sufficiently large spreads stable coexistence becomes possible. The applicability of the proposed hypothesis to the observed instances of phenological spread is discussed and shown to extend beyond that of other current theories.We thank L.-E. Liljelund, C. Solbreck and C. Wiklund for helpful comments. This work was carried out within the Swedish Coniferous Forest Project, supported by the Swedish Natural Science Research Council, the Swedish Environmental Protection Board, the Swedish Council of Forestry and Agricultural Research, and the Wallenberg foundation.     

Variance effective population size is affected by census size in sub-structured populations

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (N_e), and this ‘temporal method’ provides estimates of N_e referred to as variance effective size (N_eV). We show that N_eV of a local population that belongs to a sub-structured population (a metapopulation) is determined not only by genetic drift and migration rate (m), but also by the census size (N_c). The realized N_eV of a local population can either increase or decrease with increasing m, depending on the relationship between N_e and N_c in isolation. This is shown by explicit mathematical expressions for the factors affecting N_eV derived for an island model of migration. We verify analytical results using high-resolution computer simulations, and show that the phenomenon is not restricted to the island model migration pattern. The effect of N_c on the realized N_eV of a local subpopulation is most pronounced at high migration rates. We show that N_c only affects local N_eV, whereas N_eV for the metapopulation as a whole, inbreeding (N_eI), and linkage disequilibrium (N_eLD) effective size are all independent of N_c. Our results provide a possible explanation to the large variation of N_e/N_c ratios reported in the literature, where N_e is frequently estimated by N_eV. They are also important for the interpretation of empirical N_e estimates in genetic management where local N_eV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation N_eV as a proxy for N_eI.     

Maternal effects provide phenotypic adaptation to local environmental conditions

In outcrossing plants, seed dispersal distance is often less than pollen movement. If the scale of environmental heterogeneity within a population is greater than typical seed dispersal distances but less than pollen movement, an individual's environment will be similar to that of its mother but not necessarily its father. Under these conditions, environmental maternal effects may evolve as a source of adaptive plasticity between generations, enhancing offspring fitness in the environment that they are likely to experience. This idea is illustrated using Campanula americana, an herb that grows in understory and light-gap habitats. Estimates of seed dispersal suggest that offspring typically experience the same light environment as their mother. In a field experiment testing the effect of open vs understory maternal light environments, maternal light directly influenced offspring germination rate and season, and indirectly affected germination season by altering maternal flowering time. Results to date indicate that these maternal effects are adaptive; further experimental tests are ongoing. Evaluating maternal environmental effects in an ecological context demonstrates that they may provide phenotypic adaptation to local environmental conditions.     

一类离散Lotka-Volterra系统的灭绝和稳定性（英文）

考虑了一类受有毒物质影响的两物种非自治离散Lotka-Volterra系统.在平均增长率意义下,得到了其中一种物种灭绝的充分条件,证明了另外一种物种的稳定性.     

Leaf breakdown patterns in a NW Italian stream: Effect of leaf type, environmental conditions and patch size

We studied the decomposition process and macroinvertebrate colonisation of leaf packs to determine to what extent leaf consumption and invertebrate abundance depend on the pollution level, season, leaf type and patch size. We exposed 400 leaf packs made of two leaf types, alder and chestnut, at two sites of the Erro River (NW Italy) with different environmental alteration levels. Leaf packs were set out as three patch sizes (alone, or in groups of 6 or 12). A first experiment was carried out in winter and a second in summer. Leaf packs were retrieved after 15, 30, 45 and 60 days of submersion to determine the leaf mass loss and to quantify the associated macroinvertebrates. Natural riverbed invertebrates were collected in the same areas. Patch size, season, leaf type and pollution level significantly affected mass loss. The breakdown process was faster for alder leaves, during summer, at the unpolluted site, and in smaller patches. Leaf type and patch size did not affect macroinvertebrate density and richness, but the highest taxon richness was found in winter and at the unpolluted site. There were more shredders and predators than in the natural riverbed. Our study supports two recent ideas regarding leaf processing in streams: that patch size influences the leaf breakdown rate and that the breakdown rate can be used to evaluate water quality and environmental health.     

Recent exposure to environmental stochasticity does not determine the demographic resilience of natural populations

Escalating climatic and anthropogenic pressures expose ecosystems worldwide to increasingly stochastic environments. Yet, our ability to forecast the responses of natural populations to this increased environmental stochasticity is impeded by a limited understanding of how exposure to stochastic environments shapes demographic resilience. Here, we test the association between local environmental stochasticity and the resilience attributes (e.g. resistance, recovery) of 2242 natural populations across 369 animal and plant species. Contrary to the assumption that past exposure to frequent environmental shifts confers a greater ability to cope with current and future global change, we illustrate how recent environmental stochasticity regimes from the past 50 years do not predict the inherent resistance or recovery potential of natural populations. Instead, demographic resilience is strongly predicted by the phylogenetic relatedness among species, with survival and developmental investments shaping their responses to environmental stochasticity. Accordingly, our findings suggest that demographic resilience is a consequence of evolutionary processes and/or deep-time environmental regimes, rather than recent-past experiences.     

A neutral theory with environmental stochasticity explains static and dynamic properties of ecological communities

Understanding the forces shaping ecological communities is crucial to basic science and conservation. Neutral theory has made considerable progress in explaining static properties of communities, like species abundance distributions (SADs), with a simple and generic model, but was criticised for making unrealistic predictions of fundamental dynamic patterns and for being sensitive to interspecific differences in fitness. Here, we show that a generalised neutral theory incorporating environmental stochasticity may resolve these limitations. We apply the theory to real data (the tropical forest of Barro Colorado Island) and demonstrate that it much better explains the properties of short‐term population fluctuations and the decay of compositional similarity with time, while retaining the ability to explain SADs. Furthermore, the predictions are considerably more robust to interspecific fitness differences. Our results suggest that this integration of niches and stochasticity may serve as a minimalistic framework explaining fundamental static and dynamic characteristics of ecological communities.     

Monoterpene content in Origanum syriacum as affected by environmental conditions and flowering

A high content of essential oil in the foliage of two chemotypes of field-grown Origanum syriacum L. was found between August and October. The content of phenolic monoterpenes in the essential oil was low from November to January, while the content of p -cymene was high. The effect of environmental conditions and flowering on the two chemotypes was similar. Controlled experiments revealed that under long photoperiods the content of essential oils in the foliage and of phenolic monoterpenes in the oil increased, while that of p -cymene decreased. A similar effect was observed when an 8 h natural light day was extended by 8 h low-intensity incandescent light. When the 16 h day was composed of 12 h natural light, the effect on oil content and composition was intensified. Under short-day photoperiods, increasing temperature or light intensity enhanced the relative content of p -cymene, while that of phenolic monoterpenes and the γ-terpinene generally decreased. Flowering decreased the essential oil content in the leaves and the relative content of the phenolic monoterpenes in the essential oil. Since environmental conditions influence flowering, they had both direct and indirect effects on the essential oil content and composition.