The Allee effect, the social dysfunction and failure to mate successfully when population densityfalls below a certain threshold, is one of the most important phenomena in ecology that can profoundly affect metapopulation persistence. We have developed a continuous dynamic model by pair approximation and two derived spatial lattice models to describe the influences of Allee effects on the distribution and dynamics of metapopulation. Analytical results of pair approximation show that the initial global stable equilibrium of metapopulation size turns into a local stable equilibrium with Allee effects and sensitivity to the initial situations that can incur a threshold phenomenon in dynamics. When the intensity of the Allee effect varies within a certain range, a new positive local stable equilibrium appears. This new equilibrium has the same local intensity as the initial one and a smaller metapopulation size. However, a metapopulation with a too strong Allee effect is doomed. Simulation results from the lattice models reinforce these findings and show that the new equilibrium forms a static distribution border in space. Hence, an Allee effect with moderate intensity can incur three distribution patterns that are sensitive to the initial metapopulation size and the spatial configuration of local populations: aggregation, circumscription and extinction. The pattern of circumscription may be a new explanation for the species' current distributional range. The relationships between distribution patterns (such as random, uniform, aggregation, circumscription and extinction) and other factors (such as mean-field assumption, local interaction, demographic stochasticity and Allee effect) are also discussed.

Aimed at the special background of arid region Shapotou in China, the paper presented a measure of ecosystem health, which was based on three criteria proposed by Costanza: vigor, organization, and resilience, then modified Costanza's model, and calculated. The calculated results show that the mixed species plots had the highest overall health, this means that the monitoring and managing modes of mixed species plots are more suitable. The conclusion provide quantitative basis for restoration and rehabilitation of artificial vegetation in arid and semi-arid regions.

We have constructed a new general model of three-species food web with environmental noise by extending a simple three-species food chain model with omnivory. With this general model, the dynamical behavior of each population in four typical three-species food web structures has been numerically simulated and analyzed. We have examined how a noise signal is propagated through a food web and the responses of web components to noise; how these responses are dependent on food web structure and some possible intrinsic ecological mechanisms of noise response. The simulation results demonstrate that food web structure has significant influence on the responses of the web components to noise. The response strength depends not only on the direct influence of environmental noise but also on where a population is positioned and how it is connected to other populations in the web. So starting from relatively complex food web, the importance of web structure for the expected response of all parts of the web to noise signals could be revealed, via numerical simulation analysis on a general model of food web. This paper also implies that the responses of populations in a food web to environmental noise are determined by environmental noise, internal dynamics, and the basic food web structure in which the populations are embedded.

Niche construction means that all organisms modify their environments, also known as ecosystem engineering. Organism-environmental relations induced by niche construction profoundly influence the dynamics, competition, and diversity of metapopulations. Single-species model shows a positive feedback between metapopulation and environmental resources, which leads to threshold phenomena in dynamics. Lattice model suggests that 'ecological imprint' is formed by niche construction in spatial habitat. Ecological imprint leads to the self-organized spatial heterogeneity of environments and species' distribution limits. In competitive systems, niche construction leads to alternative competitive consequences, which implies that trade-offs between the abilities of competition, colonization, and niche construction are important to competitive coexistence. Ecological imprint in competitive systems can weaken the spatial competitive intensity by spatial heterogeneity and segregation of species' distributions. In metapopulation community, positive niche construction leads to exclusion of intermediate species with odd-numbered species richness and oscillation with even-numbered species richness; negative niche construction has opposite results. These results suggest that species richness may be critical to community's dynamics and structure. Extinction of some species can lead to dramatic change of dynamical stability, oscillations or exclusions, or even chain reactions that damage the community structure.

Factors leading to chaotic dynamics in metapopulation are studied, including Allee effect, rescue effect and overcrowding effect. We use theoretical bifurcation diagram and lattice simulation to investigate the dynamics of metapopulation in time and space. The influence of habitat destruction on the complexity of dynamics, which can decrease the fraction of suitable patches and induce the change of colonization rate and extinction rate, is also discussed. The whole scene of the implicit relationship between dynamical complexity and metapopulation persistence is given, which has five primary results. First, metapopulation persistence reaches the maximum at moderate dynamical complexity, which can occur at moderate intensity of habitat destruction. Second, the intensity of habitat destruction can be approximated by the dynamical complexity because the habitat destruction regulates the dynamics. Third, Allee effects can amazingly regulate dynamics and improve the persistence slightly before extinction. Fourth, rescue effects stabilize dynamics and improve persistence. Finally, overcrowding effect is the key to incur chaos and increase the dynamical complexity, and to improve the persistence of metapopulations. Anyway, there is no uniform correlation between dynamical complexity and metapopulation persistence.

In the present study, the effect of 'red', 'white' and 'blue' environmental noise on population dynamics in a simple three-species food chain system was analyzed. The 'colored' noise was superimposed on the three-species food chain model first put forth by Rosenzweig in different ways and the resulting power spectra were investigated. We showed that the amplitude of environmental noise, the trophic level at which a population is positioned and whether a population is directly affected by environmental noise, are all important with respect to the way in which a population responds to noise with different colors. For the deterministic case, all population dynamics are 'red' irrespective of the system dynamics. When all species are sensitive to environmental noise, the top predator's dynamics always remain 'red' regardless of the color of the noise and its amplitude, whereas the dynamics of the intermediate species turn 'blue' under disturbances of any color with high amplitude, and those of the basal species may become 'blue' only under 'blue' noise. If only one species is sensitive to environmental noise, the dynamics of the insensitive species are always 'red', irrespective of the color of the noise and its amplitude. Unlike previous results obtained by studying single-species models, our results have almost nothing to do with deterministic system dynamics. In other words, changing the deterministic system dynamics from stable via periodic to chaotic does not qualitatively change the outcome. Our results are of importance in determining how we interpret the ubiquitous 'red' power spectrum of natural ecological time series.

Natural population dynamics are very complicated. Previous theory has shown that this phenomenon can be explained by the stochastic behavior arising from stochastic disturbances of external environment factors and the highly complex and chaotic behavior generating from nonlinearities in population itself, which is considered as a leading one. However, recently many studies theoretically show that ecological factors such as immigration, omnivory, habitat-heterogeneity may impede and control chaos. In this paper, we investigate the role of intraspecific density dependence (IDD), another important ecological factor, in the dynamics of two versions (deterministic and stochastic) of a food chain. We find that the addition of IDD to a deterministic three-species food chain model stabilizes the food chain system, leading chaotic and periodic dynamics to a steady state and especially making the very famous 'teacup' chaotic attractor disappear, and that the addition of it to a stochastic one at most results in a reduction in amplitude and frequency of dynamical fluctuations and can never eliminate the stochastic behavior. Our results contribute to investigations of the relative importance of the intrinsic factors and extrinsic environmental factors in determining population size fluctuations. Also, they give a better understanding of the essential difference between chaos and stochasticity.

Starting from a non-equilibrium perspective and stochastically variable characteristic of ecosystem, this paper gives a definition of stochastic resilience, and examines, via computer simulation, the relationship between stochastic resilience and primary productivity in a range of ecologically reasonable models, including single-species stochastic ones and multi-species stochastic ecosystem models. Compared with recent Lewi Stone's conclusions on deterministic ecosystems, our simulation results, focusing on stochastic ones, are more rich and complex. Our conclusions and field studies suggest that external stochastic perturbation, partly, if not all, responsible for the high variations of primary productivity of ecosystems, is a significant one affecting resilience /productivity relationship. It can make the complex relationship arising from the intrinsic non-linearities of ecosystems become more complicated. Thus, it should not be neglected when we investigate the relationship between resilience and primary productivity in real ecosystems, which are actually subject to stochastic disturbances of biotic and abiotic factors. In addition, our results imply that at present, there is no universal pattern of this relationship. Further work from the viewpoint of non-equilibrium will be needed in the future.