一类带有扩散和时滞的非自台Lotka-Volterra系统

本文讨论有时滞的扩散系统,此系统有两个种群两个斑块,其中一种种群可以在两斑块中自由扩散,另一种群被限定在斑块中不能扩散,当系数数满足一定的条件时,得到系统有持续生存和全局稳定的解。     

基于反馈控制离散Lotka-Volterra竞争模型的持续生存和稳定性

针对一类具有偏离自变量的离散Lotka-Volterra竞争模型,考虑到不可避免的外界扰动,通过引入反馈控制,基于一定的分析技巧得到该系统持久性与全局稳定性的充分条件.生态意义上表明:在外界扰动下,具有偏离自变量的离散Lotka-Volterra竞争模型仍能持续生存并保持全局稳定发展.     

Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species

We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis.     

Species assembly in model ecosystems, I: Analysis of the population model and the invasion dynamics

Recently we have introduced a simplified model of ecosystem assembly (Capitán et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper analysis of the model, obtaining analytical results and introducing some approximations which allow us to reconstruct the results of our previous work. In particular, we show that the population dynamics equations of a very general class of trophic-level structured food-web have an unique interior equilibrium point which is globally stable. We show analytically that communities found as end states of the assembly process are pyramidal and we find that the equilibrium abundance of any species at any trophic level is approximately inversely proportional to the number of species in that level. We also find that the per capita growth rate of a top predator invading a resident community is key to understand the appearance of complex end states reported in our previous work. The sign of these rates allows us to separate regions in the space of parameters where the end state is either a single community or a complex set containing more than one community. We have also built up analytical approximations to the time evolution of species abundances that allow us to determine, with high accuracy, the sequence of extinctions that an invasion may cause. Finally we apply this analysis to obtain the communities in the end states. To test the accuracy of the transition probability matrix generated by this analytical procedure for the end states, we have compared averages over those sets with those obtained from the graph derived by numerical integration of the Lotka-Volterra equations. The agreement is excellent.     

Localized states qualitatively change the response of ecosystems to varying conditions and local disturbances

The response of dynamical systems to varying conditions and disturbances is a fundamental aspect of their analysis. In spatially extended systems, particularly in pattern-forming systems, there are many possible responses, including critical transitions, gradual transitions and locally confined responses. Here, we use the context of vegetation dynamics in drylands in order to study the response of pattern-forming ecosystems to oscillating precipitation and local disturbances. We focus on two precipitation ranges, a bistability range of bare soil with a patterned vegetation state, and a bistability range of uniform vegetation with a patterned vegetation state. In these ranges, there are many different stable states, which allow for both abrupt and gradual transitions between the system states to occur. We find that large amplitude oscillations of the precipitation rate can lead to a collapse of the vegetation in one range, while in the other range, they result in the convergence to a patterned state with a preferred wavelength. In addition, we show that a series of local disturbances results in the collapse of the vegetation in one range, while it drives the system toward fluctuations around a finite average biomass in the other range. Moreover, it is shown that under certain conditions, local disturbances can actually increase the overall vegetation density. These significant differences in the system response are attributed to the existence of localized states in one of the bistability ranges.     

Existence and stability of equilibria in age-structured population dynamics

The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.     

Ecosystem dynamics through the past 2000 years as revealed by fossil mammals from Lamar cave in Yellowstone National Park,USA

Lamar Cave, a late Holocene paleontological site in Yellowstone National Park, USA, has yielded 36 fossil mammal species from 10 stratigraphic units representing about 2000 years. The fossil fauna is similar to the mammals in the park today and affords a unique opportunity to investigate paleocommunity and ecosystem dynamics through time.

Remains of an extralimital species in Yellowstone today, Microtus ochrogaster are found only in the oldest cave deposits, dated at 1695 ± 60 yr B.P. Disappearance of this species by about 1550 years ago marks evolution into the ecosystem that has persisted into the present and is recognizable by a fossil mammal assemblage that is virtually identical to the modern one. Relative abundance fluctuations in the mammal populations imply community resilience through the past 2000 years. Trends in relative abundances of small mammals, particularly the inverse relationship between Microtus and Spermophilus are interpreted as evidence of declining grass cover near Lamar Cave between approximately 1500 and 1000 years ago. The initiation of this environmental change may well have stimulated the ecosystem change marked by Microtus ochrogaster extirpation. Support for this hypothesis is found in a pollen record from a nearby lake.     

Local structuring factors of invertebrate communities in ephemeral freshwater rock pools and the influence of more permanent water bodies in the region

We used three isolated clusters of small ephemeral rock pools on a sandstone flat in Utah to test the importance of local structuring processes on aquatic invertebrate communities. In the three clusters we characterized all ephemeral rock pools (total: 27) for their morphometry, and monitored their water quality, hydrology and community assemblage during a full hydrocycle. In each cluster we also sampled a set of more permanent interconnected freshwater systems positioned in a wash, draining the water from each cluster of rock pools. This design allowed additional testing for the potential role of more permanent water bodies in the region as source populations for the active dispersers and the effect on the community structure in the rock pools. Species richness and community composition in the rock pools correlated with level of permanence and the ammonia concentration. The length of the rock pool inundation cycle shaped community structure, most probably by inhibiting colonization by some taxa (e.g. tadpoles and insect larvae) through developmental constraints. The gradient in ammonia concentrations probably reflects differences in primary production. The more permanent water bodies in each wash differed both environmentally and in community composition from the connected set of rock pools. A limited set of active dispersers was observed in the rock pools. Our findings indicate that aquatic invertebrate communities in the ephemeral rock pools are mainly structured through habitat permanence, possibly linked with biotic interactions and primary production. Handling editor: S. I. Dodson     

非线性接触率和种群动力学对SI传染病模型的影响

本文研究了具有一般非线性接触率和易感类中具有Logistic增长的SI传染病模型的正不变集、平衡位置以及平衡位置的稳定性．     

Permanent coexistence in general models of three interacting species

We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x _i = X _i f _i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f _i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.     

A test of the generality of leaf trait relationships on the Tibetan Plateau

Leaf mass per area (LMA), nitrogen concentration (on mass and area bases, N(mass) and N(area), respectively), photosynthetic capacity (A(mass) and A(area)) and photosynthetic nitrogen use efficiency (PNUE) are key foliar traits, but few data are available from cold, high-altitude environments. Here, we systematically measured these leaf traits in 74 species at 49 research sites on the Tibetan Plateau to examine how these traits, measured near the extremes of plant tolerance, compare with global patterns. Overall, Tibetan species had higher leaf nitrogen concentrations and photosynthetic capacities compared with a global dataset, but they had a slightly lower A(mass) at a given N(mass). These leaf trait relationships were consistent with those reported from the global dataset, with slopes of the standardized major axes A(mass)-LMA, N(mass)-LMA and A(mass)-N(mass) identical to those from the global dataset. Climate only weakly modulated leaf traits. Our data indicate that covarying sets of leaf traits are consistent across environments and biogeographic regions. Our results demonstrate functional convergence of leaf trait relationships in an extreme environment.     

The return of the vole cycle in southern Finland refutes the generality of the loss of cycles through ‘climatic forcing’

Multiannual cycles in the abundance of voles and other animals have been collapsing in the last decades. It has been proposed that this phenomenon is ‘climatically forced’ by milder winters. We here consider the dynamics of bank and field voles during more than two decades in two localities (170 km apart) in southern Finland. Using wavelet analysis, we show that a clear 3‐year cycle disappeared in the mid 1990s. However, the vole cycle returned in both localities after about 5 years despite winters becoming increasingly milder. In both localities, vole cycles were mainly determined by bank voles after the period of noncyclic dynamics, whereas field voles were dominant before this irregularity. Wavelet coherency analysis shows that spatial synchrony temporarily broke down during the period of noncyclic dynamics, but was fully restored afterwards. The return of the cycle despite ongoing rapid climate change argues against ‘climatic forcing’ as a general explanation for loss of cycles. Rather, the population‐dynamical consequences of climate change may be dependent on the local species composition and mechanism of delayed density dependence.     

Predator defense along a permanence gradient: roles of case structure, behavior, and developmental phenology in caddisflies

Species replacements along freshwater permanence gradients are well documented, but underlying mechanisms are poorly understood for most taxa. In subalpine wetlands in Colorado, the relative abundance of caddisfly larvae shifts from temporary to permanent basins. Predators on caddisflies also shift along this gradient; salamanders (Ambystoma tigrinum nebulosum) in permanent ponds are replaced by predaceous diving beetles (Dytiscus dauricus) in temporary habitats. We conducted laboratory and field experiments to determine the effectiveness of caddisfly cases in reducing vulnerability to these predators. We found that larvae of a temporary-habitat caddisfly (Asynarchus nigriculus) were the most vulnerable to salamanders. Two relatively invulnerable species (Limnephilus externus, L. picturatus) exhibited behaviors that reduced the likelihood of detection and attack, whereas the least vulnerable species (Agrypnia deflata) was frequently detected and attacked, but rarely captured because cases provided an effective refuge. Vulnerability to beetle predation was also affected by cases. The stout cases of L. externus larvae frequently deterred beetle larvae, whereas the tubular cases of the other species were relatively ineffective. Two of these vulnerable species (A. nigriculus and L. picturatus) often co-occur with beetles; thus, case construction alone is insufficient to explain patterns of caddisfly coexistence along the permanence gradient. One explanation for the coexistence of these two species with beetles is that they develop rapidly during early summer and pupate before beetle larvae become abundant. One species (L. picturatus) pupates by burying into soft substrates that serve as a refuge. The other (A. nigriculus) builds stone pupal cases, which in field experiments, more than doubles survival compared to organic pupal cases. The combined results of these experiments suggest that caddisfly distributions along permanence gradients depend on a suite of primary and secondary predator defenses that include larval and pupal case structure, predator-specific escape behaviors, and the phenology of larval development.     

Transient dynamics and persistence of ecological systems

Using spatially coupled predator–prey systems as an example of a cyclic ecological system where coexistence depends on oscillations, transient dynamics of models where there are no stable persistent solutions are shown to be a reasonable explanation of persistence over ecological time scales. The parameter values leading to transients within the context of a particular model may be far from parameter values that lead to stable solutions, so transients will need to be explicitly considered in model analysis. Since natural systems with many coupled oscillating species are common, and natural communities are often reset by disturbances or seasonality, transients should play a central role in understanding natural systems.     

Throughflow centrality is a global indicator of the functional importance of species in ecosystems

To better understand and manage complex systems like ecosystems it is critical to know the relative contribution of the system components to the system function. Ecologists and social scientists have described a diversity of ways that individuals can be important; This paper makes two key contributions to this research area. First, it shows that throughflow (T_j), the total energy or matter entering or exiting a system component, is a global indicator of the relative contribution of the component to the whole system activity. It is global because it includes the direct and indirect exchanges among community members. Further, throughflow is a special case of Hubbell status or centrality as defined in social science. This recognition effectively joins the concepts, enabling ecologists to use and build on the broader centrality research in network science. Second, I characterize the distribution of throughflow in 45 empirically-based trophic ecosystem models. Consistent with theoretical expectations, this analysis shows that a small fraction of the system components are responsible for the majority of the system activity. In 73% of the ecosystem models, 20% or less of the nodes generate 80% or more of the total system throughflow. Four or fewer nodes are required to account for 50% of the total system activity and are thus defined as community dominants. 121 of the 130 dominant nodes in the 45 ecosystem models could be classified as primary producers, dead organic matter, or bacteria. Thus, throughflow centrality indicates the rank power of the ecosystems components and shows the concentration of power in the primary production and decomposition cycle. Although these results are specific to ecosystems, these techniques build on flow analysis based on economic input–output analysis. Therefore these results should be useful for ecosystem ecology, industrial ecology, the study of urban metabolism, as well as other domains using input–output analysis.     

捕食者具有流行病的捕食-被捕食(SI)模型的分析

建立并分析了捕食者具有疾病的生态-流行病(SI)模型,讨论解的有界性,得到了平衡点局部渐近稳定的充分条件,进一步,分析了平衡点的全局稳定性,得到了捕食者绝灭和疾病成为地方病的充分条件．     

Species assembly in model ecosystems, II: Results of the assembly process

In the companion paper of this set (Capitán and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitán et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.     

Persistence and stability of macroinvertebrate communities in streams of Denali National Park, Alaska: implications for biological monitoring

1. Macroinvertebrate communities were studied from 1994 to 2001/2002 (except 1997) in six streams in Denali National Park, interior Alaska. All six streams were potential reference streams with no known impairment. 2. Abundance of individual taxa varied markedly from year to year. Overall, abundance decreased over the study period, particularly with respect to mayflies. Stonefly taxa showed lower persistence and were sometimes absent from a stream in any particular year. 3. Mean community persistence for the six streams, as measured by Jaccard's similarity coefficients between years, varied from 0.48 in the year pair 1999–2000 to 0.78 in 1998–99. Tattler Creek (a small stable stream) supported the most persistent macroinvertebrate community and Highway Pass Creek (a small, unstable creek) the least. Mean community persistence showed a significant relationship with mean winter snowfall (November to March) for the six streams. 4. The highest community compositional stability was found in Tattler Creek and the lowest in Highway Pass Creek, but stability varied markedly over time for the six streams, peaking in 1994–95 and reaching a minimum in 2000–01. Compositional stability was significantly related to the Pfankuch Index of channel stability. 5. The composition metrics % Chironomidae, % dominant taxa, %EPT, % Ephemeroptera and % Plecoptera, employed as part of the Alaska Stream Condition Index, varied over almost their entire range in these pristine streams across the 9 years of the study. 6. This study demonstrates the wide range of natural variation that occurs in benthic macroinvertebrate communities in these pristine central Alaskan streams, potentially limiting the applicability of composition metrics for the biological monitoring of water quality in these systems.