On the generality of stability-complexity relationships in Lotka-Volterra ecosystems

Understanding how complexity persists in nature is a long-standing goal of ecologists. In theoretical ecology, local stability is a widely used measure of ecosystem persistence and has made a major contribution to the ecosystem stability-complexity debate over the last few decades. However, permanence is coming to be regarded as a more satisfactory definition of ecosystem persistence and has relatively recently become available as a tool for assessing the global stability of Lotka-Volterra communities. Here we document positive relationships between permanence and Lotka-Volterra food web complexity and report a positive correlation between the probability of local stability and permanence. We investigate further the frequency of discrepancy (attributed to fragile systems that are locally stable but not permanent or locally unstable systems that are permanent and have cyclic or chaotic dynamics), associate non-permanence with the local stability or instability of equilibria on the boundary of the state-space, and investigate how these vary with aspects of ecosystem complexity. We find that locally stable interior equilibria tend to have all locally unstable boundary equilibria. Since a locally stable boundary is inconsistent with permanent dynamics, this can explain the observed positive correlation between local interior stability and permanence. Our key finding is that, at least in Lotka-Volterra model ecosystems, local stability may be a better measure of persistence than previously thought.     

Qualitative permanence of Lotka–Volterra equations

In this paper, we consider permanence of Lotka-Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka-Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence.     

Two predators feeding on two prey species: a result on permanence

For biological populations the precise asymptotic behavior of the corresponding dynamic system is probably less important than the question of extinction and survival of species. An ecological differential equation is called permanent if there exists some level k greater than 0 such that if the number xi(0) of species i at time 0 is positive for i = 1,2, ..., n then xi(t) greater than k for all sufficiently large times t Characterizations for permanence in a four-species prey-predator system modeled by the Lotka-Volterra equation are presented. The method used is based on a combination of two well-known approaches to dealing with permanence. An interesting feature is the occurrence of heteroclinic cycles.     

On the stabilizing effect of predators and competitors on ecological communities

Ecological communities can lose their permanence if a predator or a competitor is removed: the remaining species no longer coexist. This well-known phenomenon is analysed for some low dimensional examples of Lotka-Volterra type, with special attention paid to the occurrence of heteroclinic cycles.     

Permanence does not predict the commonly measured food web structural attributes

Food web assembly algorithms show great promise for investigating issues involving the dynamics of whole webs, such as succession, rehabilitation, and invasibility. Permanence, which requires that all species densities remain positive and finite, has been suggested as a good stability constraint. This study tests the validity of the permanence constraint by comparing real webs and model webs from the literature to the predictions of three assembly algorithms: one constrained by permanence and feasibility, one constrained by feasibility alone, and one with no dynamical constraint. It is found that the addition of the permanence constraint does not improve the predictive ability of the algorithm. Its main effect is to increase the efficiency of species selected for the web. Dynamically constrained webs have lower connectance and indistinct trophic levels compared to real webs and webs from other models, which is a consequence of omitting species' physiology. Although webs are less likely to be permanent if they have high omnivory and cycling, the web-building process circumvents this constraint. The challenges of testing and justifying system-level hypotheses, including isolating and detecting their effects, are discussed.     

基于比率的具有反馈控制的非自治捕食系统的动力学行为

讨论了一类基于比率的具有反馈控制的非自治捕食系统,所有的参数都是时滞的.先研究了该系统的一致持久性和全局渐近稳定性,并通过构造适当的Lyapunov函数,得到了系统存在惟一渐近稳定的正概周期解的充分性条件.最后,通过一个例子说明了结论的可行性.     

Permanence of discrete-time Kolmogorov systems for two species and saturated fixed points

This paper considers the dynamics of a discrete-time Kolmogorov system for two-species populations. In particular, permanence of the system is considered. Permanence is one of the concepts to describe the species coexistence. By using the method of an average Liapunov function, we have found a simple sufficient condition for permanence of the system. That is, nonexistence of saturated boundary fixed points is enough for permanence of the system under some appropriate convexity or concavity properties for the population growth rate functions. Numerical investigations show that for the system with population growth rate functions without such properties, the nonexistence of saturated boundary fixed points is not sufficient for permanence, actually a boundary periodic orbit or a chaotic orbit can be attractive despite the existence of a stable coexistence fixed point. This result implies, in particular, that existence of a stable coexistence fixed point is not sufficient for permanence.     

Crustacean Species Richness in Temporary Pools: Relationships with Habitat Traits

We examined species richness separately for cladocerans and ostracods in 52 temporary pools in a small geographical area, relating species richness with habitat traits using multiple regressions. Habitat traits considered included surface area, water depth, permanence and sediment depth. Permanence was an important predictor of species richness of both cladocerans and ostracods. Additionally, variation in ostracod species richness was significantly explained by water depth (negative relationship) and sediment depth (positive relationship). Surface area was not a statistically significant factor in any of our analyses. The importance of permanence supports the hypothesis that extinction due to pool drying is a major driving force behind the structuring of microcrustacean communities in temporary pools.     

The effect of dispersal on single-species nonautonomous dispersal models with delays

In this paper, single-species nonautonomous dispersal models with delays are considered. An interesting result on the effect of dispersal for persistence and extinction is obtained. That is, if the species is persistent in a patch then it is also persistent in all other patches; if the species is permanent in a patch then it is also permanent in all other patches; if the species is extinct in a patch then it is also extinct in all other patches. Furthermore, some new sufficient conditions for the permanence and extinction of the species in a patch are established. The existence of positive periodic solutions is obtained in the periodic case by employing Teng and Chen's results on the existence of positive periodic solutions for functional differential equations. Received: 26 June 2000 / Revised version: 6 October 2000 / Published online: 10 April 2001     

Multisequence comparisons in protein coding genes. Search for functional constraints

A very powerful method for detecting functional constraints operative in biological macromolecules is presented. This method entails performing a base permanence analysis of protein coding genes at each codon position simultaneously in different species. It calculates the degree of permanence of subregions of the gene by dividing it into segments, c codons long, counting how many sites remain unchanged in each segment among all species compared. By comparing the base permanence among several sequences with the expectations based on a stochastic evolutionary process, gene regions showing different degrees of conservation can be selected. This means that wherever the permanence deviates significantly from the expected value generated by the simulation, the corresponding regions are considered "constrained" or "hypervariable". The constrained regions are of two types: alpha and beta. The alpha regions result from constraints at the amino acid level, whereas the beta regions are those probably involved in "control" processing. The method has been applied to mitochondrial genes coding for subunit 6 of the ATPase and subunit 1 of the cytochrome oxidase in four mammalian species: human, rat, mouse, and cow. In the two mitochondrial genes a few regions that are highly conserved in all codon positions have been identified. Among these regions a sequence, common to both genes, that is complementary to a strongly conserved region of 12S rRNA has been found. This method can also be of great help in studying molecular evolution mechanisms.     

Structuring functional groups of aquatic insects along the resistance/resilience axis when facing water flow changes

Understanding how differences in intensity and frequency of hydrological disturbances affect the resistance and resilience of aquatic organisms is key to manage aquatic systems in a fast‐changing world. Some aquatic insects have strategies that improve the permanence (resistance), while others use strategies that favor recolonization (resilience). Therefore, we carried out a manipulative experiment to understand the influence of functional characteristics of aquatic insects in their permanence and recolonization against hydrological disturbances in streams in the biodiversity hotspot of the Cerrado of Brazil. We placed 200 artificial substrates in five streams and submitted them to changing water flow regimes that differed both in frequency and intensity, and we observed the response of the aquatic community for 39 days. We used a hierarchical Bayesian approach to estimate the probabilities of permanence and recolonization of each life strategy group (nine groups). We observed that the most intense changes in the water flow tended to affect the permanence of almost all groups, but the intensity of this effect reduced over time. On the other hand, less frequent disturbances, regardless of intensity, tended to reduce the permanence of most groups of aquatic insects over time. The different effects of disturbance intensity may have been related to a greater recolonization capacity of some groups. The results we present are worrisome in a scenario of reduced riparian vegetation around streams and with the expectation of precipitation becoming more concentrated in shorter periods of time due to climate change in the Cerrado hotspot, reducing the occurrence of many groups of aquatic insects in their habitat, particularly those with traits associated with resistance against hydrological disturbance.     

Multisequence comparisons in protein coding genes

A very powerful method for detecting functional constraints operative in biological macromolecules is presented. This method entails performing a base permanence analysis of protein coding genes at each codon position simultaneously in different species. It calculates the degree of permanence of subregions of the gene by dividing it into segments,c codons long, counting how many sites remain unchanged in each segment among all species compared. By comparing the base permanence among several sequences with the expectations based on a stochastic evolutionary process, gene regions showing different degrees of conservation can be selected. This means that wherever the permanence deviates significantly from the expected value generated by the simulation, the corresponding regions are considered “constrained” or “hypervariable”. The constrained regions are of two types: α and β. The α regions result from constraints at the amino acid level, whereas the β regions are those probably involved in “control” processing. The method has been applied to mitochondrial genes coding for subunit 6 of the ATPase and subunit 1 of the cytochrome oxidase in four mammalian species: human, rat, mouse, and cow. In the two mitochondrial genes a few regions that are highly conserved in all codon positions have been identified. Among these regions a sequence, common to both genes, that is complementary to a strongly conserved region of 12S rRNA has been found. This method can also be of great help in studying molecular evolution mechanisms.     

Can bryophytes be used to characterize hydrologic permanence in forested headwater streams?

Recent court cases have questioned whether all headwater streams, particularly those that are not perennial, fall within the protective boundaries of the Clean Water Act. Rapid field-based indicators of hydrologic permanence are critically needed for jurisdictional determinations. The study objective was to determine whether characteristics of bryophyte assemblages in forested headwater streams can be useful indicators of hydrologic permanence. We sampled bryophytes from the channel thalweg at 113 sites across 10 forests in the U.S. which varied in hydrologic permanence. Hydrologic permanence was based on hydrologic status during spring (wet season) and late summer (dry season) visits. Perennial sites had flow (surface or visibly interstitial) during both spring and summer visits. Intermittent sites flowed during spring but were either dry or had surface water limited to isolated pools in summer. Ephemeral sites did not have flow during either visit. The species composition significantly differed between ephemeral and perennial stream reaches. The species composition of intermittent streams overlapped with both ephemeral and perennial streams. Three species and six families were identified as indicators of particular permanence classes. Liverworts occurred more frequently at perennial than at intermittent or ephemeral sites. Bryophytes with cushion and turf growth forms were common to ephemeral sites, whereas mat and weft forms were more common to perennial sites. Acrocarpous mosses were more frequent at ephemeral than at perennial sites. The frequencies of bryophyte-moisture associations (derived from the literature) across the three permanence categories were significantly different. Species associated with dry habitats were more frequently encountered at ephemeral than perennial sites, whereas species associated with wet habitats were more frequent at perennial than ephemeral sites. Species richness varied among forests and permanence classes. Ephemeral sites tended to have higher species richness than perennial sites; however, this pattern did not hold for all forests. Bryophytes should be included among the tools for jurisdictional determinations, much like vascular plants are used to help delineate wetlands. Growth forms and higher level taxonomy of bryophytes (i.e., phyla) can be particularly useful for making jurisdictional determinations because of their ability to discriminate ephemeral from intermittent and perennial reaches and they are measures that can be rapidly trained and routinely used by agencies making such determinations.     

Responses of hyporheic invertebrate assemblages to large-scale variation in flow permanence and surface–subsurface exchange

1. Flow permanence (the proportion of time that flowing water is present) strongly influences benthic invertebrate assemblages in ephemeral and intermittent river reaches. Effects of varying flow permanence on hyporheic invertebrate assemblages are not well understood, and have not previously been studied at large spatial scales. 2. We used a 52‐km long flow‐permanence gradient in the alluvial Selwyn River, New Zealand to assess hyporheic assemblage responses to variation in flow permanence and surface–subsurface exchange. The Selwyn mainstem consists of perennial and temporary reaches embedded in longer downwelling (losing) and upwelling (gaining) sections. 3. We predicted that hyporheic invertebrate diversity, density and assemblage stability would increase with increasing flow permanence. We further predicted that assemblage structure would be influenced by the relative contribution of downwelling and upwelling water at the reach‐scale. 4. Hyporheic invertebrates were collected at 15 river cross‐sections over a 13‐month period. As predicted, hyporheic taxon richness, density and assemblage stability varied directly with flow permanence. The distribution of taxa along the flow permanence gradient appeared to be related to desiccation resistance. However, it is possible that proximity to colonist sources also contributed to distribution patterns. 5. Taxon richness was significantly higher at sites in the gaining section compared with the losing section. Sites with high flow permanence in the gaining and losing sections supported distinct hyporheic assemblages, characterised by amphipods and isopods in the gaining section, and ostracods, Hydra sp. and the mayfly Deleatidium spp. in the losing section. 6. Results of the study suggest an expansion of the scope of the Hyporheic Corridor Concept to include large hyporheic flowpaths associated with unbounded alluvial plains rivers. Hyporheic assemblages in alluvial rivers are strongly influenced by large‐scale flow permanence gradients, large‐scale surface water–groundwater exchange, and their interactions.     

Permanence and Existence of Positive Periodic Solution for Diffusive Lotka-Volterra Model

OneOfthemostintereStingquestionSintnathematiedbiologyconcernsthes~ofSpecsinecologicalmodels.Forautonomoussystemwhichhavenodiffusion,therearemanyliteraturesabout~istenceanddondnance[1,2,3j.R~ly,manyauthorsfindthatthediffusionpzocessineCOIOgitalsystemPlaysanimPOrtantrole.Infact,diffusionoftenoccursinnatural~icalenvironxnent,thatistosay,whenonepatchisnotvaluabletolivein-spotescan~tOanother.SoLevin[4)firsteStablishedthemedelabbotautonomousLDthe-VolterraSystemwithdiffusionprocess.AfterLevin…     

Generalist and specialist predators that mediate permanence in ecological communities

 General dynamic models of systems with two prey and one or two predators are considered. After rescaling the equations so that both prey have the same intrinsic rate of growth, it is shown that there exists a generalist predator that can mediate permanence if and only if there is a population density of a prey at which its per-capita growth rate is positive yet less than its competitor’s invasion rate. In particular, this result implies that if the outcome of competition between the prey is independent of initial conditions, then there exists a generalist predator that mediates permanence. On the other hand, if the outcome of competition is contingent upon initial conditions (i.e., the prey are bistable), then there may not exist a suitable generalist predator. For example, bistable prey modeled by the Ayala–Gilpin (θ-Logistic) equations can be stabilized if and only if θ<1 for one of the prey. It is also shown that two specialist predators always can mediate permanence between bistable prey by creating a repelling heteroclinic cycle consisting of fixed points and limit cycles. Received 10 August 1996; received in revised form 21 March 1997     

母体遗传效应对青海细毛羊生产性能遗传参数估计的影响

为了研究母体遗传效应对青海细毛羊生长性状、产毛性状的影响, 文章采用平均信息最大约束似然法应用不同混合动物模型估计青海细毛羊生产性状的遗传参数, 并采用似然比检验对不同模型进行比较分析。各模型中均包括固定效应、个体直接加性遗传效应、残差效应; 随机效应为：个体永久环境效应、母体遗传效应、母体永久环境效应。不同模型对随机效应作了不同考虑：模型1不考虑个体永久环境效应、母体遗传效应、母体永久环境效应; 模型2考虑母体永久环境效应; 模型3考虑母体遗传效应; 模型4考虑母体遗传效应和母体永久环境效应; 模型5考虑个体永久环境效应和母体遗传效应; 模型6考虑个体永久环境效应、母体遗传效应、母体永久环境效应。各模型估计的初生重遗传力为：0.1896~0.3781; 断奶重遗传力为：0.2537~0.2890; 周岁重遗传力范围：0.2244~0.3225; 成年羊体重遗传力范围：0.2205~0.3983; 产毛量遗传力为：0.1218~0.1490; 羊毛细度遗传力为：0.0983~0.4802; 羊毛长度遗传力为：0.1170~0.1311。与模型1相比, 模型3对于初生重、断奶重差异显著(P<0.01), 对于周岁重、成年羊体重各模型与模型1的似然比检验差异不显著(P>0.05); 与模型6相比, 模型4、5对于羊毛细度差异显著(P<0.01), 模型4对羊毛长度差异显著(P<0.05), 对于产毛量各模型与模型6似然比检验差异不显著(P>0.05)。生长性状中初生重、断奶重受母体遗传效应影响显著, 周岁重、成年羊体重受母体遗传效应影响不显著; 产毛性状中羊毛细度、长度受母体遗传效应影响显著, 产毛量受母体遗传效应影响较弱。     

母体遗传效应对青海细毛羊生产性能遗传参数估计的影响

为了研究母体遗传效应对青海细毛羊生长性状、产毛性状的影响,文章采用平均信息最大约束似然法应用不同混合动物模型估计青海细毛羊生产性状的遗传参数,并采用似然比检验对不同模型进行比较分析。各模型中均包括固定效应、个体直接加性遗传效应、残差效应;随机效应为:个体永久环境效应、母体遗传效应、母体永久环境效应。不同模型对随机效应作了不同考虑:模型1不考虑个体永久环境效应、母体遗传效应、母体永久环境效应;模型2考虑母体永久环境效应;模型3考虑母体遗传效应;模型4考虑母体遗传效应和母体永久环境效应;模型5考虑个体永久环境效应和母体遗传效应;模型6考虑个体永久环境效应、母体遗传效应、母体永久环境效应。各模型估计的初生重遗传力为:0.1896~0.3781;断奶重遗传力为:0.2537~0.2890;周岁重遗传力范围:0.2244~0.3225;成年羊体重遗传力范围:0.2205~0.3983;产毛量遗传力为:0.1218~0.1490;羊毛细度遗传力为:0.0983~0.4802;羊毛长度遗传力为:0.1170~0.1311。与模型1相比,模型3对于初生重、断奶重差异显著(P<0.01),对于周岁重、成年羊体重各模型与模型1的似然比检验差异不显著(P>0.05);与模型6相比,模型4、5对于羊毛细度差异显著(P<0.01),模型4对羊毛长度差异显著(P<0.05),对于产毛量各模型与模型6似然比检验差异不显著(P>0.05)。生长性状中初生重、断奶重受母体遗传效应影响显著,周岁重、成年羊体重受母体遗传效应影响不显著;产毛性状中羊毛细度、长度受母体遗传效应影响显著,产毛量受母体遗传效应影响较弱。     

具有时滞的非自治差分竞争系统的持久生存性和全局稳定性(英文)

对一类具有时滞的两种群竞争系统进行了研究,利用一些不等式的技巧得到了系统持久生存的充分条件,并且通过构造一个离散的Lyapunov函数得到了系统正解全局稳定的条件.