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1.
Frequency-dependent seed predation (FDP) has been shown to be a powerful coexistence mechanism in models of annual plant communities. However, FDP undermines the competition-based coexistence mechanism called the storage effect (SEc), which relies on temporal environmental fluctuations that drive fluctuations in competition. Although environmental fluctuations also drive fluctuations in predation, a storage effect due to predation (SEp) may not arise due to a time lag between a change in the environment and the resulting change in the predation rate. Here we show how SEp can arise with multispecies FDP, and in a two-species setting with density-dependent frequency-dependence, partially compensating for the reduction in SEc, in the presence of predation. These outcomes occur when predatory behavior is flexible, and can accommodate to changes in prey abundances on a within-year time scale, leading to changes in predator preferences in response to prey abundances in a given year. When predator preferences are determined by average prey abundances over several years, FDP is still a strong coexistence mechanism but undermines SEc without creating SEp.  相似文献   

2.
Understanding the mechanisms of species coexistence is a key task for ecology. Recent theory predicts that both competition and predation (which causes apparent competition among prey) can either promote or limit species coexistence. Both mechanisms cause negative interactions between individuals, and each mechanism promotes stable coexistence if it causes negative interactions to be stronger between conspecifics than between heterospecifics. However, the relative importance of competition and predation for coexistence in natural communities is poorly known. Here, we study how competition and apparent competition via pre‐dispersal seed predators affect the long‐term fecundity of Protea shrubs in the fire‐prone Fynbos biome (South Africa). These shrubs store all viable seeds produced since the last fire in fire‐proof cones. Competitive effects on cone number and pre‐dispersal seed predation reduce their fecundity and can thus limit recruitment after the next fire. In 27 communities comprising 49 990 shrubs of 22 Protea species, we measured cone number and per‐cone seed predation rate of 2154 and 1755 focal individuals, respectively. Neighbourhood analyses related these measures to individual‐based community maps. We found that conspecific neighbours had stronger competitive effects on cone number than heterospecific neighbours. In contrast, apparent competition via seed predators was comparable between conspecifics and heterospecifics. This indicates that competition stabilizes coexistence of Protea species, whereas pre‐dispersal seed predation does not. Larger neighbours had stronger competitive effects and neighbours with large seed crops exerted stronger apparent competition. For 97% of the focal plants, competition reduced fecundity more than apparent competition. Our results show that even in communities of closely related and ecologically similar species, intraspecific competition can be stronger than interspecific competition. On the other hand, apparent competition through seed predators need not have such a stabilizing effect. These findings illustrate the potential of ‘community demography’, the demographic study of multiple interacting species, for understanding plant coexistence.  相似文献   

3.
The interaction between predation and competition: a review and synthesis   总被引:6,自引:3,他引:6  
This review discusses the interface between two of the most important types of interactions between species, interspecific competition and predation. Predation has been claimed to increase, decrease, or have little effect on, the strength, impact or importance of interspecific competition. There is confusion about both the meaning of these terms and the likelihood of, and conditions required for, each of these outcomes. In this article we distinguish among three measures of the influence of predation on competitive outcomes: short‐term per capita consumption or growth rates, long‐term changes in density, and the probability of competitive coexistence. We then outline various theoretical mechanisms that can lead to qualitatively distinct effects of predators. The qualitative effect of predators can depend both on the mechanism of competition and on the definition of competitive strength/impact. In assessing the empirical literature, we ask: (1) What definitions of competitive strength/impact have been assumed? (2) Does strong evidence exist to support one or more of the possible mechanisms that can produce a given outcome? (3) Do biases in the choice of organism or manipulation exist, and are they likely to have influenced the conclusions reached? We conclude by discussing several unanswered questions, and espouse a stronger interchange between empirical and theoretical approaches to this important question.  相似文献   

4.
The storage effect, a mechanism that promotes species coexistence in temporally variable environments, poses a dilemma to evolutionary ecologists. Ecological studies have demonstrated its importance in natural communities, but evolutionary models have predicted that selection either impedes coexistence or diminishes the storage effect if there is coexistence. Here, we develop a lottery model of competition in which two species experience a trade‐off in competitive ability between two types of years. We use an adaptive evolution framework to determine conditions favoring the evolution of the storage effect. Storage evolves via divergence of relative performance in the two environments under a wide range of biologically realistic conditions. It evolves between two initially identical species (or lineages) when the trade‐off in performance is strong enough. It evolves for species having different initial trade‐offs for both weak and strong trade‐offs. Our simple 2‐species‐2‐environment scenario can be extended to multiple species and environmental conditions. Results indicate that the storage effect should evolve in a broad range of situations that involve a trade‐off in competitive ability among years, and are consistent with empirical observations. The findings show that storage can evolve in a manner and under conditions similar to other types of resource partitioning.  相似文献   

5.
Post-dispersal seed predation is only one of many factors underlying plant demography and evolution. Nevertheless, the generalist feeding habits of many post-dispersal seed predators and the limited ability of plants either to compensate for or to respond to post-dispersal seed losses directly suggest that post-dispersal seed predation may have a considerable impact on plant populations. Seed predators probably have little direct influence on the demography of plants that regenerate exclusively by vegetative means or are buffered by a large active seed bank, but such species are only a minority in most plant communities.In general, ants are significant post-dispersal seed predators in arid and semi-arid ecosystems while they act mainly as seed dispersers rather than as predators in temperate ecosystems. Although studies have probably underestimated the importance of invertebrates and birds as seed predators, rodents appear to have greater potential to influence seed dynamics, and are particularly important in temperate ecosystems. For example, production of mast seed crops is more effective at satiating specialist invertebrate seed predators than generalist vertebrates, and recruitment may be limited by post-dispersal seed predation even during mast years.Both spatial variation in post-dispersal seed predation and differences in predation between species are important elements which facilitate the coexistence of different plant species. Where microsites are limiting, selective post-dispersal seed predators can influence pre-emptive competition for these microsites. Seed size determines the extent of density-dependent predation and the exploitation of buried seed. This suggests that post-dispersal seed predators may also play a role in the evolution of seed characteristics. However, conclusions regarding the ecological and evolutionary impact of post-dispersal seed predators will remain speculative without a more substantial empirical base.  相似文献   

6.
Temporal environmental variation is a leading hypothesis for the coexistence of desert annual plants. Environmental variation is hypothesized to cause species-specific patterns of variation in germination, which then generates the storage effect coexistence mechanism. However, it has never been shown how sufficient species differences in germination patterns for multispecies coexistence can arise from a shared fluctuating environment. Here we show that nonlinear germination responses to a single fluctuating physical environmental factor can lead to sufficient differences between species in germination pattern for the storage effect to yield coexistence of multiple species. We derive these nonlinear germination responses from experimental data on the effects of varying soil moisture duration. Although these nonlinearities lead to strong species asymmetries in germination patterns, the relative nonlinearity coexistence mechanism is minor compared with the storage effect. However, these asymmetries mean that the storage effect can be negative for some species, which then only persist in the face of interspecific competition through average fitness advantages. This work shows how a low dimensional physical environment can nevertheless stabilize multispecies coexistence when the species have different nonlinear responses to common conditions, as supported by our experimental data.  相似文献   

7.
Abstract The presence of shrubs in arid lands creates spatial heterogeneity that affects the distribution and performance of annual plants; several possible mechanisms have been implicated. A preliminary survey in a chenopod shrubland in South Australia showed differences in the distribution of annual plants under canopies of Atriplex vesicaria and Maireana sedifolia (the two dominant shrub species) and open spaces. A series of experiments were conducted to test the potential contribution to these patterns of nutrient enrichment under shrubs, differential seed accumulation, stress reduction by the canopy, competition by shrub roots, and protection against grazing. The germinable soil seed‐bank under A. vesicaria and M. sedifolia was different from that in open spaces, but these differences can only explain a fraction of the differences observed in the growing annual plant community in different microsites. The soil under A. vesicaria had higher total nitrogen content than soil in open spaces, whereas soil under M. sedifolia had lower available phosphorus than open spaces. Although annual plant densities under A. vesicaria were higher than in open spaces, experimental removal of shrubs increased their density, suggesting that shrub canopies inhibit annual plants in this system. Surprisingly, trenching of open areas close to shrubs (severing lateral shrub roots) decreased annual plant density. We suggest that water moves laterally through shrub roots, in a process akin to a hydraulic lift, increasing water availability for the annual plants. Exclusion of vertebrate grazers had a stronger effect on annual plant biomass in open spaces than under M. sedifolia, suggesting that this shrub provides shelter against herbivory. Overall our results show that shrubs can have simultaneously facilitative and inhibitory effects on the annual plant community through different mechanisms, but more importantly that different shrub species have different effects. This is a potential mechanism allowing for species coexistence of annual plants.  相似文献   

8.
Co-evolution of seed size and seed predation   总被引:3,自引:0,他引:3  
Using the evolutionarily stable strategy (ESS) approach in a model for the co-evolution of seed size and seed predation, I show that seed size variation within individual plants is favoured if there is a trade-off in the predator's attack rate for different seed sizes. A single seed size is not evolutionarily stable because a predator that is optimally adapted to one particular seed size cannot prevent invasion by plants with a different seed size. The model generates the following predictions. The ESS consists of a continuous range of seed sizes. Small seeds tend to be attacked more frequently than big seeds. Plants with many resources and plants with low (frequency-independent) juvenile mortality have more variable seeds than plants with few resources and a high juvenile mortality. Seed size variation is higher in fluctuating populations regulated by seed predation alone than in stable populations (partially) regulated by seedling competition. Predator searching behaviour does not directly affect the ESS seed size range, but may have an indirect effect by affecting population stability or the significance of seedling competition as a population regulating mechanism. Moreover, seed size distributions are found to be more skewed in favour of small seeds if predation is spatially non-uniform than if predation is more even. Application of the model to systems of several co-evolving plant and predator species is discussed.  相似文献   

9.
Gross K 《Ecology letters》2008,11(9):929-936
Although positive interactions between species are well documented, most ecological theory for investigating multispecies coexistence remains rooted in antagonistic interactions such as competition and predation. Standard resource-competition models from this theory predict that the number of coexisting species should not exceed the number of factors that limit population growth. Here I show that positive interactions among resource competitors can produce species-rich model communities supported by a single limiting resource. Simulations show that when resource competitors reduce each others' per capita mortality rate (e.g. by ameliorating an abiotic stress), stable multispecies coexistence with a single resource may be common, even while the net interspecific interaction remains negative. These results demonstrate that positive interactions may provide an important mechanism for generating species-rich communities in nature. They also show that focusing on the net interaction between species may conceal important coexistence mechanisms when species simultaneously engage in both antagonistic and positive interactions.  相似文献   

10.
L. Eigentler 《Oikos》2021,130(4):609-623
The exploration of mechanisms that enable species coexistence under competition for a sole limiting resource is widespread across ecology. Two examples of such facilitative processes are intraspecific competition and spatial self-organisation. These processes determine the outcome of competitive dynamics in many resource-limited patterned ecosystems, classical examples of which include dryland vegetation patterns, intertidal mussel beds and subalpine ribbon forests. Previous theoretical investigations have explained coexistence within patterned ecosystems by making strong assumptions on the differences between species (e.g. contrasting dispersal behaviours or different functional responses to resource availability). In this paper, I show that the interplay between the detrimental effects of intraspecific competition and the facilitative nature of self-organisation forms a coexistence mechanism that does not rely on species-specific assumptions and captures coexistence across a wide range of the environmental stress gradient. I use a theoretical model that captures the interactions of two generic consumer species with an explicitly modelled resource to show that coexistence relies on a balance between species' colonisation abilities and their local competitiveness, provided intraspecific competition is sufficiently strong. Crucially, the requirements on species' self-limitation for coexistence to occur differ on opposite ends of the resource input spectrum. For low resource levels, coexistence is facilitated by strong intraspecific dynamics of the species superior in its colonisation abilities, but for larger volumes of resource input, strong intraspecific competition of the locally superior species enables coexistence. Results presented in this paper also highlight the importance of hysteresis in understanding tipping points, in particular extinction events. Finally, the theoretical framework provides insights into spatial species distributions within single patches, supporting verbal hypotheses on coexistence of herbaceous and woody species in dryland vegetation patterns and suggesting potential empirical tests in the context of other patterned ecosystems.  相似文献   

11.
When prey are differentially affected by intra and interspecific competition, the cooccurrence of multiple prey species alters the per capita availability of food for a particular prey species which could alter how prey respond to the threat of predation, and hence the overall‐effect of predators. We conducted an experiment to examine the extent to which the nonconsumptive and overall effect of predatory water bugs on snail and tadpole traits (performance and morphology) depended on whether tadpoles and snails cooccurred. Tadpoles and snails differed in their relative susceptibility to intraspecific and interspecific competition, and predators affected both prey species via consumptive and nonconsumptive mechanisms. Furthermore, the overall effect of predators often depended on whether another prey species was present. The reasoning for why the overall effect of predators depended on whether prey species cooccurred, however, differed for each of the response variables. Predators affected snail body growth via nonconsumptive mechanisms, but the change in the overall effect of predators on snail body growth was attributable to how snails responded to competition in the absence of predators, rather than a change in how snails responded to the threat of predation. Predators did not affect tadpole body growth via nonconsumptive mechanisms, but the greater vulnerability of competitively superior prey (snails) to predators increased the strength of consumptive mechanisms (and hence the overall effect) through which predators affected tadpole growth. Predators affected tadpole morphology via nonconsumptive mechanisms, but the greater propensity for predators to kill competitively superior prey (snails) enhanced the ability of tadpoles to alter their morphology in response to the threat of predation by creating an environment where tadpoles had a higher per capita supply of food available to invest in the development of morphological defenses. Our work indicates that the mechanisms through which predators affect prey depends on the other members of the community.  相似文献   

12.
Laboratory experiments and numerical simulations have shown that the outcome of cyclic competition is significantly affected by the spatial distribution of the competitors. Short-range interaction and limited dispersion allows for coexistence of competing species that cannot coexist in a well-mixed environment. In order to elucidate the mechanisms that destroy species diversity we study the intermediate situation of imperfect mixing, typical in aquatic media, in a model of cyclic competition between toxin producing, sensitive and resistant phenotypes. It is found, that chaotic mixing, by changing the character of the spatial distribution, induces coherent oscillations in the populations. The magnitude of the oscillations increases with the strength of mixing, leading to the extinction of some species beyond a critical mixing rate. When mixing is non-uniform in space, coexistence can be sustained at much stronger mixing by the formation of partially isolated regions, that prevent global extinction. The heterogeneity of mixing may enable toxin producing and sensitive strains to coexist for very long time at strong mixing.  相似文献   

13.
1. In obligate plant/seed parasite–pollinator mutualisms, the plant is exclusively pollinated by an insect whose larvae are specific seed predators. Hence, outcomes of the interaction for the plant can vary with the number of eggs laid and the number of seeds eaten per larva. 2. In the work reported here, predation by Chiastocheta larvae on seeds of Trollius europaeus was analysed as a function of the number of eggs laid on the flower. Flowers with an increasing number of eggs were bagged in three populations and seeds were counted after the end of larval predation, in order to assess whether there was competition among larvae. 3. Seed predation on single‐egg flowers was high and variable (mean per population ranging from 15 to 40% of the developed seeds). Seed predation increased weakly with increasing egg load and was lower than gross seed production (always < 85%) whatever the number of eggs laid. This corresponds to a strong decrease in seed consumption per larva with increasing egg load, i.e. severe larval competition for resources. 4. The results suggest that both interference among Chiastocheta larvae and carpel dehiscence may protect T. europaeus seeds from total predation. Estimates of seed predation based on egg load observed in 20 natural populations in the French Alps typically ranged from 30 to 60%. The interaction was always beneficial for the plant and there was no risk of total seed destruction by Chiastocheta larvae, favouring stability of the mutualism.  相似文献   

14.
Yinghui Yang  Cang Hui 《Oikos》2021,130(2):260-273
Competitive intransitivity is mostly considered outside the main body of coexistence theories that rely primarily on the role of niche overlap and differentiation. How the interplay of competitive intransitivity and niche overlap jointly affects species coexistence has received little attention. Here, we consider a rock–paper–scissors competition system where interactions between species can represent the full spectra of transitive–intransitive continuum and niche overlap/differentiation under different levels of competition asymmetry. By comparing results from pair approximation that only considers interference competition between neighbouring cells in spatial lattices, with those under the mean-field assumption, we show that 1) species coexistence under transitive competition is only possible at high niche differentiation; 2) in communities with partial or pure intransitive interactions, high levels of niche overlap are not necessary to beget species extinction; and 3) strong spatial clustering can widen the condition for intransitive loops to facilitate species coexistence. The two mechanisms, competitive intransitivity and niche differentiation, can support species persistence and coexistence, either separately or in combination. Finally, the contribution of intransitive loops to species coexistence can be enhanced by strong local spatial correlations, modulated and maximised by moderate competition asymmetry. Our study, therefore, provides a bridge to link intransitive competition to other generic ecological theories of species coexistence.  相似文献   

15.
生态群落物种共存的进化机制   总被引:14,自引:0,他引:14  
本文概述了目前对生态群落的物种共存研究中存在的若干问题及动、植物群落物种共存机制的研究进展。植物群落的物种共存主要介绍与环境、种子再迁移、生态位分化、竞争平衡理论、种库假设、再生生态位等有关的几种假设、生态学上相似种的共存及“原”群落概念等。动物群落的物种共存机制主要从以下几方面叙述:(1)异质环境中的资源分割,主要指动物斑状滋养的不同利用;(2)避免竞争排斥的行为机制,如边缘效应、聚群效应、扩散行为、相互作用和干扰;(3)特化者和泛化者的共存,包括:竞争是物种向多功能进化的作用力、最佳觅食理论与生态学特化及特化概念的发展。最后指出进一步研究的方向。  相似文献   

16.
Interactions among species, which range from competition to facilitation, have profound effects on ecosystem functioning. Large carnivores are of particular importance in shaping community structure since they are at the top of the food chain, and many efforts are made to conserve such keystone species. Despite this, the mechanisms of carnivore interactions are far from understood, yet they are key to enabling or hindering their coexistence and hence are highly relevant for their conservation. The goal of this review is thus to provide detailed information on the extents of competition and facilitation between large carnivores and their impact in shaping their life histories. Here, we use the example of spotted hyaenas (Crocuta crocuta) and lions (Panthera leo) and provide a comprehensive knowledge of their interactions based on meta‐analyses from available literature (148 publications). Despite their strong potential for both exploitation and interference competition (range and diet overlap, intraguild predation and kleptoparasitism), we underline some mechanisms facilitating their coexistence (different prey‐age selection and scavenging opportunities). We stress the fact that prey abundance is key to their coexistence and that hyaenas forming very large groups in rich ecosystems could have a negative impact on lions. We show that the coexistence of spotted hyaenas and lions is a complex balance between competition and facilitation, and that prey availability within the ecosystem determines which predator is dominant. However, there are still many gaps in our knowledge such as the spatio‐temporal dynamics of their interactions. As both species' survival becomes increasingly dependent on protected areas, where their densities can be high, it is critical to understand their interactions to inform both reintroduction programs and protected area management.  相似文献   

17.
Natural enemies can be a powerful force when structuring natural communities, and in facilitating or preventing species coexistence depending on the nature of the trophic interaction. In particular, “keystone” predators can promote species coexistence, provided they preferentially attack the competitively dominant species. However, it is not clear whether parasites can play a similar structuring role; parasites typically form chronic associations with their victims, reducing their fitness (i.e., fecundity) rather than survival, and allowing infected hosts to remain viable competitors within the community. Therefore the density-dependent suppression of the host is likely to be more subtle than that due to predation. Using a series of simple population-dynamic models we show that specialist parasites can facilitate species coexistence, although possibly less so than predators. These results contrast with those typically found with models of generalist parasites, which can reduce the likelihood of species coexistence through apparent competition. In addition, we show that the likelihood of parasite-facilitated species coexistence depends greatly on the specific type of parasite. In particular, macroparasites (e.g., parasitic helminths) may be less likely to facilitate species coexistence than microparasites (e.g., viruses or bacteria) due to their typically highly aggregated distribution amongst their hosts. Furthermore, species coexistence is more likely if the parasite is relatively benign to its host. Parasitism by apparently “harmless” specialist parasites may provide an important but overlooked factor in the maintenance of species diversity, facilitating species invasions into new communities and the emergence of novel infectious diseases.  相似文献   

18.
  1. Resource partitioning is a stabilising mechanism known to maintain species diversity in a variety of environments. Assemblages of stream shrimp species are structured by habitat features and predation. Therefore, segregation along habitat dimensions could facilitate coexistence among species in shrimp assemblages even when segregation is a result of predation pressure by fish species. These ecological interactions take place on a background modulated by biogeographic features, such as connectivity among drainages. However, these generalisations are mainly based on studies undertaken in temperate regions.
  2. We investigated whether abundances of rainforest shrimp species are related to habitat dimensions, and whether habitat–abundance relationships might be mediated through fish-assemblage structure and the effect of drainages on connectivity.
  3. We detected effects of habitat variation on densities of shrimp species, but the magnitudes of the effects were larger for some species than others. Fish-assemblage composition also affected shrimp densities. Two of the three species of shrimp showed some degree of habitat specialisation, but only along current-velocity, depth, and pH gradients. Habitat segregation among species occurred along the current-velocity and pH gradients. Relationships between density and environmental gradients differed between catchments for only one species and only along the pH gradient.
  4. Our findings provide evidence that rainforest-stream shrimp species respond differently to environmental gradients and this could facilitate coexistence among species. However, interactions with fish seem to have a stronger effect on species densities, and consequently species segregation, than direct effects of the environmental gradients, resulting in apparent competition for these resources.
  相似文献   

19.
Abstract The long-term growth and coexistence of species with large mixed populations in varying environments were modelled for representative environments and life-history characteristics of annual and perennial plants. The effects of the relationships between the means, variances, and covariances of seed yield, establishment, and survival, were explored by Taylor's expansion. The main findings are: 1. Individual variation in reproductive success within generations has no effect on long-term growth, which is determined only by the mean growth rate of the individuals of the species. 2. In annual species with nonoverlapping generations and without seed banks, the species with the largest mean log of the annual growth rate Y, that is the product of the average seed yield per plant and the establishment probability per seed, will win in competition with other species, independent of the correlations between the growth rates of the different species. In this case there is a negative tradeoff between the mean and the variance. 3. In perennial species with a lottery type of equal access to vacant sites, a high annual survival probability allows stable coexistence between perennial species with independent or negatively correlated variance in their mean annual product of seed production and establishment Y. 4. The coexistence range and the likely number of coexisting perennial species increase as a function of the variance of the common species, and is decreased by the variance of the rare species. The coexistence range is decreased by the covariance between the growth rates of the species, and between the survival of the rare species and its growth rate. 5. If mortality in the community of long-lived perennials is synchronized, the generations become nonoverlapping, and the competitive dynamics become similar to that of annuals. 6. Coexistence between annual and perennial species is promoted if the covariances between the annual survival and the relative yield of perennials, and between the yields of perennials and annuals, decrease and become more negative. 7. Selection for seed yield and establishment in different conditions in annuals favours a generalist strategy with low variance between years which provides a moderate yield and establishment over a wide range of environmental conditions. In perennial plants, long-term growth rate is determined by the lifetime seed yield and establishment. Because of strong competition with annuals in the more common conditions, selection in perennials favours instead a specialist strategy, with a high seed yield and establishment at relatively rare occasions in space and time, in which there is only weak competition with annuals. 8. Coexistence of annual species with a long-lived seed bank in the soil is also made possible by independent variation in different years of the germination, seed yield and establishment of different species, analogous to the situation of perennial plants.  相似文献   

20.
The lottery model of competition between species in a variable environmental has been influential in understanding how coexistence may result from interactions between fluctuating environmental and competitive factors. Of most importance, it has led to the concept of the storage effect as a mechanism of species coexistence. Interactions between environment and competition in the lottery model stem from the life-history assumption that environmental variation and competition affect recruitment to the adult population, but not adult survival. The strong role of life-history attributes in this coexistence mechanism implies that its robustness should be checked for a variety of life-history scenarios. Here, age structure is added to the adult population, and the results are compared with the original lottery model. This investigation uses recently developed shape characteristics for mortality and fecundity schedules to quantify the effects of age structure on the long-term low-density growth rate of a species in competition with its competitor when applying the standard invasibility coexistence criterion. Coexistence conditions are found to be affected to a small degree by the presence of age structure in the adult population: Type III mortality broadens coexistence conditions, and type I mortality makes them narrower. The rates of recovery from low density for coexisting species, and the rates of competitive exclusion in other cases, are modified to a greater degree by age structure. The absolute rates of recovery or decline of a species from low density are increased by type I mortality or early peak reproduction, but reduced by type III mortality or late peak reproduction. Analytical approximations show how the most important effects can be considered as simple modifications of the long-term low-density growth rates for the original lottery model.  相似文献   

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