The age-structured lottery model

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.     

Competition and coexistence with multiple life-history stages

Do complex life histories affect the conditions under which competitors can coexist? We investigated this using a two-species, two-stage Ricker model. With complex life cycles, the competition coefficients associated with each life-history stage suggest one of three competitive outcomes-coexistence, alternate stable states, or competitive exclusion-that depend on the relative magnitudes of intraspecific and interspecific competition. When the two stages suggest the same outcome, only that outcome can occur. When the stages suggest different outcomes, either one may prevail. It is also possible to have emergent outcomes, in which the outcome is not suggested by either stage. This can occur when the two stages suggest competitive exclusion by opposite species or when one stage suggests alternate stable states and the other suggests coexistence. Therefore, determining the mechanisms of coexistence in species with complex life histories may require consideration of competitive interactions within all life-history stages.     

Food Web Effects of Prey Size Refugia: Variable Interactions and Alternative Stable Equilibria

Predators can have highly variable effects on the abundance and composition of food webs, ranging from strong to weak effects of top predators. Typical food web models assume that individual prey are identical in their susceptibility to predators throughout their lives, but many prey species become less vulnerable to predators through ontogeny. A simple set of models is explored where prey must pass through a vulnerable stage prior to achieving a predator-invulnerable size refuge. As productivity of the environment increases, the proportional impact of predators decreases because more individuals become and remain in the invulnerable adult stage. The addition of a competitor prey species that can not achieve size refuge results in contrasting outcomes. At low productivity, the small species wins in competition, and the system is strongly consumer controlled. At high productivity, the large species wins due to the presence of predators, and the system becomes less consumer controlled. At intermediate productivity, either the small or the large species can win depending on initial conditions, and the system can be either strongly or weakly consumer controlled. Such alternative stable equilibria derived from models with prey size refugia may help to explain many natural situations.     

Evolution of the maturation rate collapses competitive coexistence

Most theoretical studies on character displacement and the coexistence of competing species have focused attention on the evolution of competitive traits driven by inter-specific competition. We investigated the evolution of the maturation rate which is not directly related to competition and trades off with the birth rate and how it influences competitive outcomes. Evolution may result in the superior competitor becoming extinct if, initially, the inferior competitor has a lower, and the superior one a higher, maturation rate at the coexistence equilibrium. This counterintuitive result is explained by an explosive increase in the adult population of the inferior competitor as a result of the more rapid evolution of its maturation rate, which is caused by differences in the intensity and direction of selection on the maturation rates of the two species and in their adult densities, which are related to differences in their life histories. Thus, a life history trait trade-off with a competitive trait may cause a competitive ecological coexistence to collapse.     

物种对资源竞争的动力机制及数值模拟

建立了集合种群物种在两个斑块中对资源竞争的数学模型,并进行了数值模拟实验,结果表明：（1）通过R^＊来预测竞争物种的结局,存在几种可能性：一是具有低R^＊值的物种竞争取代高R^＊值的物种;二是具有不同R^＊值的物种,甚至是具有相同R^＊值的物种也存在共存的可能性;三是具有高R^＊值的物种也可以竞争排斥低R^＊值的物种,结论存在不确定性。（2）竞争物种的随机迁移形成了源一汇结构,对物种竞争共存具有促进作用,但弱的资源利用者（较高的R^＊）的迁移率不宜过高。（3）在种群统计率相同的条件下,资源增长率差异越大,越不利于消费者物种的共存;若种群统计率不相同,在资源增长率相同的情况下,物种共存又是不可能的,在自然界中,物种共存需要资源增长率的差异。（4）不同类型的资源增长对竞争物种的稳定性的影响是不同的。     

Coexistence of predator and prey in intraguild predation systems with ontogenetic niche shifts

In basic intraguild predation (IGP) systems, predators and prey also compete for a shared resource. Theory predicts that persistence of these systems is possible when intraguild prey is superior in competition and productivity is not too high. IGP often results from ontogenetic niche shifts, in which the diet of intraguild predators changes as a result of growth in body size (life-history omnivory). As a juvenile, a life-history omnivore competes with the species that becomes its prey later in life. Competition can hence limit growth of young predators, while adult predators can suppress consumers and therewith neutralize negative effects of competition. We formulate and analyze a stage-structured model that captures both basic IGP and life-history omnivory. The model predicts increasing coexistence of predators and consumers when resource use of stage-structured predators becomes more stage specific. This coexistence depends on adult predators requiring consumer biomass for reproduction and is less likely when consumers outcompete juvenile predators, in contrast to basic IGP. Therefore, coexistence occurs when predation structures the community and competition is negligible. Consequently, equilibrium patterns over productivity resemble those of three-species food chains. Life-history omnivory thus provides a mechanism that allows intraguild predators and prey to coexist over a wide range of resource productivity.     

Diffusion analysis and stationary distribution of the two-species lottery competition model

The lottery model is a stochastic population model in which juveniles compete for space. Examples include sedentary organisms such as trees in a forest and members of marine benthic communities. The behavior of this model appears to be characteristic of that found in other sorts of stochastic competition models. In a community with two species, it was previously demonstrated that coexistence of the species is possible if adult death rates are small and environmental variation is large. Environmental variation is incorporated by assuming that the birth rates and death rates are random variables. Complicated conditions for coexistence and competitive exclusion have been derived elsewhere. In this paper, simple and easily interpreted conditions are found by using the technique of diffusion approximation. Formulae are given for the stationary distribution and means and variances of population fluctuations. The shape of the stationary distribution allows the stability of the coexistence to be evaluated.     

Short-term instabilities and long-term community dynamics

Competition in a temporally variable environment leads to sequences of short-term instabilities that in some cases are the mechanism of long-term coexistence; in other cases they promote long-term instability. Recent work associates long-term stability with a positive relationship between environmental and competitive effects and with population growth rates that are buffered against jointly unfavorable environmental and competitive events. Buffered growth rates arise from population subdivision over life-history stages, microenvironments or phenotypes. A distinct but related mechanism of long-term stability relies on population growth rates that are nonlinear functions of competition. New ways of understanding and investigating species diversity follow from these results.     

Evolution of life-history traits collapses competitive coexistence

Trade-offs between competitive ability and the other life-history traits are considered to be a major mechanism of competitive coexistence. Many theoretical studies have demonstrated the robustness of such a coexistence mechanism ecologically; however, it is unknown whether the coexistence is robust evolutionarily. Here, we report that evolution of life-history traits not directly related to competition, such as longevity, and predator avoidance, easily collapses competitive coexistence in several competition systems: spatially structured, and predator-mediated two-species competition systems. In addition, we found that a superior competitor can be excluded by an inferior one by common mechanisms among the models. Our results suggest that ecological competitive coexistence due to a life-history trait trade-off balance may not be balanced on an evolutionary timescale, that is, it may be evolutionarily fragile.     

Competition and evolutionary stability of plants in a spatially structured habitat

We modelled the population dynamics of two types of plants with limited dispersal living in a lattice structured habitat. Each site of the square lattice model was either occupied by an individual or vacant. Each individual reproduced to its neighbors. We derived a criterion for the invasion of a rare type into a population composed of a resident type based on a pair-approximation method, in which the dynamics of both average densities and the nearest neighbor correlations were considered. Based on this invasibility criterion, we showed that, when there is a tradeoff between birth and death rates, the evolutionarily stable type is the one that has the highest ratio of birth rate to mortality. If these types are different species, they form segregated spatial patterns in the lattice model in which intraspecific competitive interactions occur more frequently than interspecific interactions. However, stable coexistence is not possible in the lattice model contrary to results from completely mixed population models. This clearly shows that the casual conclusion, based on traditional well mixed population models, that different species can coexist if intraspecific competition is stronger than interspecific competition, does not hold for spatially structured population models.     

Life-cycle switching and coexistence of species with no niche differentiation

The increasing evidence of coexistence of cryptic species with no recognized niche differentiation has called attention to mechanisms reducing competition that are not based on niche-differentiation. Only sex-based mechanisms have been shown to create the negative feedback needed for stable coexistence of competitors with completely overlapping niches. Here we show that density-dependent sexual and diapause investment can mediate coexistence of facultative sexual species having identical niches. We modelled the dynamics of two competing cyclical parthenogens with species-specific density-dependent sexual and diapause investment and either equal or different competitive abilities. We show that investment in sexual reproduction creates an opportunity for other species to invade and become established. This may happen even if the invading species is an inferior competitor. Our results suggests a previously unnoticed mechanism for species coexistence and can be extended to other facultative sexual species and species investing in diapause where similar density-dependent life-history switches could act to promote coexistence.     

Spatial patterns and associations of four species in an old-growth temperate forest

The spatial pattern of a tree species is an important characteristic of plant communities, providing critical information to explain species coexistence. The spatial distribution and association of four different successional species were analyzed among different life-history stages in an old-temperate forest. Significant aggregation patterns were found, and the degree of aggregation decreased with the scales and life-history stages. Significant interspecific spatial associations were detected. In comparing the relationships among the different life-history stages, positive associations were found at small scales in all of the juvenile species pairs. In the adult stage, negative associations were detected in coniferous vs. deciduous species pairs, while the deciduous species pairs, which have identical resource requirements, showed a positive association in this study. The coniferous species pairs showed a positive association at small scales. We infer that seed dispersal, competitive ability, or the requirement for specific topographic and light environments may contribute to the coexistence of these species.     

Life-history trade-offs and ecological dynamics in the evolution of longevity

Longevity is a life-history trait that is shaped by natural selection. An unexplored consequence is how selection on this trait affects diversity and diversification in species assemblages. Motivated by the diverse rockfish (Sebastes) assemblage in the North Pacific, the effects of trade-offs in longevity against competitive ability are explored. A competition model is developed and used to explore the potential for species diversification and coexistence. Invasion analyses highlight that life-history trait trade-offs in longevity can mitigate the effects of competitive ability and favour the coexistence of a finite number of species. Our results have implications for niche differentiation, limiting similarity and assembly dynamics in multispecies interactions.     

Signs of stabilisation and stable coexistence

Many empirical studies motivated by an interest in stable coexistence have quantified negative density dependence, negative frequency dependence, or negative plant–soil feedback, but the links between these empirical results and ecological theory are not straightforward. Here, we relate these analyses to theoretical conditions for stabilisation and stable coexistence in classical competition models. By stabilisation, we mean an excess of intraspecific competition relative to interspecific competition that inherently slows or even prevents competitive exclusion. We show that most, though not all, tests demonstrating negative density dependence, negative frequency dependence, and negative plant–soil feedback constitute sufficient conditions for stabilisation of two‐species interactions if applied to data for per capita population growth rates of pairs of species, but none are necessary or sufficient conditions for stable coexistence of two species. Potential inferences are even more limited when communities involve more than two species, and when performance is measured at a single life stage or vital rate. We then discuss two approaches that enable stronger tests for stable coexistence‐invasibility experiments and model parameterisation. The model parameterisation approach can be applied to typical density‐dependence, frequency‐dependence, and plant–soil feedback data sets, and generally enables better links with mechanisms and greater insights, as demonstrated by recent studies.     

Aging alters interspecific competition between two sympatric insect–parasitic nematode species

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Coexistence in a competitive parasitoid-host system

The main objective of this work is to determine the conditions for coexistence and competitive exclusion in a discrete model for a community of three species: a stage-structured host and two competing parasitoids sharing the same host developmental stage. Coexistence of the community of the species is found to depend on the host life history parameters in the first place, and on competitive ability and parasitoid efficiency in the second place. In particular, parasitoids equilibrium densities are defined by the size of the refuge. Extinction is expected with low growth rate and with low adult survival. Host life histories are also associated with oscillations in population density, and depending on the combination of host adult survival from one generation to the next and host growth rate, the minimum of fluctuations approaches zero, implying a higher potential risk of extinction because of stochastic factors. Our results suggest that equally reduced survival of parasitoids in hosts parasitized by both species determines extinction of the parasitoid with lower population density, in contrast to the case when both parasitoids benefit with 50% of all doubly parasitized hosts, leading to the hypothesis that a community where competitors in multiparasitized hosts die, easily becomes extinct. Competitive exclusion is expected for highly asymmetric competitive interactions, independent of population densities, allowing us to hypothesize that coexistence of competitors in systems with limited resources and refuges is associated with a clearly defined competitive hierarchy.     

Offspring quality and the evolution of cainism

Obligate siblicide, known as ‘cainism’ in large raptors, is a taxonomically widespread avian phenomenon that remains inexplicable as a simple consequence of food stress: two young can be raised to independence in experimentally manipulated nests, and food supplements do not decrease sibling aggression. A review of the Falconiformes identified 23 species in which obligate and facultative cainism is regular. All species have small clutches and deferred acquisition of adult plumage. Obligate cainists in particular are large, long-lived species characterized by extreme subadult mortality and intense competition for breeding sites. Hence, it can be suggested that early sibling conflict, in the absence of food stress, is the end result of selection for quality (survival) and competitive ability. Cain's domination or killing of Abel insures (1) an increase in Cain's chances of survival through the high-risk, pre-breeding period via improved nestling weight gain, and/or (2) domination of surviving sibs, enhancing Cain's competitive abilities and thereby increasing the probability of achieving breeding status. Only among long-lived species can the benefits of enhanced survival and competitive ability outweigh the major costs of sibling loss. Facultative cainists, which in more than 10% of cases raise more than one young (despite aggression and sibling hierarchies), not only lay larger, more variable clutches, but on average attain adult plumage earlier than obligate cainists. Their shorter lives and higher population turnovers are consistent with their less extreme siblicidal tendencies. Similar life-history traits and cainistic habits in other avian orders parallel those in the Falconiformes, indicating several independent evolutionary pathways to cainism. Retention of the second egg by obligate cainists, usually explained as insurance against failure, may instead allow parents adaptively to track population stability. Thus when breeding places are numerous (habitat saturation and competition low), parents laying two eggs and rearing two young may achieve greater fitness than single-young parents. When populations become saturated (competition high), selection should favour high-quality, competitive young and levels of siblicide should increase. A proximate mechanism is proposed linking population saturation with the incidence of cainism, based on demonstrable population characteristics found in several long-lived species.     

Coexistence of plant species in a biodiversity hotspot is stabilized by competition but not by seed predation

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.     

Increasing community size and connectance can increase stability in competitive communities

The relationship between community complexity and stability has been the subject of an enduring debate in ecology over the last 50 years. Results from early model communities showed that increased complexity is associated with decreased local stability. I demonstrate that increasing both the number of species in a community and the connectance between these species results in an increased probability of local stability in discrete-time competitive communities, when some species would show unstable dynamics in the absence of competition. This is shown analytically for a simple case and across a wider range of community sizes using simulations, where individual species have dynamics that can range from stable point equilibria to periodic or more complex. Increasing the number of competitive links in the community reduces per-capita growth rates through an increase in competitive feedback, stabilising oscillating dynamics. This result was robust to the introduction of a trade-off between competitive ability and intrinsic growth rate and changes in species interaction strengths. This throws new light on the discrepancy between the theoretical view that increased complexity reduces stability and the empirical view that more complex systems are more likely to be stable, giving one explanation for the relative lack of complex dynamics found in natural systems. I examine how these results relate to diversity-biomass stability relationships and show that an analytical solution derived in the region of stable equilibrium dynamics captures many features of the change in biomass fluctuations with community size in communities including species with oscillating dynamics.     

A predator–prey refuge system: Evolutionary stability in ecological systems

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individual’s fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator–prey systems are discussed from this perspective.