Spatial heterogeneity of mortality and temporal fluctuation in fertility promote coexistence but not vice versa: a random-community approach

Both spatial heterogeneity and temporal fluctuation of the environment are important mechanisms promoting species coexistence, but they work in different manners. We consider many pairs of species with randomly generated survivorship and fertility in the lottery model, and examine how the variability in demographic processes affects the outcome of competition. The results are: [1] Coexistence is easier if habitat difference in mortality is greater, or if year-to-year variation in reproductive rate is larger. But neither habitat-difference in fertility nor temporal variation in mortality promotes coexistence. [2] Mean fertility does not affect the outcome if CV remains constant. In contrast, enhanced mean mortality decreases the fraction of coexisting pairs if the environment fluctuates temporally. [3] We also investigate the effect of limited dispersal of propagules between habitats. Compared with the complete mixing case, the fraction of coexisting pairs is clearly enhanced if the spatial heterogeneity is the major source of environmental variation, but shows slight increase if the temporal fluctuation is dominant. We conclude that spatial heterogeneity is likely to work more effectively in promoting species coexistence than temporal fluctuation, especially when the species suffer relatively high mortality, and disperse their propagules in a limited spatial scale.     

Incomplete mixing promotes species coexistence in a lottery model with permanent spatial heterogeneity

For many marine organisms, the population dynamics in multiple habitats are affected by migration of planktonic larvae. We herein examine the effect of incomplete larval mixing on the condition for species coexistence. The system consists of two heterogeneous habitats, each composed of a number of sites occupied by adults of two species. Larvae produced in a habitat form a pool and migrate to the pool of the other habitat. When an adult dies, the vacant site becomes occupied by an individual randomly chosen from the larval pool. We study (1). the invasibility of a inferior species which has no advantage in either habitats, (2). the dynamics when larval migration and competition among adults are symmetric between habitats, and (3). the case with unidirectional migration. The coexistence of competitors is more likely to occur when larval migration is weak.     

Competition and coexistence in spatially subdivided habitats

While non-spatial models predict that like species cannot stably coexist, empirical studies suggest that similar species have similar distributions due to shared habitat requirements. A model is developed to discuss competition and coexistence in subdivided but locally stable habitats. The model predicts that in some cases it is possible for one species to exclude the other species from a geographic region, while in other cases two competing species can stably coexist. The equilibrium level and the fraction of doubly occupied patches, if there is coexistence, are determined by the strength of competition on colonization and exclusion in such a system. Also, it is possible for two ecologically identical species to stably coexist, and two asymmetrically competing species can coexist when there is a trade-off between local competition ability and invasion ability. When rescue effects are considered, the stable region at internal equilibrium point would be reduced, but the fraction of doubly occupied patches would be enlarged.     

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.     

Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity

Abstract In the presence of permanent spatial heterogeneity, local dispersal, especially short‐range dispersal, can facilitate coexistence by concentrating low‐density species in the areas where their rates of increase are higher. We present a framework for predicting the effects of local dispersal on coexistence for arbitrary forms of dispersal and arbitrary spatial patterns of environmental variation. Using the lottery model as an example, we find that local dispersal contributes to coexistence by enhancing the effects of environmental variation on scales longer than typical dispersal distances, which can be characterized solely by the variance of the dispersal kernel. Higher moments of the dispersal kernel are not important.     

Plant coexistence in coastal heaths: Floristic patterns and species attributes

Abstract An investigation was made of plant coexistence in coastal heaths. A 4 km stretch of Pleistocene beach sand was selected, and patterns of variation in heath vegetation on ridges and slopes in the beach system were studied. The sampling design covered variation with geographic distance among transects, plots within transects and quadrats within plots which were orthogonal to the alignment of ridges and slopes. Cover of vascular plant species was scored within each quadrat and both multivariate and univariate analyses tested the hypothesis that variation in the data was associated with environmental difference and geographic distance. There was a strong flohstic variation between the ridge and slope habitats. However, within these habitats there was no significant variation with distance at scales of kilometres, nor at hundreds of metres within transects nor at tens of metres within plots in floristic composition, in numbers of species, and in cover. Though differing floristically, the vegetation of the slopes and ridges had similar curves of importance values and fairly similar spectra of life forms and forms of post-fire regeneration in their constituent species, although the ridges had slightly more obligate-seeding species and fewer species of sedges and herbs than the slopes. The two habitats shared several genera, however, within such genera, species with similar attributes mostly occurred in different habitats. Hypotheses were suggested to explain segregation of species between the two habitats and the coexistence of species within habitats. Since patterns of variation among habitats were consistent over both smaller and larger scales of distance examined, experiments to test hypotheses may be designed so that their findings might be applied generally to the whole system studied.     

EVOLUTION OF THE STORAGE EFFECT

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.     

The species pool hypothesis: the necessity to shift emphasis

The species pool of a biological community is determined as a group of species that inhabit some area and potentially can be included in a given community. The species pool hypothesis, i.e. the assumption that the size of species pool strongly influences species richness of local community can be confirmed if there is positive linear relationship between these two variables. The results of hypothesis testing however are not obvious. For example, correlation between local richness and species pool size can be caused by their dependence on the third variable--capacity of environment. It seems that in case of decreasing area occupied by local community the environmental conditions become more important than species pool size. If that is true, the influence of species pool on local species richness is not significant. However one can estimate the degree of unsaturation of species pool on the basis of relationships between the number of species in small locations occupied by similar local communities and their species pool. We think, that study of local and regional species richness should shift the emphasis--from the analysis of species pool influence on local community richness to the estimation of historical, ecological and anthropogenic factors in variation of species pool size. The local species richness should be considered rather as a tool (allowing to compare the species capacity of biological communities), than as an object of such study.     

The stabilizing effect of a random environment

It is shown that the lottery competition model permits coexistence in a stochastic environment, but not in a constant environment. Conditions for coexistence and competitive exclusion are determined. Analysis of these conditions shows that the essential requirements for coexistence are overlapping generations and fluctuating birth rates which ensure that each species has periods when it is increasing. It is found that a species may persist provided only that it is favored sufficiently by the environment during favorable periods independently of the extent to which the other species is favored during its favorable periods.Coexistence is defined in terms of the stochastic boundedness criterion for species persistence. Using the lottery model as an example this criterion is justified and compared with other persistence criteria. Properties of the stationary distribution of population density are determined for an interesting limiting case of the lottery model and these are related to stochastic boundedness. An attempt is then made to relate stochastic boundedness for infinite population models to the behavior of finite population models.     

Plant species richness and community productivity: why the mechanism that promotes coexistence matters

This paper stresses that the mechanism of coexistence is the key to understanding the relationship between species richness and community productivity. Using model plant communities, we explored two general kinds of mechanisms based on resource heterogeneity and recruitment limitation, with and without any trade-off between reproductive and competitive abilities. We generated different levels of species richness by changing model parameters, in particular the number of species in the regional pool, the degree of recruitment limitation, and the level of heterogeneity. Different diversity–productivity patterns are obtained with different coexistence mechanisms, indicating there is no reason to expect any general relationship between species richness and productivity. We discuss these results in the context of the within-site and across-site aspects of the relationship between species richness and productivity. Furthermore, we extend these results to hypothesize the relationship between species richness and productivity for other coexistence mechanisms not explicitly considered here.     

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.     

Niche partitioning and stochastic processes shape community structure following whitefly invasions

One of the most detrimental impacts of invasive species is the exclusion of native species, which reduces biodiversity and can alter community structure. Coexistence between invaders and native species across large scales, however, might be promoted by niche partitioning and/or stochastic processes, even when one species is excluded in some habitats. Here, we examined the effects of species traits, stochastic processes, and niche partitioning on coexistence of two morphocryptic whitefly species in the Bemisia tabaci complex: the invasive Mediterranean (MED) species and the native Middle East-Asia Minor 1 (MEAM1) species. These species engage in intense reproductive interference, which can result in the exclusion of one species or the other in shared habitats. Both species, however, have coexisted in sympatry in Israel for many years, where MED is invasive and MEAM1 is native. Using a spatially explicit model, we show that both stochastic processes and niche partitioning can promote coexistence between MEAM1 and MED, although predicted community structure differs drastically in each scenario. Comparison of field observations with model results indicated that variation in habitat use leading to niche partitioning was a primary factor driving coexistence between MEAM1 and MED across landscapes, although stochastic processes affected the establishment of rare species within habitats. In many systems, combining models with field surveys can be used to isolate and test mechanisms underlying patterns of community structure following invasions.     

Scaling up from local competition to regional coexistence across two scales of spatial heterogeneity: insect larvae in the fruits of Apeiba membranacea

Species that live in patchy and ephemeral habitats can compete strongly for resources within patches at a small scale. The ramifications of these interactions for population dynamics and coexistence at regional scales will depend on the intraspecific and interspecific distributions of individuals among patches. Spatial heterogeneity due to independent aggregation of competitors among patchy habitats is an important mechanism maintaining species diversity. I describe regional patterns of aggregation for four species of insect larvae in the fruits of Apeiba membranacea, a Neotropical rainforest tree. This aggregation results from variation in densities at a small scale (among the fruits under a single tree), compounded by significant variation among trees in both mean densities and degrees of aggregation. Both the degrees of aggregation and mean densities are statistically independent within and across species at both spatial scales. I evaluate the regional consequences of these spatial patterns by using maximum likelihood methods to parameterize a model that includes both explicit measures of the strength of competition and spatial variation at both within- and among-tree spatial scales. Despite strong competitive interactions among these species, during 2 years the observed spatial variation at both scales combined was sufficient to explain the coexistence of these species, although other coexistence mechanisms may also operate simultaneously. The observed spatial variation at small spatial scales may not be sufficient for coexistence, indicating the importance of considering multiple sources of spatial heterogeneity when scaling up from experiments that investigate local interactions to regional patterns of coexistence.     

Soil texture as an influence on the distribution of the desert seed-harvester ants Pogonomyrmex rugosus and Messor pergandei

Summary Pogonomyrmex rugosus and Messor pergandei are ecologically similar species of desert seed-harvester ants that coexist in numerous areas throughout the Sonoran and Mohave Deserts. However, these two species also commonly segregate along physical gradients, with each species predominating in areas that differ in soil texture and/or topographic relief. Along gradients that included bajada and alluvial flat habitats, P. rugosus occurred alone in coarse-textured soils near mountains, while M. pergandei occurred alone in finer-textured soils further away. Conversely, along a vegetation gradient that included creosote bush and saltbush habitats, P. rugosus occurred alone in finer-textured soils than those occupied by either M. pergandei alone or both species in coexistence. However, in both situations clay content was significantly higher in areas occupied by P. rugosus alone, and at the latter site clay content was correlated with relative abundance of each species. Moreover, local distribution pattern of these two species may be related to the effects of clay on water retention, with retention being highest in areas occupied by P. rugosus alone. Differences in reproductive ecology may also affect these patterns as P. rugosus reproductive flights follow summer monsoon rains, while those of M. pergandei occur during the milder winter and spring.     

Scaling up from local competition to regional coexistence across two scales of spatial heterogeneity: insect larvae in the fruits of <Emphasis Type="Italic">Apeiba membranacea</Emphasis>

Species that live in patchy and ephemeral habitats can compete strongly for resources within patches at a small scale. The ramifications of these interactions for population dynamics and coexistence at regional scales will depend on the intraspecific and interspecific distributions of individuals among patches. Spatial heterogeneity due to independent aggregation of competitors among patchy habitats is an important mechanism maintaining species diversity. I describe regional patterns of aggregation for four species of insect larvae in the fruits of Apeiba membranacea, a Neotropical rainforest tree. This aggregation results from variation in densities at a small scale (among the fruits under a single tree), compounded by significant variation among trees in both mean densities and degrees of aggregation. Both the degrees of aggregation and mean densities are statistically independent within and across species at both spatial scales. I evaluate the regional consequences of these spatial patterns by using maximum likelihood methods to parameterize a model that includes both explicit measures of the strength of competition and spatial variation at both within- and among-tree spatial scales. Despite strong competitive interactions among these species, during 2 years the observed spatial variation at both scales combined was sufficient to explain the coexistence of these species, although other coexistence mechanisms may also operate simultaneously. The observed spatial variation at small spatial scales may not be sufficient for coexistence, indicating the importance of considering multiple sources of spatial heterogeneity when scaling up from experiments that investigate local interactions to regional patterns of coexistence.     

Maladaptation and mass effects in a metacommunity: consequences for species coexistence

Metacommunity theories predict multispecies coexistence based on the interplay between local species interactions and regional migration. To date, most metacommunity models implicitly assume that evolution can be ignored. Yet empirical studies indicate a substantial potential for contemporary evolution. I evaluate how evolution alters species diversity in a simulated mass-effects (sink-source) metacommunity. Populations inhabiting source habitats became locally adapted, while subordinate competitors became maladapted because of assumed ecological and phenotypic trade-offs between habitats. This maladaptation decreased and leveled relative abundances among subordinate populations. These two effects produced two regions of departure from nonevolutionary predictions. Assuming low proportional migration, maladaptation reduced local species richness via an overall reduction in reproductive rates in sink populations. With intermediate proportional migration, a greater absolute reduction of reproductive rates in intermediate competitors leveled reproductive rates and thereby enhanced local species richness. Although maladaptation is usually viewed as a constraint on species coexistence, simulations suggest that its effects on diversity are manifold and dependent on interpatch migration and community context. Hence, metacommunity predictions often may profit from an evolutionary perspective. Results indicate that modifications of community connectivity, such as might occur during habitat fragmentation, could elicit rapid shifts in communities from regions of high to low biodiversity.     

The effects of host-plant distribution and local abundance on the species richness of agromyzid flies attacking British umbellifers

Abstract. 1. The number of agromyzid species (Diptera: Agromyzidae) attacking British Umbelliferae generally increases with the size of the geographic range of the host, measured as occupied 10 km squares in the Atlas of the British Flora (Lawton & Price, 1979). 2. In the present study we tried to explain the large, residual variation in this species—area relationship using two new variables, namely the local abundance of the host plant, and the number of habitats within which it grows. 3. Local abundance was estimated from eight floras that map plant distributions within English countries by tetrads (2 times 2 km squares). Local abundance was defined as: Total number of occupied tetrads Total number of available tetrads within occupied 10 km squares 4. The number of habitats occupied by each host plant was taken from the only county flora to record plant habitats objectively, that for Warwickshire. 5. We expected to find a correlation between local abundance and the residuals from the national species—area relationship, with locally scarce plants having fewer agromyzids than expected from the sizes of their national ranges, and vice versa. 6. What we found was that size of geographic range and local abundance were highly correlated; hence their relative contributions to agromyzid species richness were difficult to disentangle. Residuals from the national species—area relationship were positively correlated with local abundance, but the relationship marginally failed to achieve statistical significance (P= 0.06). 7. In contrast, the number of habitats occupied by each species of umbellifer in Warwickshire had a marked effect upon agrornyzid species richness, with plants that grow in more habitats supporting more species of insects. Not surprisingly, local abundance and number of habitats occupied were highly correlated. 8. Lawton & Price's observation that aquatic umbellifers are faunally impoverished now emerges as part of the general effect of number of habitats occupied by the host plants on agromyzid species richness. 9. Once the number of habitats occupied by each host plant in Warwickshire was entered into a multiple regression, the effect of size of host geographic range on agromyzid species richness was no longer statistically significant. 10. A combination of the number of habitats occupied, and leaf-form of the host (the latter taken from Lawton & Price, 1979), explains 61% of the variation in agromyzid species richness on British Umbelliferae.     

Evidence for lottery recruitment in Mediterranean old fields

Abstract. The hypothesis of lottery establishment ( Sale 1977 ) explains coexistence of species with similar niches through processes of stochastic recruitment. This initial idea forms the basis for a variety of mathematical models, but has not been tested empirically. This study is a field investigation of lottery establishment for plants with a seed bank, using Canonical Correspondence Analysis to compare the compositions of the vegetation and the seed bank according to different hypotheses on the mechanisms of establishment. This method was used for a data set from old fields from southern France. The weighted lottery (i.e. a random draw from the seed pool, weighted by the frequencies of each species) appeared as the best suited hypothesis to explain the high degree of similarity between the vegetation and the seed bank and the relative spatial distributions of the species. Several mechanisms are probably interacting, depending on the life histories of the species. Modelling and experimental approaches are needed to further test the hypothesis of lottery recruitment.     

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.     

Variation between individuals fosters regional species coexistence

Although individual‐level variation (IV) is ubiquitous in nature, it is not clear how it influences species coexistence. Theory predicts that IV will hinder coexistence but empirical studies have shown that it can facilitate, inhibit, or have a neutral effect. We use a theoretical model to explore the consequences of IV on local and regional species coexistence in the context of spatial environmental structure. Our results show that individual variation can have a positive effect on species coexistence and that this effect will critically depend on the spatial structure of such variation. IV facilitates coexistence when a negative, concave‐up relationship between individuals’ competitive response and population growth rates propagates to a disproportionate advantage for the inferior competitor, provided that each species specialises in a habitat. While greater variation in the preferred habitat generally fosters coexistence, the opposite is true for non‐preferred habitats. Our results reconcile theory with empirical findings.