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.     

The influence of varying spatial heterogeneity on the refuge model for coexistence of specialist parasitoid assemblages

Models of host–parasitoid dynamics often assume constant levels of spatial heterogeneity in parasitoid attack rate, which tends to stabilize the interactions. Recently, authors have questioned this assumption and shown that outcomes of simple host–parasitoid models change if spatial heterogeneity is allowed to vary with parasitoid density. Here, we allow spatial heterogeneity to vary with either parasitoid density or percent parasitism in a model designed to explain specialist parasitoid coexistence on insect hosts with various levels of refuge. By examining this model we can evaluate the effect of varying spatial heterogeneity on a more complex model in which spatial heterogeneity is not considered the primary determinant of persistence. By modeling communities with one host and two parasitoid species, we show that the probability of species persistence for the competitively inferior parasitoid depends on the assumed relationship between spatial heterogeneity and both parasitoid density and percent parasitism. The probability of parasitoid coexistence is generally lower when spatial heterogeneity varies with parasitoid demographics. We conclude that the conditions for which host refuge promote specialist parasitoid coexistence are less common that proposed by the original model. Finally, we compared a model in which spatial heterogeneity varies with percent parasitism to data from laboratory trials and find a reasonable fit. We conclude that the change in spatial heterogeneity strongly influenced the outcome of the laboratory trials, and we suggest more research is necessary before researchers can assume constant spatial heterogeneity in future models.     

Reduction of species coexistence through mixing in a spatial competition model

Many ecological systems exhibit self-organized spatial patterns due to local interactions. Such patterns can promote species diversity and therefore serve as an important mechanism for biodiversity maintenance. Previous work has shown that when species interactions occurred at local spatial scales, species diversity was greatest when robust mosaic spatial patterns formed. Also, intransitive interactions led to the emergence of spiral patterns, frequently resulting in multispecies coexistence. In some instances, intransitive interactions reduced species diversity as the consequence of competitive hierarchies. Here, we extend and broaden this line of investigation and examine the role of global competition along a continuum ranging from spatial mosaics to spiral patterns. While previous models have predicted that species diversity is reduced when interactions occur over larger spatial scales, our model considers the effects of various levels of mixing on species diversity, in the context of various network structures as measured by the covariance of row and column sums of the competition matrix. First, we compare local competition (unmixed system) versus global competition (mixed systems) and show that greater species diversity is maintained under a positive covariance. Second, we show that under various levels of mixing, species diversity declines more rapidly under a negative covariance. Lastly, we demonstrate that time to extinction in our model occurs much more rapidly under a negative covariance.     

Complexity and coexistence in a simple spatial model for arid savanna ecosystems

Tree–grass coexistence is broadly observed in tropical savannas. Recent studies indicate that, in arid savannas, such coexistence is stable and related to water availability. The role of different factors (from niche separation to demographic structure) has been explored. Nevertheless, spatial mechanisms of water–vegetation interactions have been rarely taken into account, despite their well-known importance for vegetation distribution. Here, we introduce a spatial model including tree and grass biomass dynamics, together with soil and surface water dynamics. We consider two water–vegetation feedbacks. Grasses increase water infiltration into the soil, while tree shadow limits evaporation, and both mechanisms increase soil water availability, leading to positive feedbacks. The infiltration feedback can also lead to spatial pattern formation. Despite the fact that trees and grasses compete for the same resource, namely water, we observe stable coexistence as a possible model outcome. The system displays a complex behavior, with multiple stable states and possible catastrophic shifts between states, e.g., patterned grassland, bare soil and forest. In our model, coexistence is always linked with multi-stability and spatial pattern formation, driven by grass infiltration feedback. Given such complex model solutions, we expect that, under real conditions, heterogeneities and disturbances, acting on the multi-stable states, may further foster coexistence.     

How the spatial scales of dispersal, competition, and environmental heterogeneity interact to affect coexistence

Spatial coexistence depends on a variety of biological and physical processes, and the relative scales of these processes may promote or suppress coexistence. We model plant competition in a spatially varying environment to show how shifting scales of dispersal, competition, and environmental heterogeneity affect coexistence. Spatial coexistence mechanisms are partitioned into three types: the storage effect, nonlinear competitive variance, and growth-density covariance. We first describe how the strength of each of these mechanisms depends on covariances between population densities and between population densities and the environment, and we then explain how changes in the scales of dispersal, competition, and environmental heterogeneity should affect these covariances. Our quantitative approach allows us to show how changes in the scales of biological and physical processes can shift the relative importance of different classes of spatial coexistence mechanisms and gives us a more complete understanding of how environmental heterogeneity can enable coexistence. For example, we show how environmental heterogeneity can promote coexistence even when competing species have identical responses to the environment.     

Multispecies coexistence of trees in tropical forests: spatial signals of topographic niche differentiation increase with environmental heterogeneity

Neutral and niche theories give contrasting explanations for the maintenance of tropical tree species diversity. Both have some empirical support, but methods to disentangle their effects have not yet been developed. We applied a statistical measure of spatial structure to data from 14 large tropical forest plots to test a prediction of niche theory that is incompatible with neutral theory: that species in heterogeneous environments should separate out in space according to their niche preferences. We chose plots across a range of topographic heterogeneity, and tested whether pairwise spatial associations among species were more variable in more heterogeneous sites. We found strong support for this prediction, based on a strong positive relationship between variance in the spatial structure of species pairs and topographic heterogeneity across sites. We interpret this pattern as evidence of pervasive niche differentiation, which increases in importance with increasing environmental heterogeneity.     

Species traits in relation to temporal and spatial heterogeneity in streams: a test of habitat templet theory

1. The habitat templet approach depends on defining templet axes appropriate to the organism(s) of interest, predicting the traits of species associated with different parts of the templet, and testing these predictions in a range of habitats whose positions in the templet have been determined. 2. In this study of thirty-five benthic insect taxa at fifty-four tributary sites of the Taieri River on the South Island of New Zealand, we chose as the temporal axis the intensity/frequency of disturbance, defined in terms of bed movement during high discharge events. As the spatial axis, we postulated that three features would provide refugia and therefore ameliorate disturbance—percentage of the bed with low shear stress, percentage of the bed made up of large substratum particles and availability of interstitial space in the bed—from which we derived a combined multivariate refugium axis. 3. More disturbed communities contained a significantly higher percentage of individuals possessing the following traits: small size, high adult mobility, habitat generalist (each predicted to confer resilience in response to disturbance), clinger, streamlined/flattened and with two or more life stages outside the stream (each predicted to confer resistance in the face of disturbance). When analyses were performed on the percentage of taxa having particular traits, the predicted positive relationships with average bed movement were found for high adult mobility and habitat generalist traits. 4. The percentage of variance in trait scores explained by intensity of disturbance was generally higher in sites with less refugia available and lower in sites further from the headwaters. The percentage of variance explained was higher in sites recently subject to a major high discharge disturbance, suggesting that disturbances tend to strengthen the pattern of preponderance of resilience/resistance traits. 5. We mapped insect taxa onto the two-dimensional templet, following Grime et al.’s triangular terrestrial plant classification. The full variety of resistance and resilience traits were represented in insect species throughout the templet, but taxa associated with more disturbed conditions generally displayed a larger number of resilience and resistance traits, combined, than taxa associated with more stable stream beds.     

Utilization by fishes of shallow,seagrass-covered banks in Florida Bay: 1. Species composition and spatial heterogeneity

Synopsis Species composition and relative capture rates of water column fishes occurring on the shallow (<1 m), seagrass-covered mudbanks of Florida Bay were assessed using small-mesh gillnets. The fauna was largely temperate, with few tropical representatives, and was similar to the fish community in adjacent basins. There was a high variability in the catch across the Bay, reflecting heterogeneity in both the physical environment and various aspects of the seagrass canopy. The Gulf site, in the northwestern section of the Bay, had the highest species richness and highest capture rates of individual species, relative to other sites. Higher densities of potential prey, greater available foraging area, and organically rich, fine sediments are probably influential in the greater fish utilization of this bank. The greater exchange of western Florida Bay with open Atlantic or Gulf waters is proposed as a secondary factor influencing species richness; the probability of non-resident species occasionally appearing on western banks is greater than in isolated interior sections of the Bay.     

Species coexistence in temperate, mixed deciduous forests

The response of tree life-history traits to community profiles (horizontal and vertical heterogeneity, disturbances and biotic interactions) determines community assembly rules, which are currently a hot issue in community ecology. Important mechanisms of coexistence differ throughout the developing stages of tree life history. Many processes of niche partitioning and tradeoffs that potentially enable tree coexistence have been reported to be present in temperate forests, although some of these life-history traits are either correlated with each other or are not independent. Not all of the proposed mechanisms explain coexistence equally well; some could predominate in determining the community organization of forest communities. Population studies need to concentrate more on the component species of a target community to detect the ecological assembly rule. These approaches can also address how chance factors contribute to the composition of temperate tree communities, which might be less dependent on chance than are tropical ones.     

Analysis of a lottery competition model with limited nutrient availability

How a plant species utilizes a limited nutrient is important for its survival. The purpose of this work is to examine how nutrient utilization mechanisms (for seed production) affect the coexistence of competing plant species. We construct a revised lottery model that uses one of three possible kinds of nutrient utilization functions. In all cases the models suggest that two species can coexist under certain circumstances, but that three species cannot coexist, at least when the nutrient utilization functions are continuous functions of nutrient uptake. However, in the discontinuous case three species can coexist in a state of sustained oscillations. The results suggest that one need pay close attention to the differences in the nutrient utilization mechanisms among competing plant species in order to ascertain the competitive outcome.     

The nature of zooplankton spatial heterogeneity in a nonriverine impoundment

Knowledge of spatial heterogeneity characteristic of reservoir plankton communities is fundamental to a variety of ecological studies. Degree of spatial heterogeneity in the zooplankton community of Center Hill Reservoir, with water residence times of 50–250 days, was positively correlated with rate of water influx. Important spatial differences resulted from the contrast between zooplankton associated with new and longer-impounded water. The nature of spatial heterogeneity differed fundamentally from the more riverine impoundments where spatial differences are often persistent and characterized by gradual change (as opposed to contrast) in plankton assemblages with respect to location. Magnitude of plankton spatial heterogeneity in nonriverine impoundments may be predictable from inflow rates. Areas, between which major differences in plankton communities exist, may also be definable from knowledge of inflow dispersal patterns in these impoundments.     

Benthic microalgal diversity enhanced by spatial heterogeneity of grazing

This study presents model experiments on the effect of the spatial pattern of herbivory on primary producer diversity. Microalgal biofilms (periphyton) were exposed to different mixtures of two benthic herbivores, the isopod Idothea chelipes and the gastropod Littorina littorea. The herbivores are similar in their feeding selectivity but differ strongly in the spatial pattern of grazing. Idothea did not increase the spatial heterogeneity of algal cell densities beyond the level of ungrazed controls (<1 order of magnitude between local minima and maxima at the 1 mm² scale). Littorina grazing, in contrast, created a pronounced spatial heterogeneity with maximum:minmum ratios of almost 3 orders of magnitude. When algae were exposed to mixtures of both gazers, the spatial heterogeneity of microalgal cell densities increased with an increasing proportion of Littorina in the herbivore mixture. Algal species richness, diversity and evenness also increased with increasing proportions of Littorina, and was highly significantly correlated with the spatial heterogeneity of cell densities. Received: 25 May 1999 / Accepted: 14 September 1999     

Oscillatory coexistence in a food chain model with competing predators

A food chain model with two predators feeding on a single prey in a chemostat is studied. Using a multiparameter bifurcation analysis, we find parameters values for which there is stable oscillatory coexistence of the predators. It is also shown how these coexistent states provide a transition between two possible states of competitive exclusion. It is shown that the competitive exclusion principle need not hold if one or more of the predators has oscillatory behavior in the absence of other predators.This work was partially supported by National Science Foundation Grant MCS 83-01881     

Effects of microenvironmental heterogeneity on the seed-to-seedling process and tree coexistence in a riparian forest

In a temperate riparian forest, the effects of substrate types, canopy gaps and conspecific seedfall density were investigated on the seed-to-seedling process for the five dominant species (Aesculus turbinata, Fagus crenata, Acer mono, Pterocarya rhoifolia and Cercidiphyllum japonicum). Densities of seedfall and subsequent seedling recruits were measured in the stand over a period of 6 years. A model assuming that local density of seedling recruits is proportional to seedfall density in the preceding year significantly explained a spatial variation in seedling recruits for all species. Several environmental factors were then added. Substrate composition had a positive effect on P. rhoifolia and C. japonicum. P. rhoifolia was favored by gravel substrate, which also explained the adult distribution of this species in this forest. C. japonicum appeared to be facilitated by a mineral-soil substrate. However, the distributions of this substrate and adults of C. japonicum did not follow each other closely. A. mono was negatively affected by gaps, and F. crenata was negatively affected by conspecific seedfall density. In contrast, A. turbinata was not significantly affected by any of the environmental factors tested. The microenvironmental heterogeneity in this forest explained species coexistence to a limited extent in the context of seed-to-seedling processes. Performances at later stages of the life-cycle and/or catastrophic disturbances (e.g. landslides) might have a stronger influence on species coexistence in this forest.     

Impact of spatial heterogeneity on a predator-prey system dynamics

This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.     

Fitness effects of parasite-mediated spatial heterogeneity within a swarm

The fitness consequences associated with the position an individualadopts within a dynamic group are not well understood. I investigatedmate acquisition by male chironomid midges using a simple swarmingmodel and empirically collected data on midge aerobatic ability.Previous work has suggested that the aerobatic ability of amale is an important predictor of his reproductive success,although there is contrary (and counterintuitive) evidence thatinfection with ectoparasitic mites increases a male's chanceof mating, despite having negative effects on flight speed.The model used here suggests that a male's location within theswarm, brought about passively through interindividual differencesin flight speed, may explain these contradictory results. Specifically,slower flying males (including those burdened with mites) adoptedpositions nearer the center of the swarm, whereas faster malestended to occupy the periphery. This in turn affected theiraccess to females because any mechanism that brought femalesnearer the swarm's center before capture (including high femaleflight speed and selective pairing by either males or females)significantly increased the relative reproductive success ofboth larger and parasitized males, with the benefits of parasitismpeaking at around 4 mites per host. There may be selective pressureon hosts and parasites to maintain this optimal mite densitybecause both are likely to benefit from the relationship: hostsenjoy an increased reproductive success, whereas only throughhost copulation can mites transfer to a female midge and returnto water (their next life-history stage) during host oviposition.     

Host heterogeneity is a determinant of competitive exclusion or coexistence in genetically diverse malaria infections

During an infection, malaria parasites compete for limited amounts of food and enemy-free space. Competition affects parasite growth rate, transmission and virulence, and is thus important for parasite evolution. Much evolutionary theory assumes that virulent clones outgrow avirulent ones, favouring the evolution of higher virulence. We infected laboratory mice with a mixture of two Plasmodium chabaudi clones: one virulent, the other avirulent. Using real-time quantitative PCR to track the two parasite clones over the course of the infection, we found that the virulent clone overgrew the avirulent clone. However, host genotype had a major effect on the outcome of competition. In a relatively resistant mouse genotype (C57B1/6J), the avirulent clone was suppressed below detectable levels after 10 days, and apparently lost from the infection. By contrast, in more susceptible mice (CBA/Ca), the avirulent clone was initially suppressed, but it persisted, and during the chronic phase of infection it did better than it did in single infections. Thus, the qualitative outcome of competition depended on host genotype. We suggest that these differences may be explained by different immune responses in the two mouse strains. Host genotype and resistance could therefore play a key role in the outcome of within-host competition between parasite clones and in the evolution of parasite virulence.     

The effect of heterogeneity on invasion in spatial epidemics: from theory to experimental evidence in a model system

Heterogeneity in host populations is an important factor affecting the ability of a pathogen to invade, yet the quantitative investigation of its effects on epidemic spread is still an open problem. In this paper, we test recent theoretical results, which extend the established "percolation paradigm" to the spread of a pathogen in discrete heterogeneous host populations. In particular, we test the hypothesis that the probability of epidemic invasion decreases when host heterogeneity is increased. We use replicated experimental microcosms, in which the ubiquitous pathogenic fungus Rhizoctonia solani grows through a population of discrete nutrient sites on a lattice, with nutrient sites representing hosts. The degree of host heterogeneity within different populations is adjusted by changing the proportion and the nutrient concentration of nutrient sites. The experimental data are analysed via Bayesian inference methods, estimating pathogen transmission parameters for each individual population. We find a significant, negative correlation between heterogeneity and the probability of pathogen invasion, thereby validating the theory. The value of the correlation is also in remarkably good agreement with the theoretical predictions. We briefly discuss how our results can be exploited in the design and implementation of disease control strategies.