Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Population size dependence, competitive coexistence and habitat destruction

1. Spatial dynamics can lead to coexistence of competing species even with strong asymmetric competition under the assumption that the inferior competitor is a better colonizer given equal rates of extinction. Patterns of habitat fragmentation may alter competitive coexistence under this assumption.
2. Numerical models were developed to test for the previously ignored effect of population size on competitive exclusion and on extinction rates for coexistence of competing species. These models neglect spatial arrangement.
3. Cellular automata were developed to test the effect of population size on competitive coexistence of two species, given that the inferior competitor is a better colonizer. The cellular automata in the present study were stochastic in that they were based upon colonization and extinction probabilities rather than deterministic rules.
4. The effect of population size on competitive exclusion at the local scale was found to have little consequence for the coexistence of competitors at the metapopulation (or landscape) scale. In contrast, population size effects on extinction at the local scale led to much reduced landscape scale coexistence compared to simulations not including localized population size effects on extinction, especially in the cellular automata models. Spatially explicit dynamics of the cellular automata vs. deterministic rates of the numerical model resulted in decreased survival of both species. One important finding is that superior competitors that are widespread can become extinct before less common inferior competitors because of limited colonization.
5. These results suggest that population size–extinction relationships may play a large role in competitive coexistence. These results and differences are used in a model structure to help reconcile previous spatially explicit studies which provided apparently different results concerning coexistence of competing species.     

Population sex ratios, sex-specific clonal traits and tradeoffs among these traits in the liverwort Marchantia inflexa

Unisexual, female- or male-biased populations are common among some clonal plants. Within and among populations, the relative frequencies of males and females can be influenced by sex-specific demographic patterns that, in turn, can be a consequence of life-history characteristics. The objectives of this study were to describe (1)  population sex-ratio patterns among habitat patches along a river, and (2)  sex-specific patterns of and correlations among life-history clonal traits including: growth rates, number of meristematic tips and asexual reproduction in the dioecious liverwort, Marchantia inflexa . In Trinidad, a section of a stream was surveyed for the occurrence of female and male sex expressing thalli among habitat patches, and habitat characteristics (canopy openness and patch size) were recorded. The numbers of female and male inflorescences were obtained also. Of the 209 patches observed in the field, 83% did not contain sex expressing thalli, 9% contained thalli of both sexes, and the rest contained only female- (4%) or male-expressing (4%) thalli. Sex expression was less common among small patches, and there was a tendency for sex expression to be less likely among patches with the lowest canopy openness. The proportion of male inflorescences among the bisexual patches ranged from 0.22 to 0.80. In a greenhouse, we planted gemmae (asexual propagules) from field-collected isolates: ten female and eight male. On six occasions, we harvested replicates of each isolate to estimate isolate trait means. Females grew faster, produced more meristematic tips and had lower levels of asexual reproduction than males. Number of meristematic tips was negatively correlated with asexual reproduction and positively correlated with growth rate. These sex-specific patterns may lead to the high frequency of single sex patches as well as biased adult population sex ratios that are observed in the field.     

Spatially structured intraspecific trait variation can foster biodiversity in disturbed,heterogeneous environments

Trait variation within populations is an important area of research for empirical and theoretical ecologists. While differences between individuals are doubtlessly ubiquitous, their role for species coexistence is much less clear and highly debated. Both unstructured (random) and structured (linked to space, time or inheritance) intraspecific trait variation (ITV) may modify species interactions with nontrivial consequences for emerging community compositions. In many ecosystems, these compositions are further driven by prevalent disturbance regimes. I therefore explored the effects of unstructured as well as spatially structured ITV under disturbances in a generic ecological model of competing sessile species. Using spatially explicit, individual‐based simulations, I studied how intraspecific variation in life history traits together with interspecific tradeoffs and disturbance regimes shape long‐term community composition. I found that 1) unstructured ITV does not affect species coexistence in the given context, 2) spatially structured ITV may considerably increase coexistence, but 3) spatially clumped disturbances reduce this effect of spatially structured ITV, especially if interspecific tradeoffs involve dispersal distance. The findings suggest that spatially structured ITV with individual trait responses to local habitat conditions differing among species may create or expand humps in disturbance–diversity relationships. Hence, if present, these forms of spatially structured ITV should be included in ecological models and will be important for reliably assessing community responses to environmental heterogeneity and change.     

Evolution of complex dynamics in spatially structured populations

Dynamics of populations depend on demographic parameters which may change during evolution. In simple ecological models given by one-dimensional difference equations, the evolution of demographic parameters generally leads to equilibrium population dynamics. Here we show that this is not true in spatially structured ecological models. Using a multi-patch metapopulation model, we study the evolutionary dynamics of phenotypes that differ both in their response to local crowding, i.e. in their competitive behaviour within a habitat, and in their rate of dispersal between habitats. Our simulation results show that evolution can favour phenotypes that have the intrinsic potential for very complex dynamics provided that the environment is spatially structured and temporally variable. These phenotypes owe their evolutionary persistence to their large dispersal rates. They typically coexist with phenotypes that have low dispersal rates and that exhibit equilibrium dynamics when alone. This coexistence is brought about through the phenomenon of evolutionary branching, during which an initially uniform population splits into the two phenotypic classes.     

A simple landscape-scale test of a spatially explicit population model: patch occupancy in fragmented south-eastern Australian forests

The results of a landscape‐scale test of ALEX, a widely used metapopulation model for Population Viability Analysis (PVA), are described. ALEX was used to predict patch occupancy by the laughing kookkaburra and the sacred kingfisher in patches of eucalypt forest in south‐eastern Australia. These predictions were compared to field surveys to determine the accuracy of the model. Predictions also were compared to a “naïve” null model assuming no fragmentation effects.
The naïve null model significantly over‐predicted the number of eucalypt patches occupied by the sacred kingfisher, but the observed patch occupancy was not significantly different from that predicted using ALEX. ALEX produced a better fit to the field data than the naïve null model for the number of patches occupied by the laughing kookaburra. Nevertheless, ALEX still significantly over‐predicted the number of occupied patches, particularly remnants dominated by certain forest types – ribbon gum and narrow‐leaved peppermint. The predictions remained significantly different from observations, even when the habitat quality of these patches was reduced to zero. Changing the rate of dispersal improved overall predicted patch occupancy, but occupancy rates for the different forest types remained significantly different from the field observations. The lack of congruence between field data and model predictions could have arisen because the laughing kookaburra may move between an array of patches to access spatially separated food and nesting resources in response to fragmentation. Alternatively, inter‐specific competition may be heightened in a fragmented habitat. These types of responses to fragmentation are not incorporated as part of traditionally applied metapopulation models. Assessments of predictions from PVA models are rare but important because they can reveal the types of species for which forecasts are accurate and those for which they are not. This can assist the collection of additional empirical data to identify important factors affecting population dynamics.     

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。     

Grazers and Diggers: Exploitation Competition and Coexistence among Foragers with Different Feeding Strategies on a Single Resource

A mathematical model is presented that describes a system where two consumer species compete exploitatively for a single renewable resource. The resource is distributed in a patchy but homogeneous environment; that is, all patches are intrinsically identical. The two consumer species are referred to as diggers and grazers, where diggers deplete the resource within a patch to lower densities than grazers. We show that the two distinct feeding strategies can produce a heterogeneous resource distribution that enables their coexistence. Coexistence requires that grazers must either move faster than diggers between patches or convert the resources to population growth much more efficiently than diggers. The model shows that the functional form of resource renewal within a patch is also important for coexistence. These results contrast with theory that considers exploitation competition for a single resource when the resource is assumed to be well mixed throughout the system.     

A general model of local competition for space

Local competition for space across a wide array of taxa typically involves three mechanisms that we denote here as expansion (spreading into unoccupied habitat), lottery (replacing dead competitors), and overgrowth (encroaching on competitors along zones of contact). By formulating and analysing a simple, general model incorporating these features, we identify ecological conditions and life‐history features that lead to stable coexistence or competitive exclusion (with or without initial‐condition dependence) and gain insight by linking these to case studies in the literature. We demonstrate the importance of contact inhibition, a little‐studied feature of overgrowth, and we show how life‐history tradeoffs may influence and be influenced by local competition for space. The general model we present can help indicate whether local interactions are sufficient to explain patterns of coexistence or exclusion and can serve as the foundation for more specific, realistic models of spatial competition.     

Integrating nested spatial scales: implications for the coexistence of competitors on a patchy resource

1. Intraspecific aggregation at a single spatial scale can promote the coexistence of competitors. This paper demonstrates how this same mechanism can be applied to the many systems that are patchy at two scales, with patches nested within 'superpatches'.
2. Data are presented from a field study showing that insects living in rotting fruits have aggregated distributions in the fruits under a single tree, and that the mean density and degree of aggregation varies significantly among trees. Observations in this system motivate the following models.
3. A model of competition has been developed between two species which explicitly represents spatial variation at two scales. By integrating the probability distributions for each scale, the marginal distributions of competitors over all patches can be found and used to calculate coexistence criteria. This model assumes global movement of the competitors.
4. Although spatial variation at a single scale may not be sufficient for coexistence, the total variation over all patches can allow coexistence. Variation in mean densities among superpatches and variation in the degree of aggregation among superpatches both promote coexistence, but act in different ways.
5. A second model of competition between two species is described which incorporates the effects of limited movement among superpatches. Limited movement among superpatches generally promotes coexistence, and also leads to correlations among aggregation and the mean densities of competitors.     

Local movement and edge effects on competition and coexistence in ephemeral-patch models

For insects exploiting spatially structured arrays of resource patches (host plants, fungi, carrion, etc.), the distribution of individuals among patches can have important consequences for the coexistence of competitors. In general, intraspecific aggregation of consumer individuals over the landscape of patches stabilizes competition. Oviposition behavior of individual females can generate aggregation of larvae across patches and, therefore, strongly influences the outcome of competition between co-occurring species. We used simulation models to evaluate the consequences (for the coexistence of competitors) of different movement behaviors by females before and between oviposition events. Coexistence times increase when females are more likely to travel among neighboring patches than among distant ones. Coexistence times are also longer when females begin egg laying near the site of their emergence. Preoviposition dispersal is, therefore, destabilizing. We also considered responses by females to edges of resource arrays. Edge effects are generally stabilizing, delaying competitive exclusion by increasing larval aggregation, but different responses to edges have dramatically different effects on coexistence. The longest coexistence times occur when edges are "sticky", such that females encountering an edge tend to remain there.     

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.     

Habitat fragmentation and extinction thresholds on fractal landscapes

Habitat fragmentation is a potentially critical factor in determining population persistence. In this paper, we explore the effect of fragmentation when the fragmentation follows a fractal pattern. The habitat is divided into patches, each of which is suitable or unsuitable. Suitable patches are either occupied or unoccupied, and change state depending on rates of colonization and local extinction. We compare the behaviour of two models: a spatially implicit patch-occupancy (PO) model and a spatially explicit cellular automaton (CA) model. The PO model has two fixed points: extinction, and a stable equilibrium with a fixed proportion of occupied patches. Global extinction results when habitat destruction reduces the proportion of suitable patches below a critical threshold. The PO model successfully recreates the extinction patterns found in other models. We translated the PO model into a stochastic cellular automaton. Fractal arrangements of suitable and unsuitable patches were used to simulate habitat fragmentation. We found that: (i) a population on a fractal landscape can tolerate more habitat destruction than predicted by the patch-occupancy model, and (ii) the extinction threshold decreases as the fractal dimension of the landscape decreases. These effects cannot be seen in spatially implicit models. Landscape struc-ture plays a vital role in mediating the effects of habitat fragmentation on persistence.     

The trade-off between dispersability and longevity - an important aspect of plant species diversity

Abstract. Local presence of plant species is determined by population colonizations and extinctions. All traits that influence the capacity of individuals to colonize patches and survive within patches, are therefore important for community diversity. Spatial models can explain the coexistence of species provided that the inferior competitor has a greater spatial mobility and thereby can avoid competition. We searched the literature for empirical evidence for such trade-offs and included all available information on correlations between traits associated with the capacity to colonize and traits promoting the ability to survive. A lower reproductive effort of a species is associated with a longer life span and a higher competitive ability. Morphological adaptations for dispersal are less common in species which better tolerate stress, that are better competitors or possess seed dormancy. Such patterns suggest that species that are good survivors may have a limited ability to colonize new patches and vice versa. A negative correlation between dispersability and longevity has important effects on the regional dynamics of single species as well as on the coexistence of species. From a conservation perspective differences in the colonization capacity among species imply that restoration of plant biodiversity must not only focus on conditions within patches, but also consider the spatial arrangement of patches in order to enable plants to bridge gaps in time and space.     

生境破碎化对动物种群存活的影响

生境破碎是生物多样性下降的主要原因之一。通常以岛屿生物地理学、异质种群生物学和景观生态学的理论来解释不同空间尺度中生境破碎化的生态学效应。生境破碎化引起面积效应、隔离效应和边缘效应。这些效应通过影响动物种群的绝灭阈值、分布和多度、种间关系以及生态系统过程,最终影响动物种群的存活。野外研究表明,破碎化对动物的影响,因物种、生境类型和地理区域不同而有所变化,因此,预测物种在破碎生境中的存活比较困难。研究热点集中于：确定生境面积损失和生境斑块的空间格局对破碎景观中物种绝灭的相对影响,破碎景观中物种的适宜生境比例和绝灭阈值,异质种群动态以及生态系统的生态过程。随着3S技术的发展,生境破碎化模型趋于复杂,而发展有效的模型和验证模型将成为一项富有挑战性的任务。     

Cellular automaton models for competition in patchy environments: Facilitation, inhibition, and tolerance

We have developed cellular automaton models for two species competing in a patchy environment. We have modeled three common types of competition: facilitation (in which the winning species can colonize only after the losing species has arrived) inhibition (in which either species is able to prevent the other from colonizing) and tolerance (in which the species most tolerant of reduced resource levels wins). The state of a patch is defined by the presence or absence of each species. State transition probabilities are determined by rates of disturbance, competitive exclusion, and colonization. Colonization is restricted to neighboring patches. In all three models, disturbance permits regional persistence of species that are excluded by competition locally. Persistence, and hence diversity, is maximized at intermediate disturbance frequencies. If disturbance and dispersal rates are sufficiently high, the inferior competitor need not have a dispersal advantage to persist. Using a new method for measuring the spatial patterns of nominal data, we show that none of these competition models generates patchiness at equilibrium. In the inhibition model, however, transient patchiness decays very slowly. We compare the cellular automaton models to the corresponding mean-field patch-occupancy models, in which colonization is not restricted to neighboring patches and depends on spatially averaged species frequencies. The patch-occupancy model does an excellent job of predicting the equilibrium frequencies of the species and the conditions required for coexistence, but not of predicting transient behavior.     

The effect of habitat fragmentation on cyclic population dynamics: a reduction to ordinary differential equations

Habitat fragmentation is known to be a key factor affecting population dynamics. In a previous study by Strohm and Tyson (Bull Math Biol 71:1323?C1348, 2009), the effect of habitat fragmentation on cyclic population dynamics was studied using spatially explicit predator?Cprey models with four different sets of reaction terms. The difficulty with spatially explicit models is that often analytical tractability is lost and the mechanisms behind the behaviour of the models are difficult to analyse. In this study, we employ a simplification procedure based on a Fourier series first-term truncation of the spatially explicit models Strohm and Tyson (Bull Math Biol 71:1323?C1348, 2009) to obtain spatially implicit models. These simpler models capture the main features of the spatially explicit models and can be used to explain the dynamics observed by Strohm and Tyson. We find that the spatially implicit models and the spatially explicit models produce similar responses to habitat fragmentation for larger high-quality patch sizes. Additionally, we find that the critical patch size of the spatially implicit models provides an upper bound on the critical patch size of the spatially explicit models. Finally, we derive an approximation of the multi-patch habitat by a single-patch habitat with partial flux boundary conditions which allows for a lower bound on the critical patch size to be calculated.     

Maintenance of the sexes and persistence of a clonal organism in spatially complex metapopulations

Clonal organisms persist at a range of population sex ratios, from equal numbers of males and females to single-sex systems. When intersexual competition is strong enough to drive one sex locally extinct, the maintenance of the sexes is facilitated by the semi-independent dynamics of populations within a metapopulation. These semi-independent dynamics are influenced by dispersal and recolonization rates, which are affected by the spatial arrangement of populations. To establish the quantitative relationship between spatially complex metapopulations and the maintenance of the sexes, we used a mathematical model of the liverwort Marchantia inflexa. This clonal organism is found in discrete patches on rocks and along the banks of streams, which form single-sex and two-sex metapopulations. In this system, asexual propagules mainly disperse short distances. Long-distance between-patch dispersal and recolonization mainly occurs via sexual propagules, which require both sexes to be present. Dispersal of these two types of propagules could interact with the spatial arrangement of populations to affect the maintenance of the sexes. With our mathematical model, we found that at intermediate distances between populations, metapopulations maintained both sexes, and the spatial arrangement of populations changed the threshold at which one sex was lost. On the other hand, when populations were close to one another, one sex was lost and the single-sex metapopulation persisted through dispersal of asexual propagules. When populations were far apart, one sex was lost, and the metapopulation either went extinct due to lack of recolonization by asexual propagules or persisted because clumped populations facilitated recolonization. These idealized spatial arrangements help clarify the effects of the spatial arrangement on the maintenance of the sexes and the persistence of metapopulations of clonal organisms, which can help explain geographic parthenogenesis and the distribution of asexual populations, the persistence of asexual species, and inform the conservation of clonal organisms.     

Body size mediated coexistence of consumers competing for resources in space

Body size is a major phenotypic trait of individuals that commonly differentiates co-occurring species. We analyzed inter-specific competitive interactions between a large consumer and smaller competitors, whose energetics, selection and giving-up behaviour on identical resource patches scaled with individual body size. The aim was to investigate whether pure metabolic constraints on patch behaviour of vagile species can determine coexistence conditions consistent with existing theoretical and experimental evidence. We used an individual-based spatially explicit simulation model at a spatial scale defined by the home range of the large consumer, which was assumed to be parthenogenic and semelparous. Under exploitative conditions, competitive coexistence occurred in a range of body size ratios between 2 and 10. Asymmetrical competition and the mechanism underlying asymmetry, determined by the scaling of energetics and patch behaviour with consumer body size, were the proximate determinant of inter-specific coexistence. The small consumer exploited patches more efficiently, but searched for profitable patches less effectively than the larger competitor. Therefore, body-size related constraints induced niche partitioning, allowing competitive coexistence within a set of conditions where the large consumer maintained control over the small consumer and resource dynamics. The model summarises and extends the existing evidence of species coexistence on a limiting resource, and provides a mechanistic explanation for decoding the size-abundance distribution patterns commonly observed at guild and community levels.     

Difference Inadaptive Dispersal Ability Can Promote Species Coexistence in Fluctuating Environments

Theories and empirical evidence suggest that random dispersal of organisms promotes species coexistence in spatially structured environments. However, directed dispersal, where movement is adjusted with fitness-related cues, is less explored in studies of dispersal-mediated coexistence. Here, we present a metacommunity model of two consumers exhibiting directed dispersal and competing for a single resource. Our results indicated that directed dispersal promotes coexistence through two distinct mechanisms, depending on the adaptiveness of dispersal. Maladaptive directed dispersal may promote coexistence similar to random dispersal. More importantly, directed dispersal is adaptive when dispersers track patches of increased resources in fluctuating environments. Coexistence is promoted under increased adaptive dispersal ability of the inferior competitor relative to the superior competitor. This newly described dispersal-mediated coexistence mechanism is likely favored by natural selection under the trade-off between competitive and adaptive dispersal abilities.