Population biology of multispecies helminth infection: competition and coexistence

The role that interspecific interactions play in shaping parasite communities is uncertain. To date, models of competition between helminth species have assumed that interaction occurs through parasite-induced host death. To our knowledge, there has been no theoretical exploration of other forms of competition. We examine models in which competition acts at the point of establishment within the host, and at the time of egg production by the adult worm. The models used are stochastic and we allow hosts to vary in their rate of exposure to infective larvae. We derive the Lotka-Volterra model of competition when exposure is homogenous and thus demonstrate that two helminth species cannot coexist on a single limiting resource. We show that coexistence of species is promoted by heterogeneity in host exposure provided that the rates of exposure to the two species are not perfectly correlated, and, if they are positively correlated, provided that the degree of heterogeneity in host exposure is similar for the two competing helminth species. These results are robust to the mechanism of competition.     

Predicting the effect of competition on secondary plant extinctions in plant–pollinator networks

What are the limitations of models that predict the behavior of an ecological community based on a single type of species interaction? Using plant–pollinator network models as an example, we contrast the predicted vulnerability of a community to secondary extinctions under the assumption of purely mutualistic interactions versus mutualistic and competitive interactions. We find that competition among plant species increases the risk of secondary extinctions and extinction cascades. Simulations over a number of different network structures indicate that this effect is stronger in larger networks, more strongly connected networks and networks with higher plant:pollinator ratios. We conclude that efforts to model plant–pollinator communities will systematically over‐estimate community robustness to species loss if plant competition is ignored. However, because the effect of plant competition depends on network architecture, and because characterization of plant competition is work intensive, we suggest that efforts to account for plant competition in plant–pollinator network models should be focused on large, strongly connected networks with high plant:pollinator ratios.     

Competition and introduction regime shape exotic bird communities in Hawaii

Complex combinations of historical and local-regional processes determine the assembly of ecological communities. We investigated such processes in the Hawaiian introduced avifauna, comprising 140 years of historical records of invasions and extinctions of birds. Here the particular introduction regime (i.e., colonization attempts and number of introduced species) and priority effects constitute the historical (and regional) component, and competition is the local component. These processes are theoretically supported by means of a Lotka–Volterra model of species competition, finding that changes in the specific introduction regime might result in different extinction dynamics. Both field data and model outcomes support the biotic resistance hypothesis, so that the invasibility of new incomers decrease with species richness. Finally, we found that the resistance to new invaders depends on the particular introduction regime. Thus, community assembly models built to predict the success of exotic species should consider more scenarios than random introduction regimes.     

Effective competition determines the global stability of model ecosystems

We investigate the stability of Lotka-Volterra (LV) models constituted by two groups of species such as plants and animals in terms of the intragroup effective competition matrix, which allows separating the equilibrium equations of the two groups. In matrix analysis, the effective competition matrix represents the Schur complement of the species interaction matrix. It has been previously shown that the main eigenvalue of this effective competition matrix strongly influences the structural stability of the model ecosystem. Here, we show that the spectral properties of the effective competition matrix also strongly influence the dynamical stability of the model ecosystem. In particular, a necessary condition for diagonal stability of the full system, which guarantees global stability, is that the effective competition matrix is diagonally stable, which means that intergroup interactions must be weaker than intra-group competition in appropriate units. For mutualistic or competitive interactions, diagonal stability of the effective competition is a sufficient condition for global stability if the inter-group interactions are suitably correlated, in the sense that the biomass that each species provides to (removes from) the other group must be proportional to the biomass that it receives from (is removed by) it. For a non-LV mutualistic system with saturating interactions, we show that the diagonal stability of the corresponding LV system close to the fixed point is a sufficient condition for global stability.     

Disturbance, interspecific interaction and diversity in metapopulations

Metapopulation diversity patterns depend on the relations among the timescales of local biological interactions (predation, competition), the rates of dispersal among local populations and the patterns of disturbance. We investigate these relationships using a family of simple non-linear Markov chain models. We consider three models for interspecific competition; if the species are identified with early and late successional species, the models describe the facilitation, inhibition and tolerance models of ecological succession. By adding a third competing species we also compare transitive competitive hierarchies and intransitive competitive networks. Finally, we examine the effects of predation in mediating coexistence among competing prey species. In each model we find circumstances in which biotic or abiotic disturbance can increase both local and regional diversity, but those circumstances depend on the various timescales in the model in ways that arc neither obvious nor trivial.     

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities.     

Allee effect,spatial structure and species coexistence

Both positive and negative interactions among species are common in communities. Until recently, attention has focused on negative interactions such as competition. However, the importance of positive interactions such as the Allee effect has recently been recognized. We construct a single-patch model that incorporates both an Allee effect and competition between two species. A species that experiences an Allee effect cannot establish in a patch which is already occupied by a competitor unless its density is over a critical value. This effect, when translated into a metapopulation, makes migrants of a species unable to colonize patches where another species has established. This interaction between the Allee effect and inter-specific competition creates and stabilizes spatial segregation of species. Therefore, under circumstances in which competition would preclude local coexistence, the presence of an Allee effect can allow coexistence at a metapopulation scale. Furthermore, we found that a species can resist displacement if stronger competitors experience an Allee effect.     

Competition and species packing in patchy environments

In models of competition in which space is treated as a continuum, and population size as continuous, there are no limits to the number of species that can coexist. For a finite number of sites, N, the results are different. The answer will, of course, depend on the model used to ask the question. In the Tilman-May-Nowak ordinary differential equation model, the number of species is asymptotically C log N with most species packed in at the upper end of the competitive hierarchy. In contrast, for metapopulation models with discrete individuals and stochastic spatial systems with various competition neighborhoods, we find a traditional species area relationship CN(a), with no species clumping along the phenotypic gradient. The exponent a is larger by a factor of 2 for spatially explicit models. In words, a spatial distribution of competitors allows for greater diversity than a metapopulation model due to the effects of recruitment limitation in their competition.     

Direct competition results from strong competition for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka–Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur in, Theor Popul Biol 1:1–11, 1970). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional.     

Competition between similar invasive species: modeling invasional interference across a landscape

As the number of biological invasions increases, interactions between different invasive species will become increasingly important. Several studies have examined facilitative invader–invader interactions, potentially leading to invasional meltdown. However, if invader interactions are negative, invasional interference may lead to lower invader abundance and spread. To explore this possibility, we develop models of two competing invaders. A landscape simulation model examines the patterns created by two such species invading into the same region. We then apply the model to a case study of Carduus nutans L. and C. acanthoides L., two economically important invasive weeds that exhibit a spatially segregated distribution in central Pennsylvania, USA. The results of these spatially-explicit models are generally consistent with the results of classic Lotka–Volterra competition models, with widespread coexistence predicted if interspecific effects are weaker than intraspecific effects for both species. However, spatial segregation of the two species (with lower net densities and no further spread) may arise, particularly when interspecific competition is stronger than intraspecific competition. A moving area of overlap may result when one species is a superior competitor. In the Carduus system, our model suggests that invasional interference will lead to lower levels of each species when together, but a similar net level of thistle invasion due to the similarity of intra- and interspecific competition. Thus, invasional interference may have important implications for the distribution and management of invasive species.     

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.     

Colonization process determines species diversity via competitive quasi‐exclusion

A colonization model provides a useful basis to investigate a role of interspecific competition in species diversity. The model formulates colonization processes of propagules competing for spatially distinct habitats, which is known to result in stable coexistence of multiple species under various trade‐off, for example, competition–colonization and fecundity–mortality trade‐offs. Based on this model, we propose a new theory to explain patterns of species abundance, assuming a trade‐off between competitive ability and fecundity among species. This model makes testable predictions about species positions in the rank abundance diagram under a discrete species competitiveness. The predictions were tested by three data of animal communities, which supported our model, suggesting the importance of interspecific competition in community structure. Our approach provides a new insight into understanding a mechanism of species diversity.     

Competition-similarity relationships and the nonlinearity of competitive effects in consumer-resource systems

Much previous ecological and evolutionary theory about exploitative competition for a continuous spectrum of resources has used the Lotka-Volterra model with competition coefficients given by a Gaussian function of niche separation. Using explicit consumer-resource models, we show that the Lotka-Volterra model and the assumption of a Gaussian competition-similarity relationship both fail to reflect the impact of strong resource depletion, which typically reduces the influence of the most heavily used resources on the competitive interaction. Taking proper account of resource depletion reveals that strong exploitative competition between efficient consumers is usually a highly nonlinear interaction, implying that a single measure is no longer sufficient to characterize the process. The nonlinearity usually entails weak coupling of competing species when their abundances are high and equal. Rare invaders are likely to have effects on abundant residents much larger than those of the resident on the invader. Asymmetrical utilization curves often produce asymmetrical competition coefficients. Competition coefficients are typically non-Gaussian and are often nonmonotonic functions of niche separation. Utilization curve shape and resource growth functions can have major effects on competition-similarity relationships. A variety of previous theoretical findings need to be reassessed in light of these results.     

Interactions between root and shoot competition vary among species

Understanding how the competition varies with productivity is essential for differentiating among alternative models of plant community organization. Prior attempts to explain shifts in root and shoot competition along gradients have generally assumed an additive interaction between the two competitive forms, using an experimental design which does not fully separate both above‐ and belowground processes. At the most basic level, few field studies have separated root and shoot competition, and we have limited knowledge about both the relative importance of these processes, and how they interact to affect plant growth in the field. Presented here are findings from a field study in which root and shoot competition were experimentally separated by using root exclusion tubes and neighbor tiebacks in an early successional community. Individuals of four species (Abutilon theophrasti, Amaranthus retroflexus, Rumex crispus, and Plantago lanceolata) were grown at two levels of fertilization with full competition, aboveground competition only, belowground competition only, or neither above‐ nor belowground competition. Competition was measured as competitive response, which is the natural log of the relative biomass of a target plant grown with competition compared to growth without competition. In contrast to predictions from current models of productivity‐competition relationships, but in agreement with other experimental studies, there was no change in the strengths or root, shoot, or total competition with a modest increase in productivity. Despite no effect of fertilization on the strength of competition, the form of interaction between root and shoot competition varied both as a function of species identity and fertilization. For both of the rosette forming species, the combined effects of root and shoot competition were less than predicted assuming no interaction (a “negative interaction”), with one species switching from a negative to an additive interaction with fertilization. The fact that fertilization caused a shift in the root‐shoot interaction, but not in the total strength of root and shoot competition, suggests that the root‐shoot interaction is itself a highly labile variable. If root‐shoot interactions are common in natural systems, then simply measuring the strength of one form of competition in no way provides any information about the overall importance of that competitive form to plant growth.     

Interspecific Resource Competition Effects on Fisheries Revenue

In many fisheries multiple species are simultaneously caught while stock assessments and fishing quota are defined at species level. Yet species caught together often share habitat and resources, resulting in interspecific resource competition. The consequences of resource competition on population dynamics and revenue of simultaneously harvested species has received little attention due to the historical single stock approach in fisheries management. Here we present the results of a modelling study on the interaction between resource competition of sole (Solea solea) and slaice (Pleuronectus platessa) and simultaneous harvesting of these species, using a stage-structured population model. Three resources were included of which one is shared with a varied competition intensity. We find that plaice is the better competitor of the two species and adult plaice are more abundant than adult sole. When competition is high sole population biomass increases with increasing fishing effort prior to plaice extinction. As a result of this increase in the sole population, the revenue of the stocks combined as function of effort becomes bimodal with increasing resource competition. When considering a single stock quota for sole, its recovery with increasing effort may result in even more fishing effort that would drive the plaice population to extinction. When sole and plaice compete for resources the highest revenue is obtained at effort levels at which plaice is extinct. Ignoring resource competition promotes overfishing due to increasing stock of one species prior to extinction of the other species. Consequently, efforts to mitigate the decline in one species will not be effective if increased stock in the other species leads to increased quota. If a species is to be protected against extinction, management should not only be directed at this one species, but all species that compete with it for resource as well.     

病原体感染对物种间资源竞争的影响——基于资源竞争理论

病原体感染对种间竞争的影响可能是因为改变了宿主的资源利用过程,然而竞争模型（Lotka-Volterra）由于参数化竞争系数而忽略了资源的动态变化过程,因此基于此类模型的研究无法揭示病原体对宿主资源利用的影响。基于Tilman的资源竞争理论构建了病原体感染一个物种的资源竞争模型,通过分析宿主物种资源利用效率的变化探讨了病原体对种间竞争的影响。结果表明：（1）病原体降低了宿主对资源的消耗率（消费矢量变短）,抬高了对资源的最低需求（零等倾线上移）,这意味着宿主的竞争力减弱;（2）虽然感染影响了竞争物种的密度,但不会改变共存物种的共存状态;（3）病原体可以使宿主物种的竞争对手更容易入侵,形成共存局面,极大地扩大了竞争物种共存的参数范围,本质上促进了物种多样性维持;（4）病原体的传播率和毒性也复杂地影响了竞争物种共存,传播率越大越能促进物种共存,而中等强度毒性最能促进物种共存。研究结果明确了病原体对物种资源利用模式的潜在改变,强调了病原体在物种共存和生物多样性维持中的重要性。     

Why allometric scaling enhances stability in food web models

It has recently been shown that the incorporation of allometric scaling into the dynamic equations of food web models enhances network stability if predators are assigned a higher body mass than their prey. We investigate the underlying mechanisms leading to this stability increase. The dynamic equations can be written such that allometric scaling influences these equations at three places: the time scales of predator and prey dynamics become separated, the energy outflow to the predators is decreased, and intraspecific competition is increased relative to metabolic rates. For five food web topologies and various network sizes (i.e., species richness), we study the effect of each of these modifications on the percentage of surviving species separately and find that the decreased interaction strengths and the increased intraspecific competition are responsible for the enhanced stability. We also investigate the range of parameter values for which an enhanced stability is observed.     

Growth of mixed cultures on mixtures of substitutable substrates: the operating diagram for a structured model

The growth of mixed microbial cultures on mixtures of substrates is a problem of fundamental biological interest. In the last two decades, several unstructured models of mixed-substrate growth have been studied. It is well known, however, that the growth patterns in mixed-substrate environments are dictated by the enzymes that catalyse the transport of substrates into the cell. We have shown previously that a model taking due account of transport enzymes captures and explains all the observed patterns of growth of a single species on two substitutable substrates (J. Theor. Biol. 190 (1998) 241). Here, we extend the model to study the steady states of growth of two species on two substitutable substrates. The model is analysed to determine the conditions for existence and stability of the various steady states. Simulations are performed to determine the flow rates and feed concentrations at which both species coexist. We show that if the interaction between the two species is purely competitive, then at any given flow rate, coexistence is possible only if the ratio of the two feed concentrations lies within a certain interval; excessive supply of either one of the two substrates leads to annihilation of one of the species. This result simplifies the construction of the operating diagram for purely competing species. This is because the two-dimensional surface that bounds the flow rates and feed concentrations at which both species coexist has a particularly simple geometry: It is completely determined by only two coordinates, the flow rate and the ratio of the two feed concentrations. We also study commensalistic interactions between the two species by assuming that one of the species excretes a product that can support the growth of the other species. We show that such interactions enhance the coexistence region.     

Large species shifts triggered by small forces

Changes in species composition of communities seem to proceed gradually at first sight, but remarkably rapid shifts are known to occur. Although disrupting disturbances seem an obvious explanation for such shifts, evidence for large disturbances is not always apparent. Here we show that complex communities tend to move through occasional catastrophic shifts in response to gradual environmental change or evolution. This tendency is caused by multiple attractors that may exist in such systems. We show that alternative attractors arise robustly in randomly generated multispecies models, especially if competition is symmetrical and if interspecific competition is allowed to exceed intraspecific competition. Inclusion of predators as a second trophic level did not alter the results greatly, although it reduced the probability of alternative attractors somewhat. These results suggest that alternative attractors may commonly arise from interactions between large numbers of species. Consequently, the response of complex communities to environmental change is expected to be characterized by hysteresis and sudden shifts. Some unexplained regime shifts observed in ecosystems could be related to alternative attractors arising from complex species interactions. Additionally, our results support the idea that ancient mass extinctions may partly be due to an intrinsic loss of stability of species configurations.     

The evolution of traits affecting resource acquisition and predator vulnerability: character displacement under real and apparent competition

This article investigates some simple models of the evolutionary interaction between two prey species that share a common resource and a common predator. Each prey species is characterized by a trait that determines both the rate of resource capture and vulnerability to a predator. In a simple model of a three-species food chain, such traits usually increase in response to an imposed reduction in resource density. When the per capita growth rates of each of two prey species depend linearly on resource density, such traits will change in opposite directions when the two prey come into sympatry. In addition, the ratio of the effect of the predator on prey fitness to the effect of the resource on prey fitness will diverge from the corresponding ratio in a second prey species when those species coexist in sympatry. These simple predictions need not hold under several alternative assumptions, which may be more common in biological systems. Parallel changes in sympatry may occur if the relationship between resource consumption and prey growth is nonlinear, if the prey species have partial overlap in the set of resources used or in the set of predators that consume them, or if prey experience direct intraspecific competition. The responses to a second prey can also differ significantly from those predicted by the simplest model if separate traits affect vulnerability to predators and resource acquisition rate. It is important to determine whether examples of character displacement previously interpreted as responses to competition for resources might also reflect responses to altered predation risks in sympatry.