Global stability in consumer-resource cascades

 Models of population growth in consumer-resource cascades (serially arranged containers with a dynamic consumer population, v, receiving a flow of resource, u, from the previous container) with a functional response of the form h(u/v ^b ) are investigated. For b∈[0, 1], it is shown that these models have a globally stable equilibrium. As a result, two conclusions can be drawn: (1) Consumer density dependence in the functional or in the per-capita numerical response can result in persistence of the consumer population in all containers. (2) In the absence of consumer density dependence, the consumer goes extinct in all containers except possibly the first. Several variations of this model are discussed including replacing discrete containers by a spatial continuum and introducing a dynamic resource. Received 25 February 1995 / received in revised form 27 July 1995     

Can R*s Predict Invasion in Semi-arid Grasslands?

We estimated R*s and tested the applicability of R* theory on nonindigenous plant invasions in semi-arid rangeland. R* is the concentration of a resource that a species requires to survive in a habitat. R* theory predicts that a species with a lower R* for the most limiting resource will competitively displace a species with a higher R* under equilibrium conditions. In a greenhouse, annual sunflower (Helianthus annuus L.), bluebunch wheatgrass (Agropyron spicatum Pursh), and spotted knapweed (Centaurea maculosa Lam.) were grown in monoculture and 2- and 3-species mixtures for three growth periods in an attempt to reduce soil NO₃-N concentrations below each species’ R*. At the end of each growth period, aboveground biomass by species and soil plant available nitrogen were sampled. Decreasing biomass coupled with decreasing soil plant available nitrogen was used to quantify R*s for the three species. R*s for annual sunflower, bluebunch wheatgrass, and spotted knapweed were estimated to be 0.6±0.16 ppm NO₃⁻, less than 0.05 ppm NO₃⁻, and 0.6±0.13 ppm NO₃⁻, respectively. Estimated R*s did not predict the outcome of competition among species. To successfully predict plant community dynamics on semi-arid rangeland with and without the presence of a nonindigenous invasive species, a more comprehensive model that includes mechanisms in addition to competition may have to be considered. We speculate that R* theory may prove most useful for predicting the outcome of competition within functional groups.     

Competition intensity as a function of resource availability in a semiarid ecosystem

Two field experiments were conducted using three dominant perennial species of the Chihuahuan Desert: Hilaria mutica (a tussock grass), Larrea tridentata (a microphyllous shrub) and Opuntia rastrera (a flat-stemmed succulent cactus). Two hypotheses concerning competition in arid plant communities were tested. (1) Marked resource partitioning with no interspecific competition could be expected since the three species belong to different life-forms, and that plant growth in deserts is basically limited by harsh environmental conditions. (2) Alternatively, resource scarcity (particularly water) will result in strong plant competition. In a 1-year removal experiment, water status and plant growth of the three species were monitored in twelve 10 m × 10 m plots randomized in three blocks and assigned to the following treatments: (a) removal of all species, except H. mutica; (b) removal of all species, except L. tridentata; (c) removal of all species, except O. rastrera, and (d) control without any manipulation. In a watering experiment, under two neighbourhood conditions (growing isolated or in associations of plants of the three species in plots of 20 m²), the water status of the three species and the growth of H.mutica and L.tridentata were studied for 32 days after an irrigation equivalent to 30 mm of rain, similar to a strong storm event at the site. In the removal experiment, where plants were free to capture water, no evidence of competition was observed. However, during the watering experiment, in which water was forced into the soil, competitive effects were observed. Associated individuals of L. tridentata had lower xylem water potentials and osmotic potentials (OPs) and produced shorter twigs and less leaves and nodes. Although less pronounced, neighbours also had a negative effect on the OP in O. rastrera. According to these results, the intensity of the interspecific competition for water seems to depend on the level of resource availability in the soil. Thus, the validity of the two hypotheses tested in this study also depends on the level of resources. Competition could be absent or very low in years of low precipitation, as in the year of this study (173 mm against a 25-year average of 264 mm). However, when soil water availability is high, e.g. following heavy rain, the negative interactions between species could be more intense. Received: 3 October 1997 / Accepted: 23 March 1998     

A graphical method for analysing the dynamics of three-species systems

We report a series of experiments with three competing species and a novel graphical analysis that explores the dynamics of this simple multi-species system. The three competing species (Drosophila hydei, D. immigrans and D. virilis) were maintained in five very large cages, on a natural fruit resource. The analytic method involved constructing a “dynamic surface”, by interpolation, from the population trajectories. Within the dynamic surface constructed from the five experiments a small “equilibrium area” (an area of point vectors) could be identified. The implications of both the method and the results are discussed. Received: 22 July 1996 / Accepted: 29 April 1997     

Dynamics of biomass partitioning in two competing meadow plant species

The optimal allocation theory predicts that growth is allocated between the shoot and the roots so that the uptake of the most limiting resource is increased. Allocation is dynamic due to resource depletion, interaction with competitors, and the allometry of growth. We assessed the effects of intra- and inter-specific competition on growth and resource allocation of the meadow species Ranunculus acris and Agrostis capillaris, grown in environments with high (+) or low (−) availability of light (L) and nutrients (N). We took samples twice a week over the 7 weeks experiment, to follow the changes in root-to-shoot ratios in plants of different sizes, and carried out a larger scale harvest at the end of the experiment. Of all the tested factors, availability of nutrients had the largest effect on the growth rate and shoot-to-root allocation in both species, although both competition and light had significant effects as well. The highest root-to-shoot ratios were measured from the L+N− treatment, and the lowest from the L−N+ treatment, as predicted by the optimal allocation theory. Competition changed resource allocation, but not always toward acquiring the resource that is most limiting to growth. We thus conclude that the greatest variation in shoot-to-root allocation was due to the resource availability and the effects of competition were small, probably due to low density of plants in the experiment.     

Structure and function of a non-interactive, reactive insect-plant system

Rhagoletis alternata is a common tephritid fly in central Europe, whose larvae feed on the hypanthium of rose hips. The resource-consumer system is “non-interactive”, i.e. the insect has little or no impact on host plant fitness and therefore is not able to influence the rate at which larval food resources are renewed. The system is “reactive”, since fluctuations in the carrying capacity (hip density) of the host plant are important for determining year-to-year fluctuations in the insect's population size. Insect fluctuations exceed those of its carrying capacity. The insect's efficient exploitation strategy, maximizing its fitness at high as well as low resource supply, must be attributed to the variable and unpredictable relationship between resource availability and consumer density. The only regulatory mechanism is contest competition when larval densities exceed the carrying capacity. Due to the low impact of the insect, its exploitation strategy is apparently not opposed by mechanisms selecting for defence in the host plant. This lack of defence and the efficient exploitation strategy may be important factors for the frequently observed high degree of the resource utilization by the insect. Received: 3 November 1997 / Accepted: 22 January 1998     

Bacterial Competition in Activated Sludge: Theoretical Analysis of Varying Solids Retention Times on Diversity

A mechanistic model for activated sludge sewage treatment was developed to predict exploitative competition of six aerobic heterotrophic bacterial species competing for three essential resources. The central hypothesis of the model is that in a multispecies/limiting resource system the number of coexisting bacterial species, N, exceeds the number of limiting resources, K, available for them. The explanation for this is that for certain species combinations, the dynamics of the competition process generate oscillations in the abundances of species, and these oscillations allow the coexistence of greater number of species than the number of limiting resources (N > K). This result is a direct contradiction of an existing activated sludge steady state competition theory, the principle of competitive exclusion, which states that the competition process proceeds to equilibrium, allowing only N K species to coexist. The model was used to investigate the effect of varying solids retention times on the diversity of species using the conventional, completely mixed activated sludge configuration. The results of model simulations showed that for a certain range of solids retention times (2.28–5.66 days) the competition of six species for three essential resources produces oscillations within the structure of the bacterial community allowing for the sustained growth of more than three species on three resources.This revised version was published online in November 2004 with corrections to Volume 48.     

Body size and species coexistence in consumer–resource interactions: A comparison of two alternative theoretical frameworks

Species coexistence involving trophic interactions has been investigated under two theoretical frameworks—partitioning shared resources and accessing exclusive resources. The influence of body size on coexistence is well studied under the exclusive resources framework, but has received less attention under the shared-resources framework. We investigate body-size-dependent allometric extensions of a classical MacArthur-type model where two consumers compete for two shared resources. The equilibrium coexistence criteria are compared against the general predictions of the alternative framework over exclusive resources. From the asymmetry in body size allometry of resource encounter versus demand our model shows, counterintuitively, and contrary to the exclusive resource framework, that a smaller consumer should be competitively superior across a wide range of supplies of the two resource types. Experimental studies are reviewed to resolve this difference among the two frameworks that arise from their respective assumptions over resource distribution. Another prediction is that the smaller consumer may have relatively stronger control over equilibrium resource abundance, and the loss of smaller consumers from a community may induce relatively stronger trophic cascades. Finally, from satiating consumers’ functional response, our model predicts that greater difference among resource sizes can allow a broader range of consumer body sizes to coexist, and this is consistent with the predictions of the alternative framework over exclusive resources. Overall, this analysis provides an objective comparison of the two alternative approaches to understand species coexistence that have heretofore developed in relative isolation. It advances classical consumer–resource theory to show how body size can be an important factor in resource competition and coexistence.     

Interspecific competition and coexistence of the two chrysomelids,Gastrophysa atrocyanea motschulsky andGalerucella vittaticollis baly (Coleoptera: Chrysomelidae), under limited food resource conditions

Field experiments were conducted in order to investigate the mode of exploitation of food resources and the mechanism of coexistence of mixed larval populations of the two chrysomelids,Gastrophysa atrocyanea andGalerucella vittaticollis, under limited food resource conditions. The larval survival rates seemed high enough to assure coexistence when hatchlings of the two species were released in 1∶1 and 1∶3 ratios on a host plant. However, the survival rate became almost nil for both species when a 3∶1 ratio was employed, suggesting asymmetrical interspecific competition. Wasted food consumption was much higher inG. atrocyanea larvae. The population ofG. atrocyanea seemed to be regulated more by intraspecific competition, while on the other hand, the population ofG. vittaticollis was considered to be more likely affected by the interspecific competition withG. atrocyanea, depending on the initial ratio and density of the two species.     

Interspecific interactions and co-existence in dabbling ducks: observations and an experiment

We studied the possible role of resource limitation and interspecific competition in assemblages of dabbling ducks on breeding lakes in Finland and Sweden with observational and experimental data. After initial vegetation mapping and yearly censuses of ducks in 1985–1990, we collected observational data in 1991–1994 from 28 lakes with natural populations of mallard Anas platyrhynchos and teal A. crecca. Mallard and teal co-occur over vast areas in the Holarctic and they are the only breeding dabbling ducks on many oligotrophic lakes. Both species are migratory in our study regions, teal arriving later in spring than mallards. Log-linear model analysis of observational presence/absence data revealed a positive, not a negative, association between the species. This association was independent of habitat diversity as well as of lake size. Mallard-teal interaction was also studied in a cross-over introduction experiment in 32 other lakes in two years. Wing-clipped mallards were introduced to breeding lakes before the arrival of teal to induce resource limitation and interspecific competition, hypothesized to reduce lake use by teal. The density of mallard pairs on experimental lakes was 2.9–8.0 times higher than on controls, but there was no negative response by teal to the treatment. This is the first combined observational-experimental demonstration of lack of interspecific competition in waterfowl. Our results indicate that heterospecific attraction may affect species co-existence in dabbling ducks. Received: 28 October 1996 / Accepted: 13 January 1997     

Evolution of species trait through resource competition

To understand the evolution of diverse species, theoretical studies using a Lotka–Volterra type direct competition model had shown that concentrated distributions of species in continuous trait space often occurs. However, a more mechanistic approach is preferred because the competitive interaction of species usually occurs not directly but through competition for resource. We consider a chemostat-type model where species consume resource that are constantly supplied. Continuous traits in both consumer species and resource are incorporated. Consumers utilize resource whose trait values are similar with their own. We show that, even when resource-supply has a continuous distribution in trait space, a positive continuous distribution of consumer trait is impossible. Self-organized generation of distinct species occurs. We also prove global convergence to the evolutionarily stable distribution.     

Does competition between resources change the competition between their consumers to mutualism? Variations on two themes by Vandermeer

How does competition between resources affect the interaction between consumer species that share those resources? Existing theory suggests that high resource competition can lead to mutualism. However, this is based on an analysis that need only apply near equilibrium, and experimental demonstrations of such mutualism are rare. Two alternative approaches to measuring food web mutualism are examined here. These are based on the population-level effects of adding or removing a consumer species or on the amount of additional mortality that can be applied to one consumer without excluding it. Both measures suggest that mutualism is likely to be confined to two situations: when overlap in resource use by the consumers is very low and when the consumers are inefficient users of their resources. Competition between resources is also likely to increase the occurrence and magnitude of "hypercompetition" between consumers, where the reduction in population size caused by the introduced consumer is greater than that caused by a consumer that is identical to the resident species. Competition between resources can also increase the negative interaction between consumers by destabilizing the dynamics of the system. Such destabilization can cause negative indirect interactions between specialist consumers having no overlap in resource use.     

Aggressive foraging of social bees as a mechanism of floral resource partitioning in an Asian tropical rainforest

Interference competition by aggressive foraging often explains resource partitioning, but mechanisms contributing to partitioning have rarely been studied in Asian social bee guilds. Foraging of social bees at canopy flowers of Santiria laevigata (Burseraceae) and honey-water feeders was studied in a lowland mixed-dipterocarp forest in Sarawak, Malaysia. Four stingless bee species (Apidae, Meliponinae), Trigona canifrons, T.␣fimbriata, T. apicalis and T. melina, aggressively defended flower patches and feeders. At the flowers, T.␣canifrons excluded other bees only in the morning when nectar flow peaked. At the feeders, the aggression resulted in asymmetric interference competition, which produced a dominance hierarchy among seven social bee species. Interspecific partitioning of the feeders was detected in time and height but not quality. Only time of the first arrival after feeder presentation was negatively correlated with the dominance hierarchy: more aggressive species arrived at the feeders later than less aggressive species. This result suggests that a trade-off between searching ability and defensive ability at flower patches gives rise to resource partitioning in the social bee guild. Received: 22 June 1996 / Accepted: 22 November 1996     

Competition hierarchy and plant defense in a guild of ants on tropical Passiflora

In facultative ant–plant interactions, ants may compete with each other for food provided by extrafloral nectar (EFN) plants. We studied resource competition and plant defense in a guild of ants that use the same EFN resource provided by two species of Passiflora in a seasonal rain forest in tropical China. At least 22 ant species were recorded using the EFN resource, although some of those species were rare. Among these ants, Paratrechina sp.1 and Dolichoderus thoracicus were more aggressive than other species. Ant aggressiveness measured as ant behavioral dominance index (BDI) was positively correlated with ant abundance on the Passiflora species studied. Ant BDI was also positively correlated to the protection that ants provided against herbivory. In Passiflora siamica, the number of workers patrolling on the plants did negatively correlate with average leaf loss per plant. We conclude that in this facultative Passiflora–ant system, plant defense upon herbivore was indeed influenced by the total number of ants present on plant and the aggressiveness of these ants.     

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.     

Degeneracy-Driven Self-Structuring Dynamics in Selective Repertoires

Numerous biological interactions, such as interactions between T cell receptors or antibodies with antigens, interactions between enzymes and substrates, or interactions between predators and prey are often not strictly specific. In such less specific, or “sloppy,” systems, referred to here as degenerate systems, a given unit of a diverse resource (antigens, enzymatic substrates, prey) is at risk of being recognized and consumed by multiple consumers (lymphocytes, enzymes, predators). In this study, we model generalized degenerate consumer-resource systems of Lotka–Volterra and Verhulst types. In the degenerate systems of Lotka–Volterra, there is a continuum of types of consumer and resource based on variation of a single trait (characteristic, or preference). The consumers experience competition for a continuum of resource types. This non-local interaction system is modeled with partial differential-integral equations and shows spontaneous self-structuring of the consumer population that depends on the degree of interaction degeneracy between resource and consumer, but does not mirror the distribution of resource. We also show that the classical Verhulst (i.e. logistic) single population model can be generalized to a degenerate model, which shows qualitative behavior similar to that in the degenerate Lotka–Volterra model. These results provide better insight into the dynamics of selective systems in biology, suggesting that adaptation of degenerate repertoires is not a simple “mirroring” of the environment by the “fittest” elements of population.     

Interspecific displacement mechanisms by the invasive little fire ant <Emphasis Type="Italic">Wasmannia auropunctata</Emphasis>

Competition between invasive species and native ones in the new environment was found to be significant and to affect both animal and plant species. Invasive ants are notorious for displacing local ant species through competition. Competitive displacement of native species can occur through interference and or resource competition. However, for invasive ants, little is known about the relative importance of competitive displacement. We studied competitive interactions of the little fire ant, Wasmannia auropunctata, one of the most destructive invasive ant species, with two other ant species, Monomorium subopacum and Pheidole teneriffana. We compared the species’ foraging behavior and studied their aggressive interactions around food baits for the short (2 h) and long (21 days) term in the laboratory. Surprisingly we found that in short term experiments W. auropunctata had the poorest foraging abilities of the three species studied: it took the workers the longest to locate the bait and retrieve it; in addition they retrieved the lowest amount of food. When both W. auropunctata and M. subopacum were foraging the same bait, in the short term competition experiment, W. auropunctata workers did not defend the bait, and ceased foraging when encountered with competition. The long-term experiments revealed that W. auropunctata had the advantage in aggressive interactions over time; they eliminated seven of nine M. subopacum’s nests while consuming some of the workers and brood. According to our laboratory studies, W. auropunctata cannot be considered an extirpator species, unless it has a substantial numerical advantage, in contrast with previous assumptions. Otherwise it may behave as an insinuator species, i.e. the workers do not initiate aggression and by staying undetected they can continue foraging adjacent to dominant species.     

THE ECO‐EVOLUTIONARY RESPONSES OF A GENERALIST CONSUMER TO RESOURCE COMPETITION

This article explores the combined evolutionary and ecological responses of resource uptake abilities in a generalist consumer to exploitative competition for one resource using a simple 2‐resource model. It compares the sizes of ecologically and evolutionarily caused changes in population densities in cases where the original consumer has a strong or a weak trade‐off in its abilities to consume the two resources. The analysis also compares the responses of the original species to competition when the competitor's population size is or is not limited by the shared resource. Although divergence in resource use traits in the resident generalist consumer is expected under all scenarios when resources are substitutable, the changes in population densities of the resources and resident consumer frequently differ between scenarios. The population of the original consumer often decreases as a result of its own adaptive divergence, and this decrease is often much greater than the initial ecological decrease. If the evolving consumer has a strong trade‐off, the overlapped resource increases in equilibrium population density in response to being consumed by a generalist competitor. Some of these predictions differ qualitatively in alternative scenarios involving sustained variation in population densities or nutritionally essential resources.     

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.     

Competitive exclusion and persistence in models of resource and sexual competition

 We study a combined mathematical model of resource and sexual competition. The population dynamics in this model is analyzed through a coupled system of reaction-diffusion equations. It is shown that strong sexual competition and low birth rate lead to competitive exclusion of the biological species. If sexual competition is weak, then the persistence of the species is possible, depending on the initial density functions and the growth rates of the species. When sexual competition affects both species, persistence and competitive exclusion results are also obtained in terms of the ecological data in the model. Received 1 November 1995; received in revised form 13 January 1996