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.     

Convergence to stationary distributions in two-species stochastic competition models

Two sets of sufficient conditions are given for convergence to stationary distributions, for some general models of two species competing in a randomly varying environment. The models are nonlinear stochastic difference equations which define Markov chains. One set of sufficient conditions involves strong continuity and -irreducibility of the transition probability for the chain. The second set has a much weaker irreducibility condition, but is only applicable to monotonic models. The results are applied to a stochastic two-species Ricker model, and to Chesson's lottery model with vacant space, to illustrate how the assumptions can be checked in specific models.     

Epidemics with general generation interval distributions

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her “age” of infection. We focus first on early outbreak stages when stochastic effects dominate and show that epidemics tend to happen faster than deterministic calculations predict. If an outbreak is sufficiently large, stochastic effects are negligible and we modify the standard ordinary differential equation (ODE) model to accommodate age-of-infection effects. We avoid the use of partial differential equations which typically appear in related models. We introduce a “memoryless” ODE system which approximates the true solutions. Finally, we analyze the transition from the stochastic to the deterministic phase.     

Effects of competition and shading in planktonic communities

A model for several algal species which compete both for light and for nutrients, and which are also subject to settling and diffusion, is considered. The settling speeds and diffusion coefficients are assumed to be small, in a sense to be made precise later, and a singular perturbation argument is used. In certain cases vertical segregation of the algal species is observed, and the mechanism for this is interpreted biologically.Supported by the Danish Natural Science Research Council (Grant No. 11-8321)     

Two species competition in a periodic environment

The classical Lotka-Volterra equations for two competing species have constant coefficients. In this paper these equations are studied under the assumption that the coefficients are periodic functions of a common period. As a generalization of the existence theory for equilibria in the constant coefficient case, it is shown that there exists a branch of positive periodic solutions which connects (i.e. bifurcates from) the two nontrivial periodic solutions lying on the coordinate axes. This branch exists for a finite interval or spectrum of bifurcation parameter values (the bifurcation parameter being the average of the net inherent growth rate of one species). The stability of these periodic solutions is studied and is related to the theory of competitive exclusion. A specific example of independent ecological interest is examined by means of which it is shown under what circumstances two species, which could not coexist in a constant environment, can coexist in a limit cycle fashion when subjected to suitable periodic harvesting or removal rates.Research supported by National Science Foundation Grant No. MCS-7901307     

Hierarchical models of intra-specific competition: scramble versus contest

Hierarchical structured models for scramble and contest intraspecific competition are derived. The dynamical consequences of the two modes of competition are studied under the assumption that both populations divide up the same amount of a limiting resource at equal population levels. A comparison of equilibrium levels and their resiliences is made in order to determine which mode of competition is more advantageous. It is found that the concavity of the resource uptake rate is an important determining factor. Under certain circumstances contest competition is more advantageous for a population while under other circumstances scramble competition is more advantageous.Supported by NSF grant DMS-9306271     

Population dynamics and competition in chemostat models with adaptive nutrient uptake

 The standard Monod model for microbial population dynamics in the chemostat is modified to take into consideration that cells can adapt to the change of nutrient concentration in the chemostat by switching between fast and slow nutrient uptake and growing modes with asymmetric thresholds for transition from one mode to another. This is a generalization of a modified Monod model which considers adaptation by transition between active growing and quiescent cells. Global analysis of the model equations is obtained using the theory of asymptotically autonomous systems. Transient oscillatory population density and hysteresis growth pattern observed experimentally, which do not occur for the standard Monod model, can be explained by such adaptive mechanism of the cells. Competition between two species that can switch between fast and slow nutrient uptake and growing modes is also considered. It is shown that generically there is no coexistence steady state, and only one steady state, corresponding to the survival of at most one species in the chemostat, is a local attractor. Numerical simulations reproduce the qualitative feature of some experimental data which show that the population density of the winning species approaches a positive steady state via transient oscillations while that of the losing species approaches the zero steady state monotonically. Received 4 August 1995; received in revised form 15 December 1995     

Size bias in traditional analyses of substitutive competition experiments

Summary The objective of this study was to examine the claim that traditional measures of competitive performance in substitutive experiments are biased towards larger plants. Results from a three-year diallele experiment of 6 marsh plant species were analyzed using both Relative Yields (a traditional analysis) and the Relative Efficiency Index (a recently proposed analysis presumed to be size-independent). In adddition, a mechanistic model of competition was used to explore the behavior of both methods of estimating competitive performance.Results from the three-year experiment showed that Relative Yields (RYs) were correlated with the initial sizes of plants for the first two years but not the third. By the third year, RYs were highly correlated with Relative Efficiency Index values (REIs) suggesting that the effects of initial size were eventually overcome. Model results showed that RYs are inherently biased in favor of larger plants during the early phases of competition while REIs are not. Further, model analysis confirmed that the size bias associated with RYs declines with increasing duration of the experiment. It is concluded that current generalizations about the relationship between plant size and competitive ability may be biased by the procedures used to analyze competition experiments.     

Some implications of a first-order model of inter-plant competition for the means and variances of complex mixtures

Summary Factorial models commonly used in the analysis of overall and component yields of binary mixtures of genotypes are generalised to include mixtures of any number of components (size, m) and the form of an analysis of variance for fitting such a model to tertiary mixtures is outlined. Such a model contains main effects and interactions up to the mth order, and is specific to the size of mixture so that no equivalence necessarily exists between similar parameter sets for different sized mixtures. Monocultures can be regarded as a special case of the general model.A simple model of intra-and inter-component competition is defined which assumes that plants do not interact in their competitive effects on others, a condition which is equivalent to an absence of second and higher order interactions in statistical analyses of mixtures of any size. Simple scaling tests involving the yields of components or whole mixtures of different sizes can also be used to test the adequacy of the model. This competition model least to a linear relationship between the mean yield of a mixture and the reciprocal of the number of components it contains, and thus allows the prediction of means and other statistical parameters for mixtures of one size from those of others.     

Changes in pain perception and hormones pre- and post-kumdo competition

The psychological stress of competition is a powerful stimulus affecting numerous hormones, which in turn change how pain is perceived. This study investigated whether a kumdo (kendo) team competition may be related to changes in hormones and pain. Seventeen healthy male kumdo practitioners participated in this experiment. Pain experiments were conducted by applying noxious stimuli with a thermal stimulator 10 min before a kumdo competition and 30 min post-competition. Serum testosterone, cortisol, beta-endorphin levels, pain thresholds, pain ratings at 48 °C and during blood sampling (sampling pain), anxiety, blood pressure, and heart rate were measured pre- and post-competition. Anxiety, pain threshold, testosterone/cortisol ratio, and blood pressure were significantly higher pre-competition compared to post-competition, while cortisol and pain ratings were significantly lower pre-competition than post-competition. There were significant correlations between the number of previous competitions and testosterone levels both pre-competition and post-competition. In pre-competition measurements, sampling pain increased with an increase in systolic blood pressure, heart rate, and beta-endorphins, and a decrease in age. In post-competition measurements, sampling pain increased with an increase in diastolic blood pressure and a decrease in testosterone levels. These results indicate that severe psychological pre-competition stress was associated with reduced pain ratings, perhaps in order to improve athletic performance. This also suggests that competitors may be at risk of potential injury due to changes in pain perception, and careful consideration should be taken to avoid potential injury before and during competition.     

Seasonal dynamics and interspecific competition in Oneida Lake Daphnia

I investigated the population dynamics and competitive interactions of two species of the suspension-feeding crustacean Daphnia in Oneida Lake, N.Y. Both species have persisted in the lake for decades, but their water-column densities are negatively correlated. The larger Daphnia pulicaria dominates in some years, the smaller D. galeata mendotae in others, and in some years one species replaces the other seasonally. Although this pattern results in part from annual variation in vertebrate predation pressure, predation alone cannot explain the irregular daphnid dynamics. In 1992–1995, I examined the water-column abundances, birth and death rates of both species. D. pulicaria dominated in two years, D. galeata mendotae was replaced by D. pulicaria in one year and in 1994, both species persisted in low numbers. To test the effect of temporal changes on the strength of intra- and interspecific competition on both juvenile and adult daphnids, I manipulated a series of field enclosures in 1994 and 1995. The outcome of competition varied within and between years, and its effects were most evident at the highest densities and lowest resource levels. For adults of both species, the effects of interspecific competition were detected more often than those of intraspecific competition. Lipid reserves (a metric of fitness) among juveniles were generally low, with those of D. galeata mendotae often being less than those of D. pulicaria. Contrary to the results of other studies examining competition in daphnids, spatial segregation and predictable within-year reversals in competitive dominance most likely do not play a large role in fostering coexistence of the Oneida Lake daphnids. Instead, coexistence of these competitors is promoted by interannual variation and long-lived diapausing eggs. Received: 20 July 1997 / Accepted: 21 November 1997     

Global analysis of a model of plasmid-bearing,plasmid-free competition in a chemostat

A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat was proposed in a paper of Stephanopoulis and Lapidus. The model was in the form of a system of nonlinear ordinary differential equations. Such models are relevant to commercial production by genetically altered organisms in continuous culture. The analysis there was local (using index arguments). This paper provides a mathematically rigorous analysis of the global asymptotic behavior of the governing equations in the case of uninhibited specific growth rate.Research supported by the National Council of Science, Republic of ChinaResearch supported by National Science Foundation Grant, DMS-9204490Research supported by the Natural Science and Engineering Council of Canada. This author's contribution was made while on research leave visiting the Department of Ecology and Evolutionary Biology at Princeton University. She would especially like to thank Simon Levin for his guidance as well as for providing an exceptional working environment     

Aggregation pattern of individuals and the outcomes of competition within and between species: Differential equation models

The influence of spatial distribution pattern on the outcomes of intra- and interspecific competition is studied theoretically. The models developed are the generalized logistic andVolterra equations, whereLloyd 's indices of intra- and interspecies mean crowding were incorporated with their assumed linear relationship to mean density in order to express the intensity of crowding which is really effective to the existing individuals. It is shown that while the increasing patchiness of distribution has a pronounced effect of promoting the intraspecific competition and lowering the equilibrium density for individual populations, it generally relaxes the interspecific competition, making it easy for different species sharing the same niche, which would otherwise be incompatible, to coexist stably. These models thus provide a simplest theoretical basis to explain why many insect populations in nature are kept relatively rare in number and why a number of allied species often coexist freely sharing the same resource, against the “competitive exclusion principle” deduced from the originalVolterra equations.     

On a resource based ecological competition model with interference

A resource based ecological competition model with interference is proposed. The model is based on Lotka-Volterra dynamics with two predators competing for a single, limited prey. Interference effects are considered in this article. When the interference coefficient, expressing the damage effect from its rival, is small, the mathematical analysis shows that the winner in purely exploitative competition still outcompetes its rival. However, if the interference coefficient is large enough then the competition outcome will depend on initial population of predator species.     

Invasibility and stochastic boundedness in monotonic competition models

We give necessary and sufficient conditions for stochastically bounded coexistence in a class of models for two species competing in a randomly varying environment. Coexistence is implied by mutual invasibility, as conjectured by Turelli. In the absence of invasibility, a species converges to extinction with large probability if its initial population is small, and extinction of one species must occur with probability one regardless of the initial population sizes. These results are applied to a general symmetric competition model to find conditions under which environmental fluctuations imply coexistence or competitive exclusion.     

Parasite-mediated competition in Anolis lizards

Summary On many small Caribbean islands, two species of Anolis lizard coexist, but the two are typically very different in body size. The two Anolis of St. Maarten, however, are exceptional because they are similar in size and are known to be strongly competitive. One species, A. gingivinus, appears the stronger competitor and occurs throughout the island; the other, A. wattsi, is found only in the central hills. The malarial parasite Plasmodium azurophilum very rarely infects A. wattsi, but in some locations is very common in A. gingivinus. Wherever malaria infects A. gingivinus, A. wattsi is present, but wherever malaria is absent, only A. gingivinus occurs. This pattern of coincidence of malaria and coexistence of both Anolis is observed over distances of only a few hundred meters. The parasite infects both red and white blood cells of A. gingivinus and causes important pathology: immature erthrocytes increase in abundance, blood hemoglobin decreases, monocytes and neutrophils increase, and infected white cells are less likely to produce acid phosphatase. These results argue that malaria mediates competition between the two species and determines the present distribution of the lizards on St. Maarten. This kind of parasite-mediated competition could be common if susceptibility to parasitic infection varies among competitors. The distribution of malaria in the Anolis of Caribbean islands suggests this parasite can play an important role in Anolis community ecology.     

Interspecific competition between two field populations of grass-feeding bugs

Abstract. 1. We tested the hypothesis that interspecific competition between two grass-feeding stenodemine bug species ( Notostira elongata Geoffroy and Megaloceraeu recticornis Geoffroy) was capable of causing population-scale mortality in the field.
2. N.elongata nymphs were added to two field enclosures in which the M.recti-cornis population was to hatch. In one of these enclosures the grass Arrhena-therum elatius L., on which only M.recticornis can feed, was also added. Population changes of the bug species were then monitored. An unmanipulated enclosure and an unfenced plot of grassland were used as controls.
3. The results demonstrated that N.elongata lowered the survival of M.recticornis and that this effect was removed by the addition of A.elatius . The results also suggested that N.elongata suffered less from the effects of competition with M.recticornis when the latter had access to the refuge foodplant.
4. Interspecific competition was rare among members of the grass-feeding stenodemine guild in the area studied. Only one out of fifteen possible pairs competed, and this competition occurred only under special circumstances.     

Nearest-neighbour analysis and the prevelance of woody plant competition in South African savannas

Inter- and intra-specific competition has long been regarded as asignificant determinant of the structure and function of woody plantcommunitiesin African savannas. The most widely used approach to detect the presence orabsence of competition has been the use of nearest-neighbour methods. Althoughseveral studies have been published reporting the presence of competition inAcacia dominated communities, less than 20 plots have beensampled across all these studies. Results from broad-leaved communities arevariable, and also based on a small sample number. Consequently, this studysought to assess the prevalence of competition from a large number of savannasites (45), and to identify abiotic and biotic factors characterising siteswithcompetition relative to those without. Using the nearest-neighbour method onlyfour sites (9.3%) indicated the presence of inter-specific competition; twowereAcacia dominated communities (18.2% ofAcacia sites) and two were broad-leaved communities(7.7%).These four sites had a significantly higher mean annual rainfall and fewerwoodyspecies than sites without inter-specific competition. There were alsosignificant relationships between the inter-specific competition index and thedominance index and the number of species at a site. In terms of intra-specificcompetition only ten of the 31 sites tested revealed a significant correlationbetween nearest-neighbour distance and summed canopy volume of the twoneighbours. Seven were for Acacia species (55.6% of theAcacia species comparisons) and three were forbroad-leavedspecies (21.4% of the broad-leaved species comparisons). Sites lacking evidenceof intra-specific competition were at a significantly lower slope position andhad a smaller proportion of small stems. The lower prevalence of competition inSouth African savannas detected in this study using the same method as previousstudies is discussed, and the appropriateness of nearest-neighbour analysis isexamined.