Visual competition

Binocular rivalry--the alternations in perception that occur when different images are presented to the two eyes--has been the subject of intensive investigation for more than 160 years. The psychophysical properties of binocular rivalry have been well described, but newer imaging and electrophysiological techniques have not resolved the issue of where in the brain rivalry occurs. The most recent evidence supports a view of rivalry as a series of processes, each of which is implemented by neural mechanisms at different levels of the visual hierarchy. Although unanswered questions remain, this view of rivalry might allow us to resolve some of the controversies and apparent contradictions that have emerged from its study.     

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.     

A model of competition

Summary The paper considers a model of competition, based upon the Lotka-Volterra equations, which explicitly considers the effect of density independent mortality upon the outcome of competition. The model's possible application to wild Drosophila species in Europe are considered.     

Mechanisms of sperm competition

Sperm competition occurs when two (or more) males inseminate a single female during a reproductive cycle, but what determines which one of them will fertilize her eggs? Is it simply a lottery, or are there some more complex rules by which matings are translated into offspring? Several studies covering various animal groups have shown that mating order effects are often important in determining paternity patterns: in animals as different as insects and birds, the sperm from the last male to mate often has precedence over previously introduced sperm. Recently, behavioural ecologists and physiologists have started to examine the mechanisms by which sperm precedence is achieved. The study of sperm competition mechanisms complements the more behavioural studies, and a combination of the two approaches used on single species should prove to be particularly rewarding.     

Epidemics in competition

When two or more epidemic agents are simultaneously present in a population, they may interact to increase or decrease each other's effectiveness. One form of interaction is competition where each agent confers immunity to the others. Such competition occurs, for example, between different strains of myxomatosis in rabbit populations. We consider some consequences of introducing competition into mathematical epidemic models. Both deterministic and stochastic simple epidemic models are examined. In either case the conclusions are similar: the faster spreading epidemic has a considerable advantage.     

Chaotic pairwise competition

We investigate a kind of competition possible in a system of at least three populations competing for the same limited resource. As a model we use generalised Volterra equations in which the growth rates and competition coefficients of populations depend on the number of members of all populations. Because of the nonconstant values of the last quantities the system could be repelled from the state of cyclic pairwise competition described by May and Leonard (SIAM J. Appl. Math. 29 (1975) 243.). We investigate the competition in a chaotic regime of evolution of the number of members of populations. We show that the nonconstant competition coefficients can lead to a regularisation of the time intervals of domination of each population and the non-constant growth rates can lead to decreasing length of the time intervals of domination as well as to chaotisation of the occurrence of these intervals. A quantity characterising the time intervals between the successive maxima of the number of the populations individuals is discussed. By means of the wavelet transform modulus maxima method we calculate the tau(q)-spectrum and the H?lder exponent for the time series of this quantity. The results of the theory are illustrated by an example of competition among the three main political parties in Bulgaria and we discuss qualitative aspects of the dynamics of change of preferences of voters.     

Estimating competition coefficients: strong competition among three species of frugivorous flies

Despite the abundance of studies on competitive interactions, relatively few experiments have been used to fit explicit competition models and estimate competition coefficients. Such estimates are valuable for making contact between theoretical and empirical studies, which tend to measure competition in different units. To quantify the strength of competitive interactions among the larvae of three species of frugivorous flies, I manipulated the densities of each species to investigate all three pairwise interactions. The densities of each species were changed independently (i.e., using a response surface experimental design), which allowed maximum likelihood estimation of the competition coefficients for each species, based on the Hassell and Comins competition model. The effects of competitor density on larval survival, time to emergence, and the weight of emerging adults were also analyzed to investigate the responses of individual species to density. The estimates of the competition coefficients suggest that the larvae of these flies experience strong asymmetric competition for resources, and raise questions as to how these species coexist. For each pair, one of the species was largely unaffected by interspecific competition, but decreased the performance of the other. Received: 8 February 1999 / Accepted: 5 April 1999     

The caries-attrition competition

Contradictory reports on the interreation of caries and attrition concerning their destructive activity at the occlusal surface of teeth required more investigation. Some suggested that the abrasive action of attrition worked against the progress of decay. Others proposed that attrition facilitated the development of caries in dentine exposed due to the dental wear. A comparison of the condition of teeth in western societies from an intermediate stage, with the preceding period characterized by excessive attrition, and with the following period of ongoing reduction of dental wear, might elucidate the mutual relationship. For this reason the almost complete dental assemblage of fifty men, whalers buried during their short sojourn in the Arctic in the 17th and 18th centuries at a Dutch whaling station, and the data of their contemporaries, were evaluated. The results confirmed the proposition that the rise in caries incidence from (pre-) medieval times on, was associated with an ongoing fall of dental attrition. Within this sample of an intermediate phase, one sees that the percentage of carious molars decreases considerably when the degree of dental wear increases. Besides, at the occlusal surface the decay was almost exclusively located in the natural fissures and pits of teeth, not in the exposed dentine due to wear. These findings strongly suggest a competitive relationship between progress of caries and attrition. The best impression of the attrition rate is gained by linkage of degree of dental attrition (i.e. functional age) to age at death. The wide age ranges fitting to the degrees of molar wear make it hazardous to use attrition for age determination.     

Killing the competition

Sex- and age-specific rates of killing unrelated persons of one’s own sex were computed for Canada (1974–1983), England/Wales (1977–1986), Chicago (1965–1981), and Detroit (1972) from census information and data archives of all homicides known to police. Patterns in relation to sex and age were virtually identical among the four samples, although the rates varied enormously (from 3.7 per million citizens per annum in England/Wales to 216.3 in Detroit). Men’s marital status was related to the probability of committing a same-sex, nonrelative homicide, but age effects remained conspicuous when married and unmarried men were distinguished. These findings and the treatment of age and sex effects by criminologists are discussed in the light of contemporary evolutionary psychological models of sex differences and life-span development. Same-sex homicides in which killer and victim are unrelated can be interpreted as an assay of competitive conflict. In every human society for which relevant information exists, men kill one another vastly more often than do women. Lethal interpersonal competition is especially prevalent among young men, which accords with many other aspects of life-span development in suggesting that sexual selection has maximized male competitive prowess and inclination in young adulthood.     

High competition with low similarity and low competition with high similarity: exploitative and apparent competition in consumer-resource systems

This article investigates the relationship between the similarity of resource capture abilities and the amount of competition between two consumer species that exploit common resources. Most of the analysis is based on a consumer-resource model introduced by Robert MacArthur. Contrary to many statements in the literature and in textbooks, measures of competition may decrease as similarity increases and may be greatest when similarity of the two species' sets of resource capture rates is very low. High competition with low similarity may occur whether competition is measured by a competition coefficient near equilibrium or is measured by the proportional increase in a species' population density when its competitor is removed. However, these two measures may differ considerably and may change in opposite directions with a given change in similarity. The general conditions required for such counterintuitive relationships between similarity and competition are that the consumer species have relatively low resource requirements for successful reproduction and that the resources be self-reproducing. These same conditions also frequently lead to exclusion of one or more resources via apparent competition, and this is always true of MacArthur's model. A variety of other models of competition are analyzed, and circumstances most likely to produce large competitive effects with little overlap are identified.