We analyze perturbation experiments performed on real and ealized ecological communities. A community may be considered as a black box in the sense that the individual species grow and interact in complicated ways that are difficult to discern. Yet, by observing the response (output) of the system to natural or human—induced disturbances (inputs), information can be gained regarding the character and strengths of species interactions. We decline a perturbation as selective alteration of the density of one or more members of the community, and we distinguish two quite different kinds of perturbations. A PULSE perturbation is a relatively instantaneous alteration of species numbers, after which the system is studied as it "relaxes" back to its previous equilibrium state. A PRESS perturbation is a sustained alteration of species densities (often a complete elimination of particular species): it is maintained until the unperturbed species reach a new equilibrium. The measure of interest in PRESS perturbation is the net change in densities of the unperturbed species. There is a very important difference between these two approaches: PULSE experiments yield information only on direct interactions (e.g. terms in the interaction matrix), while PRESS experiments yield information on direct interactions mixed together with the indirect effects mediated through other species in the community. We develop mathematical techniques that yield measures of ecological interaction between species from both types of experimental designs. Particular caution must be exercised in interpreting results form PRESS experiments, particularly when some species are lumped into functional categories and others are neglected altogether in the experimental design. We also suggest mathematical methods to deal with temporal and random variation during experiments. Finally, we critically review techniques that rely on natural variation in numbers to estimate species interaction coefficients. The problems with such studies are formidable.

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We review the early development of metapopulation ideas, which culminated in the well-known model by Levins in 1969. We present a survey of metapopulation terminology and outline the kinds of studies that have been conducted on single-species and multispecies metapopulations. Metapopulation studies have important conceptual links with the equilibrium theory of island biogeography and with studies on the dynamics of species living in patchy environments. Metapopulation ideas play an increasingly important role in landscape ecology and conservation biology.

A linear model of interspecific competition with separate parameters for exploitation and interference is deduced. Interference is assumed to have a cost and an effect. The interfering species realizes a "profit" if some resources, which the species interfered against would have utilized, are made available as a result of the interference. Interference is favored when its cost is small, its effect is high, and the resource overlap with the species interfered against is high. Interference is likely to be an alternative strategy to high exploitation efficiency. The incorporation of interference into niche theory clarifies the competitive phenomenon of unstable equilibrium points, excess density compensation on islands, competitive avoidance by escape in time and space, the persistence of the "prudent predator," and the magnitude of the difference between the size of a species' fundamental niche and its realized niche.Interspecies competition has long been recognized to be of two types, exploitation competition and interference competition (1, 2). Nonetheless, the "niche theory" of competition in communities (3) assumes that exploitation (or utilization) of "resources", e.g., prey species or habitat types, primarily determines ecological segregation. Most actual field or laboratory studies of interspecies competition show, however, that interference was present, and often played the more important role in determining abundance and distribution.Interference was the major component of competition in the classical studies of Gause (4) on yeast and Paramecium, and of Park (5, 6) on Tribolium. It was mediated through metabolic by-products (alcohol) in yeast, through allelochemicals in Paramecium (7), and by egg predation between species of Tribolium. In the field, interspecific interference competition, e.g., aggression or poisoning, has been found to be important between species of birds (8-12), mammals (13-20), and invertebrates (21-24). In contrast, most, if not all, evidence for exploitation competition for food is inferential.Given this taxonomically broad catalogue of interference competition, it is imperative that interference competition be explicitly included in current niche theory. To this end, we shall develop a mathematical model of competition that separates the contributions from exploitation and interference.By considering the effect of interference on population adaptedness (equilibrium density), it will be possible to predict the circumstances whereunder interference competition may evolve from exploitation competition.Competition models and the evolution of interferenceThe differential equations of Lotka and Volterra are frequently used to model competition and they also serve as the basis of niche theory (25), but this model has some weaknesses. It does not account for sex, age structure, seasonality, thresholds, time delays, stochastic effects and nonlinearities. Nonetheless, the model is simple and general. If its approximate nature is appreciated, it can serve as an excellent vehicle to un...

Very precise data on the dynamics of a competitive system of two species of Drosophila have been obtained. By a curvilinear regression approach, analytical models of competition have been fitted. By statistical and biological criteria of simplicity, reality, generality, and accuracy, the best of these models has been chosen. This model represents an extension of the Lotka-Volterra model of competition; it adds a fourth parameter that controls the degree of nonlinearity in intraspecific growth regulation. It represents a similar extension of the logistic model of population growth.Population ecology is at a Keplerian stage of development. Much of the present theory is based on idealized linear interactions (which are valid first-order approximations of more general interaction), somewhat as preKeplerian astronomy was based on idealized circular motions (which approximate ellipses). For interspecies competition, the present need is to obtain precise data that disclose the global dynamics of real competition systems, that is, the rates of population growth at any combination of population densities. Simple but general analytical models may then be sought to represent such systems. Only if this attempt achieves success should the Newton-like effort of producing a law for the repulsive "forces" of intraspecies and interspecies competition be undertaken, though the obviously pluralistic nature of biological mechanisms could make this effort profitless.In the 1920s, the linear model of competition was proposed independently by Lotka (1) and Volterra (2); it isN1 is the population density of the ith species; ri is the exponential rate of growth of the ith species when both the ith and jth population densities are low; Ki is the carrying capacity of the ith species in the absence of its competitor, the jth species; and aij is the linear reduction (in terms of K1) of the ith species' rate of growth by its competitor, the jth species. This model and other analytical models of competition ignore time lags, thresholds, and stochastic effects; but this is necessary if the mathematics are to be kept tractable and should lead to no difficulties if not forgotten.Volterra, in the absence of any competition data whatsoever, felt that the above model could be globally valid. Lotka indicated that the correct competition model was likely to be nonlinear; but by making a Taylor's series expansion about the point of equilibrium and dropping the higher order terms, he was able to arrive at the same model of competition as an approximation valid in a "neighborhood" of the equilibrium point. Levins (3) and MacArthur (4) have added to the importance of this linear model by basing their niche theory on it, and they have provided independent formulas to calculate the K and a parameters. Vandermeer (5) has used the as of the Lotka-Volterra competition equations to determine the "community matrix" of a competition ecosystem. But such epitheory does nothing to validate the linear model.In 1934, Gause (9) determined the dynamics of yeast...