Global models of growth and competition

Demographic characteristics and population dynamical patterns of solitary birds

In birds and many other animals, there are large interspecific differences in the magnitude of annual variation in population size. Using time-series data on populations of solitary bird species, we found that fluctuations in population size of solitary birds were affected by the deterministic characteristics of the population dynamics as well as the stochastic factors. In species with highly variable populations, annual variation in recruitment was positively related to the return rate of adults between successive breeding seasons. In stable populations, more recruits were found in years with low return rates of breeding adults. This identifies a gradient, associated with the position of the species along a "slow-fast" continuum of life history variation, from highly variable populations with a recruitment-driven demography to stable, strongly density-regulated populations with a survival-restricted demography. These results suggest that patterns in avian population fluctuations can be predicted from a knowledge of life-history characteristics and/or temporal variation in certain demographic traits.

Estimating the time to extinction in an island population of song sparrows

We estimated and modelled how uncertainties in stochastic population dynamics and biases in parameter estimates affect the accuracy of the projections of a small island population of song sparrows which was enumerated every spring for 24 years. The estimate of the density regulation in a theta-logistic model (theta = 1.09 suggests that the dynamics are nearly logistic, with specific growth rate r1 = 0.99 and carrying capacity K = 41.54. The song sparrow population was strongly influenced by demographic (ŝigma2(d) = 0.66) and environmental (ŝigma2(d) = 0.41) stochasticity. Bootstrap replicates of the different parameters revealed that the uncertainties in the estimates of the specific growth rate r1 and the density regulation theta were larger than the uncertainties in the environmental variance sigma2(e) and the carrying capacity K. We introduce the concept of the population prediction interval (PPI), which is a stochastic interval which includes the unknown population size with probability (1 - alpha). The width of the PPI increased rapidly with time because of uncertainties in the estimates of density regulation as well as demographic and environmental variance in the stochastic population dynamics. Accepting a 10% probability of extinction within 100 years, neglecting uncertainties in the parameters will lead to a 33% overestimation of the time it takes for the extinction barrier (population size X = 1) to be included into the PPI. This study shows that ignoring uncertainties in population dynamics produces a substantial underestimation of the extinction risk.

Moose and snowshoe hare competition and a mechanistic explanation from foraging theory

Moose (Alces alces) and snowshoe hare (Lepus americanus) appear to compete with each other. This was determined using the "natural experiments" of populations found in sympatry and allopatry on islands at Isle Royale National Park, Michigan, and manipulated exclosures. The population densities from these areas are fit to a series of competition models based upon different competitive mechanisms (Schoener 1974a), using non-linear regression techniques. A model of competition for food where the food can be separated into exclusively used and shared categories is found to predict observed densities of moose and hare best. Finally, the competition model's parameters (fraction of food shared and competition coefficients) are shown to agree with values predicted independently from a foraging model.

Stability in Gilpin and Ayala's models of competition

Simple and effective conditions for global stability in a class of models for m competing species are given. A numerical method is used to establish a large finite region of attraction for the feasible equilibrium in Gilpin and Ayala's model of two competing Drosophila populations.