Can useful generalizations be drawn from these observations on population changes? Can a model be constructed of the forces which drive population changes or of population-habitat interactions which keep populations from extinction? Some conflicting theories and assumptions of population dynamics are examined and discussed below.
_The Assumption of Population Stability and of Closely Attuned Density-dependent Mortality_
During the 5 decades before 1970, it was widely accepted that most animal populations were generally stable and saturated before the arrival of the white man. Although a few field biologists vigorously dissented, "establishment" ecologists regarded fluctuations as a departure from the norm, and as such, a hazard to the population. Many theorists of both evolution and ecology argued that adaptations were required to damp fluctuations or the fluctuations would become "random walks" and the population would rapidly become extinct. As a consequence, relatively all theoretical models included stability as a central assumption.
• The basic element of this theoretical complex has been the Lotka-Volterra formula for a logistic curve of population growth and stabilization. According to this formula it has been reasoned that by establishing the inherent rate of increase of a population (i.e., its average natality relative to mortality, or _r_) and by measuring the carrying capacity of the environment (which is the density of the population at saturation, or _K_), one can predict the maximally productive population size, and maximum rate of production of new individuals (or maximum sustained yield). These assumptions have supplied the theoretical framework for virtually all game management and many fisheries practices.
Once stability was assumed, a mechanism for maintaining stability was necessary. This mechanism was found in an interaction between the population and the environment, called density-dependent mortality (Nicholson 1933). The impact of this feedback has been assumed to cause the point of inflection of the "sigmoid curve" and to regulate the density "at equilibrium."
Populations growing in relatively isolated or closed systems have been observed to follow a sigmoid curve toward a steady state. We have data on the growth of several Massachusetts gull colonies which show this type of short-period rapid increase followed by a long sequence of shallow oscillations (Drury and Nisbet 1972). But usually observations have been terminated at about the time the population passed through the point of inflection.