Density-dependent Population Growth Research Articles

Global asymptotic stability criteria for models of density-dependent population growth

A single-population, multiple-age-class model is formulated in which the fertility or mortality rates are dependent on the total biomass density of the population or a related function. The circle criterion is applied to determine conditions for which the model is globally asymptotically stable about an equilibrium age distribution.

The effect of random variations of different types on population growth.

The probability distributions of population size are derived for populations living in randomly varying environments for both density-dependent and density-independent population growth. The effects of random variation in the rate of increase, the carrying capacity, and sampling variation in numbers are examined.

Sufficient Conditions for Multiple Niche Polymorphism

Sufficient Conditions for Multiple Niche Polymorphism

Population Growth in Micro‐Organisms Limited by Food Supply

It is suggested that an hyperbolic equation of the form (1/n) (dn/dt) = rb/(b + A) where n is the population density, b the concentration of limiting food supply and A and r are constants, is widely applicable as a density-dependent growth model. An attempt is madse to state explicitly the conditions under which it would apply. A consideration of the kinetics of food uptake leads to the interpretation of the constant A as representing a ratio of two rate constants, k3 /k1 where k1 is the rate constant associated with first step in food uptake and k3 is associated with the second step which results in the freeing of the adsorption site. The constant r represents a composite expression, k3 co /(qn) where co /n is the number of adsorption sites per individual, and q is the amount of food required to produce a new individual. Density dependent population growth models must always include a second equation which describes the effect of population growth on the environment (in this case food supply). The failure of the logistic equation to provide the necessary generality for this effect is pointed out. The applicability of this model for a number of different bacterial populations using a variety of both energetic and substantive food as the growth-limiting factor has been established for several years. Data are presented to show that it is also applicable to the unicellular alga, Isochrysis galbana, growing under limiting nitrate concentration and to several species of phytoplankton growing under limiting light intensity. The quantitative effects of preconditioning light intensity on chlorophyll per cell (co /n) and on k3 are noted as examples of the usefulness of this more detailed consideration of the growth constants, r and A.