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 c_o /(qn) where c_o /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 (c_o /n) and on k₃ are noted as examples of the usefulness of this more detailed consideration of the growth constants, r and A.