Scanning electron micrograph of the bacteria Heliobacterium chlorum. Photo credit: F. R. Turner, Indiana University, Bloomington/ Courtesy: National Science Foundation.

The logistic model of population growth assumes that the growth rate of the population decreases linearly with population size. In particular, the logistic equation gives the instantaneous rate of change of a population (Δ_N) as,

where r > 0 is the growth rate of the population in the absence of intraspecific competition and α > 0 is the per individual effect of competition. Δ_N represents the rate at which the population is growing/decaying at any instant in time. For example, a population of microorganisms may grow at a rate of 10 microorganisms per day exactly two days after the population is innoculated.