Exponential growth

Definition

Population increase in which the per capita growth rate remains constant, causing the population to expand by a constant multiplicative factor over equal time intervals; mathematically, dN/dt = rN, where N is population size and r is the intrinsic rate of increase. In arthropod populations, this pattern typically occurs when resources are unlimited, predators and pathogens are scarce, and environmental conditions remain favorable, producing a J-shaped curve on arithmetic axes.

Etymology

From Latin exponere (to put out, display) and Middle English growen; mathematical usage established in 19th-century demography and ecology.

Example

A laboratory colony of Drosophila melanogaster with abundant yeast medium and no mortality factors may double every 10 days; starting with 100 flies, the population reaches 200 after 10 days, 400 after 20 days, and 3,200 after 50 days—illustrating exponential growth until crowding or food depletion initiates logistic damping.

Synonyms

• geometric growth
• Malthusian growth

Related Terms

• logistic growth
• Carrying capacity
• Intrinsic rate of increase
• doubling time
• density-dependent regulation
• Population dynamics
• r-selection

Usage Notes

Distinguished from linear growth (constant absolute increase) and logistic growth (decelerating as carrying capacity is approached). In field entomology, true exponential growth is rarely sustained for long; it characterizes initial invasion phases, laboratory colonies, or pest outbreaks before natural enemies or resource limits intervene. The term is sometimes applied loosely to any rapid increase, but specialists reserve it for the specific mathematical pattern. Geometric growth is preferred for discrete generations (many insects), exponential for continuous reproduction.