Practice question

When a constant finite multiplier exceeds unity, geometric growth compounds abundance at each discrete interval. Early increases may appear modest, but every increment enlarges the base from which the next increment is produced. Plotting population size against time therefore yields a trajectory that bends progressively upward, conventionally called a J-shaped curve. This shape is the discrete-time counterpart of continuous exponential growth. It differs from the sigmoid or S-shaped logistic curve, in which density dependence progressively lowers per-capita growth as abundance approaches carrying capacity. A J-shaped trajectory is expected only while resources, space, and other constraints do not appreciably reduce survival or reproduction. Real populations may show a temporary J phase after colonization or release from limitation, followed by slowing, oscillation, or a crash. The name describes the graph’s geometry rather than a separate biological mechanism: multiplicative growth produces the curvature. If λ equals 1 the graph is horizontal, and if λ is below 1 the trajectory declines geometrically instead of forming an increasing J.