Population Growth

The increase in the number of individuals of a species in a given area over a period of time is called population growth.

The rate at which new individuals are added to a population through reproduction is called natality.

The rate at which individuals die in a population during a given period of time is called mortality.

The rate of change in population size per individual per unit time is called population growth rate.

The maximum growth rate of a population under ideal conditions with maximum reproduction and minimum mortality is called intrinsic rate of growth.

The reproductive capacity of a population measured as the number of births during a given period is called fecundity.

The addition of individuals to a population from neighbouring populations is called immigration.

The movement of individuals out of a population to other areas is called emigration.

\[\mathbf{N_{t+1}}=\mathbf{N_{t}}+[(\mathbf{B+I})-(\mathbf{D+E})]\]

\[\frac{\mathrm{dN}}{\mathrm{dt}}=\mathrm{rN}\]

Integral form: \[\mathbf{N_{t}}=\mathbf{N_{0}}\mathbf{e^{rt}}\]

Verhulst-Pearl Logistic Growth:

\[\frac{\mathrm{d~N}}{\mathrm{d~t}}=\mathbf{rN}\left[\frac{\mathrm{K}-\mathrm{N}}{\mathrm{K}}\right]\]

• Population growth is studied mainly by two models: exponential growth and logistic growth.
• Population density (N) changes due to four factors: Natality (B), Mortality (D), Immigration (I), and Emigration (E).
• Exponential growth → Occurs when resources are unlimited; population increases rapidly and forms a J-shaped curve.
• Logistic growth → Occurs when resources are limited; growth slows down and forms an S-shaped (sigmoid) curve.
• Phases of logistic growth → Lag phase → Log (exponential) phase → Diminishing growth phase → Stationary phase.
• Carrying capacity (K) → Maximum population size that the environment can support; population stabilises at this level.