Practice question

The finite rate of increase λ is the ratio of population sizes at successive discrete censuses: λ = N(t+1)/N(t). If censuses are annual, it represents the population multiplication factor per year, often described as annual finite growth. Thus λ = 1.10 means the next year’s population is expected to be 110% of the current one, whereas λ = 0.90 indicates a 10% decline. The time unit is set by the census interval and need not always be a year. Net reproductive rate R0 differs because it measures replacement over a generation, usually expected daughters per female across her lifetime. Carrying capacity is K, and migration is represented through immigration and emigration rates. The relationship to continuous growth is λ = e^r for equivalent intervals, so ln λ gives the instantaneous rate r. Unlike an additive growth amount, λ is a dimensionless ratio. Interpreting it requires stating the interval, since the same biological trajectory has different numerical multipliers when measured monthly versus annually.