Population Viability Analysis Calculator

Demographic variability is scaled by dividing demographic variance by the current population size before adding it to environmental variance. In a small population, that division produces a much larger contribution to total variance, which pulls the stochastic growth rate (mu) down further below your entered mean growth rate. In a large population, the same demographic variance input barely moves total variance at all. This reflects the real biological pattern that individual birth and death randomness swings small populations much more than large ones.

It's the population size below which you consider the species functionally extinct — not necessarily zero individuals, but a level too low to be viable (e.g., below the point where finding mates becomes difficult). The calculator computes the log-ratio between your current population and this threshold; raising the threshold shrinks that ratio, which mathematically increases the calculated probability of the population diffusing down to it within your time horizon, all else equal.

They're fixed constants (mvpShortTerm = 50, mvpLongTerm = 500) representing the classic "50/500 rule" first proposed in conservation genetics by Franklin (1980) and Soulé (1980) — 50 breeding individuals (effective population size) to avoid short-term inbreeding depression, 500 to retain enough genetic diversity for long-term evolutionary adaptation. Unlike every other output in this calculator, these two numbers are not derived from your population size, growth rate, or variance inputs at all; they're reference benchmarks displayed alongside your calculated results for comparison. The rule remains debated in the literature — some conservation geneticists argue for higher thresholds (e.g., 100/1000) — so treat 50/500 as a historically standard floor, not a guarantee of viability.

9999 is used as a stand-in for "effectively infinite" in two situations: when your stochastic growth rate (mu) is 0.01 or higher, meaning the population is expected to grow rather than decline, or when there's no variance at all and the growth rate isn't negative. The diffusion model's mean-time-to-extinction formula only produces a meaningful finite answer for populations with a negative stochastic growth rate, since a growing or stable population isn't expected to hit the extinction threshold on any predictable timeline.