Ecology & Biodiversity formula solvers
Lincoln-Petersen Mark-Recapture Estimate
Ecology & BiodiversityStatisticsPopulation size estimated from two samples: mark M individuals, later catch C, and count how many of those carry a mark. Assumes a closed population, equal catchability and no lost marks — every one of those failing biases the answer, and the Chapman correction is what small samples actually use.
Logistic Population Growth
Ecology & BiodiversityStatisticsPopulation at time t under density-dependent growth toward a carrying capacity K. Growth is nearly exponential while the population is small, slows through an inflection at K/2, and flattens as the resource runs out.
Pielou's Evenness (J′)
Ecology & BiodiversityStatisticsShannon diversity as a fraction of the largest value it could take for that many species, so a community with every species equally abundant scores 1 and a community dominated by one species scores near 0. A proportion, never a count.
Shannon Diversity Index (H′)
Ecology & BiodiversityStatisticsDiversity of a community of up to four species from their proportional abundances, in nats. It rises with both the number of species and the evenness of their shares, and it is Shannon's information entropy with species where the symbols were.
Simpson's Index of Diversity (1 − D)
Ecology & BiodiversityStatisticsProbability that two individuals drawn at random from a community of up to four species belong to DIFFERENT species. This page returns 1 − D, which rises with diversity; Simpson's own D = Σ pᵢ² is the dominance and runs the opposite way.
Species-Area Relationship (S = cA^z)
Ecology & BiodiversityStatisticsExpected number of species in an area, as a power law fitted to survey data. The exponent z is typically 0.20 to 0.35 for nested samples within a region and 0.25 to 0.45 for true islands; c is a fitted constant whose units depend on z and on the area unit it was fitted in.