How this calculator works
Dominance is the probability that two selected individuals belong to the same species. Without replacement, use n_i(n_i - 1) terms and total N(N - 1). With replacement, use squared observed proportions. Diversity is the complementary probability and reciprocal dominance is another common index. Names differ across sources, so all three quantities are labelled by formula. Empty categories do not increase observed richness.
Formula
Without replacement: D = Σn_i(n_i - 1)/(N(N - 1)). With replacement: D = Σ(n_i/N)². Diversity = 1 - D; reciprocal = 1/D.
Worked example
Two species with counts 2 and 2 have finite dominance (2 + 2)/(4 × 3) = 1/3, diversity 2/3 and reciprocal 3. Squared proportions instead give D = 1/2.
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Frequently asked questions
Does a larger number always mean more diversity?
Larger 1 - D or 1/D means greater diversity, while larger D means greater dominance. Always check which quantity is reported.
Why can finite reciprocal exceed observed richness?
Finite without-replacement dominance differs from squared-proportion dominance. Its reciprocal is not the same effective-species measure and can even be undefined.
What if every individual belongs to a different species?
Finite dominance is zero, diversity is one and reciprocal dominance is undefined. The tool reports that explicitly.