Statistical & Clinical Analysis
Margalef Richness, Menhinick Index & Berger-Parker Dominance Formula
Calculate three rapid ecological bioassessment indices from species counts: Margalef Richness D_Mg = (S - 1) / LN(N), Menhinick Richness D_Mn = S / SQRT(N), and Berger-Parker Dominance d_BP = N_max / N (plus reciprocal 1 / d_BP).
Pair logarithmic/square-root Richness normalization with Berger-Parker Top-Taxon Dominance!
In benthic macroinvertebrate water-quality biomonitoring and rapid ecological triage, raw species count S climbs mechanically with total individuals counted N. Ramón Margalef (1958) normalized S against logarithmic sample effort D_Mg = (S - 1) / LN(N) (requiring N >= 2), while Edward F. Menhinick (1964) normalized against square-root effort D_Mn = S / SQRT(N)!
Because nutrient pollution or invasive-species blooms often leave S temporarily unchanged while a single tolerant taxon explodes to 70%+ of all individuals, Wolfgang H. Berger and Frances L. Parker (1970, Science) paired richness with pure top-species dominance d_BP = MAX(n_i) / N (and its intuitive inverse 1 / d_BP, which climbs as dominance falls)!
| Rapid Ecological Metric (Counts [45, 22, 15, 11, 7, 0]; S = 5, N = 100) | Formula | Evaluated Value |
|---|---|---|
| Observed Present Species S (Count > 0) | =COUNTIF(B2:B7, ">0") | 5 species |
| Margalef Richness Index D_Mg | (S - 1) / LN(N) | 0.8686 |
| Menhinick Richness Index D_Mn | S / SQRT(N) | 0.5000 |
| Berger-Parker Dominance d_BP (and 1 / d_BP) | MAX(n_i) / N | 0.4500 (Reciprocal 2.2222) |
Margalef Species Richness Index D_Mg = (S - 1) / LN(N)
Counts strictly positive species abundances S = COUNTIF(B2:B7, ">0") and divides S - 1 by LN(SUM(B2:B7)) for N >= 2.
=IF(OR(MIN(B2:B7) < 0, SUM(B2:B7) < 2), "Requires Non-Negative Counts & Total N >= 2", ROUND((COUNTIF(B2:B7, ">0") - 1) / LN(SUM(B2:B7)), 4))Menhinick Richness S / SQRT(N) & Berger-Parker Dominance N_max / N
Computes Berger-Parker top-taxon share MAX(B2:B7) / SUM(B2:B7) (or Menhinick COUNTIF(B2:B7, ">0") / SQRT(SUM(B2:B7))).
=IF(OR(MIN(B2:B7) < 0, SUM(B2:B7) <= 0), "Requires Positive Total Individuals N", ROUND(MAX(B2:B7) / SUM(B2:B7), 4))Try the example
Use the original values or change them to test your understanding.