lnH

lnH denotes the natural logarithm of H, with ln representing the natural logarithm (base e). The expression is defined for positive values of H; if H is zero or negative, lnH is undefined without modification or offsetting.

Context and interpretation: H is a variable used in many disciplines. In mathematics and applied sciences, H can denote a positive real quantity. In population genetics and ecology, H often represents heterozygosity or a related diversity measure. Consequently, lnH is the natural logarithm of that quantity, and its meaning depends on how H is defined in a given context. Log-transforming H to lnH is common to stabilize variance, linearize multiplicative relationships, or compress wide ranges of H.

Properties and examples: The natural log is strictly increasing, so larger H yields larger lnH. It maps (0, ∞) to (−∞, ∞). For 0 < H < 1, lnH is negative; at H = 1 it is zero; for H > 1 it is positive. Examples: if H = 5, lnH ≈ 1.609; if H = 0.5, lnH ≈ −0.693. When H represents a proportion or a diversity measure bounded between 0 and 1, the transformation lnH emphasizes small values of H and can be useful in statistical analyses that assume normality after transformation.

See also: natural logarithm, log transformation, heterozygosity.