qdiv.diversity.func_alpha

qdiv.diversity.func_alpha(tab, distmat, *, q=1, index='FD', use_values_in_tab=False)[source]

Compute functional alpha diversity (Hill numbers) of order q.

Implements the framework of Chiu et al. (2014, PLoS ONE), where functional diversity is derived from pairwise trait distances and species abundances.

For each sample, functional diversity is computed from:

Q = Σᵢ Σⱼ pᵢ pⱼ dᵢⱼ (Rao’s quadratic entropy)

and the functional Hill number of order q:

q = 1:
FD₁ = exp( -½ Σᵢ Σⱼ (pᵢ pⱼ ln(pᵢ pⱼ)) dᵢⱼ / Q )

q ≠ 1:
FD_q = ( Σᵢ Σⱼ (pᵢ pⱼ)ᵠ dᵢⱼ / Q )^( 1 / (2(1−q)) )

Parameters:

tab (DataFrame | MicrobiomeData-like | dict) – Abundance table (features x samples) or convertible structure.
distmat (pandas.DataFrame) – Functional distance matrix (features × features).
q (float, default=1) – Diversity order.
index ({'FD', 'D', 'MD'}, default='FD') – Output type: - ‘D’ : functional Hill number - ‘MD’ : mean functional diversity (D × Q) - ‘FD’ : functional diversity (D × MD)
use_values_in_tab (bool, default=False) – If False, convert abundances to relative abundances. If True, assume tab already contains relative abundances.

Returns:

Functional diversity values for each sample.

Return type:

pandas.Series

Notes