Table 1.

Summary of notation

Notation	Description
i	Sample index, i = 1, 2, …, n.
j	Taxon index, j = 1, 2, …, d.
k	Index of fixed effects, k = 1, 2, …, p.
l	Index of random effects, l = 1, 2, …, q.
xik	The kth fixed effect of interest for the ith sample.
zil	The lth random effect of interest for the ith sample.
Aijb	True absolute abundance of jth taxon in a unit volume of ecosystem of ith sample.
Oij b	Observed count of jth taxon in a random specimen taken from a unit volume of ecosystem of ith sample.
Eij b	Random error for taxon j in sample i.
Si a	Sample-specific sampling fraction.
Cj a	Taxon-specific sequencing efficiency.
aij b	$\log A_{ij}$.
oij b	$\log O_{ij}$.
eij b	Random error for taxon j in sample i in log scale.
si a	Sample-specific sampling fraction in log scale.
cj a	Taxon-specific sequencing efficiency in log scale.

^aParameter.

^bRandom variable.