Table 3.

The observed marginal correlation of the motivating data set

	${\mathit{C}}_{\mathbf{1}}^{(\mathbf{1})}$	${\mathit{C}}_{\mathbf{2}}^{(\mathbf{1})}$	${\mathit{C}}_{\mathbf{3}}^{(\mathbf{1})}$	${\mathit{C}}_{\mathbf{4}}^{(\mathbf{1})}$	${\mathit{C}}_{\mathbf{5}}^{(\mathbf{1})}$	${\mathit{C}}_{\mathbf{6}}^{(\mathbf{1})}$	${\mathit{C}}_{\mathbf{1}}^{(\mathbf{2})}$	${\mathit{C}}_{\mathbf{2}}^{(\mathbf{2})}$	${\mathit{C}}_{\mathbf{3}}^{(\mathbf{2})}$	${\mathit{C}}_{\mathbf{4}}^{(\mathbf{2})}$	${\mathit{C}}_{\mathbf{5}}^{(\mathbf{2})}$	${\mathit{C}}_{\mathbf{6}}^{(\mathbf{2})}$
$C_1^{(1)}$	1	−0.46	−0.43	−0.48	−0.12	−0.23
$C_2^{(1)}$	·	1	−0.29	0.13	0.02	0
$C_3^{(1)}$	·	·	1	−0.27	−0.19	0
$C_4^{(1)}$	·	·	·	1	0.1	0.06
$C_5^{(1)}$	·	·	·	·	1	0.01
$C_6^{(1)}$	·	·	·	·	·	1
$C_1^{(2)}$	0.14	−0.11	−0.05	−0.01	0	−0.13	1	−0.27	−0.53	−0.57	0.04	−0.14
$C_2^{(2)}$	−0.14	0.17	0.04	0.03	−0.01	−0.05	·	1	−0.27	−0.15	−0.05	0.01
$C_3^{(2)}$	0.04	0.05	0.01	−0.07	−0.08	−0.1	·	·	1	−0.07	−0.22	−0.11
$C_4^{(2)}$	−0.11	−0.02	0.01	0.07	0.05	0.3	·	·	·	1	0.02	0.09
$C_5^{(2)}$	0.06	−0.25	0.09	0.01	0.05	0.01	·	·	·	·	1	−0.05
$C_6^{(2)}$	−0.07	0.08	−0.06	−0.01	0.23	0.17	·	·	·	·	·	1

$C_j^{(t)}$ represents the bacterial phyla j,j = 1,…,6 at time‐point t. The order of j are Firmicutes, Actinobacteria, Bacteroidetes, Proteobacteria, Unclassified and pooled category.