Table 2.

A fictitious numerical example demonstrating for several orders a of Rényi-diversity the diversity components $v_T$, $v_C$, $v_{\mathit{TC}}$, the minimally required numbers of communities ($N_C^{\circ }$) and types ($N_T^{\circ }$) as well as their associated effective numbers of types ($N_{T<C}^e$) and communities ($N_{C<T}^e$), respectively, and the dual $\beta$-diversities $N_C/N_C^{\circ }$ and $N_T/N_T^{\circ }$

Joint and marginal frequencies
	$C_1$	$C_2$	$C_3$	${\sum }_T$
$T_1$	0.18	0.00	0.28	0.46
$T_2$	0.00	0.08	0.09	0.17
$T_3$	0.00	0.00	0.20	0.20
$T_4$	0.09	0.08	0.00	0.17
${\sum }_C$	0.27	0.16	0.57	1.00

Diversity components, minimum numbers, effective numbers and $\beta$-diversities
Order	$v_T^e$	$v_C^e$	$v_{\mathit{TC}}^e$	$N_C^{\circ }$	$N_{T<C}^e$	$N_T^{\circ }$	$N_{C<T}^e$	$\frac{N_C}{N_C^{\circ }}$	$\frac{N_T}{N_T^{\circ }}$
$a=0$	4.000	3.000	7.000	1.750	4.000	2.333	3.000	1.714	1.714
$a=1$	3.602	2.630	6.200	1.721	3.602	2.357	2.630	1.743	1.697
$a=2$	3.232	2.362	5.562	1.721	3.232	2.355	2.362	1.743	1.699
$a=\infty$	2.174	1.754	3.571	1.643	2.174	2.036	1.754	1.826	1.965