difference only represents a part of nestedness, and a correct assessment of
nestedness should include the common species (a). See Sect. 8.4.3.3 for a comparison of nestedness indices.
8.4.3.2 The Baselga Family of Indices
This family contains indices of replacement (sometimes called turnover) and
nestedness. The replacement indices can be easily compared to those of the Podani
family, but the nestedness indices are different in their purpose and formulation from
the richness and abundance difference indices of the Podani family. They also differ
from the Podani and Schmera (2011) index of nestedness.
Baselga (2010) described a replacement index (called turnover in his paper)
based on the Sørensen dissimilarity D S , and proposed to subtract it from the
Sørensen dissimilarity to obtain the nestedness component. These two indices are
called Repl BS and Nes BS in Table 8.5. The same line of reasoning led to indices
summing up to Jaccard’s dissimilarity D J . For quantitative data, the quantities a,
b and c are replaced by A, B and C respectively. These indices are presented (with
numerical examples) in Table 8.5.
Table 8.5 Replacement (turnover) and nestedness indices of the Baselga family, with numerical
examples based on Tables 8.2 and 8.3
Presence-absence
Abundance
Jaccard – Ružička group
Dissimilarity
Examples
D J ¼ (b + c)/(a + b + c)
8 / 12 ¼ 0.667
D Ru ¼ (B + C)/(A + B + C)
108 / 149 ¼ 0.725
Replacement
(turnover)
Examples
Repl BJ ¼
2min b;c
ð Þ
aþ2min b;c
ð Þ
6 / [4 + (2 Â 3)] ¼ 0.600
Repl BR ¼
2min B;C
ð
Þ
Aþ2min B;C
ð
Þ
(2 Â 37)/[41 + (2 Â 37)] ¼ 0.643
Nestedness
Examples
Nes BJ ¼
bÀc
j
j
aþbþc Â
a
aþ2min b;c
ð Þ
(2/12) Â [4/(4 + 2 Â 3)] ¼ 0.067
Nes BR ¼
BÀC
j
j
AþBþC Â
A
Aþ2min B;C
ð
Þ
Nes BR ¼ (34/149) Â [41/(41 + (2 Â 37))] ¼ 0.081
Sørensen – % difference group
Dissimilarity
Examples
D S ¼ (b + c)/(2a + b + c)
8 / 16 ¼ 0.500
D 14 ¼ (B + C)/(2A + B + C)
108 / 190 ¼ 0.568
Replacement
(turnover)
Examples
Repl BS ¼
min b;c
ð Þ
aþmin b;c
ð Þ
3 / (4 + 3) ¼ 0.429
Repl B:D14 ¼
min B;C
ð
Þ
Aþmin B;C
ð
Þ
(37)/[41 + 37] ¼ 0.474
Nestedness
Examples
Nes BS ¼
bÀc
j
j
2aþbþc Â
a
aþmin b;c
ð Þ
(2/16) Â [4/(4 + 3)] ¼ 0.071
Nes BS ¼
BÀC
j
j
2AþBþC Â
A
Aþmin B;C
ð
Þ
Nes BR ¼ (34/190) Â [41/(41 + 37)] ¼ 0.094
392
8 Community Diversity
nestedness should include the common species (a). See Sect. 8.4.3.3 for a comparison of nestedness indices.
8.4.3.2 The Baselga Family of Indices
This family contains indices of replacement (sometimes called turnover) and
nestedness. The replacement indices can be easily compared to those of the Podani
family, but the nestedness indices are different in their purpose and formulation from
the richness and abundance difference indices of the Podani family. They also differ
from the Podani and Schmera (2011) index of nestedness.
Baselga (2010) described a replacement index (called turnover in his paper)
based on the Sørensen dissimilarity D S , and proposed to subtract it from the
Sørensen dissimilarity to obtain the nestedness component. These two indices are
called Repl BS and Nes BS in Table 8.5. The same line of reasoning led to indices
summing up to Jaccard’s dissimilarity D J . For quantitative data, the quantities a,
b and c are replaced by A, B and C respectively. These indices are presented (with
numerical examples) in Table 8.5.
Table 8.5 Replacement (turnover) and nestedness indices of the Baselga family, with numerical
examples based on Tables 8.2 and 8.3
Presence-absence
Abundance
Jaccard – Ružička group
Dissimilarity
Examples
D J ¼ (b + c)/(a + b + c)
8 / 12 ¼ 0.667
D Ru ¼ (B + C)/(A + B + C)
108 / 149 ¼ 0.725
Replacement
(turnover)
Examples
Repl BJ ¼
2min b;c
ð Þ
aþ2min b;c
ð Þ
6 / [4 + (2 Â 3)] ¼ 0.600
Repl BR ¼
2min B;C
ð
Þ
Aþ2min B;C
ð
Þ
(2 Â 37)/[41 + (2 Â 37)] ¼ 0.643
Nestedness
Examples
Nes BJ ¼
bÀc
j
j
aþbþc Â
a
aþ2min b;c
ð Þ
(2/12) Â [4/(4 + 2 Â 3)] ¼ 0.067
Nes BR ¼
BÀC
j
j
AþBþC Â
A
Aþ2min B;C
ð
Þ
Nes BR ¼ (34/149) Â [41/(41 + (2 Â 37))] ¼ 0.081
Sørensen – % difference group
Dissimilarity
Examples
D S ¼ (b + c)/(2a + b + c)
8 / 16 ¼ 0.500
D 14 ¼ (B + C)/(2A + B + C)
108 / 190 ¼ 0.568
Replacement
(turnover)
Examples
Repl BS ¼
min b;c
ð Þ
aþmin b;c
ð Þ
3 / (4 + 3) ¼ 0.429
Repl B:D14 ¼
min B;C
ð
Þ
Aþmin B;C
ð
Þ
(37)/[41 + 37] ¼ 0.474
Nestedness
Examples
Nes BS ¼
bÀc
j
j
2aþbþc Â
a
aþmin b;c
ð Þ
(2/16) Â [4/(4 + 3)] ¼ 0.071
Nes BS ¼
BÀC
j
j
2AþBþC Â
A
Aþmin B;C
ð
Þ
Nes BR ¼ (34/190) Â [41/(41 + 37)] ¼ 0.094
392
8 Community Diversity