One can easily get confused by all these indices. In his 2014 paper, Legendre put
things in order and shed some light into the resemblances and differences among
these coefficients. The conclusions of this work can be summarized as follows.
1. It is the numerators of the proposed indices that estimate (1) replacement and
(2) either richness difference or nestedness. The denominators proposed by the
various authors can all be applied to scale the indices. However, the choice of a
denominator influences the positioning of the sites in an ordination based on these
quantities, when compared to the use of the numerators only.
2. The indices of the Podani family measure replacement and richness
(or abundance) difference. Those in the Baselga family are replacement (sometimes called turnover) and nestedness indices. Richness difference is not equal to
nestedness. See Sect. 8.4.3.3 below.
3. In the two families, replacement and richness difference (Podani) or replacement
and nestedness (Baselga) sum to four dissimilarity measures that are appropriate
for beta diversity assessment, following the criteria of Legendre and De Cáceres
(2013) (see Sect. 8.4.2.3).
4. The replacement and richness difference indices of the Podani family are easy to
interpret in ecological terms, as well as the replacement indices in the Baselga
family. Baselga’s nestedness indices are less obvious, but logical nevertheless.
5. Matrices of indices can be used to produce ordinations of the sites through
principal coordinate analysis (PCoA, Sect. 5.5). In this context, the Podani
indices of richness or abundance difference in the Sørensen group are particularly
well adapted since they are Euclidean. See Legendre (2014, Table S1.4).
6. There have been some discussions about the overestimation of species replacement by Baselga’s index Repl BS (Carvalho et al. 2012) and, conversely, of
underestimation by Podani’s Repl J (Baselga 2012). These properties result from
the denominators used to scale the indices. In the opinion of Legendre (2014),
“one can [...] scale the indices [...] with denominators of one’s choice, depending
on the purpose of the study”.
8.4.3.3 The Flavours of Nestedness
While the concepts of species (or abundance) replacement and richness
(or abundance) difference are easy to understand, nestedness is more elusive and
its definition and measurement have caused some controversies in the literature; see
Legendre (2014) for details. Here we show several examples with various numbers
of common and unique species to highlight and compare the behaviour of the Podani
and Baselga nestedness indices.
The examples, which are constructed on the indices derived from the Jaccard
dissimilarity, are presented in Table 8.6. They range from the case of complete
dissimilarity (no species in common) to complete similarity (all species in common),
going through different proportions of unique species. The formulae used to compute the nestedness values below are the ones presented above:
8.4 Beta Diversity
393
things in order and shed some light into the resemblances and differences among
these coefficients. The conclusions of this work can be summarized as follows.
1. It is the numerators of the proposed indices that estimate (1) replacement and
(2) either richness difference or nestedness. The denominators proposed by the
various authors can all be applied to scale the indices. However, the choice of a
denominator influences the positioning of the sites in an ordination based on these
quantities, when compared to the use of the numerators only.
2. The indices of the Podani family measure replacement and richness
(or abundance) difference. Those in the Baselga family are replacement (sometimes called turnover) and nestedness indices. Richness difference is not equal to
nestedness. See Sect. 8.4.3.3 below.
3. In the two families, replacement and richness difference (Podani) or replacement
and nestedness (Baselga) sum to four dissimilarity measures that are appropriate
for beta diversity assessment, following the criteria of Legendre and De Cáceres
(2013) (see Sect. 8.4.2.3).
4. The replacement and richness difference indices of the Podani family are easy to
interpret in ecological terms, as well as the replacement indices in the Baselga
family. Baselga’s nestedness indices are less obvious, but logical nevertheless.
5. Matrices of indices can be used to produce ordinations of the sites through
principal coordinate analysis (PCoA, Sect. 5.5). In this context, the Podani
indices of richness or abundance difference in the Sørensen group are particularly
well adapted since they are Euclidean. See Legendre (2014, Table S1.4).
6. There have been some discussions about the overestimation of species replacement by Baselga’s index Repl BS (Carvalho et al. 2012) and, conversely, of
underestimation by Podani’s Repl J (Baselga 2012). These properties result from
the denominators used to scale the indices. In the opinion of Legendre (2014),
“one can [...] scale the indices [...] with denominators of one’s choice, depending
on the purpose of the study”.
8.4.3.3 The Flavours of Nestedness
While the concepts of species (or abundance) replacement and richness
(or abundance) difference are easy to understand, nestedness is more elusive and
its definition and measurement have caused some controversies in the literature; see
Legendre (2014) for details. Here we show several examples with various numbers
of common and unique species to highlight and compare the behaviour of the Podani
and Baselga nestedness indices.
The examples, which are constructed on the indices derived from the Jaccard
dissimilarity, are presented in Table 8.6. They range from the case of complete
dissimilarity (no species in common) to complete similarity (all species in common),
going through different proportions of unique species. The formulae used to compute the nestedness values below are the ones presented above:
8.4 Beta Diversity
393