favourable, or the absence of the species is due to different non-optimal conditions
on any of the important dimensions of its ecological niche, or the species is present
but has not been observed or captured by the researcher, or the species does not show
a regular distribution among the sites under study. The key points here are that (1) in
most situations, the absence of a species from two sites cannot readily be counted as
an indication of resemblance between these sites, because this double absence may
be due to completely different reasons, and (2) the number of un-interpretable double
zeros in a species matrix depends on the number of species and thus increases
strongly with the number of rare species in the matrix.
The information “presence” thus has a clearer interpretation than the information
“absence”. One can distinguish two classes of association measures based on this
problem: the coefficients that consider the double zeros (sometimes also called
“negative matches”) as indications of resemblance (like any other value) are said
to be symmetrical, the others, asymmetrical
4 . In most cases, it is preferable to use
asymmetrical coefficients when analysing species data, unless one has compelling
reasons to consider the absence of a species from two sites as being due to the same
cause, and this for all cases of double-zeros. Possible examples of such exceptions
are controlled experiments with known community compositions or ecologically
homogeneous areas with disturbed zones.
3.2.3 Association Measures for Qualitative or
Quantitative Data
Some variables are qualitative (nominal or categorical, either binary or multiclass),
others are semi-quantitative (ordinal) or quantitative (discrete or continuous). Association coefficients exist for all types of variables, but most of them fall into two
classes: coefficients for binary variables (hereunder called binary coefficients for
short, although it is the variables that are binary, not the values of the association
measures) and coefficients for quantitative variables (called quantitative coefficients
hereafter).
3.2.4 To Summarize. . .
Keep track on what kind of association measure you need. Before any analysis, ask
the following questions:
4 The use of the words symmetrical/asymmetrical for this distinction, as opposed to symmetric/
asymmetric (same value of the coefficient between n 1 and n 2 as between n 2 and n 1 ), follows
Legendre and Legendre (2012). Legendre and De Cáceres (2013) use the expressions doublezero symmetrical and double-zero asymmetrical.
3.2 The Main Categories of Association Measures (Short Overview)
37
on any of the important dimensions of its ecological niche, or the species is present
but has not been observed or captured by the researcher, or the species does not show
a regular distribution among the sites under study. The key points here are that (1) in
most situations, the absence of a species from two sites cannot readily be counted as
an indication of resemblance between these sites, because this double absence may
be due to completely different reasons, and (2) the number of un-interpretable double
zeros in a species matrix depends on the number of species and thus increases
strongly with the number of rare species in the matrix.
The information “presence” thus has a clearer interpretation than the information
“absence”. One can distinguish two classes of association measures based on this
problem: the coefficients that consider the double zeros (sometimes also called
“negative matches”) as indications of resemblance (like any other value) are said
to be symmetrical, the others, asymmetrical
4 . In most cases, it is preferable to use
asymmetrical coefficients when analysing species data, unless one has compelling
reasons to consider the absence of a species from two sites as being due to the same
cause, and this for all cases of double-zeros. Possible examples of such exceptions
are controlled experiments with known community compositions or ecologically
homogeneous areas with disturbed zones.
3.2.3 Association Measures for Qualitative or
Quantitative Data
Some variables are qualitative (nominal or categorical, either binary or multiclass),
others are semi-quantitative (ordinal) or quantitative (discrete or continuous). Association coefficients exist for all types of variables, but most of them fall into two
classes: coefficients for binary variables (hereunder called binary coefficients for
short, although it is the variables that are binary, not the values of the association
measures) and coefficients for quantitative variables (called quantitative coefficients
hereafter).
3.2.4 To Summarize. . .
Keep track on what kind of association measure you need. Before any analysis, ask
the following questions:
4 The use of the words symmetrical/asymmetrical for this distinction, as opposed to symmetric/
asymmetric (same value of the coefficient between n 1 and n 2 as between n 2 and n 1 ), follows
Legendre and Legendre (2012). Legendre and De Cáceres (2013) use the expressions doublezero symmetrical and double-zero asymmetrical.
3.2 The Main Categories of Association Measures (Short Overview)
37