Other multiplicative indices have been proposed. See Legendre and Legendre (2012,
p. 260) and references therein.
An alternative, additive, ANOVA-type approach also exists. The principle,
exposed in detail by Lande (1996), is to compute a quantity
D T ¼ D among À
D within where D T is gamma diversity and D within is an average
measure of diversity at the level of the sites (alpha diversity). Thus, D among is the
variation of diversity among sites, i.e., beta diversity. The diversity components
D can be based on species richness (N 0 ), Shannon information H 1 or Simpson
diversity 1 – λ (but not N 2 ¼ 1/λ). See Lande (1996) and the Forum section in
Ecology (2010: 1962–1992) for details.
Another approach to multiplicative or additive partitioning of community diversity has been recently advocated, compatible with the general framework based on
Hill numbers (Jost 2006, Jost 2007, de Bello et al. 2010).
Gamma species richness, i.e. the number of species observed in a collection of
communities sampled within a given regional range, is simple to obtain from the
species data frame, since it is the number of columns of the data frame. Different
algorithms are available to estimate the species pool, including species that could
have been missed by the sampling. The specpool() function of package vegan
does this job. Predictions are based on the number of the less frequent species in the
dataset (species observed in only one or two sites).
# Gamma richness and expected species pool
?specpool
(gobs <- ncol(spe))
(gthe <- specpool(spe))
Compare the observed gamma species richness with the expected species pool
predicted by four models (Chao, first and second order jackknife, bootstrap). How
many unobserved species may contribute to the “dark diversity”?
Using the d() function of package vegetarian is the easiest way of computing mean alpha, multiplicative beta and gamma diversities based on Hill numbers. The argument lev is used to select the component and the argument q the
order of the diversity index (any null or positive numeric value, integer or real; the
higher the order, the higher the importance given to the abundant species; argument
q corresponds to the subscript a in Table 8.1). Thanks to this framework, it is
possible to plot multiplicative beta diversity as a function of the order of the diversity
index.
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8 Community Diversity
p. 260) and references therein.
An alternative, additive, ANOVA-type approach also exists. The principle,
exposed in detail by Lande (1996), is to compute a quantity
D T ¼ D among À
D within where D T is gamma diversity and D within is an average
measure of diversity at the level of the sites (alpha diversity). Thus, D among is the
variation of diversity among sites, i.e., beta diversity. The diversity components
D can be based on species richness (N 0 ), Shannon information H 1 or Simpson
diversity 1 – λ (but not N 2 ¼ 1/λ). See Lande (1996) and the Forum section in
Ecology (2010: 1962–1992) for details.
Another approach to multiplicative or additive partitioning of community diversity has been recently advocated, compatible with the general framework based on
Hill numbers (Jost 2006, Jost 2007, de Bello et al. 2010).
Gamma species richness, i.e. the number of species observed in a collection of
communities sampled within a given regional range, is simple to obtain from the
species data frame, since it is the number of columns of the data frame. Different
algorithms are available to estimate the species pool, including species that could
have been missed by the sampling. The specpool() function of package vegan
does this job. Predictions are based on the number of the less frequent species in the
dataset (species observed in only one or two sites).
# Gamma richness and expected species pool
?specpool
(gobs <- ncol(spe))
(gthe <- specpool(spe))
Compare the observed gamma species richness with the expected species pool
predicted by four models (Chao, first and second order jackknife, bootstrap). How
many unobserved species may contribute to the “dark diversity”?
Using the d() function of package vegetarian is the easiest way of computing mean alpha, multiplicative beta and gamma diversities based on Hill numbers. The argument lev is used to select the component and the argument q the
order of the diversity index (any null or positive numeric value, integer or real; the
higher the order, the higher the importance given to the abundant species; argument
q corresponds to the subscript a in Table 8.1). Thanks to this framework, it is
possible to plot multiplicative beta diversity as a function of the order of the diversity
index.
380
8 Community Diversity