rare_phylo: Phylogenetic Diversity Rarefaction Curves
In Rarefy: Rarefaction Methods
rare_phylo R Documentation
Phylogenetic Diversity Rarefaction Curves
Description
rare_phylo calculates classic rarefaction curves using different indexes of phylogenetic diversity.
ser_phylo calculates spatially-explicit rarefaction curves using different indexes of phylogenetic diversity.
Usage
rare_phylo(comm,tree=NULL,method=c("faith","barker","Ia","hill","tsallis",
"renyi","fun_div"),exp=0,resampling=99,fun_div=NULL,args=NULL,verbose=FALSE)
ser_phylo(comm,tree=NULL,dist_xy,method=c("faith","barker","Ia","hill","tsallis"
,"renyi","fun_div"),exp=0,fun_div=NULL,args=NULL,verbose=FALSE,
comparison=FALSE,resampling=99)
Arguments
comm
a community dataframe or matrix with N plots as rows, S species as columns. Both the presence/absence (1/0) or the abundances of species in plots are allowed as entries. Plot and species names should be provided as row names and column names.
tree
an object of class phylo or phylo4 containing the phylogenetic tree of the species which are present in comm.
dist_xy
an object of class dist containing the pairwise geographic distances among the plots or an object of class, an object of class vector containing the order of the sampling units along a gradient or an object of class matrix or data.frame where each column represents a gradient along which the sampling units are ordered. The names of the labels must be the same as the rows of comm. If dist_xy is not of class dist, then a distance matrix is calculated using the Euclidean distance coefficient.
method
the diversity index for the calculation of the rarefaction curve, one among "faith", "barker", "Ia", "hill", "tsallis", "renyi" or "fun_div". See details.
exp
parameter that determines the sensitivity of the measure to the relative abundance of the species for "Ia", "hill", "tsallis" and "renyi" indexes.
resampling
number of times plots (rows) are randomly resampled from comm to calculate the mean accumulation curve for the non-spatially-explicit rarefaction.
fun_div
a string with the name of the user-defined function for the diversity index in the rarefaction. The function must calculate the value of the chosen diversity index per plot and return a numeric vector with the values calculated.
args
a list with the arguments for fun_div. The value NA should be given in place of the community matrix in the list. The names of the elements must correspond to the names of the arguments of the function passed.
verbose
if TRUE, the arguments of fun_div are inserted interactively by the user.
comparison
if TRUE, both non-spatially explicit and spatially explicit phylogenetic rarefactions are calculated.
Details
The available methods are:
faith: Faith's phylogenetic diversity (PD) is defined as the sum of branch lengths in a phylogenetic tree for the assemblage of species (Faith 1992):
PD= \sum_{i \in B}L_{i}
where L_i is the branch length of the branch i and B is the number of branches in the tree.
barker: Barker's index is the abundance weighted Faith's PD. The number of branches (B) is multiplied by the weighted mean branch length, with weights equal to the average abundance of species sharing that branch (Vellend et al. 2010):
PDw= B \times \frac{\sum_{i}^{B}L_{i} A_{i}}{\sum_{i}^{B}A_{i}}
where L_i is the branch length of the branch i, and A_i is the average abundance of the species sharing the branch i. B is the number of branches in the tree.
Ia: Ia index, by Pavoine et al. (2009), calculates PD partitioned between evolutionary periods and between plots defined in terms of spatial and time units. Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988) (that measures diversity by regrouping individuals into categories) is computed for each period of the phylogenetic tree, from the number of lineages that descend from the period and from the relative abundances summed within these lineages within the focal community. With exp=0, HCDT is the richness (number of species) minus one and Ia is Faith's PD minus the height of the phylogenetic tree; with exp tending to 1 HCDT is a generalization of the Shannon index while with exp=2 HCDT is the Simpson index and Ia is Rao's QE applied to phylogenetic distances between species. To apply Ia, the phylogeny must be ultrametric:
Ha= \frac{(1-\sum_{i=1}^{n}p_{i}^{a})}{(a-1)}
the equation for the HCDT entropy, where p_i is the relative abundance of the species i and a is the scaling constant that weights the importance of rarity of the species.
I_{a}= \sum_{K=1}^{N}(t_{K}-t_{K-1})H_{a,K}
where H_{a,K} is Ha applied to the period K and t_K-t_{K-1} is the length of the period K.
Hill index (hill) and the HCDT (tsallis) and Renyi (renyi) entropies are adapted for the calculation of the phylogenetic diversity replacing the species with the units of the branch length in the phylogenetic tree (Pavoine & Ricotta 2019):
Hill=\left [ \sum_{i \in B} L_{i}(p_{i})^{q}]\right ]^{\frac{1}{1-q}}
HCDT= \frac{1-\sum_{i \in B} L_{i}(p_{i})^q}{q-1}
Renyi= \frac{1}{1-q}log\left [ \sum_{i \in B} L_{i}(p_{i})^q\right ]
where L_i is the branch length of the branch i, p_i is the relative abundance of the species sharing the branch i and q is the scaling constant that weights the importance of rarity of the species. B is the number of branches in the tree.
Value
An object of class data.frame with 3 columns is returned:
- Rarefaction: : mean of the values of the accumulation curves for all the sampling dimensions;
- IC_up: upper confidence interval;
- IC_low: lower confidence interval.
If comparison is TRUE, the data.frame object will have six columns, with the values of the accumulation curve and confidence intervals for both spatially explicit and non-spatially explicit rarefaction.
Author(s)
Elisa Thouverai elisa.th95@gmail.com
with contributions of Sandrine Pavoine.
References
Chao, A., Chiu, C.-H., Hsieh, T.C., Davis, T., Nipperess, D.A., Faith, D.P. (2014) Rarefaction and extrapolation of phylogenetic diversity. Methods in Ecology and Evolution, 6, 380–388.
Daroczy, Z. (1970) Generalized information functions. Information and Control, 16, 36–51.
Faith, D.P. (1992) Conservation evaluation and phylogenetic diversity. Biological Conservation, 61, 1–10.
Havrda, M., Charvat F. (1967) Quantification method of classification processes: concept of structural alpha-entropy. Kybernetik, 3, 30–35
Pavoine, S., Love, M., Bonsall, M.B. (2009) Hierarchical partitioning of evolutionary and ecological patterns in the organization of phylogenetically-structured species assemblages: application to rockfish (genus: Sebastes) in the Southern California Bight. Ecology Letters, 12, 898–908.
Pavoine, S., Ricotta, C. (2019) A simple translation from indices of species diversity to indices of phylogenetic diversity. Ecological Indicators, 101, 552–561.
Swenson, N.G. (2014) Functional and Phylogenetic Ecology in R. Springer UseR! Series, Springer, New York, New York, U.S.A.
Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 480–487.
Vellend, M., Cornwell, W.K., Magnuson-Ford, K., Mooers, A. (2010) Measuring phylogenetic biodiversity. Magurran & McGill, 194–207.
Examples
## Not run:
#Time consuming
require(picante)
require(geiger)
data(phylocom)
phylo<-treedata(phylocom$phylo,phylocom$sample[1,],warnings = FALSE)$phy
## Non-spatially explicit rarefaction
raref<-rare_phylo(phylocom$sample,phylo,resampling=999) ##Faith index
plot(raref [,1], ylab="Faith", xlab="Number of plots", type="l", ylim=range(raref, na.rm
=TRUE))
lines(raref[,2], lty=2)
lines(raref[,3], lty=2)
rareb<-rare_phylo(phylocom$sample,phylo,method='barker',resampling=999) ##Barker index
plot(rareb [,1], ylab="Barker", xlab="Number of plots", type="l", ylim=range(rareb, na.rm
=TRUE))
lines(rareb[,2], lty=2)
lines(rareb[,3], lty=2)
rareia<-rare_phylo(phylocom$sample,phylo,method='Ia',resampling=999,exp=2) ##Ia index
plot(rareia [,1], ylab="Ia", xlab="Number of plots", type="l", ylim=range(rareia, na.rm
=TRUE))
lines(rareia[,2], lty=2)
lines(rareia[,3], lty=2)
## End(Not run)
Rarefy documentation built on July 9, 2023, 6:16 p.m.
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| rare_phylo | R Documentation |
Phylogenetic Diversity Rarefaction Curves
Description
rare_phylo calculates classic rarefaction curves using different indexes of phylogenetic diversity.
ser_phylo calculates spatially-explicit rarefaction curves using different indexes of phylogenetic diversity.
Usage
rare_phylo(comm,tree=NULL,method=c("faith","barker","Ia","hill","tsallis",
"renyi","fun_div"),exp=0,resampling=99,fun_div=NULL,args=NULL,verbose=FALSE)
ser_phylo(comm,tree=NULL,dist_xy,method=c("faith","barker","Ia","hill","tsallis"
,"renyi","fun_div"),exp=0,fun_div=NULL,args=NULL,verbose=FALSE,
comparison=FALSE,resampling=99)
Arguments
comm |
a community dataframe or matrix with N plots as rows, S species as columns. Both the presence/absence (1/0) or the abundances of species in plots are allowed as entries. Plot and species names should be provided as row names and column names. |
tree |
an object of class |
dist_xy |
an object of class |
method |
the diversity index for the calculation of the rarefaction curve, one among "faith", "barker", "Ia", "hill", "tsallis", "renyi" or "fun_div". See details. |
exp |
parameter that determines the sensitivity of the measure to the relative abundance of the species for "Ia", "hill", "tsallis" and "renyi" indexes. |
resampling |
number of times plots (rows) are randomly resampled from comm to calculate the mean accumulation curve for the non-spatially-explicit rarefaction. |
fun_div |
a string with the name of the user-defined function for the diversity index in the rarefaction. The function must calculate the value of the chosen diversity index per plot and return a numeric vector with the values calculated. |
args |
a list with the arguments for fun_div. The value NA should be given in place of the community matrix in the list. The names of the elements must correspond to the names of the arguments of the function passed. |
verbose |
if TRUE, the arguments of |
comparison |
if TRUE, both non-spatially explicit and spatially explicit phylogenetic rarefactions are calculated. |
Details
The available methods are:
faith: Faith's phylogenetic diversity (PD) is defined as the sum of branch lengths in a phylogenetic tree for the assemblage of species (Faith 1992):
PD= \sum_{i \in B}L_{i}
where L_i is the branch length of the branch i and B is the number of branches in the tree.
barker: Barker's index is the abundance weighted Faith's PD. The number of branches (B) is multiplied by the weighted mean branch length, with weights equal to the average abundance of species sharing that branch (Vellend et al. 2010):
PDw= B \times \frac{\sum_{i}^{B}L_{i} A_{i}}{\sum_{i}^{B}A_{i}}
where L_i is the branch length of the branch i, and A_i is the average abundance of the species sharing the branch i. B is the number of branches in the tree.
Ia: Ia index, by Pavoine et al. (2009), calculates PD partitioned between evolutionary periods and between plots defined in terms of spatial and time units. Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988) (that measures diversity by regrouping individuals into categories) is computed for each period of the phylogenetic tree, from the number of lineages that descend from the period and from the relative abundances summed within these lineages within the focal community. With exp=0, HCDT is the richness (number of species) minus one and Ia is Faith's PD minus the height of the phylogenetic tree; with exp tending to 1 HCDT is a generalization of the Shannon index while with exp=2 HCDT is the Simpson index and Ia is Rao's QE applied to phylogenetic distances between species. To apply Ia, the phylogeny must be ultrametric:
Ha= \frac{(1-\sum_{i=1}^{n}p_{i}^{a})}{(a-1)}
the equation for the HCDT entropy, where p_i is the relative abundance of the species i and a is the scaling constant that weights the importance of rarity of the species.
I_{a}= \sum_{K=1}^{N}(t_{K}-t_{K-1})H_{a,K}
where H_{a,K} is Ha applied to the period K and t_K-t_{K-1} is the length of the period K.
Hill index (hill) and the HCDT (tsallis) and Renyi (renyi) entropies are adapted for the calculation of the phylogenetic diversity replacing the species with the units of the branch length in the phylogenetic tree (Pavoine & Ricotta 2019):
Hill=\left [ \sum_{i \in B} L_{i}(p_{i})^{q}]\right ]^{\frac{1}{1-q}}
HCDT= \frac{1-\sum_{i \in B} L_{i}(p_{i})^q}{q-1}
Renyi= \frac{1}{1-q}log\left [ \sum_{i \in B} L_{i}(p_{i})^q\right ]
where L_i is the branch length of the branch i, p_i is the relative abundance of the species sharing the branch i and q is the scaling constant that weights the importance of rarity of the species. B is the number of branches in the tree.
Value
An object of class data.frame with 3 columns is returned:
- Rarefaction: : mean of the values of the accumulation curves for all the sampling dimensions;
- IC_up: upper confidence interval;
- IC_low: lower confidence interval.
If comparison is TRUE, the data.frame object will have six columns, with the values of the accumulation curve and confidence intervals for both spatially explicit and non-spatially explicit rarefaction.
Author(s)
Elisa Thouverai elisa.th95@gmail.com
with contributions of Sandrine Pavoine.
References
Chao, A., Chiu, C.-H., Hsieh, T.C., Davis, T., Nipperess, D.A., Faith, D.P. (2014) Rarefaction and extrapolation of phylogenetic diversity. Methods in Ecology and Evolution, 6, 380–388.
Daroczy, Z. (1970) Generalized information functions. Information and Control, 16, 36–51.
Faith, D.P. (1992) Conservation evaluation and phylogenetic diversity. Biological Conservation, 61, 1–10.
Havrda, M., Charvat F. (1967) Quantification method of classification processes: concept of structural alpha-entropy. Kybernetik, 3, 30–35
Pavoine, S., Love, M., Bonsall, M.B. (2009) Hierarchical partitioning of evolutionary and ecological patterns in the organization of phylogenetically-structured species assemblages: application to rockfish (genus: Sebastes) in the Southern California Bight. Ecology Letters, 12, 898–908.
Pavoine, S., Ricotta, C. (2019) A simple translation from indices of species diversity to indices of phylogenetic diversity. Ecological Indicators, 101, 552–561.
Swenson, N.G. (2014) Functional and Phylogenetic Ecology in R. Springer UseR! Series, Springer, New York, New York, U.S.A.
Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 480–487.
Vellend, M., Cornwell, W.K., Magnuson-Ford, K., Mooers, A. (2010) Measuring phylogenetic biodiversity. Magurran & McGill, 194–207.
Examples
## Not run:
#Time consuming
require(picante)
require(geiger)
data(phylocom)
phylo<-treedata(phylocom$phylo,phylocom$sample[1,],warnings = FALSE)$phy
## Non-spatially explicit rarefaction
raref<-rare_phylo(phylocom$sample,phylo,resampling=999) ##Faith index
plot(raref [,1], ylab="Faith", xlab="Number of plots", type="l", ylim=range(raref, na.rm
=TRUE))
lines(raref[,2], lty=2)
lines(raref[,3], lty=2)
rareb<-rare_phylo(phylocom$sample,phylo,method='barker',resampling=999) ##Barker index
plot(rareb [,1], ylab="Barker", xlab="Number of plots", type="l", ylim=range(rareb, na.rm
=TRUE))
lines(rareb[,2], lty=2)
lines(rareb[,3], lty=2)
rareia<-rare_phylo(phylocom$sample,phylo,method='Ia',resampling=999,exp=2) ##Ia index
plot(rareia [,1], ylab="Ia", xlab="Number of plots", type="l", ylim=range(rareia, na.rm
=TRUE))
lines(rareia[,2], lty=2)
lines(rareia[,3], lty=2)
## End(Not run)R Package Documentation
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