# Phylogenetic Beta Entropy of a community

### Description

Calculates the phylogenetic beta entropy of order *q* of a a community belonging to a metacommunity.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
PhyloBetaEntropy(NorP, NorPexp = NULL, q = 1, Tree, Normalize = TRUE,
Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL,
Pexp = NULL, Nexp = NULL)
bcPhyloBetaEntropy(Ns, Nexp, q = 1, Tree, Normalize = TRUE,
Correction = "Best", CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
PhyloBetaEntropy(NorP, NorPexp = NULL, q = 1, Tree, Normalize = TRUE,
Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL,
Pexp = NULL, Nexp = NULL)
## S3 method for class 'AbdVector'
PhyloBetaEntropy(NorP, NorPexp = NULL, q = 1, Tree, Normalize = TRUE,
Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL,
Pexp = NULL, Nexp = NULL)
## S3 method for class 'integer'
PhyloBetaEntropy(NorP, NorPexp = NULL, q = 1, Tree, Normalize = TRUE,
Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL,
Pexp = NULL, Nexp = NULL)
## S3 method for class 'numeric'
PhyloBetaEntropy(NorP, NorPexp = NULL, q = 1, Tree, Normalize = TRUE,
Correction = "Best", CheckArguments = TRUE, Ps = NULL, Ns = NULL,
Pexp = NULL, Nexp = NULL)
``` |

### Arguments

`Ps` |
The probability vector of species of the community. |

`Pexp` |
The probability vector of species of the metacommunity. |

`Ns` |
A numeric vector containing species abundances of the community. |

`Nexp` |
A numeric vector containing species abundances of the metacommunity. |

`NorP` |
A numeric vector, an integer vector, an abundance vector ( |

`NorPexp` |
A numeric vector, an integer vector, an abundance vector ( |

`q` |
A number: the order of entropy. Default is 1. |

`Tree` |
An object of class |

`Normalize` |
If |

`Correction` |
A string containing one of the possible corrections: currently, only |

`CheckArguments` |
Logical; if |

### Details

The phylogenetic entropy is the generalization of HCDT entropy to unequal species distances (Pavoine et al., 2009).

Calculation relies on `TsallisBeta`

and `PhyloApply`

.

Bias correction requires the number of individuals to estimate sample `Coverage`

. Use `bcPhyloBetaEntropy`

and choose the `Correction`

.

Note that beta entropy value is related to alpha entropy (if *q* is not 1) and cannot be compared accross communities (Jost, 2007). Beta entropy of a community is not meaningful in general, do rather calculate the `PhyloDiversity`

of the metacommunity.

The functions are designed to be used as simply as possible. `PhyloBetaEntropy`

is a generic method. If its first argument is an abundance vector, an integer vector or a numeric vector which does not sum to 1, the bias corrected function `bcPhyloBetaEntropy`

is called. Explicit calls to `bcPhyloBetaEntropy`

(with bias correction) or to `PhyloBetaEntropy.ProbaVector`

(without correction) are possible to avoid ambiguity. The `.integer`

and `.numeric`

methods accept `Ps`

or `Ns`

arguments instead of `NorP`

for backward compatibility.

### Value

A `PhyloEntropy`

object containing entropy values at each cut of the tree.

### Author(s)

Eric Marcon <Eric.Marcon@ecofog.gf>

### References

Jost (2007), Partitioning diversity into independent alpha and beta components. *Ecology* 88(10): 2427-2439.

Marcon, E., Herault, B. (2015). Decomposing Phylodiversity. *Methods in Ecology and Evolution* 6(3): 333-339.

Pavoine, S., Love, M. S. and 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(9): 898-908.

### See Also

`TsallisBeta`

, `bcPhyloBetaEntropy`

, `PhyloDiversity`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest
# and their taxonomy)
data(Paracou618)
# Ps is the vector of probabilities
Ps <- as.ProbaVector(Paracou618.MC$Ps)
# Probability distribution of the first plot
Ps1 <- as.ProbaVector(Paracou618.MC$Psi[, 1])
# Calculate the phylogenetic Shannon beta entropy of the plot
summary(PhyloBetaEntropy(Ps1, Ps, 1, Paracou618.Taxonomy) -> e)
plot(e)
# Ns is the vector of abundances of the metacommunity
Ns <- as.AbdVector(Paracou618.MC$Ns)
# Abundances in the first plot
Ns1 <- as.AbdVector(Paracou618.MC$Nsi[, 1])
# Calculate the phylogenetic Shannon beta entropy of the plot
summary(bcPhyloBetaEntropy(Ns1, Ns, 1, Paracou618.Taxonomy, Correction = "Best") -> e)
plot(e)
``` |

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