# Phylogenetic Entropy of a community

### Description

Calculates the phylogenetic entropy of order *q* of a probability vector.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
PhyloEntropy(NorP, q = 1, Tree, Normalize = TRUE, Correction = "Best",
CheckArguments = TRUE, Ps = NULL, Ns = NULL)
bcPhyloEntropy(Ns, q = 1, Tree, Normalize = TRUE, Correction = "Best",
CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
PhyloEntropy(NorP, q = 1, Tree, Normalize = TRUE, Correction = "Best",
CheckArguments = TRUE, Ps = NULL, Ns = NULL)
## S3 method for class 'AbdVector'
PhyloEntropy(NorP, q = 1, Tree, Normalize = TRUE, Correction = "Best",
CheckArguments = TRUE, Ps = NULL, Ns = NULL)
## S3 method for class 'integer'
PhyloEntropy(NorP, q = 1, Tree, Normalize = TRUE, Correction = "Best",
CheckArguments = TRUE, Ps = NULL, Ns = NULL)
## S3 method for class 'numeric'
PhyloEntropy(NorP, q = 1, Tree, Normalize = TRUE, Correction = "Best",
CheckArguments = TRUE, Ps = NULL, Ns = NULL)
is.PhyloEntropy(x)
## S3 method for class 'PhyloEntropy'
summary(object, ...)
``` |

### Arguments

`Ps` |
A probability vector, summing to 1. |

`Ns` |
A numeric vector containing species abundances. |

`NorP` |
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: |

`CheckArguments` |
Logical; if |

`x` |
An object to be tested or plotted |

`object` |
A |

`...` |
Additional arguments to be passed to the generic methods. |

### Details

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

Calculation relies on `Tsallis`

and `PhyloApply`

.

Intervals separate two cuts in a tree: no node is found at heights contained in an interval.

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

. Use `bcPhyloEntropy`

and choose the `Correction`

.

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

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 `bcPhyloEntropy`

is called. Explicit calls to `bcPhyloEntropy`

(with bias correction) or to `PhyloEntropy.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

An object of class `PhyloEntropy`

is a list:

`Distribution` |
The distribution used to calculate entropy |

`Function` |
The function used to calculate entropy |

`Tree` |
The functional or phylogenetic tree used to calculate entropy |

`Normalized` |
Logical. Indicates whether phyloentropy is normalized or proportional to the height of the tree. |

`Type` |
The type of entropy ("alpha", "beta" or "gamma"). |

`Order` |
The order of entropy |

`Cuts` |
A named vector containing values of neutral entropy along the tree. Names are cut ends, |

`Total` |
A value equal the total entropy multiplied by the tree height if |

`is.PhyloEntropy`

returns `TRUE`

if the object is of class `PhyloEntropy`

.

`summary.PhyloEntropy`

returns a summary of the object's value.

`PhyloEntropy`

objects can be plotted by `plot.PhyloValue`

because `PhyloEntropy`

objects are also of class `PhyloValue`

.

### Note

The tree must contain all species of the probability vector. If it contains extra species, computation time will just be increased.

### Author(s)

Eric Marcon <Eric.Marcon@ecofog.gf>

### References

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

`Tsallis`

, `PhyloDiversity`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# 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$Ps)
# Calculate the phylogenetic Shannon entropy of the plot
summary(PhyloEntropy(Ps, 1, Paracou618.Taxonomy) -> e)
plot(e)
# Ns is the vector of abundances of the metacommunity
Ns <- as.AbdVector(Paracou618.MC$Ns)
# Calculate the phylogenetic Shannon entropy of the plot
summary(bcPhyloEntropy(Ns, 1, Paracou618.Taxonomy, Correction = "Best") -> e)
plot(e)
``` |