evodivparam {adiv} | R Documentation |

## Parametric Indices of Phylogenetic Diversity

### Description

Function `evodivparam`

calculates phylogenetic diversity in communities using parametric indices derived from Tsallis and Hill compositional indices. It can also be applied to functional trees rather than phylogenies, to calculate a functional diversity.
The function `plot.evodivparam`

plots the results of function `evodivparam`

.

### Usage

```
evodivparam(phyl, comm,
method = c("hill", "tsallis", "renyi"),
q = 2, tol = 1e-08)
## S3 method for class 'evodivparam'
plot(x, legend = TRUE,
legendposi = "topright", axisLABEL = "Tree-based diversity",
type="b", col = if(is.numeric(x)) NULL
else sample(colors(distinct = TRUE), nrow(x$div)),
lty = if(is.numeric(x)) NULL else rep(1, nrow(x$div)),
pch = if(is.numeric(x)) NULL else rep(19, nrow(x$div)),
...)
```

### Arguments

`phyl` |
an object inheriting the class |

`comm` |
a data frame or a matrix typically with communities as rows, species as columns and abundance as entry. Species should be labeled as in the phylogenetic tree where they are the tips. |

`method` |
a string: either "hill" for the Hill numbers (Hill 1973), "tsallis" for the Tsallis or HCDT entropy (Harvda and Charvat 1967; Daroczy 1970; Tsallis 1988), or "renyi" for Renyi's entropy (Renyi 1960). If several values are given, only the first one is considered. See details. |

`q` |
a vector with nonnegative value(s) for parameter |

`tol` |
numeric tolerance threshold: values between - |

`x` |
an object of class |

`legend` |
a logical. If TRUE a legend is given with the colour, the type of line (etc.) used to define the diversity curve of each community. |

`legendposi` |
a string that gives the position of the legend to be passed to function |

`axisLABEL` |
a string to display on the main axis of the plot to designate what we are measuring. The default is |

`type` |
a string to be passed to the graphic argument |

`col` |
vector of colours to be passed to the graphic argument |

`lty` |
vector of type of line (plain, broken etc.) to be passed to the graphic argument |

`pch` |
type of point (open circle, close circle, square etc.) to be passed to the graphic argument |

`...` |
other arguments can be added and passed to the functions |

### Details

Consider a phylogenetic tree *T*, `b_T`

the set of branches in *T*, *k* a branch, `L_k`

the length of branch *k*, *j* a community (*j*=1,...,*m*), `a_{jk}`

the abundance associated with branch *k* in community *j* (sum of abundance of all species descending from the branch). *q* is the parameter that increases with the importance given to abundant species compared to rare species in diversity.

The methods available to calculate the phylogenetic diversity in community *j* are:
`tsallis`

:

```
^q{evoTsallis}_j=
\left[1-\sum_{k \in b_T} L_k \left(\frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q \right]/(q-1)
```

`hill`

:

`^q{evoHill}_j=\left[\sum_{k \in b_T} L_k \left(\frac{a_{jk}}{\sum_{k \in b_T} L_k a_{jk}}\right)^q \right]^{1/(1-q)}`

`renyi`

:

`^q{evoRenyi}_j=log(^q{evoHill}_j)`

### Value

If only one value of `q`

is given, a vector with the phylogenetic diversity of each community is returned.
If more than one value of `q`

is given, a list of two objects is returned:

`q` |
the vector of values for |

`div` |
a data frame with the phylogenetic diversity of each community calculated for all values of |

The function `plot.evodivparam`

returns a graphic.

### Author(s)

Sandrine Pavoine sandrine.pavoine@mnhn.fr

### References

The methodologies and scripts were developed by

Pavoine, S., Ricotta, C. (2019) A simple translation from indices of species diversity to indices of phylogenetic diversity. *Ecological Indicators*, **101**, 552–561.

using earlier work by:

Chao, A., Chiu, C.-H., Jost, L. (2010) Phylogenetic diversity measures based on Hill numbers. *Philosophical Transactions of the Royal Society London Series B*, **365**, 3599–3609.

Daroczy, Z. (1970) Generalized information functions. *Information and Control*, **16**, 36–51.

Havrda, M., Charvat F. (1967) Quantification method of classification processes: concept of structural alpha-
entropy. *Kybernetik*, **3**, 30–35.

Hill, M.O. (1973) Diversity and evenness: a unifying notation and its consequences. *Ecology*, **54**, 427–432.

Pavoine, S. (2016) A guide through a family of phylogenetic dissimilarity measures among sites. *Oikos*, **125**, 1719–1732.

Renyi, A. (1960) On measures of entropy and information. *Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability*, **1**, 547–561.

Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics. *Journal of Statistical Physics*, **52**, 480–487.

### See Also

### Examples

```
## Not run:
if(require(ape)){
data(batcomm)
phy <- read.tree(text=batcomm$tre)
ab <- batcomm$ab[, phy$tip.label]
plot(evodivparam(phy, ab))
plot(evodivparam(phy, ab, q=seq(0, 10, length=20)))
}
## End(Not run)
```

*adiv*version 2.2.1 Index]