get_tree_beta {apTreeshape} R Documentation

## Beta parameter as a function of the proportion of remaining tips

### Description

Computes the maximum likelihood estimate of the parameter beta in trees simulated by the model, as a function of the proportion of conserved species

### Usage

```get_tree_beta(epsilon, beta, alpha, N, sampl.frac, ntree, equal.ab = TRUE, eta = 1)
```

### Arguments

 `epsilon` Minimum size of unsampled splits (see appendix 1) `beta` Imbalance index `alpha` Clade age-richness index `N` Initial tip number `sampl.frac` Vector of tips fractions for which we want to compute the beta statistic `ntree` Number of simulated trees `equal.ab` If set to TRUE, all species have the same probability to go extinct first (default to TRUE) `eta` Clade abundance-richness index (if equal.ab == FALSE)

### Value

A table of size length(sample.fract)*ntree. The element in ligne i and column j is the Maximum Likelihood Estimate for the beta statistic of the j^th tree in wich a fraction sample.frac[i] has been sampled.

### Author(s)

Odile Maliet, Fanny Gascuel & Amaury Lambert

### References

Maliet O., Gascuel F., Lambert A. (2018) Ranked tree shapes, non-random extinctions and the loss of phylogenetic diversity, bioRxiv 224295, doi: https://doi.org/10.1101/224295

### Examples

```# With the field of bullets hypothesis

set.seed(813)
sampl.frac=seq(0.2,1,0.2)
Beta=get_tree_beta(epsilon=0.01, beta=-1, alpha=-1, N=20, sampl.frac=sampl.frac, ntree=3)

Beta_quantiles=sapply(1:nrow(Beta),function(x){quantile(Beta[x,],c(0.05,0.5,0.95))})

plot(1, type="n", xlab="Fraction of extinct species, p", ylab="Beta statistic",
ylim=c(-2,10), xlim=c(0,1))
polygon(c(1-sampl.frac, rev(1-sampl.frac)), c(Beta_quantiles[1,(1:length(sampl.frac))],
rev(Beta_quantiles[3,(1:length(sampl.frac))])), border=NA, col=grey(0.7))
points(1-sampl.frac, Beta_quantiles[2,(1:length(sampl.frac))],t="l")

# With nonrandom extinctions

## Not run:
set.seed(813)
sampl.frac=seq(0.2,1,0.2)
Beta=get_tree_beta(epsilon=0.01, beta=5, alpha=2, eta=2, N=20,
sampl.frac=sampl.frac, ntree=3)

Beta_quantiles=sapply(1:nrow(Beta),function(x){quantile(Beta[x,],c(0.05,0.5,0.95))})

plot(1, type="n", xlab="Fraction of extinct species, p",
ylab="Beta statistic", ylim=c(-2,10), xlim=c(0,1))
polygon(c(1-sampl.frac, rev(1-sampl.frac)),
c(Beta_quantiles[1,(1:length(sampl.frac))],
rev(Beta_quantiles[3,(1:length(sampl.frac))])), border=NA, col=grey(0.7))
points(1-sampl.frac, Beta_quantiles[2,(1:length(sampl.frac))],t="l")

## End(Not run)

```

[Package apTreeshape version 1.5-0.1 Index]