Plotting the edges of a tree in sigmoid style using the generalized logistic function

On a whim today, I decided to try to write a function to plot a phylogeny with the edges graphed using sigmoid curves. (This is the type of thing that Luke Harmon & I cover in Chapter 13 of our book.)

I decided to use the generalized logistic function from among the wide variety of different sigmoid functions that are available.

I'm not sure I got it exactly right, but here's what I came up with.

sigmoidPhylogram<-function(tree,b=5,m1=0.01,m2=0.9,v=1,...){
    if(hasArg(use.edge.length)) 
        use.edge.length<-list(...)$use.edge.length
    else use.edge.length<-TRUE
    if(!use.edge.length) tree<-compute.brlen(tree)
    h<-max(nodeHeights(tree))
    args<-list(...)
    args$tree<-tree
    args$color<-"transparent"
    do.call(plotTree,args)
    pp<-get("last_plot.phylo",envir=.PlotPhyloEnv)
    ## Yt<-A+(K-A)/(C+exp(-B*(t-M)))^(1/v)
    for(i in 1:nrow(tree$edge)){
        A<-pp$yy[tree$edge[i,1]]
        K<-pp$yy[tree$edge[i,2]]
        if(i==1) dy<-abs(A-K)
        B<-b*Ntip(tree)/h
        t<-seq(pp$xx[tree$edge[i,1]],pp$xx[tree$edge[i,2]],
            length.out=1000)
        dd<-diff(range(t))
        M<-t[1] + if(m1*h>(m2*dd)) m2*dd else m1*h
        C<-1
        Yt<-A+(K-A)/((C+exp(-B*(t-M)))^(1/v))
        t<-c(t[1],t,t[length(t)])
        Yt<-c(A,Yt,K)
        lines(t,Yt)
    }
}

OK, let's try to use it.

First, using a 90 taxon phylogeny of primates from Kirk & Kay (2004) that also features in our book.

library(phytools)
primate.tree<-read.tree(file="http://www.phytools.org/Rbook/3/primateEyes.phy")
sigmoidPhylogram(primate.tree,ftype="i",fsize=0.5)

That's surprisingly not that bad. Here's another example using a phylogeny of bony fish from Benun Sutton & Wilson (2019). The arguments b and m1 control the general shape of the sigmoid function used to plot the edges.

bonyfish.tree<-read.tree(file="http://www.phytools.org/Rbook/7/bonyfish.tre")
sigmoidPhylogram(bonyfish.tree,ftype="i",fsize=0.5,b=10,m1=0.005)

Here's a much smaller phylogeny of centrarchid fishes from Revell & Collar (2008).

sunfish.tree<-read.nexus(file="http://www.phytools.org/Rbook/5/Centrarchidae.nex")
sigmoidPhylogram(sunfish.tree,ftype="i",b=10,m1=0.03,m2=0.5)

Lastly, here's a much larger phylogeny of flowering plants from Williams et al. (2014).

plant.tree<-read.tree(file="http://www.phytools.org/Rbook/7/pollen-tree.phy")
plant.tree<-ladderize(plant.tree)
sigmoidPhylogram(plant.tree,ftype="off",m1=0.001,b=1)