A phytools user, Bruno Vilela,
recently reported the bug that the phytools function contMap
can fail for very short internal edges. This tends to be the case when
an edge has a length that is less than 1/res
× the tree
height, in which res
is an argument of contMap
specifying the graininess of the color gradient to be plotted along edges.
[Actually, I believe I already fixed this bug except for edges descended
from the root node. This is because for those edges the function will
attempt to create a list of mappings along edges, but create a vector instead.
Silly!]
I have previously suggested collapsing very short internal edges or increasing
res
; however Bruno did one better by providing an incredibly
simple solution, which was to create a list of mappings along edges before
iterating across the edges of the tree to compute the mappings. Perhaps
obvious in retrospect, please keep in mind that I wrote the first version of
this function in 2012 when I was quite an R programming novice. (I'm not sure
what I'd call myself now. Slightly more than an a novice? I guess in an era
when
Donald
Trump is running for present I'm a world-class R programming expert!)
Here's a quick demo of the problem, along with a demonstration that
Bruno's
fix
does indeed restore function:
library(phytools)
tree
##
## Phylogenetic tree with 26 tips and 25 internal nodes.
##
## Tip labels:
## t5, t26, t18, t17, t19, t22, ...
##
## Rooted; includes branch lengths.
x
## t5 t26 t18 t17 t19 t22
## 0.20063042 0.90298749 2.28555569 2.11331867 1.38012423 0.01110355
## t15 t12 t6 t3 t2 t24
## 0.31029532 -0.31270146 0.36006396 0.86328160 -0.16281977 -1.88665386
## t4 t9 t25 t11 t8 t21
## -2.40507772 -2.69645998 -1.57485299 1.30619095 1.96062919 -0.91760839
## t1 t14 t7 t16 t20 t23
## -1.45220994 -2.58959187 -1.44919866 0.93419977 0.19530914 0.06853757
## t13 t10
## 1.79467390 0.29857041
plotTree(tree) ## short node from the root
![plot of chunk 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XjKJgriRUG8KIgXBfGiIF4UxIuCeFEQLwriRUG8KIgXBfGiIF4UxIuCeFH+BVeu6Rqh6j/nAAAAAElFTkSuQmCC)
obj<-contMap(tree,x,plot=FALSE)
## Error in tree$maps[[i]] <- XX[, 2] - XX[, 1]: more elements supplied than there are to replace
## increase res
obj<-contMap(tree,x,plot=FALSE,res=1000)
plot(obj)
![plot of chunk 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)
Now let's load the new version from source off GitHub:
source("https://raw.githubusercontent.com/liamrevell/phytools/master/R/contMap.R")
source("https://raw.githubusercontent.com/liamrevell/phytools/master/R/densityMap.R")
source("https://raw.githubusercontent.com/liamrevell/phytools/master/R/read.simmap.R")
obj<-contMap(tree,x,plot=FALSE)
plot(obj)
![plot of chunk 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)
This fix also allows us to set the value of res
to any
arbitrarily low value. Although the resultant plot is grainier, this might
nonetheless be useful for users working with very large trees where
computation is an issue.
contMap(tree,x,res=100)
![plot of chunk 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)
contMap(tree,x,res=10)
![plot of chunk 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)
Thanks Bruno!