## Thursday, August 13, 2015

### Marking changes on a stochastic map tree, and some other updates to object classes in phytools

I have posted recently (e.g., 1, 2, 3) about a phytools function to mark changes on a plotted stochastic character map tree.

Well, one creative use of the latest update to this function might be, it occured to me, plotting arrows for changes of a particular type (say, decrease or increase in a discrete character trait on the tree, corresponding to 'up' or 'down' arrows, respectively). If a character tended to be lost but not regained, then, (for example, the number of digits) perhaps we would see losses but relatively few reaquisitions.

In the code below, I use a version of phytools that is not yet posted, but code for all the functions is already available on phytools.org.

Let's simulate data with a high rate of loss, & a low rate of reaquisition:

``````set.seed(872)
library(phytools)
Q<-matrix(c(-0.1,1,0,0,0,0,
0.1,-1.1,1,0,0,0,
0,0.1,-1.1,1,0,0,
0,0,0.1,-1.1,1,0,
0,0,0,0.1,-1.1,1,
0,0,0,0,0.1,-1),6,6,byrow=TRUE)
colnames(Q)<-rownames(Q)<-0:5
Q
``````
``````##      0    1    2    3    4  5
## 0 -0.1  1.0  0.0  0.0  0.0  0
## 1  0.1 -1.1  1.0  0.0  0.0  0
## 2  0.0  0.1 -1.1  1.0  0.0  0
## 3  0.0  0.0  0.1 -1.1  1.0  0
## 4  0.0  0.0  0.0  0.1 -1.1  1
## 5  0.0  0.0  0.0  0.0  0.1 -1
``````
``````tree<-sim.history(pbtree(n=50,scale=2),Q=Q,anc="5")
``````
``````## Note - the rate of substitution from i->j should be given by Q[j,i].
## Done simulation(s).
``````
``````colors<-setNames(grey(seq(1,0,-0.2)),0:5)
plotTree(tree,lwd=6,ftype="off",ylim=c(-1,Ntip(tree)))
ylim=c(-1,Ntip(tree)))
vertical=FALSE)
obj<-markChanges(tree,plot=FALSE)
for(i in 1:nrow(obj)){
states<-as.numeric(strsplit(rownames(obj)[i],"->")[[1]])
up<-if(states[1]>states[2]) TRUE else FALSE
cex<-0.8
arrows(obj[i,1],obj[i,2]-0.8*mean(strheight(LETTERS)*cex),
obj[i,1],obj[i,2]+0.8*mean(strheight(LETTERS)*cex),
length=0.5*mean(strheight(LETTERS,units="inches")*cex),
lwd=3,col="red",ljoin=1,code=if(up) 1 else 2)
}
``````

``````x<-getStates(tree,"tips") ## our data from simulation
sort(unique(x))
``````
``````## [1] "0" "1" "2" "3" "4" "5"
``````

OK, this is the real history. Now, let's imagine we don't know the history, but we suppose that loss & gain occur at different rates:

``````model<-matrix(c(0,1,0,0,0,0,
2,0,1,0,0,0,
0,2,0,1,0,0,
0,0,2,0,1,0,
0,0,0,2,0,1,
0,0,0,0,2,0),6,6)
rownames(model)<-colnames(model)<-0:5
model
``````
``````##   0 1 2 3 4 5
## 0 0 2 0 0 0 0
## 1 1 0 2 0 0 0
## 2 0 1 0 2 0 0
## 3 0 0 1 0 2 0
## 4 0 0 0 1 0 2
## 5 0 0 0 0 1 0
``````
``````x<-to.matrix(x,as.character(0:5))
smapsI<-make.simmap(tree,x,nsim=100,model=model)
``````
``````## make.simmap is sampling character histories conditioned on the transition matrix
## Q =
``````
``````##           0         1         2         3         4         5
## 0 -0.540027  0.540027  0.000000  0.000000  0.000000  0.000000
## 1  1.274384 -1.814411  0.540027  0.000000  0.000000  0.000000
## 2  0.000000  1.274384 -1.814411  0.540027  0.000000  0.000000
## 3  0.000000  0.000000  1.274384 -1.814411  0.540027  0.000000
## 4  0.000000  0.000000  0.000000  1.274384 -1.814411  0.540027
## 5  0.000000  0.000000  0.000000  0.000000  1.274384 -1.274384
``````
``````## (estimated using likelihood);
## and (mean) root node prior probabilities
## pi =
``````
``````##         0         1         2         3         4         5
## 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
``````
``````## Done.
``````
``````smapsI
``````
``````## 100 phylogenetic trees with mapped discrete characters
``````
``````obj<-summary(smapsI)
obj
``````
``````## 100 trees with a mapped discrete character with states:
##  0, 1, 2, 3, 4, 5
##
## trees have 60.19 changes between states on average
##
## changes are of the following types:
##       0,1 0,2 0,3 0,4 0,5  1,0  1,2 1,3 1,4 1,5 2,0  2,1  2,3 2,4 2,5 3,0
## x->y 2.66   0   0   0   0 5.94 1.33   0   0   0   0 6.11 1.74   0   0   0
##      3,1  3,2  3,4 3,5 4,0 4,1 4,2   4,3  4,5 5,0 5,1 5,2 5,3   5,4
## x->y   0 9.54 4.25   0   0   0   0 10.41 6.56   0   0   0   0 11.65
##
## mean total time spent in each state is:
##              0         1          2         3          4         5
## raw  5.1938181 4.5646540 3.83968729 5.9647057 10.4758124 9.2228060
## prop 0.1322879 0.1162629 0.09779781 0.1519226  0.2668216 0.2349072
##         total
## raw  39.26148
## prop  1.00000
``````
``````plot(obj,colors=colors,ylim=c(-1,Ntip(smapsI[[1]])),ftype="off")
vertical=FALSE)
``````

We can similarly plot the location of reconstructed changes on any of stochastic mapped trees, for instance:

``````plotTree(smapsI[[1]],lwd=6,ftype="off",ylim=c(-1,Ntip(smapsI[[1]])))
ylim=c(-1,Ntip(smapsI[[1]])))
vertical=FALSE)
obj<-markChanges(smapsI[[1]],plot=FALSE)
for(i in 1:nrow(obj)){
states<-as.numeric(strsplit(rownames(obj)[i],"->")[[1]])
up<-if(states[1]>states[2]) TRUE else FALSE
cex<-0.8
arrows(obj[i,1],obj[i,2]-0.8*mean(strheight(LETTERS)*cex),
obj[i,1],obj[i,2]+0.8*mean(strheight(LETTERS)*cex),
length=0.5*mean(strheight(LETTERS,units="inches")*cex),
lwd=3,col="red",ljoin=1,code=if(up) 1 else 2)
}
``````

In this case, showing a pattern that is broadly similar to the generating pattern.

Finally, if we (for instance), knew that the ancestral state should have a particular value a priori - for instance, in this case, `"5"`, we code set a strong prior on the state at the root to be `"5"`. E.g.:

``````prior<-setNames(c(rep(0,5),1),0:5)
prior
``````
``````## 0 1 2 3 4 5
## 0 0 0 0 0 1
``````
``````smapsII<-make.simmap(tree,x,nsim=100,model=model,pi=prior)
``````
``````## make.simmap is sampling character histories conditioned on the transition matrix
## Q =
``````
``````##           0         1         2         3         4         5
## 0 -0.540027  0.540027  0.000000  0.000000  0.000000  0.000000
## 1  1.274384 -1.814411  0.540027  0.000000  0.000000  0.000000
## 2  0.000000  1.274384 -1.814411  0.540027  0.000000  0.000000
## 3  0.000000  0.000000  1.274384 -1.814411  0.540027  0.000000
## 4  0.000000  0.000000  0.000000  1.274384 -1.814411  0.540027
## 5  0.000000  0.000000  0.000000  0.000000  1.274384 -1.274384
``````
``````## (estimated using likelihood);
## and (mean) root node prior probabilities
## pi =
``````
``````## 0 1 2 3 4 5
## 0 0 0 0 0 1
``````
``````## Done.
``````
``````obj<-summary(smapsII)
obj
``````
``````## 100 trees with a mapped discrete character with states:
##  0, 1, 2, 3, 4, 5
##
## trees have 59.41 changes between states on average
##
## changes are of the following types:
##       0,1 0,2 0,3 0,4 0,5  1,0  1,2 1,3 1,4 1,5 2,0  2,1  2,3 2,4 2,5 3,0
## x->y 2.26   0   0   0   0 5.58 1.14   0   0   0   0 5.98 1.48   0   0   0
##      3,1  3,2  3,4 3,5 4,0 4,1 4,2   4,3  4,5 5,0 5,1 5,2 5,3   5,4
## x->y   0 9.47 3.55   0   0   0   0 10.96 5.03   0   0   0   0 13.96
##
## mean total time spent in each state is:
##              0         1          2         3         4          5
## raw  5.1728761 4.5440518 3.68522497 5.1720941 9.6365903 11.0506463
## prop 0.1317545 0.1157382 0.09386362 0.1317346 0.2454464  0.2814628
##         total
## raw  39.26148
## prop  1.00000
``````
``````plot(obj,colors=colors,ylim=c(-1,Ntip(smapsII[[1]])),ftype="off")