According to Splitstree, these are the different splits for your two trees:

Tree S1:

0.161175 Split t5,

0.161175 Split t5 t4 t2 t1 t3,

0.104381 Split t5 t6 t2 t1 t3,

0.075411 Split t5 t6 t4 t1 t3,

0.075411 Split t5 t6 t4 t2 t3,

0.028969 Split t5 t6 t4 t3,

0.06584 Split t5 t6 t3,

0.170221 Split t5 t6 t4 t2 t1,

0.77554 Split t5 t6,

Tree S2:

2.161175 Split t5,

0.161175 Split t5 t4 t2 t1 t3,

0.104381 Split t5 t6 t2 t1 t3,

0.075411 Split t5 t6 t4 t1 t3,

0.075411 Split t5 t6 t4 t2 t3,

1.0 Split t5 t6 t4 t3,

0.06584 Split t5 t6 t3,

0.170221 Split t5 t6 t4 t2 t1,

0.77554 Split t5 t6,

So Split t5, and Split t5 t6 t4 t3, are different. Calculate the absolute difference:

Split t5 => 2.161175 - 0.161175 = 2

Split t5 t6 t4 t3 => 1 - 0.028969 = 0.971031

Sum = 2.971031

Robinson-Foulds distance, as I understand it has nothing to do with branch lengths. It's a topology comparison _only_ statistic. It ignores branch length. http://en.wikipedia.org/wiki/Robinson%E2%80%93Foulds_metric

Hi Joseph,

Thanks for the reply. Just to clarify: Do the workings above refer to the "euclidean distance" which is defined on the dendropy website (http://pythonhosted.org/DendroPy/tutorial/treestats.html) as:

"The sum of absolute differences in branch lengths for equivalent splits between two trees, with the branch length for a missing split taken to be 0.0."

Would you say this is a correct definition of the above calculation (it seems to be)? In the dendropy example however they give an answer of 2.2232636377544162 for euclidean distance.

On the other hand they define the Robinson Foulds algorithm as:

"the sum of the square of differences in branch lengths for equivalent splits between two trees, with the branch length for a missing split taken to be 0.0."

I would take this (based on the above) to be:

Split t5 => 2.161175 - 0.161175 = 2^2 = 4

Split t5 t6 t4 t3 => 1 - 0.028969 = 0.971031^2 = 0.94290120

Sum = 4.94290120

Any further clarification greatly appreciated.

I think you've found a disconnect between the docs and the code here, they may say Dendropy is using euclidean distances for weighted RF, but the results it returns are based on absolute differences.

This is easy to show in the test case (but would be harder if the edges didn't line up so nicely) using R:

library(ape)
tr1 <- read.tree(text= "((t5:0.161175,t6:0.161175):0.392293,((t4:0.104381,(t2:0.075411,t1:0.075411):0.028969):0.065840,t3:0.170221):0.383247);")
tr2 <- read.tree(text= "((t5:2.161175,t6:0.161175):0.392293,((t4:0.104381,(t2:0.075411,t1:0.075411):1):0.065840,t3:0.170221):0.383247);")

dist(rbind(tr1$edge.length, tr2$edge.length), method="euclidean")
##         1
## 2 2.223264

dist(rbind(tr1$edge.length, tr2$edge.length), method="manhattan")
##1
##2 2.971031

The only problem is that I have no idea which of the these is _real_ RF-weighted distance! The paper is here but behind a pay wall for me. As Ross suggests, when people talk about Robinson-Foulds distance they usually mean the topology-only version, so it's hard to find other implementations.

Certainly something to email the Dendropy devs about, anyway.

EDIT

I think I was thrown off my the use of the word "euclidean" in comments. The value you've correctly calculated is the sum of squared differences,

sum(abs(tr1$edge.length- tr2$edge.length)^2)
## 4.942901

which is different from the euclidean distance, which is the square root of the sum of squared differences:

sqrt(sum(abs(tr1$edge.length- tr2$edge.length)^2))
## 2.223264