# What is the distribution of the expected number of lineages in a birth-death tree after time T?

I've been looking at The reconstructed evolutionary process by Nee et al. 1994 and they provide a number of equations dealing with the birth-death process, specifically the "reconstructed" birth-death process where you only have information about lineages that currently exist today.

I am interested in this equation for the likelihood of observing N lineages after time T:

What I want is the distribution of the expected number of lineages N after time T given per-lineage birth and death rates lambda and mu. I've looked around and haven't found anything providing such an equation.

• You are actually asking the explanation of the entire paper. There are 20 equations that precede this one. Have you understood them all? – WYSIWYG Aug 20 '15 at 8:37
• @CactusWoman I reread your post and got confused. What do you mean by distribution of the expected number? Distribution over what parameter(s)? Expected value of which distribution? – Remi.b Aug 20 '15 at 14:45
• Maybe it is more strategic to direct your question more in reaction to the content of the paper. Pick a particular step you don't understand and ask what it means. – Remi.b Aug 20 '15 at 14:46
• @Remi.b I was beginning to write an answer but figured out that even the first equation relies on many assumptions which are not really defined in this paper. The equation in the question follows equation(3) which is from a 1948 paper by Kendall. That's why I asked the OP if they have understood the previous equations. – WYSIWYG Aug 20 '15 at 14:56