<p>In molecular evolution, I know that the instantaneous rate of the rate matrix is the limit of the rate as time approaches 0, but what I don't understand is how this rate is established or what I can do with this number.</p>
<p>For instance, if a discrete character is thought to have changed from 0 to 1 five times on a tree with a root age of 40 million years, is the proportion 5 / 40 million the same as the instantaneous rate of change? If not, how exactly are they different?</p>
<p>From a different perspective, let's assume an (absolute) instantaneous rate of 0.0001 and let's say I have a tree with a root age of 2 million years. Can I multiply 0.0001 by two million to get the expected number of transitions of that character across the tree?</p>

CC BY-SA 4.0
2021-03-15T19:28:56.553Z
related: https://bioinformatics.stackexchange.com/questions/13605/what-does-instantaneous-rate-matrix-mean
Maximilian Press
CC BY-SA 4.0
2021-03-16T20:10:16.867Z
@MaximilianPress I saw this post. Although both questions concern rate matrices, they are nevertheless quite distinct.
Namenlos
CC BY-SA 4.0
2021-03-16T20:14:59.420Z
I agree; note that I didn't mark it as duplicate. However, they have a substantial overlap and it is worth annotating as such, for anyone coming across this question.
Maximilian Press
<phylogenetics><substitution-model>
How is the instantaneous rate of an instantaneous rate matrix determined?
# How is the instantaneous rate of an instantaneous rate matrix determined?

(Asked by: username_0 on 2021-03-12)

In molecular evolution, I know that the instantaneous rate of the rate matrix is the limit of the rate as time approaches 0, but what I don't understand is how this rate is established or what I can do with this number.

For instance, if a discrete character is thought to have changed from 0 to 1 five times on a tree with a root age of 40 million years, is the proportion 5 / 40 million the same as the instantaneous rate of change? If not, how exactly are they different?

From a different perspective, let's assume an (absolute) instantaneous rate of 0.0001 and let's say I have a tree with a root age of 2 million years. Can I multiply 0.0001 by two million to get the expected number of transitions of that character across the tree?

**Tags:** phylogenetics, substitution-model
> **Comments:**
> **username_1**: related: https://bioinformatics.stackexchange.com/questions/13605/what-does-instantaneous-rate-matrix-mean  
> **username_0**: @MaximilianPress I saw this post. Although both questions concern rate matrices, they are nevertheless quite distinct.  
> **username_1**: I agree; note that I didn't mark it as duplicate. However, they have a substantial overlap and it is worth annotating as such, for anyone coming across this question.  

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## 0 answers

