Body: <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>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-03-15T19:28:56.553Z
Comments.Text: related: https://bioinformatics.stackexchange.com/questions/13605/what-does-instantaneous-rate-matrix-mean
Comments.UserDisplayName: Maximilian Press
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-03-16T20:10:16.867Z
Comments.Text: @MaximilianPress I saw this post. Although both questions concern rate matrices, they are nevertheless quite distinct.
Comments.UserDisplayName: Namenlos
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-03-16T20:14:59.420Z
Comments.Text: 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.
Comments.UserDisplayName: Maximilian Press
Tags: <phylogenetics><substitution-model>
Title: How is the instantaneous rate of an instantaneous rate matrix determined?
ThreadText: # 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**: @username_1 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
  
  