Shape parameter of the gamma distribution of rate variation

Question

[dieter]

Hello all, I have another question for the experts where I did not find any answer, yet. It's about the shape parameter of the gamma distribution of rate variation. Known as Alpha. I know what the parameter is, and I know that if when Alpha = 1 the gamma distribution matches the exponential distribution. My question is: What does the setting "exponential" for example at MrBayes mean? At MrBayes I can set Shapepr=exponential(value). And I can set Shapepr=fixed(value). What is the difference? All the best Dieter

[natasha.sernova]

See this pdf-file for details of gamma-distribution:

https://www.google.ru/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&ved=0ahUKEwiypbSgvfPXAhXKHJoKHQWxCakQFghtMAg&url=http%3A%2F%2Fmath.bme.hu%2F~nandori%2FVirtual_lab%2Fstat%2Fspecial%2FGamma.pdf&usg=AOvVaw0cPMyeFnsVsX0wWHuD4ruJ

This Biostar posts on MrBayes and gamma distibution:

The Effect Of The "Invgamma" Setting On Computing The Site Likelihood In Mrbayes?

and ask stackoverflow if the above ones are not enough:

https://stackoverflow.com/questions/29902770/how-to-specify-gamma-distribution-using-shape-and-rate-in-python

[dieter]

Thanks Natasha, But I'm sorry, the pdf only describes the gamma distribution (which I already know) - all is clear there - but it does not answr my questions. The second link leads to a discussion about the Invar Model - this has nothing to do with my question. But thanks anyway. All the best Dieter

Answer 1

[Kevin Blighe]

Hi Dieter, from what I understand, the use of exponential means that the tested gamma distributions become virtually infinite, as it would then be based on an exponential range of α (alpha). I think that the value that's passed to Exponential may relate to λ (lambda).

The other options for Shapepr are:

• uniform (the default, I believe), α values between 0 and 1.0 are tested
• fixed, fixed at a specific value of α

You may wish to confirm with the author of MrBayes.

[dieter]

Hello Kevin, I checked it again and: You are right! It is exactly how you said. I found the proof here: http://hydrodictyon.eeb.uconn.edu/eebedia/index.php/Phylogenetics:_MrBayes_Lab It is the exponetial distribution and tha parameter is no longer alpha but lambda. The interesting thing is that the new standard setting at MrBayes is the exponetial distribution with Lambda = 1 [setting Shapepr=exponential(1)]. So thanks for all. All the best Dieter

[Kevin Blighe]

Great!