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Distribution of branch lengths following simulation under GTR+G

I have used GTR+G in R using PhyloSim to simulate the evolution of nucleotide sequences along a perfect star topology (I'm doing some work on homoplasy and branch attraction).

G was set to have four categories, and a shape parameter of 0.334437.

At the end of the simulation, when I fit the simulated sequences to the star tree to get branch lengths, I have a more-or-less normal distribution of branch lengths.

Should I expect the distribution of branch lengths to be normal? Or should I expect it to reflect the gamma distribution I set with the shape parameter in the simulations?

I'm just having trouble getting my head around what I should expect to see.

Thank you to anyone who can help.

r phylogenetics

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