How to modify DNA evolution model to fit actual data? I'm working on understanding the evolution of a gene in a phylogenetic tree. I know the rates of evolution of each organism (from the tree).
I am taking a random DNA sequence with my gene, evolving it along the tree with the said rates and comparing this to the actual gene in these various organisms.
I am 'evolving' the gene if randomly at a probability determined by the rate at each step in the tree.
The gene from my simulation is different from what is actually in these organisms. How do I modify my model, so that my simulation gives the same results?
Mutation is not a random process because there are many mutational biases, e.g. the transition vs. transversion ratio. Ideally use a proper evolutionary model. Maybe try a tool that incorporates substitution and indel models. I'm not up-to-date on the best packages, but e.g.

INDELible http://abacus.gene.ucl.ac.uk/software/indelible/
Evolver https://www.drive5.com/evolver/ (not to be confused with the PAML package of the same name)