The impracticalities of multiplicatively-closed codon models: a retreat to linear alternatives (Q2192661)

The paper presents a link between Markov chains theory and the matrix Lie algebra, namely, the closure under matrix multiplication which can be successfully applied on phylogenetics. To estimate the non-synonymous/ synonymous rate ratio the authors propose two approaches ``the first is the linear closure which is the smallest linear space which contains the model, and the second is the linear version which changes multiplicative constraints in the model to additive ones''; they describe in detail the mathematical and algorithmic details of the idea and also highlight the parameter-driven limitations of these models.