  In this work, we develop a stochastic model of gene gain and loss with the
aim of inferring when (if at all) in evolutionary history and association
between two genes arises. The data we consider is a species tree along with
information on the presence or absence of two genes in each of the species. The
biological motivation for our model is that if two genes are involved in the
same biochemical pathway, i.e. they are both required for some function, then
the rate of gain or loss of one gene in the pathway should depend upon the
presence or absence of the other gene in the pathway. However, if the two genes
are not functionally linked, then the rate of gain or loss of one gene should
be independent of the state of another gene.
  We simulate data under this model to determine under what conditions a shift
from the independent rates class to the dependent rates class can be detected.
For example, how large a tree is required and how large a shift in the rates is
needed before Akaike information criterion (AIC) supports a model with two rate
classes over a simpler model with just one rate class? If a model with two rate
classes is preferred, can it correctly detect where on the evolutionary tree
the shift occurred?
