A Simple Evolutionary Model of Genetic Robustness After Gene Duplication.

When a dispensable gene is duplicated (referred to the ancestral dispensability denoted by O+), genetic buffering and duplicate compensation together maintain the duplicate redundancy, whereas duplicate compensation is the only mechanism when an essential gene is duplicated (referred to the ancestral essentiality denoted by O-). To investigate these evolutionary scenarios of genetic robustness, I formulated a simple mixture model for analyzing duplicate pairs with one of the following states: double dispensable (DD), semi-dispensable (one dispensable one essential, DE), or double essential (EE). This model was applied to the yeast duplicate pairs from a whole-genome duplication (WGD) occurred about 100 million years ago (mya), and the mouse duplicate pairs from a WGD occurred about more than 500 mya. Both case studies revealed that the proportion of essentiality for those duplicates with ancestral essentiality [PE(O-)] was much higher than that for those with ancestral dispensability [PE(O+)]. While it was negligible in the yeast duplicate pairs, PE(O+) (about 20%) was shown statistically significant in the mouse duplicate pairs. These findings, together, support the hypothesis that both sub-functionalization and neo-functionalization may play some roles after gene duplication, though the former may be much faster than the later.