Expectations of duplicate gene retention under the gene duplicability hypothesis

Gene duplication is an important process in evolution. What causes some genes to be retained after duplication and others to be lost is a process not well understood. The most prevalent theory is the gene duplicability hypothesis, that something about the function and number of interacting partners (number of subunits of protein complex, etc.), determines whether copies have more opportunity to be retained for long evolutionary periods. Some genes are also more susceptible to dosage balance effects following WGD events, making them more likely to be retained for longer periods of time. One would expect these processes that affect the retention of duplicate copies to affect the conditional probability ratio after consecutive whole genome duplication events. The probability that a gene will be retained after a second whole genome duplication event (WGD2), given that it was retained after the first whole genome duplication event (WGD1) versus the probability a gene will be retained after WGD2, given it was lost after WGD1 defines the probability ratio that is calculated. Since duplicate gene retention is a time heterogeneous process, the time between the events (t1) and the time since the most recent event (t2) are relevant factors in calculating the expectation for observation in any genome. Here, we use a survival analysis framework to predict the probability ratio for genomes with different values of t1 and t2 under the gene duplicability hypothesis, that some genes are more susceptible to selectable functional shifts, some more susceptible to dosage compensation, and others only drifting. We also predict the probability ratio with different values of t1 and t2 under the mutational opportunity hypothesis, that probability of retention for certain genes changes in subsequent events depending upon how they were previously retained. These models are nested such that the mutational opportunity model encompasses the gene duplicability model with shifting duplicability over time. Here we present a formalization of the gene duplicability and mutational opportunity hypotheses to characterize evolutionary dynamics and explanatory power in a recently developed statistical framework. This work presents expectations of the gene duplicability and mutational opportunity hypotheses over time under different sets of assumptions. This expectation will enable formal testing of processes leading to duplicate gene retention.