Obviously, the probability of a duplicate gene being essential is the probability for both mechanisms failure, that is, (1) P E = (1 − g ) (1 − e − λ t ).
Here we propose considering the birth and death process as a fixation and maintenance index, fixation being the probability that a duplicate will spread in a population, and maintenance being the probability that a duplicate is preserved in the long term.
In this review, we define fixation rate as the probability that a duplicate, regardless of its functionality, spreads into a population (i.e., becomes fixed), and maintenance rate as the probability that a duplicate is stabilized in a population (preservation).
The evolutionary significance of gene duplication is explained by the duplication-degeneration-complementation (DDC) model, which states that the probability of a duplicate gene to be preserved increases with the occurrence of degenerative mutations in its regulatory region [36].
For states that only indicate a voters' decade of birth, the probability of a duplicate for any given voter is 58.6percentt.
A positive (respectively, negative) coefficient indicates a positive (negative) correlation between that variable in the diploid species S. tropicalis and the probability that a duplicate is retained in the tetraploid species X. laevis.
Without genetic buffering, we assume that the probability of a duplicate remains nonessential, that is, functionally compensated by another duplicate copy in the same genome, and decayed exponentially with the time t (the age of gene duplication), that is, e− λt, where λ is the loss rate of duplicate compensation by mutations.
Substituting λ(t) into the expression Λ (t | k ) for λ and calculating Φ (k ) by integrating across all possible divergence times give the probability that a duplicate gene with a given d S value will fail to fix (fig. 1) assuming a set of proteins of average length, as well as protein lengths at the 25% and 75% percentile.
In the duplication model, at each iteration, we randomly pick a vertex to duplicate with probability proportional to its degree and randomly drop the duplicated edges with probability at 0.5 in order to t the degree distributions and sparsity of biological networks.
In the case where the two duplicates' probabilities of retention differ by a factor r, the two duplicates have probabilities 0.5(1±r) along each branch, and, assuming independent loss along each branch, the probability that X and C retain the same duplicate is [0.5(1+r)]2+[0.5(1−r)]2 = 0.5(1+r2), giving an average internal branch length of d-r2 d-e), which is less than d-r2 d-e
The probability of subfunctionalization or neofunctionalization of a duplicate gene increases with recombination rate [ 49, 50], and once the new gene copy has reached fixation, the probability of the duplicate gene's survival also increases with recombination rate [ 51].
