These affinities [[ 94], p.199] were of structure and "economy" [[ 94], p.195], the latter term connoting features of reproduction, nutrition, physiology and ecology; branch lengths correspond with degree of affinity, and gaps may occur at any point due to extinction of families [[ 94], pp.206,214].
Perhaps most notably, DupliPHY-ML now contains a new model of gene family evolution that contains a parameter for the extinction of a family.
Subsequently, we expanded the BDIM framework by introducing stochastic BDIMs, which account not only for the stationary state of the gene ensemble but also for the characteristics of evolution of the system, such as the probability of the formation of a family of the given size before extinction and the mean times of formation and extinction of a family of a given size [ 43].
Below we compute the mean time to extinction of a family of the given size for different versions of BDIM; the mean time to extinction of the largest family in the given genome is of particular interest.
Even without local patch extinction, local extinction of the family occurs due to the recurrent inflow of other immigrants.
If this does not occur, it implies extinction of the family lineage and unrest for the soul of the deceased.
The number of successful emigrants is counted until local extinction of the family descended from the immigrant.
The mean number of elementary events before the extinction of a family of the given size, e n, is computed using formulas (A.7.13 - A.7.15) and Figures 31 and 32 show the corresponding dependences for family extinction.
The mean time to extinction of the family of initial size n, E(S(n)), is given by the general formula A.3.2.
Furthermore, although the random extinctions could produce high MPD and MNTD values, those rarely came from the extinction of derived families.
The times of formation and extinction of gene families are random variables with unknown distributions.
