Functional phylogenies for two species at evolutionary distances
t1 and
t2, counted from their last common ancestor at time
ta = 0. Branch segments with neutral evolution are shown in blue with evolution under selection in red. (
a) Neutral evolution of nonfunctional loci, described by the energy pair distribution

. (
b) Evolution of functional loci under time-independent selection, described by the distribution
Qt. (
c) Evolution under time-dependent selection generating a functional locus in species 1 and a nonfunctional locus in species 2, described by the distribution

. This mode involves either a gain of function between ancestor and 1 or a loss of function between ancestor and 2. The switching event at time
t′ is denoted by a green arrow. The corresponding mode where the roles of the two species are interchanged is described by the distribution

.