Dependence of the rates of gains, losses, expansion and reductions on phylogenetic depth. (a) Gains, (b) losses, (c) expansions and (d) reductions per unit of branch length vs the phylogenetic depth. The figure excludes singletons, i.e., gains in the terminal branches of the tree are not represented. Both x and y axes have a logarithmic scale. The phylogenetic depth is measured in the number of nucleotide substitutions per site.