  We propose and study a class-expansion/innovation/loss model of genome
evolution taking into account biological roles of genes and their constituent
domains. In our model numbers of genes in different functional categories are
coupled to each other. For example, an increase in the number of metabolic
enzymes in a genome is usually accompanied by addition of new transcription
factors regulating these enzymes. Such coupling can be thought of as a
proportional "recipe" for genome composition of the type "a spoonful of sugar
for each egg yolk". The model jointly reproduces two known empirical laws: the
distribution of family sizes and the nonlinear scaling of the number of genes
in certain functional categories (e.g. transcription factors) with genome size.
In addition, it allows us to derive a novel relation between the exponents
characterising these two scaling laws, establishing a direct quantitative
connection between evolutionary and functional categories. It predicts that
functional categories that grow faster-than-linearly with genome size to be
characterised by flatter-than-average family size distributions. This relation
is confirmed by our bioinformatics analysis of prokaryotic genomes. This proves
that the joint quantitative trends of functional and evolutionary classes can
be understood in terms of evolutionary growth with proportional recipes.
