PROCAIN combines residue substitution constraints at individual sequence positions with sequence motif matching, residue conservation and SS scoring.
Furthermore, we predict that introns might be equally as efficient for retracing the phylogeny of voles and lemmings – as recently shown for similar recent evolutionary radiations [ 14, 29, 59] – because of their relaxed substitution constraints and their potentially greater number of informative sites.
Like the A. kamchatica homeologs, for the two diploid species, genes with high expression showed lower proportions of neutral substitutions (relaxed constraint) and higher proportions of strongly deleterious substitutions compared with lowly expressed genes.
We must then recursively compute the set of satisfying substitutions of constraint (S C,a_1,b_1) = C,a_1,(T^3,a_1)).
Again, we must recursively compute the set of satisfying substitutions of constraint (S_1(C,a_2,b_2) = C,a_2,(T^5,and)), and the process goes on forever.
Consider again Example 2: we want to obtain the set of satisfying substitutions for constraint (pi =C,a, T,a)), given (Theta = { forall a,b.,C, a, b Rightarrow C,(T^2, a), b }) (computation with input (pi ) by the function in Fig. 3 does not terminate).
The most important steps are substitution of complex constraints with sets of simpler ones and insertion of redundant constraints by solving triangles and determining sums and differences of adjacent angles.
Following the standard analysis of Armington functions, changing import demand and supply is a function of change in relative prices, demand and substitution elasticities, supply constraints and trade shares (Minor and Tsigas 2008).
Since the rate of synonymous substitutions is usually higher than that of nonsynonymous substitutions, ignoring overlap constraints would result in the underestimation of the rate of synonymous substitutions.
For any substitution (S) and constraint set (P) we have that (lfloor S P rfloor subseteq lfloor P rfloor ).
Both lineages show overall increased rates of nucleotide substitution, relaxed selective constraint, and lack any appreciable shift in synonymous codon usage in spite of loss of multiple tRNAs [ 46](Table 5).
