Fig. 4. Heterogeneity of substitution rates among alleles on static SPFLs imitates entrenchment.

a Consider three classes of alleles, characterized by different constant substitution rates: fast (red), moderate (green), and slow (blue) alleles. For each allele, we can calculate the substitution frequency on the phylogenetic branches located at different evolutionary distances from the gain of that allele (each dot corresponds to a single branch). If the dynamics of replacement of these alleles are analyzed separately for each substitution-rate class, no spurious signal of entrenchment or senescence is observed (left). However, if alleles from different classes are pooled together, the substitution frequency appears to decrease with time, mimicking the signal of entrenchment (right). On a static flat SPFL (b, log fitness vector = [0, 0, ..., 0]), i.e., when the substitution rates for all 20 alleles are the same, the frequency of replacement of the current allele on some branch of the phylogenetic tree does not depend on the time since the allele gain (each dot corresponds to a single branch). However, on a gamma-distributed SPFL (c), the heterogeneity of fitness of the alleles produces entrenchment-like decline of replacement rate of the current allele with time, although the SPFL remains static. The effect is even more pronounced on a more rugged SPFL (d, log fitness vector = [10, 0, ..., 0]). The p values are obtained with linear regression.