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Viral capsids are structurally constrained by interactions amongst the aminoacids of the constituting proteins. Therefore, epistasis is expected to evolveamongst sites engaged in physical interactions, and to influence theirsubstitution rates. In order to study the distribution of structural epistasis,we modeled \emph{in silico} the capsid of 18 species of the \phix \, family,including the wild type. \phix \, is amongst the simplest organisms, making itsuitable for experimental evolution and \emph{in silico} modeling. We foundnearly 40 variable amino acid sites in the main capsid protein across the 18species. To study how epistasis evolved in this group, we reconstructed theancestral sequences using a Bayesian phylogenetic framework. The ancestralstates include 8 variable amino acids, for a total of 256 possible haplotypes.The $dN/dS$ ratio is low, suggesting strong purifying selection, consistentwith the idea that the structure is constrained by some form of stabilizingselection. For each haplotype in the ancestral node and for the extant specieswe estimated \emph{in silico} the distribution of free energies and ofepistasis. We found that free energy has not significantly increased butepistasis has. We decomposed epistasis up to fifth order and found thathigh-order epistasis can sometimes compensate pairwise interactions, oftenmaking the free energy seem additive. By synthesizing some of the ancestralhaplotypes of the capsid gene, we measured their fitness experimentally, andfound that the predicted deviations in the coat protein free energy do notsignificantly affect fitness, which is consistent with the stabilizingselection hypothesis.

Evolutionary interplay between structure, energy and epistasis in the coat protein of the $\phi \chi 174$ phage family