Fig. 1: Gene expression inheritance categories, types of cis- and trans-regulation and their models through fractional occupancies of specific binding sites.

A Gene expression inheritance categories sensu Yoo et al.³⁵; the pictograms indicate expression levels in parental species A and B whose diploid genomes are denoted as AA and BB, respectively, while hybrid is denoted as AB. Simplified figure contains 8 out of 12 total categories; details provided in Supplementary Note 1. B Types of cis- and trans-regulation of hybrids’ allele expression. For each hypothetical gene (represented by a randomly chosen individual dot), the scatterplot demonstrates its expression divergence between parental species A and B on the \(x\)-axis (i.e. the \({\log }_{2}\) fold change difference between the gene’s expression in parents corresponding to \({\log }_{2}({f}_{{{\rm{A}}}}/{f}_{{{\rm{B}}}})\) ratio in our model notation) and relative expression of hybrid’s alleles A_hyb and B_hyb on the \({{\rm{y}}}\)-axis (i.e. RAE corresponding to \({\log }_{2}({f}_{{{\rm{H}}}}^{{{\rm{A}}}}/{f}_{{{\rm{H}}}}^{{{\rm{B}}}})\) in our model notation, see Eq. 20 ad 21). Four types of cis-/trans-regulatory interactions are depicted, depending on the slope of correlation \(a\) between \({{\log }_{2}}(f_{{{\rm{H}}}}^{{{\rm{A}}}}/{f}_{{{\rm{H}}}}^{{{\rm{B}}}})\) and \({{\log }_{2}}(f_{{{\rm{A}}}}/{f}_{{{\rm{B}}}})\) ratios: (1) pure cis regulation (\(a \sim 1\); blue dots); (2) pure trans regulation (\(a \sim 0\); red dots) when the RAE is balanced irrespective of parental divergence implying that both alleles are equally regulated by a common suite of TFs (i.e., when \({\log }_{2}({f}_{{{\rm{H}}}}^{{{\rm{A}}}}/{f}_{{{\rm{H}}}}^{{{\rm{B}}}})=0\)); (3) compensating cis-/trans-interaction (\(a \, > \, 1\); yellow dots) and (4) enhancing cis-/trans-interaction (\(0 \, < \, a \, < \, 1\) black dots). Details are provided in Supplementary Note 1. C Fractional occupancies of specific binding sites (of A- and/or B-origin) under the reference scenario 1. Fractional occupancies are weighted by their genomic dosages; scenario 1 assumes single specific site per chromosome and negligible concentration of free TFs. X-axis shows the expression divergence between parental species in terms of fractional occupancies \({\log }_{2}({f}_{{{\rm{A}}}}/{f}_{{{\rm{B}}}})\), \(y\)-axis indicates the occupancies of all specific sites in an individual. Note: Types of individuals and strength of cross regulation are denoted by line colours, styles and symbols. Species A is indicated by cyan line, species B by yellow line, their average expression (i.e. [expression of AA+ expression of BB]/2) are denoted by grey line, diploid hybrid AB by red lines. Dotted lines show results for \({{\rho }}=1\) (full cross-regulation), slashed lines show for \({{\rho }}=2\) (limited cross-regulation) and full lines show \({{\rho }}=10000\) (no cross-regulation).