Ohnolog motif frequencies provide a method for estimating ancestral connectivity and rewiring parameters. (

*A*) Immediately after duplication, ohnolog motifs can be one of six zero-order motifs with probability vector m

_{0} (row vector shown as its transpose). The probabilities of observing each ancestral configuration, and hence each zero-order motif, are listed as functions of the ancestral interaction (

*P*_{i}) and self-interaction (

*P*_{si}) probabilities. Thirteen of the 19 motifs cannot arise in this fashion, enforcing a strong constraint on the initial conditions of the system. (

*B*) The six zero-order motifs can evolve into any one of the 19 possible motifs. The transition probabilities are given by a matrix T, whose entries T

_{ij} represent the probability of a member of the motif class in row

*i* becoming a member of the motif class in column

*j*. This matrix is represented iconographically, with each entry showing the interaction changes necessary to go from one motif to another. Edges are colored as in

*B* and symmetry axes are shown by dotted lines. Horizontal and vertical symmetry axes indicate reflections that yield alternative icon-procedures for getting from class

*i* to class

*j*. A diagonal symmetry axis indicates that exchanging the positions of the vertices in either ohnolog pair yields an alternative icon-procedure for getting from class

*i* to class

*j* (SI Table 3). The value of each entry is given by

*T*_{i,j} = 2

^{S}*P*_{+}^{nG}*P*_{−}^{nL}(1 −

*P*_{−})

^{nR}(1 −

*P*_{+})

^{nA}, where

*n*_{G},

*n*_{L},

*n*_{R}, and

*n*_{A} represent the number of edges that are gained (green), lost (red), retained (black), or remain absent (gray). The values of the icons in each row sums to 1. As an illustration, the probability of a motif in class

becoming a motif of class

graphically is

that equals 2

^{2} ·

*P*_{+}^{2} ·

*P*_{−}^{1} · (1-

*P*_{+})

^{3} · (1-

*P*_{−})

^{0} = 4

*P*_{+}^{2} *P*_{−} (1-

*P*_{+})

^{3}.

## PubMed Commons