Fig. 2

Diversity profile intersection predicts differential sub-repertoire clonal expansion. a Intersecting Diversity (^α D) profiles of two immune repertoires with different clonal frequency distributions are shown (immune repertoire 1 with clonal frequencies of 33 %, 29 %, 28 %, 5 %, 4 %, 1 %; immune repertoire 2 with clonal frequencies of 42 %, 30 %, 10 %, 8 %, 5 %, 5 %). b Intersection of frequency-ordered cumulative frequency distributions of immune repertoires shown in (a). The Diversity (^α D) function is Schur-concave, which predicts intersection of cumulative frequency curves if intersection in the profile space has occurred. Since cumulative frequency curves were derived from frequency-ordered clonal frequency distributions, the exact delineation of differentially expanded sub-repertoires becomes possible. Here, until clonal rank 2 immune repertoire 2 is higher clonally expanded (area I) whereas the opposite is true from clonal rank 3 onward (area II). The grey-shaded area indicates the clonal expansion difference between the two immune repertoires. Since the difference in clonal expansion is expressed in percent, the determination of relative oligo-/polyclonality with respect to a given region of the immune repertoires becomes possible