The Collaborative Cross is a cross among eight inbred strains of mice using a combinatorial design to yield many distinct eight-line hybrids that will be inbred to produce recombinant inbred (RI) strains.  The goal of this cross at Oak Ridge National Laboratory is to initiate the production of 1680 (8x7x6x5) independent lines, and inbreed as many as possible.  To maximize the utility of these RI strains, the genetic contributions of each progenitor, and pairwise combinations of progenitors, should be equal when averaged across all hybrid lines.  Although each progenitor contributes autosomal genes with equal probability, sex chromosomes and mitochondrial genomes come preferentially from certain progenitors.

Four pairwise chromosome combinations may be significant (Y and mitochondria, X and Y, pairwise X combinations, and autosomal combinations in the first mating).  Eight progenitor lines yield, for each chromosome combination, 56 pairwise combinations, each of which should be represented by 1680/56 = 30 strains.  The variance of the number of hybrid lines for each chromosome combination (calculated over 56 strain combinations) is a convenient measure of balance.  Using this criterion, and using a greedy algorithm to add new hybrid combinations (from ~40,000 available) to lines already breeding, we can construct a set of 1680 hybrid lines in which each strain combination for each chromosome combination is represented by 30.0 +/- 0.2 lines.

Recently the plan for the Cross has been recalculated to accommodate the inability to obtain first-generation crosses NZO x CAST and NZO x PWK and infertility of PWK x 129 males.  Even with this deficit, three chromosome combination types can still be balanced well: Y and mitochondria, X and Y chromosomes, and pairwise X combinations.  Frequencies of these combinations vary by 0.8% to 2.1% across 56 strain combinations.  Frequencies of the G1 autosome combinations vary by 8.7%, excluding the NZO x CAST and NZO x PWK frequencies, which are necessarily zero.

Supported by The Ellison Medical Foundation, NHGRI (P41HG001656), NCI MMHCC (U01CA105417)