MMM: A deterministic Mendelian mismatch matrix framework for germplasm collection quality assessment, demonstrated in apple and sweet cherry

Abstract

Pedigree errors, duplicate accessions, and undocumented kinship limit the effective use of large genebank collections. Existing tools such as CERVUS and COLONY require allele-frequency estimates and return relationship-level assignments, providing no collection-wide view of Mendelian consistency. We developed the Mendelian Mismatch Matrix (MMM) framework and its open-source implementation, MMMAS (Mendelian Mismatch Matrix Analysis System). We applied MMM to apple (Malus x domestica; 1,085 accessions, 15 SSRs) and sweet cherry (Prunus avium; 383 accessions, 13 SSRs) datasets from the German Fruit Genebank. MMM converts pairwise Mendelian mismatch numbers (Mmn) into an N x N symmetric matrix, from which we derive four collection-scale indices (Mmin, the Mendelian minimum mismatch number; Mavg, the Mendelian average mismatch number; Mzmp, the Mendelian zero-mismatch partner number; Mmmd, the Mendelian mismatch-mode duplication index) and the Mendelian Exhaustive Stratification (MES) grading system. Apple showed a gradient-type structure (Mendelian Grade-gap Index, MGI = 0.125), sweet cherry a broken-type structure (MGI = 0.545). The Mmin-Mavg strategy identified 20 and 10 distinct accessions in apple and sweet cherry, including the scab-resistance donor Malus x floribunda 821 (Rvi6) and the fire-blight donor M. x robusta 5. The Mmmd index flagged one literature-confirmed pair of duplicate genotypes in sweet cherry. Of CERVUS-confirmed parent-offspring pairs, 97.31% in apple and 100% of high-confidence pairs in sweet cherry fell within Mmn <= 1. Mzmp rankings matched documented breeding history, with 'Cox Orange' (Mzmp = 57) and 'Luebecker Bunte' (Mzmp = 49) ranking first in each species. The complete end-to-end analysis of all 588,070 apple pairwise comparisons took 7.24 s on an ordinary workstation. This deterministic pre-screening framework, with a parameter-free core, supports routine quality assessment in germplasm collections.