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bioRxiv · 10.64898/2026.08.02.742285

MMMAS: A Mendelian Mismatch Matrix Analysis System for Deterministic Pre-Screening of Germplasm Collections

Chen, Q.·chen, L.·Fan, J.·Yang, X.·Zhang, J.·Du, W.·Liu, Z.·Hu, H.
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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.

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Chen, Q., chen, L., Fan, J., Yang, X., Zhang, J., Du, W., Liu, Z., Hu, H.. 2026-08-06. MMMAS: A Mendelian Mismatch Matrix Analysis System for Deterministic Pre-Screening of Germplasm Collections. https://doi.org/10.64898/2026.08.02.742285

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