## 5 Conclusions  
Based on a novel modelling approach allowing GWAS with SNP by farming system interaction effects, we identified significant main and interaction effects for specific pathogens and cell fractions in milk. The detailed udder health phenotyping strategy, combined with the novel GWAS, contributed to the detection of significant SNPs for PMN, sN, bN, MAJOR, MINOR, cultural negative, CNS, AER, and AESC. For the traits PMN and sN, MINOR and CNS, and MINOR and cultural negative, we identified overlapping significant SNP effects, indicating similar genetic and physiological mechanisms. In this regard, we inferred the potential candidate genes _EVA1A_ and _CTNNA3_ which are involved in the pathways for autophagy and programmed cell death (_EVA1A_), in the MAPK pathway, and in the adherens-junctional complex in epithelial cells for cellular adherence (_CTNNA3_). Interestingly, for the traits PMN, MAJOR, MINOR, cultural negative, AER, and AESC, we identified significant SNP by farming system interactions, indicating opposite effects of the same SNP markers in cubic and compost. Annotated potential candidate genes were _CHL1_ and _HEMKI_, which are involved in pathways regulating the immune system dependent on stress levels and in the development of the immune system. From a practical perspective, our results suggest farming system-specific breeding strategies in order to improve udder health in both systems. In addition, our new modelling approach considering SNP main and interactions effects simultaneously simplifies the estimations and removes the need to split the data. For future breeding strategies to improve udder health, a very precise definition of mastitis traits is imperative as we identified different genetic mechanisms in response to specific pathogens. **Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/an11061839/s1](https://www.mdpi.com/article/10.3390/an11061839/s1)]([https://www.mdpi.com/article/10.3390/an11061839/s1](https://www.mdpi.com/article/10.3390/an11061839/s1)), Figure S1: Manhattan plots displaying the GWAS results (\(p\)-values) for the main SNP effects for: (a) segmented neutrophils, (c) banded neutrophils, (e) MINOR pathogens (_Coagulase-negative staphylococci_ and _Corynebacterium sp._), (g) cultural negative, (i) _Aerobic bacilli_, (k) _Aesculin hydrolyzing streptococci_, and (m) _Coagulase-negative staphylococci_. Manhattan plot displaying the GWAS results (\(p\)-values) for the interaction of the SNP and housing system effects for: (b) segmented neutrophils, (d) banded neutrophils, (f) MINOR pathogens (_Coagulase-negative staphylococci_ and _Corynebacterium sp._), (h) cultural negative, (j) _Aerobic bacilli_, (l) _Aesculin hydrolyzing streptococci_, and (n) _Coagulase-negative staphylococci_. Bonferroni-corrected genome-wide significance (red line) and less conservative threshold (grey line) (\(p_{\text{sugg}}=0.05/4479=1.12\times 10^{-5}\)) are shown. Red triangles highlight the significant SNP. **Author Contributions:** Conceptualization, S.K. ; data curation, P.W., K.B., P.E. and C.W. ; formal analysis, P.W., T.Y. and K.B. ; investigation, P.W., K.B., P.E. and C.W. ; methodology, P.W. and T.Y. ; laboratory, P.W., K.B., P.E., C.W. and K.S. ; project administration, K.B., P.E. and S.K. ; supervision, S.K. ; validation, P.W. and K.B. ; visualization, P.W. ; writing--original draft, P.W. ; writing--reviewand editing, T.Y., K.B. and S.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Ethical review and approval were waived for this study, due to the data for this study considered milk samples from routine milking. No additional experiments were conducted. Thus, in concordance with German animal welfare legislation, no ethical approval was required for this study.