Objective Using the abundance of Escherichia coli strains and functional mapping model as the research foundation, this study explored the impact of mixed effects on the performance of the functional mapping model by introducing fixed effects of the population and random effects caused by kinship relationships among individuals into the functional mapping model.

Method Based on the framework of functional mapping, this study employed the growth data from dynamic cultures of Escherichia coli as a practical case. Subgroups and SNP genotypes were considered as sources of fixed effects, and these fixed effect factors were integrated into the mapping model, leading to the extension of the Q-matrix model. While maintaining the use of the variance-covariance model for modeling random residuals, the Legendre model was employed to model random effects. A mixed-effects model analysis combining fixed effects with general random effects (Model 1) was conducted. Additionally, the restricted maximum likelihood estimation method was utilized to derive variance-covariance parameters, random effects, and fixed effects, enabling the analysis of a mixed model combining fixed effects with random effects arising from kinship relationships (Model 2). Finally, the Zwald test method was utilized to derive the calculation method for p-values at each marker locus.

Result (1) In both models, 95% of the markers exhibited p-values that were consistent with the expected values, resulting in satisfactory upward curvature in the QQ plot. (2) Compared to Model 1, Model 2 detected a greater number of SNP loci, indicating that Model 2 provides a stronger explanation for the random effects caused by kinship relationships. (3) Computer simulation results revealed that when the sample size is small and the heritability is low, the false-positive rate of the model is 4.77%. However, when the sample size reaches 800 and the heritability is 1%, the discovery rate of QTLs by the model can exceed 70%. Alternatively, when the sample size is 400 and the heritability exceeds 1.5%, the QTL discovery rate can also exceed 70%.

Conclusion The mixed model approach proposed in this study, which introduces fixed effects and random effects caused by kinship relationships into the functional mapping model, effectively improves the theory of functional localization. This approach exhibits excellent calibration capabilities for covariate factors in fixed effects and can effectively dissect random effects from residual residuals. This lays a solid foundation for subsequent improvements in functional localization and the development of software packages for the fixed effects plus kinship (Q + K) model.