The study of common heritability, or co-heritability, among multiple traits has been widely established in quantitative and molecular genetics. However, in bacteria, genome-based estimation of heritability has only been considered very recently and no methods are currently available for considering co-heritability. Here we introduce such a method and demonstrate its usefulness by multi-trait analyses of the three major human pathogens \textit{Escherichia coli}, \textit{Neisseria gonorrhoeae} and \textit{Streprococcus pneumoniae}. We anticipate that the increased availability of high-throughput genomic and phenotypic screens of bacterial populations will spawn ample future opportunities to understand the common molecular basis of different traits in bacteria.
