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Instead, specific alkaloids and their linked loci/alleles were favored by selection imposed by different herbivores. This has led to population differentiation in plant defenses and thus, to local adaptation driven by plant-herbivore interactions.We consider the problem of jointly modeling multiple covariance matrices by partial common principal component analysis (PCPCA), which assumes a proportion of eigenvectors to be shared across covariance matrices and the rest to be individual-specific. This paper proposes consistent estimators of t