Population Divergence along a Genetic Line of Least Resistance in the Tree Species Eucalyptus globulus

The evolutionary response to selection depends on the distribution of genetic variation in traits under selection within populations, as defined by the additive genetic variance-covariance matrix (G). The structure and evolutionary stability of G will thus influence the course of phenotypic evolution. However, there are few studies assessing the stability of G and its relationship with population divergence within foundation tree species. We compared the G-matrices of Mainland and Island population groups of the forest tree Eucalyptus globulus, and determined the extent to which population divergence aligned with within-population genetic (co)variation. Four key wood property traits exhibiting signals of divergent selection were studied—wood density, extractive content, and lignin content and composition. The comparison of G-matrices of the mainland and island populations indicated that the G-eigenstructure was relatively well preserved at an intra-specific level. Population divergence tended to occur along a major direction of genetic variation in G. The observed conservatism of G, the moderate evolutionary timescale, and close relationship between genetic architecture and population trajectories suggest that genetic constraints may have influenced the evolution and diversification of the E. globulus populations for the traits studied. However, alternative scenarios, including selection aligning genetic architecture and population divergence, are discussed.

Do traits separated by metamorphosis evolve independently? Concepts and methods

Despite the ubiquity of complex life cycles, we know little of the evolutionary constraints exerted by metamorphosis. Here, we present pitfalls and methods to answer whether animals with a complex life cycle can independently adapt to the environments encountered at each life stage, with a specific focus on the microevolution of quantitative characters. We first discuss challenges associated with study traits and populations. We further emphasize the benefits of using a combination of approaches. We then develop how multivariate methods can limit several issues by revealing genetic patterns that are invisible when only considering trait-by-trait genetic correlations. Finally, we detail how Lande's work on sexual dimorphism can be applied in measuring G matrices across life stages. The methods and tools described here will contribute towards building a predictive framework for trait evolution across life stages.

Sign patterns of J-orthogonal matrices

This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator and Theorem 3.2 on the characterization of J-orthogonal matrices in the paper “J-orthogonal matrices: properties and generation", SIAM Review 45 (3) (2003), 504-519, by Higham. As a result, it follows that for n ≤4 all n×n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. In addition, the 3 × 3 sign patterns of the J-orthogonal matrices which have zero entries are characterized.