Digest: Within and between sex covariances can enhance the response to climatic selection*

Being able to predict if and to what extent populations can respond to selection is an increasingly important topic in the age of rapid environmental change. The multivariate breeder's equation (Lande 1979), at the heart of evolutionary quantitative genetics, elegantly allows us to do this. In populations with two sexes, the breeder's equation predicts the short-term response to selection in each sex (males: _m; females: _f) as a product of the genetic covariances within and between sexes (G_mf), and selection acting on each sex (males: β_m; females: β_f) (Lande 1980):

where G_m and G_f represent male and female additive genetic (co)variances for the set of traits expressed in both sexes, B represents the cross-sex additive genetic (co)variance for the same traits, and B' denotes the matrix transposition of B. For this equation to make accurate predictions, we must know or assume two things. First, the direction of multivariate selection acting in each sex, and second, that G_mf itself does not change (too much) in response to selection. Both of these, however, are hard to estimate. This poses a real challenge for studies aiming to predict the capacity for rapid adaptation in natural populations.

In this issue, Hangartner et al. (2019) leverage populations of Drosophila melanogaster sampled from three locations along a latitudinal cline on the east coast of Australia to address three critical questions. First, how stable is G_mf across the latitudinal cline? Second, what is the direction of selection along the cline? And third, how do different components of G_mf affect the predicted response to selection? The authors naturally focus on four climatically relevant traits: cold recovery, heat knockdown, desiccation resistance, and wing size, which is often closely related to body size. Addressing all three of these questions in a single study provides a rare and comprehensive glimpse into how these factors interact to determine the potential for rapid adaptation to climate change, setting the benchmark for future studies in this area. The authors’ basic approach and results can be summarized in the schematic shown in Figure 1.

To determine whether G_mf was stable, the authors estimated the variation among the three G_mf matrices and compared that variation to what you would find if you sampled three random matrices. Variation among G_mf was estimated using an approach called a fourth-order genetic covariance tensor (Basser and Pajevic 2007; Hine et al. 2009). A tensor can be thought of as an array of numbers, where the dimensions of the array are related to the order of the tensor. For example, a one-dimensional array holds a vector, which is a first-order tensor. A two-dimensional array holds a matrix, which is a second-order tensor, and so on. In a quantitative genetic context, an individual's vector of breeding values for n traits is a first-order tensor of dimension n. The variation and covariation among breeding values for all individuals in a population is a second-order tensor of dimension n × n, a G-matrix. To utilize the information captured in G to its full extent, we do not focus on the individual variances and covariances of the matrix, but on its eigenvectors (principal components) (e.g., Walsh and Blows 2009). If some eigenvectors of G account for more variation in the data than expected by chance, then the trait combinations described by the eigenvectors are inferred to have significant genetic variation. Likewise, the variation and covariation among p G matrices, is a fourth-order tensor of dimension n × n × n × n. An eigenanalysis of this fourth order tensor yields p second order tensors that are each matrices of dimension n × n. If any of the p second-order tensors account for more variation in the data than expected by chance, then we can conclude that the set of G-matrices vary significantly in genetic variance and/or covariance.

The authors found no more variation among G-matrices than expected by chance, and therefore conclude that G is stable across the cline. In many cases, however, it may be difficult to detect variation among G-matrices simply as a consequence of low power. This is not meant as a criticism of the current study, but simply a reminder that estimating variances with precision takes a large sample, and that estimating variances of variances is even more challenging. Overall, this research provides compelling evidence that cross-sex genetic covariances largely facilitate the predicted response to climatic selection. There have only been a few studies to show that cross-sex covariances can facilitate the response to selection (e.g., Holman and Jacomb 2017, Sztepanacz and Houle 2019), and none with such a clear ecological context. This work highlights the importance of considering both sexes and their shared genetics when making evolutionary predictions in rapidly changing environments, setting a standard for future studies in this growing field.

Associate Editor: K. Moore

Handling Editor: T. Chapman