Exploratory analysis of multi-trait coadaptations in light of population history

During the process of range expansion, populations encounter a variety of environments. They respond to the local environments by modifying their mutually interacting traits. Common approaches of landscape analysis include first focusing on the genes that undergo diversifying selection or directional selection in response to environmental variation. To understand the whole history of populations, it is ideal to capture the history of their range expansion with reference to the series of surrounding environments and to infer the multitrait coadaptation. To this end, we propose a complementary approach; it is an exploratory analysis using up-to-date methods that integrate population genetic features and features of selection on multiple traits. First, we conduct correspondence analysis of site frequency spectra, traits, and environments with auxiliary information of population-specific fixation index (F _ST). This visualizes the structure and the ages of populations and helps infer the history of range expansion, encountered environmental changes, and selection on multiple traits. Next, we further investigate the inferred history using an admixture graph that describes the population split and admixture. Finally, principal component analysis of the selection on edge-by-trait (SET) matrix identifies multitrait coadaptation and the associated edges of the admixture graph. We introduce a newly defined factor loadings of environmental variables in order to identify the environmental factors that caused the coadaptation. A numerical simulation of one-dimensional stepping-stone population expansion showed that the exploratory analysis reconstructed the pattern of the environmental selection that was missed by analysis of individual traits. Analysis of a public dataset of natural populations of black cottonwood in northwestern America identified the first principal component (PC) coadaptation of photosynthesis- vs growth-related traits responding to the geographical clines of temperature and day length. The second PC coadaptation of volume-related traits suggested that soil condition was a limiting factor for aboveground environmental selection.