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\begin{document}

\title{Exploratory analysis of multiple traits co-adaptations in the population
history}



\author[1]{Reiichiro Nakamichi}%
\author[2]{Shuichi Kitada}%
\author[3]{Hirohisa Kishino}%
\affil[1]{Japan Fisheries Research and Education Agency}%
\affil[2]{Tokyo University of Marine Science and Technology}%
\affil[3]{The University of Tokyo Graduate School of Agricultural and Life Sciences Faculty of Agriculture}%


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  \date{June 15, 2024}


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\begin{abstract}
During the history of range expansion, the populations encounter with
variety of environments. They respond to the local environments by
modifying the mutually interacting traits. Therefore, to understand the
whole life history of the populations, it is ideal to capture the
history of their range expansion with reference to the series of
surrounding environments and to infer the coadaptation of the multiple
traits. Toward this end, we provide an exploratory analysis based on the
features of populations: site frequency spectra of populations,
population-specific FST, association between genes and environments,
positive selections on traits mapped on the admixture graph, and GWAS
results. Correspondence analysis of genes, environments, and traits
provides a bird's-eye view of the history of population differentiation
and range expansion and various types of environmental selections at the
times. Principal component analysis of the estimated trait-specific
polygenic adaptations mapped on the admixture graph enables to
understand the coadaptation of multiple traits. The potential usefulness
was confirmed by analyzing a public dataset of wild poplar in
northwestern America. In response to the northern cold temperature and
longer daylength, the populations increased the photosynthetic activity
and nutrient use efficiency at the expense of the risk of pathogen
invasion, and in response to warm temperature, they increased the
growth. At higher altitude, they shifted the maximum activity to earlier
period in spring to reduce the activity in dry summer. The R codes for
our representation method and simulations of population colonization
used in this study are available as supplementary script.%
\end{abstract}%



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