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Using Fourier transform to connect phenotype and fitness of complex traits
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  • Yi Dai,
  • Shaojun Pei,
  • Mengmeng Chen,
  • Goutao Chen,
  • Guohui Shi,
  • Stephen S.-T. Yau,
  • Qi Wu
Shaojun Pei
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Mengmeng Chen
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Goutao Chen
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Guohui Shi
Institute of Microbiology Chinese Academy of Sciences
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Stephen S.-T. Yau
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Qi Wu

Corresponding Author:[email protected]

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The response of traits and trait-related fitness to natural selection is crucial for the study of natural selection in populations. In this paper, we used a complex number to describe a quantitative trait, in which the frequency in a population and the fitness of the trait denote the modular square and the argument of the complex number. Based on this description, we introduced Fourier transform to relate the population distribution of a quantitative trait with the population distribution of its fitness and applied the uncertainty principle of the Fourier transform to describe the response of trait and fitness to natural selection in an inequality. This formula showed that under certain selection conditions, there was a minimum in the combined response of the fitness and the trait to the selection, which we called the principle of least response (PLR) to natural selection. It was suitable for the long-term evolutionary dynamics of polygenic adaptation, allowing for gene interactions (epistatic effects), not requiring the assumption of a normal distribution of traits in a population, and using only the variance of phenotype and fitness without the need to use complex statistics such as higher-order moments. The simulation results verified the high accuracy of the inequality relation in the case of a single population size. We hoped that this point could throw novel light on the theoretical basis of the evolution of complex traits.