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\begin{document}

\title{Morphology-performance Mapping Determines Least Functional Resistance in
Morphospace: A Case of Dual Locomotor Systems in Chinese Sturgeon}



\author[1]{Yi Qu}%
\author[2]{Chaoshuo Zhang}%
\author[3]{Ying Zhang}%
\author[4]{Gang Yang}%
\author[2]{Shaoqiu Hu}%
\author[2]{Xiangyuan Mi}%
\author[2]{Dongxu Zhang}%
\author[5]{Steven  Cooke}%
\author[6]{Jim Rohlf}%
\author[2]{Ming Duan}%
\affil[1]{Taizhou Ecological Environment Monitoring Center}%
\affil[2]{Institute of Hydrobiology Chinese Academy of Sciences}%
\affil[3]{Taizhou Vocational and Technical College}%
\affil[4]{Chinese Academy of Fishery Sciences East China Sea Fishery Research Institute}%
\affil[5]{Carleton University}%
\affil[6]{State University of New York at Stony Brook}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
Morphology-performance (M-P) mapping seems to be predictive of how
morphology may evolve along ``functional lines of least resistance'',
regardless of genetic effect, but as yet it is not clear the strict (or
mathematical) definition of the least functional resistance and how M-P
mapping determines it. We recorded station-holding and swimming
performance using a published critical swimming speed (Ucrit) test in
Chinese sturgeon Acipenser sinensis, and used Ucrit as a proxy for
fitness. We addressed a geometric morphometric framework to initiate
Arnold's ``morphology-performance-fitness'' path model (Arnold, 1983),
assessing and visualizing apparent and direct M-P mapping. We quantified
them as that one unit of the most-performance-covaried shape vector
generated fapparent and f units of standardized performance,
respectively. We defined the least functional resistance as the
theoretically minimum morphological variation on an arbitrary direction
in morphospace required by one unit of standardized fitness,
(\textbar{}b-1\textbar{}min), which was calculated as a multivariate
function of direct M-P mapping (f), together with the angle between
paired most-performance-covaried shape vectors in morphospace (\selectlanguage{greek}θ\selectlanguage{english}) and
direct performance effect on fitness (w), given dual performance
systems. The simulated and empirical data suggested that
\textbar{}b-1\textbar{}min was constrained by larger sum of absolute
direct effects (\textbar{}fhold\textbar{} + \textbar{}fswim\textbar{})
and absolute functional interaction (\textbar{}fhold fswim cos
\selectlanguage{greek}θ\selectlanguage{english}\textbar{}), and its direction was biased by magnitude of direct M-P
mapping.%
\end{abstract}%



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