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\begin{document}

\title{Reproductive dispersion and damping time scale with life-history speed}



\author[1]{Sha Jiang}%
\author[1]{Harman Jaggi}%
\author[1]{WENYUN ZUO}%
\author[2]{Madan Oli}%
\author[3]{Tim Coulson}%
\author[4]{Jean-Michel Gaillard}%
\author[1]{Shripad Tuljapurkar}%
\affil[1]{Stanford University}%
\affil[2]{University of Florida}%
\affil[3]{Oxford}%
\affil[4]{UMR-CNRS 5558}%


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  \date{May 25, 2024}


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\begin{abstract}
Generation time has previously been the focus of comparative life
history analyses. Here we examine three metrics: generation time
\emph{T\textsubscript{c}}, reproductive dispersion \emph{S} (the
distribution of ages of reproduction), and damping time \selectlanguage{greek}\emph{τ} \selectlanguage{english}(time
to converge to stable (st)age distribution). We use data on 633 species
of animals and plants, and perform phylogenetically corrected analyses.
First we find that \emph{S} varies allometrically and isometrically with
\emph{T\textsubscript{c}}. As a result, \selectlanguage{greek}\emph{τ} \selectlanguage{english}varies allometrically
with either \emph{T\textsubscript{c}} or \emph{S} but not both. Second,
we find a trade-off between \selectlanguage{greek}\emph{τ} \selectlanguage{english}and \emph{S}, so that \selectlanguage{greek}\emph{τ} \selectlanguage{english}does
not vary isometrically with \emph{T\textsubscript{c}}. This trade-off is
a novel demographic component to the relationship between \selectlanguage{greek}\emph{τ},
\selectlanguage{english}\emph{T\textsubscript{c}} and \emph{S} that is otherwise partly
determined by their similarity as biological times. Our results indicate
that species at the slow end of the slow-fast continuum take longer to
converge to stable distribution than species with fast life-histories.%
\end{abstract}%



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