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\begin{document}

\title{Two path length effects emerging from ontogenetically stable axial xylem
design affect the conductance of inner sapwood rings}



\author[1]{Giai Petit}%
\author[2]{Maurizio Mencuccini}%
\author[1]{Marco Carrer}%
\author[1]{Angela Luisa Prendin}%
\author[3]{Teemu Holtta}%
\affil[1]{Università degli Studi di Padova Dept TeSAF Viale dell’Università 16 35020 Legnaro (PD) Italy}%
\affil[2]{CREAF Bellaterra (Cerdanyola del Vallès) E08193 Spain}%
\affil[3]{Institute for Atmospheric and Earth System Research / Forest Sciences Faculty of Agriculture and Forestry University of Helsinki Latokartanonkaari 7 FI 00014 Helsinki Finland}%


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  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
The process of sapwood/heartwood transition in trees is not fully
understood. We tested whether the ontogenetically-stable apex-to-base
conduit widening generates path length effects limiting the conductance
of inner sapwood rings. The axial scaling ( \emph{b}) of conduit
hydraulic diameter ( \emph{Dh}) was estimated at annual resolution in a
spruce and beech tree. We compiled a global dataset of sapwood ring
number ( \emph{NSWr}), their average width ( \emph{SWrw}), tree height (
\emph{H}) and stem elongation rate ( \selectlanguage{greek}\emph{ΔH}\selectlanguage{english}) in conifer and
angiosperm trees. A numerical model simulated the effects of \emph{H}
and \selectlanguage{greek}\emph{ΔH}\selectlanguage{english} on the conductance of each xylem ring (
\emph{K\textsubscript{RING}}). \emph{b} resulted ontogenetically stable.
Simulations well predicted the observed patterns of increasing
\emph{NSWr} with \emph{H} and decreasing \emph{NSWr} with \selectlanguage{greek}\emph{ΔH}\selectlanguage{english},
assuming that heartwood forms when the marginal conductance gain of
maintaining the functionality of an inner ring becomes negligible.
Sapwood/heartwood transition minimizes the C costs associated to
allocation to secondary growth and maintenance of living sapwood
required to attain a given sapwood conductance. The number of sapwood
rings depends on the effects of \emph{H} and \selectlanguage{greek}\emph{ΔH}\selectlanguage{english} on the
conductance of inner sapwood rings. The width of sapwood rings
contributes to compensate for the lower conductance of inner sapwood
rings at high \selectlanguage{greek}\emph{ΔH}\selectlanguage{english}.%
\end{abstract}%



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