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\begin{document}

\title{Change point analysis to detect the effect of pruning severity on tree
growth}



\author[1]{Yutaka Iguchi}%
\affil[1]{Laboratory of Biology}%


\vspace{-1em}



  
  \date{May 22, 2024}


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\selectlanguage{english}
\begin{abstract}
The effect of pruning severity on tree growth was analyzed by change
point detection using segmented regression. The present study applied
this analysis to a well-known published data set including diameter
growth response, tree age, pruning severity and pretreatment crown size.
First, multiple regression analysis was performed to assess the effect
of tree age, pruning severity and pretreatment crown size on diameter
growth response. Next. segmented regression analysis was performed to
assess the effect of pruning severity on diameter growth response. The
results of the multiple regression showed that diameter growth response
was significantly influenced by pruning severity and pretreatment crown
size. The results of the segmented regression showed that in the whole
data set, an abrupt change toward a decrease in diameter growth response
was detected at 25\% of the live crown removed. However, in the group of
fully crowned and open-grown, diameter growth response continuously
decreased with increasing pruning severity with no significant abrupt
change, whereas in the group of 70-90\% live crown, diameter growth
response did not significantly decrease up to the break point (53\%
crown removed) and then abruptly decreased. This may be the first study
to show the numerical evaluation of the effect of pruning severity on
tree growth by change point analysis.%
\end{abstract}%



\sloppy


Yutaka Iguchi*

Laboratory of Biology, Yamashita-cho 1--10--6, Okaya City, Nagano
Prefecture, 394--0005, Japan

* Correspondence:

Corresponding Author

bio-igu@f8.dion.ne.jp

\par\null

\section*{1. Introduction}

{\label{985801}}

Tree pruning aims to craft canopy structure and shape by removing and
shortening branches and encouraging growth in selected areas of the
crown (Gilman et al., 2006). However, there has been a long-standing
controversial issue of how pruning severity affects tree growth (Clark
\& Matheny, 2010). Pruning can negatively affect growth through
excessive intensity (Rais et al., 2020). Therefore, most pruning
prescriptions are based on empirical data combining operational needs
with tree growth responses (Maurin \& DesRochers, 2013; Shimada, 2017)
or based on previous pruning studies. For example, O'Hara (1991) has
been frequently cited as a well-known review suggesting that one-third
of the live crown could be pruned without serious growth impact
(Robbins, 2000; Clark \& Matheny, 2010; Rais et al. 2020; Suchocka et
al., 2021). However, O'Hara (1991) did not show how the removal limit of
one-third was estimated.

~ The present article proposes a change point analysis to detect the
effect of pruning severity on tree growth. Regarding O'Hara's (1991)
estimation, it seems plausible that there exists an abrupt change point
in the relationship between pruning severity and tree growth. Therefore,
the present article aims to introduce a segmented regression model as a
tool of the detection of an abrupt change point (Muggeo, 2008) and apply
it to the data of O'Hara (1991).

~ Segmented regression models (also called broken-line models) are
regression models where the relationships between the response and one
or more explanatory variables are piecewise linear, namely represented
by two or more straight lines connected at unknown values (Muggeo,
2008). Change point analysis using segmented regression models has been
rarely reported in arboriculture and its related fields except for
Hilbert et al. (2022). Therefore, the use of segmented regression and
the results shown here may help further studies explore the relationship
between pruning severity and tree growth.

~ As mentioned by O'Hara (1991) as well as other studies (Pothier et
al., 2013, Shimada, 2023), the growth of diameter or circumference at
breast height is considered an index of tree vigor. Therefore, the
present article explores the relationship between diameter growth
response and other measurement variables shown in O'Hara (1991).

\section*{2. Materials and Methods}

{\label{418638}}

\subsection*{2.1. Data and Analysis}

{\label{764590}}

The data analyzed here were obtained from Table 1 of O'Hara (1991). Some
pruning severity values (\% crown removed) were shown as the interval
such as 15 -- 35. In this case, the mid-value of the interval such as 25
was used for computational convenience.

~ In the following sections, a multiple regression analysis is first
performed to examine the influence of the tree age, pruning severity and
pretreatment crown size on diameter growth response. Next, a segmented
regression model is employed to detect a change point in the
relationships between pruning severity and growth response diameter.

~ Statistical analysis was performed using the stats, car, and segment
packages in the R software (R Core Team, 2023) at a significance level
of 0.05.

\par\null

\subsection*{2.2. Multiple Regression
Analysis}

{\label{659968}}

In the multiple regression analysis, the response variable was diameter
growth response, and the explanatory variables were tree age, pruning
severity (percent of crown removed), and pretreatment crown size. There
were missing data in the Table 1 of O'Hara (1991).~ Therefore, multiple
imputation was used to fill in the missing data. The calculation was
performed using the function mice in the mice package and the function
lm in the stats package.

~ The variable pretreatment crown size was defined as a categorical
variable The category names were derived from the Table 1 of O'Hara
(1991): 70\% live crown, 80\% live crown, 90\% live crown, fully
crowned, and open-grown. The70\% live crown category served as the
reference category.

\subsection*{2.3 Segmented Regression
Analysis}

{\label{408228}}

In the segmented regression analysis, the response variable was diameter
growth response, and the explanatory variable were pruning severity. The
analysis was performed using the function segmented in the segmented
package. In order to avoid multiple values of the response variable for
one value of the explanatory variable, small random numbers with the
range {[}-0.01, 0.01{]} were added to the explanatory variable. The
random numbers were created by the function runif in the stats package.
Score test by the function pscore.test in the segmented package was also
used to test for the existence of a breakpoint.

\section*{3. Results}

{\label{817159}}

\subsection*{3.1. Results of Multiple Regression
Analysis}

{\label{728565}}

The results of the multiple regression analysis are shown in Table 1.
Diameter growth response was significantly influenced by pruning
severity and pretreatment crown size. In the categories of pretreatment
crown size, the fully crowned category significantly influenced diameter
growth response and the open-grown category was almost significant.\selectlanguage{english}
\begin{table}[H]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCCCC}
Variable &  & Regression Coefficient & SE & t value & df & p value \\
Pruning Severity &  & -0.72 & 0.08 & -8.07 & 23.1 & 0.0  \\
Age &  & -0.09 & 0.27 & -0.32 & 16.5 & 0.76  \\
Pretreatment Crown Size &  &  &  &  &  &  \\
 & 80\% Live Crown & -8.65 & 10.93 & -0.79 & 22.2 & 0.44  \\
 & 90\% Live Crown & -5.7 & 10.07 & -0.57 & 23.1 & 0.58  \\
 & Fully Crowned & -13.79 & 5.74 & -2.4 & 22.3 & 0.03  \\
 & Open-grown & -14.91 & 7.76 & -1.92 & 22.8 & 0.07  \\
\end{tabulary}
\caption{{Multiple regression analysis showing the predictors of diameter growth
response.
{\label{164305}}%
}}
\end{table}\subsection*{3.2. Results of Segmented Regression
Analysis}

{\label{314350}}

First, a segmented regression was applied to all the data sets of
pruning severity and diameter growth response. The results are depicted
in Figure 1. A breakpoint was found at 25\% crown removed and almost
significantly supported by score test (\emph{p} = 0.07). The first
segmented line (\selectlanguage{greek}\emph{β} \selectlanguage{english}= -0.25, 0 \textless{} severity \textless{} 25)
was not significant (\emph{p} = 0.57).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure1/Figure1}
\caption{{Segmented regression of diameter growth response on pruning severity.
The data were obtained from the Table 1 of O'Hara (1991).
{\label{573287}}%
}}
\end{center}
\end{figure}

~ Second, based on the results of the multiple regression analysis, the
data were divided into two groups regarding pretreatment crown size: one
consists of fully crowned and open-grown, and the other consists of 70\%
live crown, 80\% live crown, and 90\% live crown. The results of the
segmented regression are depicted in Figure 2.

~ In the group of fully crowned and open-grown, a breakpoint was found
at 67\% crown removed, but not significantly supported by score test (p
= 0.78). The first segmented line (\selectlanguage{greek}\emph{β} \selectlanguage{english}= -0.81, 0 \textless{}
severity \textless{} 67) was significantly negative (\emph{p}
\textless{} 0.001) (the left panel of Figure 2).

~ On the other hand, in the group of 70-90\% live crown, a breakpoint
was found at 53\% crown removed and significantly supported by score
test (\emph{p} \textless{} 0.001). The first segmented line (\selectlanguage{greek}\emph{β} \selectlanguage{english}=
-0.16, 0 \textless{} severity \textless{} 53) was not significant
(\emph{p} = 0.14) (the right panel of Figure 2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure2/Figure2}
\caption{{Segmented regression of diameter growth response on pruning severity in
the two groups based on pretreatment crown size. The data were obtained
from the Table 1 of O'Hara (1991).
{\label{662028}}%
}}
\end{center}
\end{figure}



\section*{\texorpdfstring{{4.
Discussion}}{4. Discussion}}

{\label{855614}}

Several previous studies have referred to O'Hara (1991) and explained
that the removal of up to one-third, or 33\% of the live crown did not
noticeably reduce diameter growth (Robbins, 2000; Clark \& Matheny,
2010; Kirby, 2016; Rais et al. 2020; Suchocka et al., 2021).
Nevertheless, there remained the question of how the limit value of 33\%
was obtained by calculation.

~ The present study applied segmented regression to the data of O'Hara
(1991) and revealed that in the whole data set, an abrupt change toward
a decrease in diameter growth response was detected at 25\% of the live
crown removed. This value was a little smaller than the limit value of
33\% estimated by O'Hara (1991) and cited by the above-mentioned
studies.

~ O'Hara (1991) mentioned the effect of different pretreatments on tree
growth, but did not take it into consideration when evaluating the crown
removal limit. However, the present results revealed that the different
pretreatments produced different relationships between pruning severity
and growth response diameter.

~ In the group of fully crowned and open-grown, diameter growth response
continuously decreased with increasing pruning severity with no
significant abrupt change. Therefore, it seemed difficult to determine
the crown removal limit. However, in the group of 70-90\% live crown,
diameter growth response did not significantly decrease up to the break
point (53\% crown removed) and then abruptly decreased. Consequently,
the difference in pretreatments was found to have a great impact on the
relationships between pruning severity and growth response diameter.

\par\null

\section*{5. Conclusion}

{\label{186555}}

This is probably the first study that evaluated the effect of pruning
severity on tree growth by change point analysis using segmented
regression. The advantage of segmented regression is that it enables us
to analyze continuous data as they are. In other words, segmented
regression does not treat continuous predictors such as pruning severity
as categorical predictors. Therefore, the present study with segmented
regression was able to analyze the relationship between pruning severity
and growth response diameter to estimate the limit value up to which
pruning can be done without serious growth losses. The results will
recommend the use of change point analysis in future studies on pruning
severity.

\section*{Acknowledgements}

{\label{552309}}

The author declares that the research was conducted in the absence of
any commercial or financial relationships that could be construed as a
potential conflict of interest. The author confirms sole responsibility
for the following: study conception and design, data collection,
analysis and interpretation of results, and manuscript preparation.

\section*{References}

{\label{393526}}

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Pruning: A Review of the Literature. Arboriculture \& Urban Forestry,
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Gilman, E. F., Anderson, P. J., \& Harchick, C. (2006). Pruning Lower
Branches of Live Oak (\emph{Quercus virginiana} Mill.) Cultivars and
Seedlings during Nursery Production: Balancing Growth and Efficiency.
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\url{https://doi.org/10.24266/0738-2898-24.4.201}

Hilbert, D. R., Koeser, A. K., Roman, L. A., Andreu, M. G., Hansen, G.,
Thetford, M., \& Northrop, R. J. (2022). Selecting and Assessing
Underutilized Trees for Diverse Urban Forests: A Participatory Research
Approach. Frontiers in Ecology and Evolution, 10,
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Kirby, J. W. (2016). Stem and Branch Diameter Response in Pruned
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Northwest. Master's Thesis, Seattle: University of Washington.

{Maurin, V., \& DesRochers, A. (2013). Physiological and Growth
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Muggeo, V. M. R. (2008). Segmented: An R Package to Fit Regression
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{O'Hara, K. L. (1991). Technical Commentary: A Biological Justification
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Pothier, D., Fortin, M., Auty, D., Delisle-Boulianne, S., Gagn\selectlanguage{ngerman}é, L. V.,
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R Core Team (2023). R: A Language and Environment for Statistical
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{Rais, A., Poschenrieder, W., van de Kuilen, J. W. G., \& Pretzsch, H.
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Robbins, J. M. (2000). Influence of Spacing and Crown Recession on Wood
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{Shimada, H. (2017). Maintenance of Trees in a Residential Section
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\par\selectlanguage{polish}\null

{Suchocka, M., Swoczyna, T., Kosno-Jończy, J., \& Kalaji, H. M. (2021).
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\par\null

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