Change point analysis to detect the effect of
pruning severity on tree growth
Laboratory of Biology, Yamashita-cho 1–10–6, Okaya City, Nagano Prefecture, 394–0005, Japan
* Correspondence:
Corresponding Author
bio-igu@f8.dion.ne.jp
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 towards 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.
Keywords
Regression analysis, Crown removal limit, Tree
growth, Pretreatment, Abrupt change
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'Harafs (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 value (Muggeo, 2008). Change point analysis using segmented
regression models has been rarely reported in arboriculture and its related
field 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 expected to
be associated with tree vigor. Therefore, the present article focuses on the
relationship between diameter growth response and other measurement variables
shown in O'Hara (1991).
The data
analyzed here were obtained from Table 1 of O'Hara (1991). Some pruning
severity (% crown removed) data 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.
2.1 Multiple Regression Analysis
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.
2.1 Segmented Regression
Analysis
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.
3.
Results
3.1 Results of Multiple Regression Analysis
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.
Table 1. Multiple regression analysis showing
the predictors of diameter growth response.
Variable |
Regression Coefficient |
SE |
t value |
df |
p value |
|
Pruning Severity |
-0.72 |
0.08 |
-8,07 |
23.1 |
0.00 |
|
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 |
-5.70 |
10.07 |
-0.57 |
23.1 |
0.58 |
|
-13.79 |
5.74 |
-2.40 |
22.3 |
0.03 |
|
|
Open-grown |
-14.91 |
7.76 |
-1.92 |
22.8 |
0.07 |
3.2
Results of Segmented Regression Analysis
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
(p = 0.07). The first segmented line (ภ = -0.25, 0 < severity < 25) was
not significant (p = 0.57).
Figure 1
Segmented regression of diameter growth
response on pruning severity. The data were obtained from the Table 1 of O'Hara (1991).
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 (ภ = -0.81, 0 < severity < 67) was
significantly negative (p < 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 (p < 0.001). The first segmented line (ภ = -0.16, 0
< severity < 53) was not significant (p = 0.14) (the right panel
of Figure 2).
Figure 2
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).
4.
Discussion
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 towards 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.
4.
Conclusion
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.
Acknowledgements
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.
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