482

Revista de Biología Tropical, ISSN electrónico: 2215-2075 Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

Principal component regression analysis demonstrates

the collinearity-free effect of sub estimated climatic variables

on tree growth in the central Amazon

Ricardo Antonio Marenco

*; Orcid: 0000-0002-9490-2624

Saul Alfredo Antezana-Vera

; Orcid: 0000-0001-7949-352X

1. Coordenação de Dinâmica Ambiental, Instituto Nacional de Pesquisas da Amazônia, Manaus, Amazonas, Brazil;

rmarenco@inpa.gov.br (*Correspondence).

2. Programa de Pósgraduação em Botânica, Instituto Nacional de Pesquisas da Amazônia, Manaus, Amazonas, Brazil;

saulantezana5@gmail.com

Received 07-XI-2020. Corrected 24-II-2021. Accepted 26-II-2021.

ABSTRACT

Introduction: Climatic variables show a seasonal pattern in the central Amazon, but the intra-annual variability

effect on tree growth is still unclear. For variables such as relative humidity (RH) and air vapor pressure deficit

(VPD), whose individual effects on tree growth can be underestimated, we hypothesize that such influences

can be detected by removing the effect of collinearity between regressors. Objective: This study aimed to

determine the collinearity-free effect of climatic variability on tree growth in the central Amazon. Methods:

Monthly radial growth was measured in 325 trees from January 2013 to December 2017. Irradiance, air tem-

perature, rainfall, RH, and VPD data were also recorded. Principal Component Regression was used to assess

the effect of micrometeorological variability on tree growth over time. For comparison, standard Multiple Linear

Regression (MLR) was also used for data analysis. Results: Tree growth increased with increasing rainfall

and relative humidity, but it decreased with rising maximum VPD, irradiance, and maximum temperature.

Therefore, trees grew more slowly during the dry season, when irradiance, temperature and VPD were higher.

Micrometeorological variability did not affect tree growth when MLR was applied. These findings indicate that

ignoring the correlation between climatic variables can lead to imprecise results. Conclusions: A novelty of this

study is to demonstrate the orthogonal effect of maximum VPD and minimum relative humidity on tree growth.

Key words: Amazon rainforest; atmospheric dryness; dry season; relative humidity; wet season.

Marenco R.A., & Antezana-Vera, S.A. (2021). Principal

component regression analysis demonstrates the

collinearity-free effect of sub estimated climatic

variables on tree growth in the central Amazon.

Revista de Biología Tropical, 69(2), 482-493. DOI

10.15517/rbt.v69i2.44489

The Amazon rainforest has a significant

impact on both water and carbon cycles, due

to its enormous extension (~ 5.1 × 10

)

and the high amount of carbon stored in its

vegetation, about 86 Pg (Saatchi, Houghton,

Alvalá, Soares, & Yu, 2007). Tree growth can

be defined as the increase of biomass through

time and it is often estimated by measuring

the increment of stem diameter over time – a

proxy of biomass gains at the ecosystem level

(Wagner, Rossi, Stahl, Bonal, & Herault, 2012;

Wagner et al., 2014; Dias & Marenco, 2016;

Antezana-Vera & Marenco, 2020). As tree

growth is greatly affected by factors that affect

photosynthesis, sun-induced fluorescence – a

proxy of ecosystem photosynthesis has been

used to estimate the effect of environmental

factors on total carbon gain of the ecosys-

tem (Lee et al., 2013; Yang et al., 2018;

Green et al., 2020).

DOI 10.15517/rbt.v69i2.44489

483

Revista de Biología Tropical, ISSN electrónico: 2215-2075, Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

Tree growth can be affected by intrinsic

factors (e.g., genetic make-up) and environ-

mental factors, such as nutrient availability,

irradiance, temperature, rainfall, and soil water

content (SWC). The influence of environmen-

tal factors on tropical tree growth has been

widely studied (Wagner et al., 2012; Mendes,

Marenco, & Magalhães, 2013; Wagner et al.,

2014; Dias & Marenco, 2016; Méndez, 2018).

However, the drivers of tree growth are rather

difficult to elucidate because they are often

correlated (Bowman, Brienen, Gloor, Phillips,

& Prior, 2013; Wagner et al., 2014). Therefore,

the effects of climatic parameters, such as tem-

perature, rainfall or SWC on tree growth, are

still under investigation in the Amazon (Laur-

ance et al., 2009; Wagner et al., 2014; Dias &

Marenco, 2016). Rainfall and SWC seem to be

the major factors that affect tree growth in the

Amazon region, but there is still under debate

whether Amazonian trees grow faster in the

wet season than in the dry season. Although in

most studies tree growth or ecosystem photo-

synthesis seems to decrease in the dry season

(Méndez, 2018; Wagner et al., 2014; Yang et

al., 2018; Antezana-Vera & Marenco, 2020),

the opposite effect has also been reported (Lau-

rance et al., 2009; Green, et al., 2020). Whereas

Laurance et al. (2009) reported that tree growth

was fastest during the dry period and positively

correlated with maximum temperatures (T

max

Wagner et al. (2014) found no significant effect

of T

max

on tree growth.

Climatic parameters are often correlated,

and hence collinearity can lead to impre-

cise results by increasing the Variance Infla-

tion Factor (VIF), as an increase in VIF can

lead to false non-significant effects. Moreover,

because of collinearity, the sign of a regres-

sion coefficient may change (from positive

to negative or vice versa, Montgomery, Peck,

& Vining, 2012). This is important because

the significance and sign of regression coef-

ficients are crucial to understand the effect of

climatic variables on tree growth. Principal

Component Analysis (PCA) is commonly used

to deal with the collinearity problem, whereby

a new set of independent variables (orthogonal

components) is computed from the original

regressors. However, PCA’s disadvantage is the

lack of a direct association between a response

variable and the extracted components. To

overcome this difficulty, PCA’s orthogonal

components can be used to perform Principal

Component Regression (PCR). An accurate

estimate of the effect of climatic variability on

tree growth is essential due to the influence of

the Amazon forest on the global carbon bal-

ance and regional climate. Thus, this study

aimed to determine the collinearity-free effect

of climatic variability on tree growth in the

central Amazon. We hypothesize that the influ-

ence of highly correlated climatic variables

such as relative humidity and VPD on tree

growth can only be detected after removing the

effect of collinearity.

MATERIALS AND METHODS

Study site and plant material: The study

was conducted from January 2013 to December

2017 (the experimental period) at the Tropi-

cal Forest Experiment Station (ZF2 Reserve),

in central Amazonia, located 60 km North of

Manaus (02°36’21” S & 60°08’11” W). The

area is a terra-firme rainforest plateau at about

120 m above sea level. Annual rainfall is 2 420

mm, with a mild dry season, with the driest

months from July through September (≤ 100

mm per month. The soil is an Oxisol with low

fertility, clay texture and pH of 4.2 to 4.5 In

this site, tree density is high, about 600 tree

–1

(> 10 cm diameter at breast height-DBH),

canopy height can reach 35-40 m, and most of

trees have less than 30 cm in diameter, while

leaf area index varies from 4.7 in dry season

to 5.0 in the wet season. Mean wood density is

about 0.75 g cm

-3

, and species diversity is high

(Dias & Marenco, 2016). At a site 30 km of

Manaus, Prance, Rodrigues, and Silva (1976)

recorded 179 species of trees in one hectare (≥

15 cm DBH).

During the experimental period, air tem-

perature (T), photosynthetically active radia-

tion (PAR), RH, and rainfall data were daily

recorded above the forest canopy, at the top

484

Revista de Biología Tropical, ISSN electrónico: 2215-2075 Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

of a 40-m-tall observation tower (02°35’20” S

& 60°06’55” W). Temperature, RH and PAR

data were logged at 15 min (PAR) or 30 min

intervals (T and RH) with specific sensors

(Humitter 50y, Vaisala, Ov, Finland; LI-190SA,

Li-Cor, Lincoln, NE, USA) connected to a data

logger (Li-1400, Li-Cor), while daily rainfall

data were collected with a tipping bucket gauge

(ECR-100, Em5b, Decagon Devices, Pullman,

WA, USA). The PAR data were integrated over

a 24-h period to obtain a daily value (mol m

-2

day

-1

). We also computed VPD and poten-

tial evapotranspiration (EVT) and measured

soil water content (SWC, %, v/v). VPD was

obtained as VP

sat

– RH × VP

sat

, where VP

sat

is the saturation vapor pressure; VP

sat

(kPa)

= 0.61365exp[17.502T

/(240.97 + T )], being

T (ºC) the air temperature (Buck, 1981). EVT

was obtained as: EVT = 0.0023R

× (T

mean

+ 17.8) (T

max

– T

min

)

0.5

, where R

denotes

the extraterrestrial radiation (Hargreaves &

Samani, 1985). Undisturbed soil samples were

collected at a depth of 100 to 200 mm every

two weeks to determine SWC after drying the

samples at 105 °C, and then a mean monthly

value was obtained.

In this study we collected data from

325 trees from more than 48 species (Digital

Appendix), which had a mean diameter at

breast height (DBH, diameter at 1.3 m from

the ground) of 23.1 ± 11.8 cm. From tree

diameter, tree height was estimated to be 22.5

± 5.2 m (Nogueira, Nelson, Fearnside, França,

& Oliveira, 2008). In these trees we measured

radial growth at breast height at monthly inter-

vals over 60 months (2013-2017) using stain-

less steel dendrometer bands, which had been

installed three years before the beginning of

the study.

Statistical analyses: To assess the effects

of the monthly microclimatic variability on

tree growth Principal Component Regression

(PCR) was used. We used this approach to

remove the effect of collinearity among climat-

ic variables. In this analysis, we used detrended

tree growth (T

, hereafter referred to as sim-

ply tree growth) instead of undetrended tree

growth (T

, i.e., raw data), because a time-

related trend in growth data can affect PCR

results (Monserud & Marshall, 2001). This step

was accomplished by using a first-order autore-

gression (Montgomery et al., 2012). Then the

tree growth of the whole data set (N = 325) was

randomly split into two subsets, one with 75

% of the trees (244 trees) was used to estimate

the regression coefficients, and the remaining

(25 %, i.e., 81 trees) was used for validation.

Prior to PCR analysis the climatic data were

standardized. In the PCR model, instead of

including all the examined factors, we only

used those that combined explained most of the

variance (i.e., eigenvalues equal or greater than

one). Also, for comparison the significance of

the regression coefficients based on standard

Multiple Linear Regression (MLR) were also

computed. A MLR model can be represented

by (Montgomery et al., 2012):

(Equation 1)

In Equation 1, y

denotes the dependent

variable, x

the regressor, ß

the intercept, ß

the slope of the regression, and ϵ the error term,

being ß

given by:

(Equation 2)

For standardized regressors, with mean x

and standard deviation s

, y

and ß

become:

(Equation 3)

(Equation 4)

The coefficients obtained from standard-

ized regressors (hereafter denoted by the super-

script s) can be transformed back to the original

regressor units, as follows:

(Equation 5)

485

Revista de Biología Tropical, ISSN electrónico: 2215-2075, Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

(Equation 6)

Likewise, the variance of b

and standard

error (SE) of b

can be transformed back to the

original coefficients:

(Equation 7)

(Equation 8)

In matrix notation Equation 1 can be rep-

resented by:

(Equation 9)

In Equation 9, Y represents the vector

of observations (dependent variable); X, the

matrix of the corresponding regressors, β the

vector of coefficients, and ϵ the vector of

random error terms. The normal equations of

the linear regression are given in Equation

10, while the estimates of β (often termed

, and hereafter denoted by b) are given by

Equation 11.

(Equation 10)

(Equation 11)

The sum of square (SS) of the model

(Equation 12), SS of regression (Equation 13),

SS of residual (Equation 14), and the covari-

ance-matrix of b (Equation 15) are given by:

(Equation 12)

(Equation 13)

(Equation 14)

(Equation 15)

Being the mean square error (MSE = s

)

an estimator of σ

, and s = √(MSE). When

the regressors are highly correlated principal

components can be used for transforming those

regressors into a new set of uncorrelated vari-

ables (orthogonal variables with each other).

In terms of standardized regressors, the PCR

can be computed, as follows (Montgomery et

al., 2012):

(Equation 16)

(Equation 17)

(Equation 18)

(Equation 19)

(Equation 20)

In Equation 17, T is a matrix whose col-

umns represent eigenvectors (derived from

X data), while in Equation 20, the columns

of Z represent a new set of orthogonal scores

(i.e., the z-scores), which are termed principal

components (Montgomery et al., 2012). The α̂

coefficients (Equation 21) and the covariance

of α̂ (Equation22) are given by:

(Equation 21)

(Equation 22)

(Equation 23)

(Equation 24)

The standardized regressors, b

are given

by Equation 25, while the variance and stan-

dard error (SE) of b

are given by Equation

486

Revista de Biología Tropical, ISSN electrónico: 2215-2075 Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

26 and Equation 27, respectively. In Equation

25, the “pc” indicates that the principal compo-

nents corresponding to near-zero eigenvalues

have been removed from the analysis.

(Equation 25)

(Equation 26)

(Equation 27)

The step described in Equation 25 is

important to obtain a new set of coefficients,

after removing the smallest λ

. This is a crucial

step in principal component regression. The

second part of Equation 25 shows the computa-

tion. Note that Z = XT, then Z´=T´X´, and ∧

–1

Z´Y = α̂ (Equation 21).

In Equation 27, the MSE is obtained as

the regression of Y on the u- principal compo-

nents retained in the reduced model, while t

denotes the j

element of the eigenvector t

(m = 1 …u). The significance of the principal

component estimator (b

) can be tested on

individual coefficients by using the statistic t

n-k-

, where k represents the number of principal

components in the reduced model, as described

in Equation 28.

(Equation 28)

Statistical analyses were carried out using

Statistica 7.0 (Stat Soft Inc., 2004).

RESULTS

Monthly means of the climatic variables

were 26.4 °C (temperature), 78.9 % (RH), and

28.9 mol m

–2

day

–1

(PAR). Mean rainfall was

213.7 mm month

–1

, SWC 44.3 % (v,v), VPD-

mean

7.41 hPa, and EVT 120.7 mm month

–1

On the other hand, the mean values between

seasons were (dry vs wet season): T

mean

(27.0

vs 26.0 °C, P = 0.001), RH

mean

(74.5 vs 82.1 %,

P < 0.001), VPD

mean

(9.2 vs 6.1 hPa, p < 0.001),

and evapotranspiration (126.2 vs 117.7 mm

month

–1

, P = 0.034). Rainfall, PAR, and the

other climatic variables varied within the wet

and dry season as described in (Fig. 1).

The undetrended radial tree growth was

0.105 ± 0.11 mm per month (N = 325 trees),

with a lower radial increment across the dri-

est season (Fig. 1A). A preliminary analysis

showed that by including all the 13 factors in

the PCR model (full model), no effect on tree

growth was observed, even when the regression

explained 23.7 % of the total variance (F

(13,46)

= 1.10, P = 0.382, R

= 0.237). In fact, the full

PCR model corresponds to the MLR model of

tree growth on all the climatic variables (full

model MLR). The principal component analy-

sis (PCA) showed that the first four factors out

of the 13 factors extracted by PCA (in bold face

in Fig. 2) together accounted for 92.9 % of the

total variance and had eigenvalues higher than

one (λ

= 8.16, 1.86, 1.05, and 1.01). Whereas

the values of λ

to λ

were lower than 1.0 (Fig.

2). Therefore, we retained the first four factors

(Kaiser criterion) and used their corresponding

eigenvectors to obtain the z

scores, hereaf-

ter referred to as principal components (z

In comparison with the full PCR model, the

significance of the four-principal component

model was improved (F

(4,55)

= 2.45, P = 0.056,

= 0.151). By reducing the complexity of the

model, the amount of variance on tree growth

explained by the regression model was also

reduced (23.7 against 15.1 %). Moreover, the

four-factor model showed that only the prin-

cipal components z

and z

had a significant

effect on tree growth, whereas z

and z

did

not (i.e., z

: P = 0.03,

: P = 0.46, z

: P = 0.04,

and z

: P = 0.86). Therefore, only z

and z

were retained for further analysis and hereafter

referred to as the reduced model. As expected,

significance of the reduced model was further

improved by retaining only the two significant

components, i.e., z

and z

(2,57)

= 4.73, P

= 0.012, R

= 0.142), with both regression

487

Revista de Biología Tropical, ISSN electrónico: 2215-2075, Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

coefficients being significant (α

= -0.003927,

P = 0.03) and α

= -0.010267, P = 0.04). As

and z

were retained in the reduced PCR

model, only Factor 1 and Factor 3 are shown

(Fig. 2), and for further information tree growth

) is included in Fig. 2 as a supplementary

variable. In Fig. 2, by taking T

as a reference

point, climatic variables were separated into

three groups. The first group comprised RH

min

mean

, rainfall, and SWC; which together

with T

are in quadrant (III) on the factor

plane. These results suggest a positive correla-

tion between each of them and T

. The second

group (PAR, EVT, T

max

and VPD

max

) is located

in quadrant I (i.e., diagonally opposite to T

and thereby indicating a negative correlation

between the variables of this group and T

The third group included variables located in

adjacent quadrants, i.e., quadrant II (RH

max

)

and quadrant IV (T

min

, T

mean

, VPD

min

and

VPD

mean

), and then indicating a low correlation

between each of these variables and T

. We

further investigated the relationship between

the climatic variables and T

after removing

the effect of collinearity (i.e., by PCR).

The PCR regression coefficients (α

and

) were used to compute the beta coefficients,

(in b

, the subscript pc stands for principal

components) and their SE (Equation 25 and

Equation 27). The coefficients b

based on

standardized regressors are shown in Table 1,

while those coefficients (b

) obtained by MLR

are shown and Table 2.

After removing the effect of collinearity,

we found that tree growth was significantly

responsive to variation in PAR (x

), rainfall

), T

max

), RH

mean

), RH

min

), VPD

max

), SWC(x

), and EVT (x

). Whereas T

min

mean

, RH

max

, VPD

min

, and VPD

mean

had no

significant effect on tree growth (Table 1). Tree

growth increased with a rise in rainfall, SWC,

mean

, and RH

min

, whereas it decreased with

Fig. 1. Undetrended tree growth (T

) and climatic variables recorded in the wet season (November to May) and dry season

(June to October) during the years of 2013 to 2017. A. Undetrended tree growth, B. RH

min

and RH

max

, C. PAR, D. T

min

and

max

, E. Rainfall, and F. VPD

min

and VPD

max

. Abbreviations are shown in Table 1.

488

Revista de Biología Tropical, ISSN electrónico: 2215-2075 Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

increasing PAR, T

max

, EVT, and VPD

max

, as

shown in Equation 29 (based on standard-

ized regressors, Table 1) and Equation 30, for

regressors in the original scale. To validate the

PCR model (Equation 30) we used growth data

of 81 trees, which showed that the R

derived

from the validation data set was even slightly

higher than the R

of data used to build the

model (R

= 0.12 vs. 0.17, Fig. 3).

(Equation 29)

Fig. 2. Principal Component Analysis of climatic variables. The eigenvalues of the first four factors account for 92.9 % of

total variance. In the factor plane, tree growth (T

) was included as a supplementary variable. Abbreviations are shown

in Table 1.

TABLE 1

Regression coefficients of standardized climatic variables (b

), standard error (SE) of b

, variance inflation factor

(VIF), and t

(57df)

and P values obtained by principal component regression (PCR) of tree growth (T

) on principal

component z

and z

(2.57)

= 4.73, MSE = 0.001473, P = 0.0125, R

= 0.142)

Variable

Beta (b

) SE (b

)

VIF

(57)

P value

PAR -0.005019 0.002164 1.0 -2.348939

0.022

Rainfall 0.005498 0.002188 1.0 2.545052

0.014

mean

0.001380 0.001250 1.0 1.118301 0.268

min

0.006063 0.003198 1.0 1.919855 0.060

max

-0.001872 0.000628 1.0 -3.019680

0.004

mean

0.001374 0.000583 1.0 2.387525

0.020

min

0.001812 0.000632 1.0 2.905751

0.005

max

-0.001084 0.001128 1.0 -0.972707 0.335

VPD

mean

-0.000745 0.000667 1.0 -1.131649 0.262

VPD

min

0.001446 0.001312 1.0 1.116269 0.269

VPD

max

-0.001571 0.000616 1.0 -2.582338

0.012

SWC 0.002088 0.000691 1.0 3.059548

0.003

EVT -0.002726 0.000939 1.0 -2.938550

0.005

EVT: potential evapotranspiration, PAR: photosynthetically active radiation, T: temperature, T

max

: mean maximum T, T

mean

mean T, T

min

: mean minimum T, RH: relative humidity, RH

max

: mean maximum RH, RH

mean

: mean RH, RH

min

: mean

minimum RH, VPD: air vapor pressure deficit, VPD

max

: mean maximum VPD, VPD

min

: mean minimum VPD, VPD

mean

VPD mean, and MSE: mean square error. Climatic data were standardized prior to statistical analysis. For T

N = 244.

Significant P values are in bold face.

489

Revista de Biología Tropical, ISSN electrónico: 2215-2075, Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

(Equation 30)

By applying the standard MLR approach,

we found that none of the climatic param-

eters modified tree growth (F

(13,46)

= 1.10, P

= 0.382, R

= 0.237, Table 2). Furthermore, in

comparison with the results obtained with the

PCR reduced model (only factor 1 and factor

3), the MLR coefficients (b

) had much larger

SE (Table 2). For instance, the SE of RH

mean

and VPD

mean

were more than two orders of

magnitude higher than those obtained by PCR,

due to the effect of collinearity. Besides having

larger SE, some coefficients (T

max

, RH

min

and

EVT) had opposite sign. In retrospect, using

the result from PCR and hence discarding from

the MLR model those climatic variables with

no significant effect on tree growth (Table 1)

did not yield any significant regression coef-

ficient (F

(8,51)

= 1.55, P = 0.16, R

= 0.19).

DISCUSSION

Most of the climatic variables assessed

had a significant effect on tree growth. The

exceptions were T

min

, T

mean

, RH

max

, VPD-

min

and VPD

mean

which did not modify tree

growth. Thus, these results partially support

our hypothesis, as highly correlated variables

TABLE 2

Regression coefficients (b

), standard error (SE), VIF, and t

(46 df)

and P values obtained by standard multiple linear

regression (MLR) of tree growth (T

) on climatic variables (F

(13,46)

= 1.10, MSE = 0.001624, P = 0.382, R

= 0.237)

Variable

SE(b

) VIF

t value

P value

PAR -0.000863 0.008981 2.9 -0.09609 0.923870

Rainfall 0.005264 0.011935 5.2 0.44107 0.661226

mean

-0.043624 0.038490 53.8 -1.13341 0.262915

min

0.020023 0.016432 9.8 1.21854 0.229230

max

0.060980 0.058528 124.5 1.04189 0.302907

mean

0.229039 0.200442 1459.8 1.14267 0.259088

min

-0.093012 0.117944 505.4 -0.78861 0.434383

max

-0.295352 0.225920 1854.5 -1.30733 0.197599

VPD

mean

0.309690 0.237523 2049.8 1.30383 0.198778

VPD

min

-0.292876 0.228333 1894.3 -1.28267 0.206034

VPD

max

-0.201591 0.175032 1113.1 -1.15174 0.255380

SWC 0.007049 0.009000 2.9 0.78321 0.437519

EVT 0.001124 0.019793 14.2 0.05679 0.954959

Climatic data were standardized prior to statistical analysis. Note that in comparison with PCR coefficients (Table 1) T

max

min

and EVT had opposite sign. Abbreviations as described in Table 1.

Fig. 3. A. Tree growth (T

, square, N = 244) and the

regression line (solid line, T

GC-PCR

) as a function time. B.

The validation of the PCR model on growth data (N = 81

trees) is also shown. The solid blue line corresponds to

the regression line, while the diamond represents the T

of validation trees. PCR: principal component regression,

GC-PCR

: PCR line fitted to data.

490

Revista de Biología Tropical, ISSN electrónico: 2215-2075 Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

such RH

max

, VPD

min

and VPD

mean

influenced

tree growth. We found that PCR explained 12

% of the total variance (R

= 0.12), which is

not unexpected, as many factors can affect tree

growth (Bowman et al., 2013). For instance,

Wagner et al. (2012) found that only about 9 %

of the variation in tree growth can be attributed

to seasonal climate variability, which is slightly

lower than the proportion of total variance

explained by climatic variability in our study.

The standard MLR explained 23.7 % of

total variance in tree growth. Nevertheless,

due to the large standard error (SE) associated

with each coefficient (Table 2), none of the

regression coefficients significantly affected

tree growth. On the other hand, even small-

magnitude coefficients obtained by PCR, such

as RH

mean

and RH

min

, showed a significant

effect on tree growth. This finding supports

our hypothesis, as the detrimental effect of col-

linearity becomes evident when the correlation

between climatic variables was disregarded

and the data subjected to MLR. The large SE

of MLR coefficients undermined the predic-

tive power of the MLR model, and therefore,

the influence of the climatic variables on tree

growth was underestimated. For instance, the

VIF of RH

mean

, RH

max

, and VPD computed

by MLR (Table 2) were over three orders of

magnitude greater than that of genuinely inde-

pendent orthogonal regressors (Table 1), which

magnified the SE up to 200-300 times (e.g.,

max

, VPD

mean

and VPD

max

) as compared

with the SE obtained by PCR. We found that

some MLR coefficients (e.g., T

max

and RH

min

)

had opposite sign.

The misleading effect of collinearity can

occur because the variance of a regression

coefficient (say b

) is inversely proportional

to the amplitude of the regressor [i.e., var(b

)

= σ

/∑(x

– x

)

]. Hence, when the variance is

so large, and the actual value of a coefficient

is close to zero, a regression coefficient with

opposite sign can result (Montgomery et al.,

2012). This is remarkable because it can be

concluded that a variable x

has a positive (or

negative) effect on Y, when in fact the opposite

is true. Tree growth increased with rising mean

and minimum RH, whereas it decreased with

increasing VPD

max

and EVT. Thus, by observ-

ing the VIF factor presented in Table 2, it is

tempting to discard from the regression model

not only RH but also VPD. Firstly, because a

VIF value above 10 is an indicative of strong

collinearity among regressors (Montgomery

et al., 2012). Secondly, because it may be

expected that the effects of these variables

are already included within the effect of tem-

perature. However, discarding these variables

from the model may weaken its predictive

strength as EVT, RH

mean

, RH

min

and VPD

max

had a truly independent effect on tree growth.

Collinearity dramatically increases the VIF,

making it difficult to quantify the individual

contribution of a regressor with little but real

independent effect on a dependent variable,

such as tree growth (Montgomery et al., 2012;

Bowman et al., 2013).

Tree growth was positively responsive to

an increase in rainfall intensity, whereas T

max

and PAR had a negative effect on growth rates.

The effect of T

max

on tree growth found in

this study agrees with the results of Way and

Oren (2010), who reported that tree growth

of tropical species can be negatively affected

by warming. On the other hand, our results

disagree with those of Wagner et al. (2014) and

Laurance et al. (2009). Wagner et al. (2014)

reported no effect of T

max

, whereas Laurance et

al. (2009) found a positive effect of maximum

temperature on tree growth. This discrepancy

can be ascribed to difference in environmental

conditions during data collection. For instance,

Green et al. (2020) reported that ecosystem

photosynthesis increases in the central Amazon

when VPD increased from 0.1 to 10 hPa. In

tropical rainforests, the optimum temperature

for photosynthesis is about 29 °C (Liu, 2020),

with decreasing photosynthetic rates at higher

temperatures. This can help explain the decline

in tree growth with rising T

max

. Beside the

effect of temperature on photosynthesis, a raise

in temperature has also an effect on transpira-

tion via the effect of temperature on water

viscosity (Darcy´s Law). In fact, in this experi-

mental site, EVT can increase in the dry season

491

Revista de Biología Tropical, ISSN electrónico: 2215-2075, Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

when temperatures are higher (Antezana-Vera

& Marenco, 2020).

There are reports associating tree growth

or ecosystem photosynthesis to variations in

temporal rainfall variability in the Amazon

region (Lee et al., 2013; Méndez, 2018; Yang

et al., 2018) or VPD (Lee et al. 2013; Green et

al., 2020). Some studies that aim to assess the

effect of rainfall seasonality on tree growth in

the Amazon have led to different results. Dias

and Marenco (2016) and Silva et al., (2003)

found no increase in tree growth during the wet

season, whereas Wagner et al. (2014), Mén-

dez (2018), and Antezana-Vera and Marenco

(2020) reported that tree growth increased with

an increase in rainfall intensity. Likewise, Lee

et al. (2013) and Yang et al. (2018) reported

a decline in photosynthesis-related activity

during the dry season. Altogether these results

indicate that the magnitude of the effect of

drought on tree growth is related to the length

of the dry season. In this study, we demonstrat-

ed that PCR could be a handy tool. We provide

evidence that an increase in VPD

max

(from 17

hPa – wet season to 23 hPa in the dry season)

leads to a reduction in tree growth. Interesting-

ly, such effect was only observed after remov-

ing the effect of collinearity. Marenco et al.

(2014) showed that photosynthesis of canopy

leaves (22-27 m tall trees) is closely related to

stomatal conductance (g

). They reported that

increased and reached its maximum value

at a VPD of 16 hPa, and then it declined and

became almost null at a VPD of 28 hPa. Like-

wise, Mendes and Marenco (2017) observed

that g

increased with increasing VPD in the

range of 5 to 10 hPa. These results show that

the effect of VPD on photosynthesis depended

on the level of atmospheric moisture. Green

et al. (2020) reported that ecosystem photo-

synthesis can increase at VPD values lower

than 10 hPa, Lee et al. (2013), on the other

hand, estimated that ecosystem photosynthe-

sis declined as VPD progressively increased

from 3.5 hPa (wet season) to 32 hPa in the dry

season, which is in agreement with the results

found in our study.

Solar radiation is intrinsically associated

with tree growth via its effect on photosyn-

thesis, and it has been reported that in tropical

rainforests an increase in solar radiation can

lead to an increase in tree growth (Wagner

et al., 2014). On the contrary, we found that

an increase in PAR leads to a decline in tree

growth, which agrees with the results of Yang

et al. (2018) and Méndez (2018). Yang et al.

(2018) observed a decrease in solar-induced

fluorescence during the drought of 2015-2016

in the Amazon region. Likewise, in a study

carried out at the same experimental site,

Antezana-Vera and Marenco (2020) found that

transpiration significantly increased with an

increase in PAR and VPD. An increase in

transpiration rates does not mean an increase

in g

and photosynthesis. In fact, most of the

time, g

decreases as transpiration increases in

response to an increase in VPD (Dai, Edwards,

& Ku, 1992), which can explain the negative

effect of PAR and VPD on tree growth reported

in this study.

Our results are relevant because of the

global importance of the Amazon forest and

because of the effects of the ongoing climate

changes, which have increased the temperature

(about 0.16 °C per decade) and altered rainfall

distribution, ranging from lower rainfall inten-

sity (longer dry seasons) in Eastern and South-

ern Amazonia to higher rainfall intensity in the

Northern Amazon (Marengo et al., 2018). The

dry season is associated with a rise in solar

radiation, temperature, and VPD (Lee et al.,

2013; Green et al., 2020), which ultimately can

lead to a decline in photosynthesis (Lee et al.,

2013; Marenco et al., 2014; Yang et al., 2018).

Because most of the climatic variables are cor-

related, assessing the collinearity-free effect is

important to accurately quantify the climatic

drivers of tree growth. Increased dry season

length has been forecasted for some parts of

the Amazon (Marengo et al., 2018), which

ultimately may reduce tree growth, not only

reducing soil water availability, but also by

increasing VPD and reducing RH. Our results

demonstrate that trees of the central Amazon

grow more slowly during the dry season, not

492

Revista de Biología Tropical, ISSN electrónico: 2215-2075 Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

only due the effect of a drop in rainfall intensity,

but also in response to the effect of an increase

in maximum temperature, evapotranspiration,

and maximum vapor pressure deficit, and a

decline in mean and minimum relative humid-

ity. To our knowledge this is the first time the

collinearity-free effect of RH

min

, RH

mean

, EVT

and VPD

max

on tree growth in the Amazon

region has been evaluated. The novelty of this

study is to demonstrate the orthogonal effect

of VPD

max

and RH

min

on tree growth in the

central Amazon, which contributes to enhance

the current knowledge of the ecophysiology of

Amazonian trees.

Ethical statement: authors declare that

they all agree with this publication and made

significant contributions; that there is no con-

flict of interest of any kind; and that we fol-

lowed all pertinent ethical and legal procedures

and requirements. All financial sources are

fully and clearly stated in the acknowledge-

ments section. A signed document has been

filed in the journal archives.

ACKNOWLEDGMENTS

To Ministry of Science, Technology and

Innovations (MCTI-INPA), the Foundation for

Research Support of the State of Amazonas

(FAPEAM), Coordination for the Improve-

ment of Higher Education Personnel (CAPES

code 0001) and the National Council for Sci-

entific and Technological Development (CNPq,

303907/2018-5). We thank the Editors and

anonymous reviewers for their valuable com-

ments and suggestions.

RESUMEN

El análisis de regresión por componentes principales

muestra el efecto libre de colinealidad de variables

climáticas subestimadas sobre el crecimiento de los

árboles en la Amazonía central

Introducción: Las variables climáticas muestran un

patrón estacional en la Amazonía central, pero el efecto de

la variabilidad intra-anual en el crecimiento de los árboles

aún no está claro. Para variables como la humedad relativa

(HR) y el déficit de presión de vapor (VPD), cuyo efecto

individual en el crecimiento de los árboles puede ser sub-

estimada, planteamos la hipótesis de que tales influencias

pueden detectarse eliminando el efecto de colinealidad

entre regresores. Objetivo: Este estudio tuvo como obje-

tivo determinar el efecto libre de colinealidad de la varia-

bilidad climática sobre el crecimiento de los árboles en la

Amazonía central. Métodos: Se midió el crecimiento radial

mensual en 325 árboles desde enero 2013 hasta diciembre

2017. También se registraron datos de irradiancia (PAR),

temperatura del aire, lluvia, humedad relativa (RH) y défi-

cit de presión de vapor de aire (VPD). Se utilizó la regre-

sión de componentes principales para evaluar el efecto de

la variabilidad micrometeorológica a lo largo del tiempo

sobre el crecimiento de los árboles. Para comparación, tam-

bién se utilizó la regresión lineal múltiple (MLR) estándar

para el análisis de datos. Resultados: El crecimiento de los

árboles incrementó con el aumento de las precipitaciones

y la humedad relativa, y disminuyó con el aumento de la

VPD máxima, la irradiancia y la temperatura máxima. Por

lo tanto, los árboles crecieron más lentamente durante la

estación seca, cuando la irradiancia, la temperatura y la

VPD eran más altas. La variabilidad micrometeorológica

no afectó el crecimiento de los árboles cuando se aplicó

MLR. Estos hallazgos indican que ignorar la correlación

entre las variables climáticas puede conducir a resultados

imprecisos. Conclusiones: Una novedad de este estudio es

demostrar el efecto ortogonal del VPD máximo y la hume-

dad relativa mínima sobre el crecimiento de los árboles.

Palabras clave: floresta húmeda amazónica; sequedad

atmosférica; estación seca; humedad relativa; temporada

húmeda.

REFERENCES

Antezana-Vera, S.A., & Marenco, R.A. (2020). Sap flow

rates of Minquartia guianensis in central Ama-

zonia during the prolonged dry season of 2015-

2016. Journal Forestry Research. DOI: 10.1007/

s11676-020-01193-9

Bowman, D.M., Brienen, R.J., Gloor, E., Phillips, O.L., &

Prior, L.D. (2013). Detecting trends in tree growth:

not so simple. Trends in Plant Science, 18, 11-17.

Buck, A.L. (1981). New equations for computing vapor-

pressure and enhancement factor. Journal of Applied

Meteorology, 20, 1527-1532.

Dai, Z., Edwards, G.E., & Ku, M.S. (1992). Control of

photosynthesis and stomatal conductance in Ricinus

communis L. (castor bean) by leaf to air vapor pressu-

re deficit. Plant Physiology, 99, 1426-1434.

Dias, D.P., & Marenco, R.A. (2016). Tree growth, wood

and bark water content of 28 Amazonian tree species

in response to variations in rainfall and wood density.

iForest - Biogeosciences and Forestry, 9(3), 1-7.

493

Revista de Biología Tropical, ISSN electrónico: 2215-2075, Vol. 69(2): 482-493, April-June 2021 (Published Apr. 01, 2021)

Green, J.K., Berry, J., Ciais, P., Zhang, Y., & Gentine, P.

(2020). Amazon rainforest photosynthesis increases

in response to atmospheric dryness. Science Advan-

ces, 6, eabb7232.

Hargreaves, G.H., & Samani, Z.A. (1985). Reference crop

evapotranspiration from temperature. Applied Engi-

neering in Agriculture, 1, 96-99.

Laurance, S.G., Laurance, W.F., Nascimento, H.E., Andra-

de, A., Fearnside, P.M., Rebello, E.R., & Condit, R.

(2009). Long-term variation in Amazon forest dyna-

mics. Journal of Vegetation Science, 20, 323-333.

Lee, J.E., Frankenberg, C., van der Tol, C., Berry, J.A.,

Guanter, L., Boyce, C.K., Fisher, J.B., Morrow, E.,

Worden, J.R., Asefi, S., Badgley, G., & Saatchi, S.

(2013). Forest productivity and water stress in Ama-

zonia: observations from GOSAT chlorophyll fluo-

rescence. Proceedings of the Royal Society Biological

Sciences, 280, 20130171.

Liu, Y. (2020). Optimum temperature for photosynthesis:

from leaf-to ecosystem-scale. Science Bulletin, 65,

601-604.

Marenco, R.A., Antezana-Vera, S.A., Santos, P.R.G.,

Camargo, M.A.B., Oliveira, M.F., & Santos, J.K.S.

(2014). Fisiologia de espécies florestais da Ama-

zônia: fotossíntese, respiração e relações hídricas.

Revista Ceres, 61, 786-799.

Marengo, J.A., Souza, C.M., Thonicke, K., Burton, C.,

Halladay, K., Betts, R.A., Alves, L.M., & Soares,

W.R. (2018). Changes in climate and land use over

the Amazon region: current and future variability

and trends. Frontiers in Earth Science, 6, 228. DOI:

10.3389/feart.2018.00228

Mendes, K.R., & Marenco, R.A. (2017). Stomatal opening

in response to the simultaneous increase in vapor

pressure deficit and temperature over a 24-h period

under constant light in a tropical rainforest of the

central Amazon. Theoretical and Experimental Plant

Physiology, 29, 187-194.

Mendes, K.R., Marenco, R.A., & Magalhães, N.D.S.

(2013). Growth and photosynthetic use efficiency of

nitrogen and phosphorus in saplings of Amazonian

tree species. Revista Arvore, 37, 707-716.

Méndez, C.R. (2018). Influência do El Niño 2015-2016

no incremento diamétrico das árvores da Amazônia

Central (Master’s thesis). Instituto Nacional de Pes-

quisas da Amazônia, Manaus, Brazil.

Monserud, R.A., & Marshall, J.D. (2001). Time-series

analysis of δ13C from tree rings. I. Time trends and

autocorrelation. Tree Physiology, 21, 1087-102.

Montgomery, D.C., Peck, E.A., & Vining, G.G. (2012).

Introduction to linear regression analysis. Hoboken,

USA: John Wiley & Sons.

Nogueira, E.M., Nelson, B.W., Fearnside, P.M., França,

M.B., & Oliveira, A.C. (2008). Tree height in Brazil’s

‘arc of deforestation’: shorter trees in south and

southwest Amazonia imply lower biomass. Forest

Ecology and Management, 255, 2963-2972.

Prance, G.T., Rodrigues, W.A., & Silva, M.F. (1976).

Inventario florestal de um hectare de mata de terra

firme km 30 de Estrada Manaus-Itacoatiara. Acta

Amazonica, 6, 9-35.

Saatchi, S.S., Houghton, R.A., Alvalá, R.C.S., Soares,

J.V., & Yu, Y. (2007). Distribution of aboveground

live biomass in the Amazon basin. Global Change

Biology, 13, 816-837.

Silva, R.P., Nakamura, S., Azevedo, C.P., Chambers, J.,

Rocha, R.D., Pinto, A.C., Santos, J., & Higuchi, N.

(2003). Use of metallic dendrometers for individual

diameter growth patterns of trees at Cuieiras river

basin. Acta Amazonica, 33, 67-84.

Stat Soft Inc. (2004). STATISTICA (Version 7, software).

Tulsa, OK, USA.

Wagner, F., Rossi, V., Aubry-Kientz, M., Bonal, D., Dalitz,

H., Gliniars, R., Stahl, C., Trabucco, A., & Herault,

B. (2014). Pan-tropical analysis of climate effects on

seasonal tree growth. PLoS ONE, 9, e92337.

Wagner, F., Rossi, V., Stahl, C., Bonal, D., & Herault, B.

(2012). Water availability is the main climate driver

of neotropical tree growth. PLoS ONE, 7, e34074.

Way, D.A., & Oren, R. (2010). Differential responses to

changes in growth temperature between trees from

different functional groups and biomes: a review and

synthesis of data. Tree Physiology, 30, 669-88.

Yang, J., Tian, H., Pan, S., Chen, G., Zhang, B., & Dangal,

S. (2018). Amazon drought and forest response:

Largely reduced forest photosynthesis but slightly

increased canopy greenness during the extreme

drought of 2015/2016. Global Change Biology, 24,

1919-1934.