Evaluation of Bent Trees in Juvenile Teak (tectona Grandis L.f.) Plantations in Costa Rica: Effects on Tree Morphology and Wood Properties

Bent trees have been observed during the early years in juvenile plantations (less than 5 years-old) of Tectona grandis in Costa Rica. The relationship between bending and the morphological characteristics of the trees was explored. An evaluation of bent trees was conducted in six juvenile plantations (8, 17, 27, 28, 31, and 54 months old) of Tectona grandis. Site 1 with 8-month-old plantations did not display any relationship with any tree morphological variable (diameter, height, and crown weight of tree), whereas for the sites 2, 3, and 4 with 17-, 27-, and 28-month-old plantations, respectively, all the tree morphological variables were statistically correlated with the bent trees. A multiple regression analysis showed that the most influential variables were height to crown base, crown weight, diameter, and total height of the tree. An evaluation of the bending risk factor (RF) was correlated with the height to crown base, crown weight, and form factor. The modulus of elasticity and chemical compositions of bent trees differed from those of straight trees. The causes of tree bending are complex, involving, among other factors, the morphology of the trees, plantation conditions, and other factors specific to the xylem, such as the specific gravity, modulus of elasticity, and presence of calcium and magnesium in the wood.


Introduction
Tectona grandis is widely used for reforestation in the tropical regions of America, Asia, and Africa [1].The estimated planted area of this species is approximately 4.35 million hectares, and it is distributed in 52 different tropical countries [1].Teak wood is well known in international markets for its natural resistance to fungal attack, excellent mechanical characteristics, and exceptional esthetical properties [2].Teak, mahogany (Swietenia spp.), and red cedar (Cedrela odorata) are the tropical hardwoods with the greatest demand in the high-end market [3].Currently, teakwood comes from fast-growing clonal plantations and is intensively managed with shorter rotations [1].
The teak silvicultural package has been undergoing important improvements in recent years in Latin America.Increasing initial spacing from 3 m × 3 m to 3 m × 4 m [4], together with the use of better genetic materials, results in a reduction in crop rotation to less than 30 years [5].Tree development during the first years is affected by plantation stocking and influenced by the initial tree spacing [6], which determines site occupancy, and tree selection for final harvest [7].A high initial density promotes a faster height growth [8], but restricts the diameter growth rate [7].
The height/diameter ratio is important in plantation management in order to maintain the verticality and stability of trees [9][10][11].The susceptibility of trees to bending, crown breakage, or uprooting is one of the main problems associated with tree stability in teak and other species [12].The presence of strong winds or storms can hinder the quality of plantation trees [12,13].However, tree stability can also be related to the species, climate, topography, altitude, wind exposure, soil properties, stand structure, and tree morphology [14,15].
Tree bending, uprooting, or breaking in plantations can also be influenced by silvicultural management practices.For example, a high stand density results in smaller diameter growth, a higher diameter/height ratio, smaller crown size, higher tree mortality, and higher form factor [16].It has also been reported [12,17] that tree morphology may affect resistance to uprooting (tree root system toppling).
Specific studies in bending trees were reported by Moore [18], who studied the resistive bending in Pinus radiata and found that bending was significantly and positively correlated with tree height, diameter, and stem volume.The study also found that trees with higher taper (lower ratio of tree height to diameter) exhibited a higher maximum resistive bending.In this species, bending trees show a larger production of resin bags in wood [19].
Bending can also affect some wood properties.Van Gelder et al. [20] found that the wood density of tropical trees was strongly positively related to wood strength and stiffness.The species safety factor for buckling has also been positively related to wood density and stiffness.In contrast, Anten and Schieving [21] found that trees with low wood density need to produce thicker stems, but at the same time, they need to invest less biomass per unit of stem length.
With the exception of eucalyptus species-which have been the focus of some studies-studies on tree bending, breaking, and uprooting in tropical species plantations remain scarce [6,22].There are only two studies on Tectona grandis that report on tree bending under plantation conditions.Monteuuis et al. [23] and Chaix et al. [24] report that bending is 50% hereditary in plantations with seedlings between 49 and 106 months old.Although it was found that bending is not significant in clonal plantations less than 49 months old, it is significant at ages between 49 and 106 months old.However, although there are two reports on bending, studies in T. grandis are still scarce.
Tree bending and stem breaking have been observed in juvenile teak plantations in Costa Rica, with its consequent negative impact on growth and the returns of investors [25].Tree shape and development during its first years are probably influenced by climatic conditions in Costa Rica [26].The initial height growth rate in teak follows a faster pattern than diameter, which can cause the trees to bend as expected.In addition, this growth dynamic can affect other intrinsic wood properties in trees, such as the specific gravity and mechanical properties.
Given the described situation, the aim of this study was to investigate the incidence of bending and the height at which the damage begins in six different sites for juvenile plantations of Tectona grandis (8 to 54 months old) in Costa Rica.Additionally, the relationship between bending and tree characteristics (diameter, height, and crown weight) was analyzed.Destructive sampling was performed in Site 6 with a 54-month-old plantation to determine the influence of mechanical and wood density properties and to examine the nutrient content in the trunks of the bent trees.Based on this information, aspects that influence tree bending, such as tree characteristics, wood properties, or nutrient content, were identified, with the aim of contributing towards the understanding of how to handle bending in juvenile plantations of T. grandis.

Studied Plantations
Six juvenile T. grandis plantations planted in six different sites in the Southern Pacific region of Costa Rica were studied.All six plantations exhibited important evidence and a high percentage of bending trees (Figure 1a).Ages ranged between 8 and 54 months (0.67 to 4.15 years old), located in four sectors: plantations in Site 2 and 6 (17-and 54-month-old) are in separate sectors; the plantations in Site 1 and 3 (8-and 27-month-old) are both in the same sector and are close to the plantation in Site 2, and plantations in Site 5 and 6 (28-and 31-month-old) are in a same area or site (Figure 1a).The six juvenile T. grandis plantations were established with seedlings.The plantations belong to the BARCA S.A. forestry company.Climatic, topographic, and wind conditions are detailed in Table 1.

per-humid
September and October.The topography is rugged in some sectors and in others is flat.The annual average rainfall is 4000 mm, with an average of three dry months from January to March.Site 4 and 6, 28-and 31month-old Soil is younger, with a second horizon.0 meters above sea level and basal tropical wet forest.
The topography is flat.The annual average rainfall is 4000 mm.The rainfall is concentrated from May to November.

Sampling Procedures
The sampled plantations ranged from 7.3 to 113.2 hectares (Table 2), and the incidence of tree bending was assessed in the whole plantation.For this study population, sample percentage varied from 15.2% to 19.1% per plantation.Table 2 shows the sample intensity in detail.Systematic sampling was used, and rectangular plots that were 10 m wide × 50 m long and continuously distributed along transects were established.The location of the first transect was randomly selected to avoid subjectivity.From this starting point, the remaining sampling transects or strips were placed systematically every 50 m.The topography is flat.The annual average rainfall is 4000 mm.The rainfall is concentrated from May to November.

Sampling Procedures
The sampled plantations ranged from 7.3 to 113.2 hectares (Table 2), and the incidence of tree bending was assessed in the whole plantation.For this study population, sample percentage varied from 15.2% to 19.1% per plantation.Table 2 shows the sample intensity in detail.Systematic sampling was used, and rectangular plots that were 10 m wide × 50 m long and continuously distributed along transects were established.The location of the first transect was randomly selected to avoid subjectivity.From this starting point, the remaining sampling transects or strips were placed systematically every 50 m.Note: Sampling intensity corresponds to the total area of sampling plots (with 10 m by 50 m in each) related to the total planted area.

Information Collected
The following variables were measured for each tree within the sampling plots: diameter at 1.3 m above the ground (d) with a diameter band meter, total height (Ht), height at crown base (Hcb), and bending height (Hb).These heights were measured using a telescoping height meter.This last variable corresponds to the distance from the ground up to the point at which the tree loses its verticality and starts to bend.It was measured using a meter stick or a telescopic pole.For bent trees, the cardinal bending orientation was recorded.Bent trees were classified into three different types, and one class was added, which corresponded to broken trees: • Class 1: no bending observed (Figure 2a).

•
Class 4: the tree is broken and has lost its crown (Figure 2d).Note: Sampling intensity corresponds to the total area of sampling plots (with 10 m by 50 m in each) related to the total planted area.

Information Collected
The following variables were measured for each tree within the sampling plots: diameter at 1.3 m above the ground (d) with a diameter band meter, total height (Ht), height at crown base (Hcb), and bending height (Hb).These heights were measured using a telescoping height meter.This last variable corresponds to the distance from the ground up to the point at which the tree loses its verticality and starts to bend.It was measured using a meter stick or a telescopic pole.For bent trees, the cardinal bending orientation was recorded.Bent trees were classified into three different types, and one class was added, which corresponded to broken trees:

Analysis of Field Data
Several ratios were determined from field data: (i) the diameter/total height ratio (d/Ht); (ii) the height at crown base/total height ratio (Hcb/Ht); and (iii) the bending height/total height ratio (Hb/Ht).A Pearson correlation matrix was developed, where the bending heights of classes 2 and 3 from each sampled plantation were correlated against d, Ht, Hcb, d/Ht ratio, and Hcb/Ht ratio using a significance level of α = 0.05.Forward stepwise multiple regression analysis was applied to determine which variables are significantly related to bending.In addition, an analysis of variance (ANOVA) was applied to determine likely differences among the morphological variables evaluated for classes 2, 3, and 4, and Tukey's multiple comparison test was used to estimate differences among plantations and bent class.The SAS 8.1 statistics program for Windows (SAS Institute Inc., Cary, NC, USA) was used to carry out the analyses.

Destructive Study in Site 6 (54-Month-Old Plantation)
Sampling: Site 6 was selected for more detailed analysis of the conditions that may explain causes of tree bending in juvenile plantations.In this plantation, 10 trees were randomly selected for each bending class (Classes 1, 2, and 3) from the total number of trees in the sampling plots (i.e., 30 trees were sampled for felling and their properties were measured).Class 4 was not considered in this analysis because the trees were broken.
Variables measured: After felling, the following variables were measured for each tree selected: the diameter at 1.3 m above the ground (d), total height (Ht), height at crown base (Hcb), and bending height (Hb).Then, each tree was cut at the lowest branch insertion point on the trunk (i.e., at the height at which the first branch at the base of the crown appears).The crown, trunk, branches, and leaves were weighed.These fresh weights were used to determine the live-crown weight (Wc), which included the crown, branches, and leaves.The trunk weight (Wt) free of branches was also determined.The tree information was used to determine the risk factor (RF) proposed by Jaquen et al. [27], which was then computed using Equations ( 1)- (3).RF measures the risk of stem bending (i.e., situations where buckling risk is a major ecological constraint, with a transition from self-supporting to liana habit for natural trees).Higher values indicate greater risk [27].
Tree bending risk factor = Total tree height Critical buckling height (1) Critical buckling height = 0.792 3 Modulus of elasticity Total weight/Volume) where total tree height is in m, the critical buckling height is in m, and the modulus of elasticity is in MPa.The coefficient of determination is indicated above, and the total weight is in kg, the volume is in m 3 , and d is the diameter at 1.3 m above the ground in cm.

Wood properties:
The specific gravity, modulus of elasticity, and inorganic composition of the trunk were determined for the 30 trees selected.Three 2.5-cm-thick cross-sections were cut from each tree trunk.The first cross-section was cut at the base of the trunk, the second at a height of 2.5 m, and the third at the upper part of the tree where the trunk diameter narrows to 2.5 cm.The first 2.5 m log cut from the base of the tree was utilized for the analysis of the modulus of elasticity (Figure 1b).
The discs were cut in half to remove the remains of the pith (in some cases, the parenchyma tissue residues are present in teak trees, which can alter the volume of the cross-section when it is measured by water immersion); then, the basic specific gravity was determined.The bark was removed on both sides of the discs.Then, they were polished to prevent bubble formation when measuring the volume by displacing water.Later, the samples were dried at 103 • C for 24 h to measure their dry weight.The moisture content was also determined for the discs from the three different heights by using the ASTM D-4442-92 standard [28].The discs were previously fresh weighed and then kiln dried at 103 • C for 24 h.
To calculate the modulus of elasticity (MOE), the methodology proposed by the ASTM D-1036-99 [29] standard "Static bending tests of poles, Cantilever Test Method" was employed, as described in Figure 1c.This method was used because it measures the bending capacity of the trunk and it approaches the bending conditions of standing trees.
To determine deformation, loads ranging from 0 kg to 100 kg, at intervals of 10 kg, were applied to each log.The deformation of the table was measured for each calibration.Load vs. deformation values were plotted to establish the limit of proportionality (the wood stops being elastic to become plastic), and the values of load and deformation at that point were recorded.Based on this information, the MOE at the limit of proportionality was calculated using Equation (5).
where MOE is the modulus of elasticity at the flexural point (kg/cm 2 ), P' is the applied load (kg), a is the span (m), δ PAC is the deflection (mm), C 1 is the circumference of the log at the ground line (cm), and C 2 is the circumference at the point of load application (cm) The inorganic composition of trunks was analyzed using the method described by Sparks [30].Concentrations of nitrogen (N), phosphorus (P), calcium (Ca), magnesium (Mg), potassium (K), and sulfur (S), whose concentrations were reported as percentages, were determined.In addition, iron (Fe), manganese (Mn), cupper (Cu), zinc (Zn), and boron (B), whose concentrations were reported as milligrams of inorganic element per ash gram, were determined.For this analysis, only 9 of the 30 sampled trees were used, three per bending class, and only the trunk tissue was used.A section of the trunk (approximately 5 cm in each sampled tree) was milled.Then, all of the material from each class was mixed, and three samples were used to determine the inorganic composition.
The information obtained in this plantation was analyzed by an ANOVA for each wood property, morphological characteristic of the tree, or inorganic composition.The response variable was the bending class (1, 2, and 3), and the independent variables were the properties of wood, morphological characteristics of the tree, or inorganic compositions.Tukey's multiple range was used to estimate the differences between the averages of each class when the ANOVA test was significant.

Results
Although there are many uncontrolled factors during plantation development, such as soil fertility, wind intensity, and growth rate, a comparative study was carried out between the different sites to establish which factors affected the development of bending trees.

Incidence of Bent Trees and Bending Height
The evaluation of bent trees showed that the percentage of bent trees (Classes 2 and 3) increases with the age of the plantation, whereas the quantity of straight trees (Class 1) diminishes from 97.8% in the youngest plantation to 78% in the oldest plantations (Table 3).Although bending increases with age, no consistency was found regarding the increment of the classes of damage.Concerning Class 2, a reduction in the percentage of this type of damage in plantations in Site 4 and 5 occurred due to the increase in the percentage of Class 4 (trees with broken crowns).For Class 3 (severely damaged trees), the percentage decreased from 10.6% to 4.5% as the age of the plantation increased from Site 5 to Site 6 (Table 3).The height to the start of bending increased with the age of the plantation for Classes 2, 3, and 4 (Figure 4a-c).For Class 2, the height varied from 0.8 to 6.5 m (Figure 4a), whereas for Class 3, the bending heights were lower, ranging from 0.3 to 5.7 m (Figure 4b).Class 4 trees (broken crown) (Figure 4c) presented a height of breaking point that was higher than the bending height of trees of Class 3 (Figure 4b).The relative height of bending trees shows that the different classes (2, 3, and 4) varied with Site (Figure 4d).Class 3 presents the lowest height percentages relative to the other damage classes (Figure 4d).For Classes 2 and 4, in plantation in Site 1, 2, 4, 5, and 6, the percentage ranges between 40% and 50% of the tree's total height.

Incidence of Bent Trees and Bending Height
The evaluation of bent trees showed that the percentage of bent trees (Classes 2 and 3) increases with the age of the plantation, whereas the quantity of straight trees (Class 1) diminishes from 97.8% in the youngest plantation to 78% in the oldest plantations (Table 3).Although bending increases with age, no consistency was found regarding the increment of the classes of damage.Concerning Class 2, a reduction in the percentage of this type of damage in plantations in Site 4 and 5 occurred due to the increase in the percentage of Class 4 (trees with broken crowns).For Class 3 (severely damaged trees), the percentage decreased from 10.6% to 4.5% as the age of the plantation increased from Site 5 to Site 6 (Table 3).The height to the start of bending increased with the age of the plantation for Classes 2, 3, and 4 (Figure 4a-c).For Class 2, the height varied from 0.8 to 6.5 m (Figure 4a), whereas for Class 3, the bending heights were lower, ranging from 0.3 to 5.7 m (Figure 4b).Class 4 trees (broken crown) (Figure 4c) presented a height of breaking point that was higher than the bending height of trees of Class 3 (Figure 4b).The relative height of bending trees shows that the different classes (2, 3, and 4) varied with Site (Figure 4d).Class 3 presents the lowest height percentages relative to the other damage classes (Figure 4d).For Classes 2 and 4, in plantation in Site 1, 2, 4, 5, and 6, the percentage ranges between 40% and 50% of the tree's total height.

Relationship between the Morphological Characteristics and Bending Height
Relative to the morphological characteristics (d, Ht, Hcb, d/Ht ratio, and Hcb/Ht ratio) no relationship was found with the bending height (Hb) for the youngest plantation in Site 1; then, Hb did not increase or decrease for these morphological parameters.In contrast, all of the morphological variables were statistically correlated with Hb for the plantations in site 2, 3, and 4. Except for the d/Ht ratio, the variables were all positively correlated (Table 4), which means that Hb increases with an increase in the d/Ht ratio.The forward stepwise analysis showed that for these sites (2, 3, and 4), the height to crown base (Hcb) is the variable that influences bending the most.The final model explained from 29% to 49% of the variation of Hb (Table 5).The second most important variable in the variation of Hb for plantation in Site 3 and 4 is Ht, and it is the Hcb/Ht ratio for plantation in Site 3.Only Hcb influences the plantation in Site 2, and explains 47% of variation of Hb (Table 5).
For the plantation in Site 5, according to the forward stepwise regression analysis, the most influential variables are Hcb and d (Table 5), explaining 39% and 7% of the variation of Hb, respectively.The variables correlated with Hb in the oldest plantation (Site 6 or 54 months old) were Hcb and the Hcb/Ht ratio (Table 4); in this plantation Hb increases with increases in Hcb and the Hcb/Ht ratio.Hcb accounted for 13% of the influence on the variation of Hb (Table 5).

Relationship between the Morphological Characteristics and Bending Height
Relative to the morphological characteristics (d, Ht, Hcb, d/Ht ratio, and Hcb/Ht ratio) no relationship was found with the bending height (Hb) for the youngest plantation in Site 1; then, Hb did not increase or decrease for these morphological parameters.In contrast, all of the morphological variables were statistically correlated with Hb for the plantations in site 2, 3, and 4. Except for the d/Ht ratio, the variables were all positively correlated (Table 4), which means that Hb increases with an increase in the d/Ht ratio.The forward stepwise analysis showed that for these sites (2, 3, and 4), the height to crown base (Hcb) is the variable that influences bending the most.The final model explained from 29% to 49% of the variation of Hb (Table 5).The second most important variable in the variation of Hb for plantation in Site 3 and 4 is Ht, and it is the Hcb/Ht ratio for plantation in Site 3.Only Hcb influences the plantation in Site 2, and explains 47% of variation of Hb (Table 5).For the plantation in Site 5, according to the forward stepwise regression analysis, the most influential variables are Hcb and d (Table 5), explaining 39% and 7% of the variation of Hb, respectively.The variables correlated with Hb in the oldest plantation (Site 6 or 54 months old) were Hcb and the Hcb/Ht ratio (Table 4); in this plantation Hb increases with increases in Hcb and the Hcb/Ht ratio.Hcb accounted for 13% of the influence on the variation of Hb (Table 5).
The evaluation of the different morphological variables in the bending class (Figure 2) demonstrated that the bending class is negatively correlated with the Hcb (r = −0.60;p < 0.0001), positively correlated with Wc (r = 0.47; p = 0.0067), and positively correlated with Hb (r = 0.57; p < 0.0001), but d (r = 0.19; p = 0.13), Ht (r = −0.15;p = 0.15), and Wt (r = 0.09; p = 0.67) presented no effect on the bending class.Considering the significant variables (Hcb, Wc, and Hb) in the forward stepwise multiple regression analysis (Table 5), it was demonstrated that Hcb is again the most influential variable, accounting for 36% of the variation of the bending class, followed by Wc and Ht, explaining 7% and 9%, respectively.
The analysis of the different morphological characteristics, SG, MOE, and trunk chemistry showed that some of these properties vary between bending classes.The morphological variables d and Ht were not related to bending class (Table 6).However, Hcb decreased with the increase in the bending class, as opposed to Wc, which increases with greater damage class (Table 6) and is approximately 20% higher for Hcb and 20% lower for Wc in bent trees.Concerning the properties of the wood, specific gravity did not differ between the bending classes (Figure 6a), whereas MOE was 8% lower for bent trees (Classes 2 and 3) than for straight trees (Class 1) (Figure 6b).In relation to the nutrient contents in the trunk, the contents of Ca and Mg were significantly different in the different types of damage (Table 6).The Ca and Mg contents were approximately 30% higher in the bent trees (Classes 2 and 3) than in the straight trees (Class 1).

Discussion
DBH, height, height, and height to crown base ((Figure 3) increased as the age of the plantation increased [31].Only the plantations that were between 27 and 28 months of age (plantations in Site 3 and 4) did not present differences, probably due to their similar ages.Growth values of the plantations sampled (Figure 3) are consistent with growth reported for T. grandis in Costa Rica [7,31,32].Additionally, the low density of the 54-month-old plantation (the plantation in Site 6) is attributed to a 50% thinning conducted in the plantation 6 months before the bending analysis was carried out.However, care must be taken in considering the results, because there are many uncontrolled factors during plantation development, such as soil fertility, wind intensity, and growth rate.Then a comparative study was carried out between the different sites to establish which factors affected the development of bending trees.
The increase in the percentage of bent trees in Classes 2 and 3 with age of the plantation (Table 3) is the result of the decreasing number of straight trees (Class 1).As trees grow, the biomass added in the upper parts of the tree develops greater self-loading due to increased weight.Then, the biomass in the crown of trees and the presence of wind create flexural moments, generally at the base of the tree, which result in the bending of tree [33].
During the first years, the low branches [34] and low diameter growth in relation to the tree's height [7] prevent teak from having the morphological structure required to support the moments created by the wind against the biomass accumulated in the upper parts of the tree, which bends the stem without causing uprooting, as normally occurs with this species.
Thinning, which affects stand density, can reduce the incidence of bent trees because some bent trees are removed, resulting in a lower stand density [19].However, it was not possible to confirm this situation in the teak plantations.The plantation in Site 6 (54-month-old) was thinned and therefore had a low density, but the incidence of tree bending was the highest (Figure 4a-c).This result indicated that the thinning was applied in the juvenile stage to reduce the stand density and that neither condition helped decrease the incidence of bent trees.The trees of this age probably have not yet developed a diameter that is able to withstand bending [35].
The forward stepwise regression analysis confirmed this because for all sites, Hcb has an impact on the Hb of the tree (Table 5) and on the bending class.Likewise, the study conducted in the plantation in Site 6 also confirms the effect of biomass accumulation on bent trees due to Wc (Table 5).In addition, as expected, important morphological characteristics (Hcb, Wc, and Hb) exert an influence on bending.Regarding the mechanical stability of the tree, increases in trunk bending with plantation age can be explained by the fact that the highest concentration of biomass and the distance of support of the tree (tree base embedded in the ground) produce a high moment value during wind events, creating an area of weakness in the trunk [35] where the tree bends.
From the perspective of stem quality for the future utilization of the logs, Class 3 is more critical compared to Class 2 because a greater bending of the log produces a lower lumber recovery factor (lumber volume production relative to the total log volume) [36,37].Therefore, a higher percentage of Class 3 trees in plantations in Site 3, 4, and 5 (Table 3) means lower quality logs.It was observed,

Discussion
DBH, height, height, and height to crown base ((Figure 3) increased as the age of the plantation increased [31].Only the plantations that were between 27 and 28 months of age (plantations in Site 3 and 4) did not present differences, probably due to their similar ages.Growth values of the plantations sampled (Figure 3) are consistent with growth reported for T. grandis in Costa Rica [7,31,32].Additionally, the low density of the 54-month-old plantation (the plantation in Site 6) is attributed to a 50% thinning conducted in the plantation 6 months before the bending analysis was carried out.However, care must be taken in considering the results, because there are many uncontrolled factors during plantation development, such as soil fertility, wind intensity, and growth rate.Then a comparative study was carried out between the different sites to establish which factors affected the development of bending trees.
The increase in the percentage of bent trees in Classes 2 and 3 with age of the plantation (Table 3) is the result of the decreasing number of straight trees (Class 1).As trees grow, the biomass added in the upper parts of the tree develops greater self-loading due to increased weight.Then, the biomass in the crown of trees and the presence of wind create flexural moments, generally at the base of the tree, which result in the bending of tree [33].
During the first years, the low branches [34] and low diameter growth in relation to the tree's height [7] prevent teak from having the morphological structure required to support the moments created by the wind against the biomass accumulated in the upper parts of the tree, which bends the stem without causing uprooting, as normally occurs with this species.
Thinning, which affects stand density, can reduce the incidence of bent trees because some bent trees are removed, resulting in a lower stand density [19].However, it was not possible to confirm this situation in the teak plantations.The plantation in Site 6 (54-month-old) was thinned and therefore had a low density, but the incidence of tree bending was the highest (Figure 4a-c).This result indicated that the thinning was applied in the juvenile stage to reduce the stand density and that neither condition helped decrease the incidence of bent trees.The trees of this age probably have not yet developed a diameter that is able to withstand bending [35].
The forward stepwise regression analysis confirmed this because for all sites, Hcb has an impact on the Hb of the tree (Table 5) and on the bending class.Likewise, the study conducted in the plantation in Site 6 also confirms the effect of biomass accumulation on bent trees due to Wc (Table 5).In addition, as expected, important morphological characteristics (Hcb, Wc, and Hb) exert an influence on bending.Regarding the mechanical stability of the tree, increases in trunk bending with plantation age can be explained by the fact that the highest concentration of biomass and the distance of support of the tree (tree base embedded in the ground) produce a high moment value during wind events, creating an area of weakness in the trunk [35] where the tree bends.
From the perspective of stem quality for the future utilization of the logs, Class 3 is more critical compared to Class 2 because a greater bending of the log produces a lower lumber recovery factor (lumber volume production relative to the total log volume) [36,37].Therefore, a higher percentage of Class 3 trees in plantations in Site 3, 4, and 5 (Table 3) means lower quality logs.It was observed, nevertheless, that the percentage of Class 3 trees decreased to 4.5% in plantations in which thinning had been applied, with a slight increase in both straight and bent trees in Class 2 (Table 3).
By comparing the results obtained regarding the number of straight trees with other studies, it becomes evident that they are within the range reported by Monteuuis et al. [23], who reports a wide range of percentages of straight trees (from 15% to 95%) for 42 provenances of 106-month-old teak in Sabah.However, according to these authors, the remaining bifurcated and bent trees were classified jointly; therefore, the percentage of bent trees was not established.Chaix et al. [24], in contrast, report a much lower range of percentages of bent trees for different provenances of teak in Sabah than the percentages found in the plantations analyzed in the present work.
As for the initial bending height, there is a positive correlation with increasing Ht (Figure 4).Moreover, consistent with the correlation analysis (Table 3) and the forward stepwise multiple regression (Table 4) of all of the plantations, the increasing Hb in most ages is related to increases in Hcb, followed by Ht in the plantations in Site 3 and 4 and d in the case of plantations in Site 5 and 6, with a slight influence from the ratio Hcb/Ht in the plantations in Site 3 and 4 (Table 4).Likewise, the specific analysis of the plantation in Site 6 confirms that Hb is linked both to the mentioned variables and to the Wc (Table 5).
The results found in teak trees agree with studies carried out by Moore [18] in Pinus radiata.He found that resistive bending was significantly and positively correlated with tree height, d, and stem volume, at a similar significance level to that found in teak in Costa Rica.
Mechanically explained, tree stability depends on the canopy as a lumped mass on a column [38] and the trunk as a weightless elastic column [39], modeling the stability of the tree as a series of n logs with lumped masses representing branch whorls along the trunk [40,41].The strength of the wind impairs tree stability [13].As the tree ages, Hcb and Ht increase [7,32], and the canopy weight and distance of support of the tree are also augmented, leading to tree bending as a result of the push of external factors, such as winds in the region.
An important aspect to highlight relative to the morphology of the tree that is not addressed in the present work on T. grandis is the resistance to bending or the mechanical stability of the tree [38].Marked taper is considered an adaptive characteristic of the tree to resist the wind [38]; however, this characteristic is hardly noticeable during the first years of growth of T. grandis [32].Therefore, tree bending due to a lack of mechanical resistance required to withstand the winds of southern Costa Rica is common.
The specific study in the plantation in Site 6 showed the importance of the tree's morphological variables to the tree bending risk factor (RF).This parameter measures the capacity of the tree to coexist under competent conditions without bending [27].Although this parameter has been applied to tree stability and tree interactions in natural forests [42], it can also be applied to trees growing in forest plantations.In the case of plantations, the RF increases in value with increasing Hcb and Wc (Figure 5b), probably as a consequence of greater weight concentration in higher parts of the tree.However, the RF decreases as the tree's form factor increases (Figure 5d).Such behavior is explained by Mattheck [43], who indicated that for the same amount of material, a cone can be built higher than a cylinder.Indeed, a cone has both a lower load in its distal part where the lever arm is the largest and a higher bending inertia in the basal part that is subjected to the highest bending moment.
An important aspect to highlight is the relationship between the RF and Hb, which are negatively correlated (Figure 5a), indicating that trees with low values of RF are prone to bend at lower heights, whereas low values of this factor indicate that the tree will tend to bend at greater heights.
The specific study conducted in the 54-month-old plantation also suggests that other wood properties influence the tendency of teak trees to bend, in addition to the influence of Wc and Hcb on bending (Figure 5c,d).This behavior is consistent with the study by Skatter and Kucera [44] in Scots pine, which investigated the influence of the crown on flaws and stem bending.It is important to mention that Ht and total weight are included in the RF (Equations ( 1) and ( 2)), but these variables did not influence the RF.This means that there are other morphological characteristics that have a greater influence on the RF.The results found in teak trees agree with studies carried out by Moore [18] in Pinus radiata, where trees with higher taper (lower ratio of tree height to d) had higher maximum resistive bending times than trees with low taper.
Although researchers have investigated the influence of various wood properties on the flexural properties of the trunk of the tree [13,45], several studies indicate that MOE is most commonly and strongly related to bending, which is consistent with the results found in this study (Figure 6b).However, changes in the SG (Figure 6a) and in calcium (Ca) and magnesium (Mg) contents were also related to the bending of young teak (Table 6).Other studies have found similar effects on wood properties; for example, Van Gelder et al. [20] found that the wood density of tropical trees was positively related to wood strength and stiffness, and the species safety factor for buckling was positively related to wood density and stiffness.Another important parameter that affects stiffness is the microfibril angle [45], but it was not considered in this study.
Some elements are directly related to tree resistance.Calcium (Ca) is an essential element for teak meristematic development because it is one of the major structural components that forms the cell wall [46].This nutrient provides rigidity and resistance to the roots [47].In contrast, potassium (K) maintains the turgidity of tissues, prevents drought effects, increases resistance to diseases, reduces uprooting, and aids nitrogen fixation.It was found that fertilization with K in species such as pine positively influences the cell wall thickness of the early stem and the modulus of elasticity of the wood [46].
Finally, according to the results obtained, bent trees account for 78% to 98% (780 to 980 trees ha −1 ) of the trees in the plantations (Table 3).This percentage will be reduced by future thinning applied as the plantation ages because the target stand density of the plantation is approximately 250-280 trees ha −1 [7].Then, although the sites where teak trees are planted present characteristics that make trees susceptible to bending, plantation conditions should be sought to achieve at least the aforementioned density at the age when the plantation is to be felled.

Conclusions
Tree bending, analysed by the height where bending occurred (bending height) is influenced by the following morphological characteristics of Tectona grandis: positively correlation with height to crown base in the first place, crown weight, the diameter and total height of the tree, when the bending height is studied in a juvenile plantation (from 8 to 54 month old).The evaluation of bent trees showed that the percentage of bent trees (Classes 2 and 3) increases with the age of the plantation, while the quantity of straight trees (Class 1) diminishes from 97.8% in the youngest plantation to 78% in the oldest plantations.Nevertheless, the specific study conducted in the 54-month-old plantation suggests that, in addition to morphological characteristics of the tree, there are factors specific to the xylem (wood) that also have an effect on tree bending, such as modulus of elasticity and the presence of calcium and magnesium in the wood.Besides, teak tree bending increases as the tree ages and varies from 0.8 to 6.5 meters in height, which means a ratio between 10 and 50% of the total height.The results indicate that bending of teak trees in young plantations occurs in approximately 30% of the trees present, and occurs mainly between 27 and 54 months of age of the tree in conditions of total height above 10 meters, height to crown base above 5 meters and diameter above 10 cm.

Figure 1 .
Figure 1.Geographic localization of sampled plantations with tree bending problems in southern Costa Rica indicating the wind direction in the site where the plantation was sampled.(a) Log extracted from sample tree for modulus of elasticity (MOE) determination; (b) Diagram of the static bending tests of poles; (c) the Cantilever Test Method was employed to measure the MOE.

Figure 1 .
Figure 1.Geographic localization of sampled plantations with tree bending problems in southern Costa Rica indicating the wind direction in the site where the plantation was sampled.(a) Log extracted from sample tree for modulus of elasticity (MOE) determination; (b) Diagram of the static bending tests of poles; (c) the Cantilever Test Method was employed to measure the MOE.

Figure 2 .
Figure 2. Bent tree classification according to bending damage for Tectona grandis plantations in Costa Rica: (a) straight trees; (b) partial bending; (c) severe bending; and (d) broken trees.

Figure 2 .
Figure 2. Bent tree classification according to bending damage for Tectona grandis plantations in Costa Rica: (a) straight trees; (b) partial bending; (c) severe bending; and (d) broken trees.

Figure 3 .
Figure 3. Variation of diameter (a); total height (b); and height to crown base (c) in trees growing in fast-growth plantations of Tectona grandis in Costa Rica.Note: the standard deviation and the average bar are presented.The letters next to these values indicate that the values are significantly different at a confidence level of 95% for morphological properties.

Figure 3 .
Figure 3. Variation of diameter (a); total height (b); and height to crown base (c) in trees growing in fast-growth plantations of Tectona grandis in Costa Rica.Note: the standard deviation and the average bar are presented.The letters next to these values indicate that the values are significantly different at a confidence level of 95% for morphological properties.

Figure 4 .
Figure 4. Total height and bending height for class 2 (a); class 3 (b); and height of breaking point in class 4 (c) of bending damage and percentage of the total tree height at which bending occurs (d) for plantations of Tectona grandis in Costa Rica.Note: the standard deviation and average bar are presented.

Figure 4 .
Figure 4. Total height and bending height for class 2 (a); class 3 (b); and height of breaking point in class 4 (c) of bending damage and percentage of the total tree height at which bending occurs (d) for plantations of Tectona grandis in Costa Rica.Note: the standard deviation and average bar are presented.
ratio R 2 = 0.01 NS Note: ** coefficient of correlation significant at p < 0.01; n: number of observation or number of pairs of scores; d: diameter at 1.3 m from the ground; Ht: total height; Hcb: height to crown base; Hb: bending height.

Figure 5 .
Figure 5. Correlation between tree bending risk factor and bending height (a), height to crown base (b), crown weight (c) and form factor (d) in Site 6, a 54-month-old plantation of Tectona grandis in Costa Rica.

Figure 5 .
Figure 5. Correlation between tree bending risk factor and bending height (a), height to crown base (b), crown weight (c) and form factor (d) in Site 6, a 54-month-old plantation of Tectona grandis in Costa Rica.

Figure 6 .
Figure 6.Specific gravity (a) and modulus of elasticity (b) for trees in Class 1, Class 2, and Class 3 bending damage in Site 6, a 54-month-old plantation of Tectona grandis in Costa Rica.

Figure 6 .
Figure 6.Specific gravity (a) and modulus of elasticity (b) for trees in Class 1, Class 2, and Class 3 bending damage in Site 6, a 54-month-old plantation of Tectona grandis in Costa Rica.

Table 1 .
Site description and climatic conditions of the sampled plantations in the study of tree bending in Tectona grandis in the Southern Pacific region of Costa Rica.

Table 2 .
General information and sampling intensity used for the tree bending study in juvenile Tectona grandis plantations in southern Pacific of Costa Rica.

Table 2 .
General information and sampling intensity used for the tree bending study in juvenile Tectona grandis plantations in southern Pacific of Costa Rica.

Table 3 .
Percentage of trees per damage class in juvenile plantations of Tectona grandis in Costa Rica.
Note: the standard deviation is presented in brackets.The plot measurements are provided in detail in Table2.

Table 3 .
Percentage of trees per damage class in juvenile plantations of Tectona grandis in Costa Rica.
Note: the standard deviation is presented in brackets.The plot measurements are provided in detail in Table2.

Table 4 .
Pearson correlation matrix between the bending height (Hb) and the morphological variables of Tectona grandis in plantations of different ages.
Note: * coefficient of correlation significant at p < 0.05; **coefficient of correlation significant at p < 0.01; n: number of observation or number of pairs of scores; d: diameter at 1.3 m from the ground; Ht: total height; Hcb: height to crown base; Hb: bending height.

Table 5 .
Forward stepwise multiple regression analysis of the effect of the morphological variables (d, Ht, Hcb, Hb) on the bending height (Hb) for Classes 2 and 3 in Tectona grandis in plantations of different ages.

Table 6 .
Average of the morphological characteristics and nutrient content in the trunk of bent trees in Site 6, a 54-month-old plantation of Tectona grandis in Costa Rica.
Legend: the letters next to these values indicate that the values are statistically different at a confidence level of 95% for different class bend.d: diameter at breast height (at 1.3 m height); Ht: total height; Hcb: height to crown base; SF: safety factor, Hb: bending height, and Wc: crown weight.

Table 6 .
Average of the morphological characteristics and nutrient content in the trunk of bent trees in Site 6, a 54-month-old plantation of Tectona grandis in Costa Rica.Legend: the letters next to these values indicate that the values are statistically different at a confidence level of 95% for different class bend.d: diameter at breast height (at 1.3 m height); Ht: total height; Hcb: height to crown base; SF: safety factor, Hb: bending height, and Wc: crown weight.