Long-term effects of plant spacing on the growth and morphometry of Bertholletia excelsa

Plant spacing is a potential driver of tree form and yield in forest plantations. However, its effects on the productivity of tree plantations in the Amazon are still little known. This study examined the effects of six spacing regimes (3 x 4, 4 x 4, 4 x 5, 5 x 5, 5 x 6, and 6 x 6 m) on the growth and morphometry of a 20-year-old plantation of Bertholletia excelsa. We observed high, spacing-independent survival (> 70%). For timber production purposes, intermediate and two large spacing regimes tended to higher values of yield components, mainly diameter, biomass, and volume, although some did not differ significantly from the smallest spacing. One of the intermediate spacings (5 x 5 m) tended to higher commercial height. Tree crowns tended to be wider and longer in the larger spacings, which indicates the potential of these regimes for fruit production. Tree crowns exceeded the vital growth space in all spacing regimes, which suggests the need for thinning before the age of 20 years in all spacings to reduce intraspecific competition and increase yield. We estimated that a density of 84 remaining trees per hectare would be necessary to reach an average diameter of 40 cm at the age of 20 years. Thus, B. excelsa had high survival in the tested range of spacing regimes, while the intermediate and the largest spacing regimes led to better tree growth and morphometry.


INTRODUCTION
There are many tree species of commercial interest in the Amazon region, but the use of native species in industrial plantations is still a challenge (Rolim et al. 2019;Nunes et al. 2020). In agroforestry systems, the inclusion of the native tree species Bertholletia excelsa Bonpl. is a common practice, especially among small farmers in the Brazilian Amazon region (Hoch et al. 2009). The main product of this species is the nut, which is among the main sources of income for Amazonian rural populations (Cronkleton et al. 2012). However, the species can also provide good quality wood (Borém et al. 2009), when it comes from reforestation, since felling wild specimens is prohibited by Brazilian legislation (Locatelli et al. 2015). In this sense, plantations are important to enable the use of the species' wood. The use of this species for reforestation of degraded areas in different planting systems has also been evaluated (Scoles et al. 2011;Ferreira et al. 2012). Regarding homogeneous plantations of B. excelsa, the company Agropecuária Aruanã, located in Central Amazonia, is the main example of a large-scale reforestation project using this species (Ferreira et al. 2016). However, silvicultural practices, such as spacing regime, have not yet been systematically defined for the best management of plantations.
To support public policies for the promotion of silviculture using native species, information on several aspects is required, such as quality of seed and seedling production, plant density, timing of thinning and pruning, and other aspects that may vary according to the planting location (Rolim et al. 2019). Despite important advances in scientific research and silvicultural techniques on native species in the Amazon region in recent decades dos Santos et al. 2020;Scoles and Gribel 2021), the still low representativeness of native species in industrial plantations is partly due to gaps in knowledge about the silvicultural aspects of these species and the management practices for the establishment and tending of plantations (Walters et al. 2005;Nunes et al. 2020).
The vital growth space of trees, determined by plant spacing, is one of the most important aspects during the planning and implementation of reforestation projects. This aspect will affect tree development, volumetric growth, wood quality, and production of fruit and wood per planted area (Botelho 1997;Inoue et al. 2011;Benomar et al. 2012). The selection of the most appropriate spacing regime depends on silvicultural and ecophysiological characteristics of the planted species, planting purpose, site quality, and management practices (Smith and Strub 1990;Botelho 1997). Analyses of morphometric parameters, such as diameter and crown area, can indicate the best spacing for the cultivation of each species . Morphometric variables can predict stability, vitality, yield, degree of competition, the space occupied by each tree, and even the adequate period for thinning (Durlo and Denardi 1998;. Larger spacings can increase plant diameter from the positive relationship between crown diameter and diameter at breast height . Nevertheless, the positive relationship between crown length and diameter at breast height  suggests that a larger crown due to a large spacing regime may result in lower commercial height. In turn, the fruit production of B. excelsa correlates positively with diameter at breast height and crown length (Tonini et al. 2008), which suggests that larger spacings may favor fruit production.
Thus, the knowledge about the effects of spacing on tree growth is essential to guide the most appropriate practices for the establishment and management of stands. In this sense, defining the most suitable spacing regimes for B. excelsa can contribute to optimize yield and increase the planted area. We specifically sought to analyze whether: i) spacing regimes affect the survival and growth of B. excelsa trees; and ii) plant spacing influences crown morphometry in B. excelsa trees.

Study site and experimental design
We collected dendrometric and morphometric data from B. excelsa plantations of the company Agropecuária Aruanã in Amazonas State, Brazil (03°00'29"S, 58°49'53"W) ( Figure  1). According to the Köppen-Geiger classification system, the climate of the region is Af, and the predominant vegetation is equatorial tropical forest (Alvares et al. 2013). The rainfall regime (1980-2019) includes a wet season (January to May), with a monthly average of 319 mm, and a dry season (August to September), with a monthly average of 76 mm (allways below 100 mm). Average annual rainfall and temperature are 2,483 mm and 27.1 °C, respectively (INMET 2020). The predominant soil is a Dystrophic Yellow Latosol (IBGE  (Ferreira et al. 2016), high acidity (pH 4.2), high aluminum content (1.08 cmol c dm -3 ), low cation exchange capacity (2.03 cmol c dm -3 ), and medium organic matter content (43.3 g kg -1 ) up to 10 cm depth (Ronquim 2010;Lima and Souza 2014;Brasil et al. 2020).
The planting of B. excelsa stands took place in March 1996, in areas previously used for pasture. The seedlings grew in nurseries on the property and came from seeds of selected matrices located on the property. The planting procedure included mechanical soil grading, and no fertilizers were used during or after planting. A total of 566 seedlings aged 12 to 18 months and an average height of 40 cm were planted in six spacing regimes (3 x 4 m; 4 x 4 m; 4 x 5 m; 5 x 5 m; 5 x 6 m; and 6 x 6 m), with two plots for each treatment (Table 1; Figure 1). The useful plot consisted of all trees within a plot, excluding the border row.
Ellipse area=(CR 1 x CR 2 )x π (1) where: CR n = crown radius (CD n .2 -1 ) From the TH and CL measurements, we calculated the crown ratio (CR) according to Tonini et al. (2008): (2) where: CR = crown ratio; CL = crown length; and TH = total height Commercial height (CH) corresponded to the height of the lowest alive branch, measured with a laser measuring tape (Bosch ® , model GLM40). The mean annual increment in diameter (MAId) and the mean annual increment in height (MAIh) were estimated from the ratio between diameter or height and the age of the tree.

Destructive sampling and modelling
We made a destructive sampling per diametric class in each spacing regime. This classification followed the Sturges formula (3), which considers the number of individuals (Machado and Figueiredo Filho 2006). In each diametric class, we chose one tree with a DBH value close to the average value of the class. Therefore, we selected 5 to 7 trees in each spacing regime, totaling 36 trees.

K=1+3.3 .log log n
(3) where: K = number of classes; n = number of observations We measured stem volume (SV) through rigorous cubing by the Smalian method (Leite et al. 2006). We sectioned trees every two meters up to a limit diameter of 5 cm. To determine aboveground biomass (AB), stem biomass (SB), branch biomass (BB), and leaf biomass (LB), we analyzed leaves (Le), branches (Br), and stem (St) following Higuchi et al. (1998). For that, we weighed these plant parts in the field with a mechanical platform scale (Micheletti, MIC 2A) with a capacity of 200 kg and an accuracy of 100 g. We calculated dry biomass from 3-cm aliquots of discs along the stem and branches (base, middle, and apex) and aliquots of 30 leaves from each third of the crown (lower, middle, and upper). We immediately weighed these aliquots in the field on a digital scale (Uranus, US 20/2 POP-S) and sent them to the laboratory for oven drying at 100 -105 °C for a minimum of 72 hours (Cienlab, CE 220/81) or until constant weight. We dried the leaves at 70 °C for a minimum of 48 hours. We calculated the coefficient for biomass extrapolation (k) from the ratio between dry and fresh biomass of aliquots according to equation (4). For extrapolation, we used equation (5).

Survival, dendrometric, and morphometric measurements
We collected the data 20 years after planting (between July and September 2016). We calculated survival (S) as the ratio between the number of individuals present at the time of survey and the number of individuals planted in each useful plot. We measured the diameter at breast height (DBH) and total height (TH) of all individuals in the useful plots. DBH was determined by measuring the circumference at breast height (1.3 m from the ground) with a measuring tape. To determine TH, we used a Haglöf hypsometer (Haglöf Sweden ® , Model ECII, Sweden).
We measured crown variables in six trees per plot, totaling 12 trees per treatment. The sampling was randomized but with a restriction of a minimum distance of six meters between tree stems. We measured crown diameter (CD) between and within planting rows. We considered crown length (CL) as the difference between TH and the height of the lowest alive branch, measured with a laser measuring tool (Bosch ® , model GLM40). We calculated the projected crown area (PCA) using the ellipse area formula (m²) according to Scoles et al. (2016): From the adjusted equations, we estimated the volume and biomass of uncut trees. The choice of the best models followed the criteria of higher adjusted determination coefficient (R² adj ), lower estimation standard error (S yx ), uniformity and no bias in residual distribution (Res%) (Sanquetta et al. 2014). The selection of the best model considered the difficulty in obtaining height data in the field. We adjusted nonlinear allometric models by the nonlinear least square method using the Gauss-Newton iterative process. For that, we used the function nls of the package stats of the statistical software R (R Core Team 2020). The equation to estimate stem volume followed the nonlinear Schumacher-Hall model (R² adj = 0.94 and S yx = 0.10). We selected the nonlinear model of Berkhout-Husch for aboveground biomass (R² = 0.91 and S yx = 102.97) and for stem biomass (R² adj = 0.92 and S yx = 71.24); and the modified nonlinear model of Schumacher-Hall for branch biomass (R² adj = 0.83 and S yx = 31.28) and for leaf biomass (R² adj = 0.83 and S yx = 7.88) ( Table 2).

Statistical analyses
We performed analysis of variance (ANOVA) to test plant spacing effects on growth and crown morphometry variables, with exception of CR and survival, which analyzed with the Kruskal-Wallis rank test and the Dunn test (P < 0.05), which is more appropriate for proportion variables. Prior to ANOVA, we analyzed the assumptions of normality (Shapiro-Wilk test) and homogeneity of variance (Levene test). We transformed data that did not meet the assumptions using the square root function (CL, PCA, SV), logarithmic function (AB, SB, BB), or Box-Cox function (LB). We performed the Duncan post hoc test (P < 0.05) after ANOVA to make pairwise comparisons among plant spacings. We have also developed a nonlinear model of PCA as a function of DBH to estimate the vital growth space needed for trees to reach a target diameter at the age of 20 years. We performed all statistical analyses using the packages stats, car, and agricolae of software R (Fox and Weisberg 2019; Mendiburu 2020; R Core Team 2020).

Survival and growth
Survival was above 70% in all spacing regimes and ranged from 71% (5 x 6-m spacing) to 92% (4 x 4 m). Despite this amplitude, there was no significant difference among treatments (Figure 2).
The magnitude of differences among spacings for TH and DBH was 35 and 95%, respectively, with a tendency for higher values in one intermediate (5 x 5 m) and the two larger spacings, which mostly differed significantly from the 5 x 4 and 4 x 4-m, spacings, but less so from the smallest spacing (3 x 4 m) (Figure 3a, b). The same magnitude of differences occurred for MAId and MAIh, respectively (Figure 4). The 5 x 5-m spacing resulted in a 0.8-fold higher average CH than    The intermediate 5 x 5-m spacing also stood out in terms of volumetric yield per hectare, with approximately 11.2 m 3 ha -1 year -1 , discounting mortality, followed by the smallest spacing (3 x 4 m), with 10.9 m 3 ha -1 year -1 , the largest spacing (6 x 6 m) with 9.9 m 3 ha -1 year -1 , the 4 x 4-m spacing, with 9, 4 m 3 ha -1 year -1 , 5 x 4 m with 6.5 m 3 ha -1 year -1 , and 5 x 6 m with 5.6 m 3 ha -1 year -1 .

Morphometry
Spacing significantly affected CL, CD, and PCA, and, overall, crown measurements tended to increase with spacing ( Figure 5). The average values of CL, CD, and PCA in the smallest spacing were 0.7, 0.7, and 1.7-fold higher than in the largest spacing. The projected crown area (PCA) exceeded the spacing limit in all regimes ( Figure 5) and exceeded the vital growth space by 1.4, 0.8, 0.5, 0.9, 0.9, and 1.2-fold in the spacing regimes 3 x 4, 4 x 4, 5 x 4, 5 x 5, 5 x 6, and 6 x 6 m, respectively. The average value of CR was 43% higher in the largest compared to the smallest spacing, although there was not a clear significant difference among the intermediate spacings ( Figure 5). There was a significant (R² adj . = 0.78; P < 0.001) and exponential relationship between PCA and DBH ( Figure 6), from which we estimated that 84 remaining trees per hectare (vital growth space of 119 m²) would be necessary for the trees to reach an average diameter of 40 cm at the age of 20 years.

Volume and biomass
Spacing significantly affected volume and biomass variables (SV, AB, SB, BB, and LB), which tended to significantly higher values in the three largest spacing regimes (Figure 7). The average values of SV, AB, SB, BB, and LB in the three largest spacing regimes were 106, 117, 115, 234, and 231% higher than those of the three smallest. Likewise, at the population level, the three largest spacings had higher

DISCUSSION
Bertholletia excelsa has been highly persistent in disturbed sites, with recorded survival rates between 77% and 100%, even in low-light environments (Scoles et al. 2011(Scoles et al. , 2014Lima and Souza 2014), despite divergent results by some studies, possibly attributed to low light or severe predation by rodents (Oliveira 2000;Scoles and Gribel 2021). It is noteworthy in our study that B. excelsa survival was high even twenty years after planting in an area previously used for grazing, independently of the spacing regime. Smaller spacing regimes generally increase intraspecific competition, mainly for light, increasing tree mortality in forest plantations during crown closure Akers et al. 2013;Schneider et al. 2015). However, photosynthetic plasticity in B. excelsa enhances survival in contrasting light environments (Souza et al. 2017;Lopes et al. 2019), which may have contributed to the spacing-independent survival in our study. It is also possible that the smallest spacing in our study may not have been sufficient to induce high intraspecific competition and higher mortality, which could have occurred in the denser spacings currently used in production forests.
A larger plant spacing allows better crown development and, consequently, more biomass allocation to branches, improving crown projection area and crown length (Sanquetta et al. 2003). For timber production purposes, the two largest spacings in our study led to the best yields, yet the intermediate spacing of 5 x 5 m tended to lower values of crown length and crown ratio, consequently providing a higher commercial height in comparison to the largest spacings. The 5 x 5-m spacing also stood out in terms of volumetric yield per hectare. Hence, our results suggest that a 5 x 5-m spacing is better than the larger ones tested to obtain B. excelsa trees with a higher CH and volume for timber production. Although there were no no significant differences between the 5 x 5 and 3 x 4-m spacings for some parameters, the 5 x 5-m regime tended to higher commercial height and volume. Other studies have found different results for B. excelsa and other native species. In the same study area, Lima and Souza (2014) recommended the 3 x 4-m spacing regime as an initial spacing for B. excelsa due to the higher production per hectare at the age of 15 years. However, the authors did not consider commercial height. Oliveira et al. (2018) analyzed 38-year-old Cariniana legalis (Mart.) Kuntze trees and found greater individual growth in the largest tested spacing of 3 x 2.5 m. Notwithstanding, their smallest spacing (3 x 1.5 m) was more advantageous, since it provided a larger volume of wood (17 m³ ha -1 year -1 versus 14 m³ ha -1 year -1 in the largest spacing), although this wood was less dense in comparison to that of trees grown in larger spacings.
Regarding fruit production, B. excelsa trees with wide crowns and in better shape are more productive than those with suppressed crowns (Kainer et al. 2007;Tonini et al. 2008;Scoles et al. 2016). In native stands, for example, B. excelsa trees with higher CR values (over 47%) have higher fruit production; i.e., trees with longer crowns were more productive (Tonini et al. 2008). In our study, crown morphometric variables and biomass allocation to branches and leaves increased with spacing after 20 years, and, although we did not measure fruit production, we can assume that the more structured and leafy crown of trees grown with the larger spacings is a good approximation of the fruit production potential. Moreover, trees with large crowns accumulated high amounts of biomass at the whole-tree and stand level. The biomass accumulation in our B. excelsa stands -at the age of 20 years -corroborates observations in neotropical secondary forests (Poorter et al. 2016). These stands have high carbon sequestration potential and therefore can meet reforestation goals. Crown measurements are also important for the management of tropical tree plantations. Determining the crown diameter, for example, is of fundamental importance since it allows to design the vital growth space for each tree (Dionisio et al. 2018).  estimated that it would take a maximum of 281 remaining trees per hectare (spacing of 6 x 6 m) for B. excelsa trees to reach an average diameter of 14 cm at seven years of age, i.e., a mean annual increment in diameter (MAId) of 2 cm year -1 . Using the same adjustment equation of these authors to reach a DBH of 40 cm, we obtained the value of 85 remaining trees per hectare (spacing of 11 x 11 m), supporting the result of our study.
Another crown trait of great importance for planting management is the crown ratio (CR), which is the ratio between crown length and tree height. The trend to lower CR values with reduced spacing may be due to increased competition for light. The greater shading among individuals can stimulate natural pruning and reduce the live crown ratio (Onyekwelu et al. 2011). Crown ratio is a common indicator of tree vigor (Comfort et al. 2010), determining the time for thinning and the potential response of trees (Dyer and Burkhart 1987). Moreover, this index can be an indirect indicator of photosynthetic capacity, with application in forest growth and production models (Leites et al. 2009). The normal rates of diameter growth in Pinus sp. trees remain unaffected if the CR is 40% or higher, and thinning should take place soon after the CR average drops below 50% (Harrington 2001). Considering only this criterion, only the smallest spacing regime (3 x 4 m) in our study would require thinning, however it has to be considered that Pinus sp is a fast-growing exotic gymnosperm that is phylogenetically distant from B. excelsa. Furthermore, the exponential model of PCA as a function of DBH indicated that thinning should take place before the age of 20 years to give enough space for the trees to reach a DBH of 40 cm. Additional studies on ring-growth or permanent plots are necessary to reconstruct the curve of the mean annual increment (MAI) and current annual increment (CAI) in different spacings to determine the best time for thinning.
Our results show that B. excelsa has planting potential even in dense spacing due to its tolerance to intraspecific competition, however, wider spacing regimes must be evaluated to further test to support these results. Nevertheless, the intermediate spacing of 5 x 5 m has an advantage in terms of CH, and volumetric yield per hectare. Our study also showed the importance of monitoring both morphometric and dendrometric variables such as PCA and DBH to determine the ideal period for thinning. The model adjusted to the PCA values as a function of DBH can be used to plan the number of trees to be maintained in the plantation considering a target diameter to meet the demand for roundwood.

CONCLUSIONS
Our main findings on Bertholletia excelsa grown over 20 years in spacing regimes from 3 x 4 to 6 x 6 m were: i) high survival was spacing-independent; ii) B. excelsa is a good option for reforestation purposes due to its long-term survival in several spacings, even in environments previously used for pasture; iii) tree growth increased with the spacing regime; iv) spacing influenced morphometric parameters, with implications for timber and fruit production and forest management; v) the intermediate spacing of 5 x 5 m lead to the best timber yield as trees had larger commercial height and trended to larger volumetric yield per hectare; vi) larger spacings also provided trees with larger diameters and crowns with potential for fruit production; and vii) thinning should probably take place before trees reach the age of 20 years for all tested spacing regimes.