INFLUENCE OF GROWTH PARAMETERS ON WOOD DENSITY OF Acacia auriculiformis

Understanding the drivers of wood density variation both within a tree and between trees is important in predicting the quality of wood logs and improving this quality through adequate forestry management. This study examined the effect of the diameter growth of Acacia auriculiformis on its wood density variation. The study was conducted in the South of Benin in four plantations of Acacia auriculiformis . Near infrared spectroscopy (NIRS) method was used to predict the basic density of 225 tree wood cores of Acacia auriculiformis . A predicting model of the average tree density using the diameter as predictor was established. The relationship between wood density and tree diameter was best described by a linear mixed-effect model. The average wood density of trees increased with the diameter. The study concluded that the quality of the species logs can be improved through regular thinning and genetic selection.


INTRODUCTION
Density is a major functional trait of wood (Hietz et al. 2013, Ducey 2012. It is related to the physico-mechanical characteristics and natural durability of the wood (Hietz et al. 2013, Pérez-Peña et al. 2020 and is correlated with the longevity of trees. Trees with low wood density usually have higher mortality risks (Hietz et al. 2013). Also, wood density represents a good indicator of forest biomass and the rate of carbon sequestered in wood (Morel et al. 2018, Nabais et al. 2018. Wood density is among the most important parameters used in tree breeding programs (Alves et al. 2010). It varies inside species with the height and the radial posi-tion (Guller et al. 2012, Hietz et al. 2013. Hence, wood density is a combined effect of several intrinsic and extrinsic factors, including the environment, genetic factors, age and growth parameters (Nabais et al. 2018, Morel et al. 2018, Mevanarivo et al. 2020).
Tree growth is usually expressed in several ways, including height increment, and diameter growth (DeBell et al. 1994, Silva et al. 2019. Tree growth influence several characteristics of wood such as wood density. The effect of tree growth on wood density is not consistent across species. In general, fast-growing species have low density (DeBell et al. 1994). The increase in tree growth would lead to an increase in the ring's width, a low wood density (Wang et al. 2000, Gapare et al. 2010 and an inter-annual variability in the wood density. On the contrary, DeBell et al. (2001) found that the wood density of Eucalyptus saligna increased with the diameter, particularly on nutrient rich soil whereas Jakubowski et al. (2020) found no significant effect of tree growth on wood density for Betula pendula. The relation between tree growth and wood density is apparently site-specific (e.g. climatic factors and soil water reserve) and species-specific (Bouriaud et al. 2005).
Several methods are used to estimate wood density. Direct measurements from felled trees, with wood density corresponding to the mass over the volume of a sample, provide quite accurate results (Alves et al. 2010). Still, indirect measurements through near infrared spectroscopy (NIRS) could be used for predicting wood properties with high precision based on calibrated and validated Partial Least Squares (PLS) regression models (Alves et al. 2010, Cooper et al. 2011, Diesel et al. 2014. This method allows to evaluate a large amount of data very quickly and efficiently (Cooper et al. 2011). It also has the advantage of using samples from un-felled trees to determine wood characteristics.
Knowledge on the distribution of wood density in individual trees and its formation process is required to improve both the silvicultural processes and the wood production so as to obtain a wood of the desired quality (Guller et al. 2012, Mäkinen andHynynen 2012). But the complexity of the wood density formation usually limits the interpretation of the models because a similar average density of two woods can result from different anatomical parameters and environmental factors. Thus, understanding the intraspecific variability of wood density can enable the identification of appropriate silvicultural practices to produce wood at a higher yield and of a better quality (Hai et al. 2010).
Acacia auriculiformis is native to Asia (Wickneswari and Norwati 1993) where its wood shows distinct rings. The number of rings may be inconsistent with the age of the tree (Chowdhury et al. 2009) and the determination of the radial variation of its wood is of definite interest. In West Africa, the species was introduced in 1980 (Tandjiekpon and Dah-Dovonon 1997) mainly for firewood production but also currently include timber prospects (Tonouéwa et al. 2019). The species produces a wood with quite good characteristics (Hounlonon et al. 2018, Tonouéwa et al. 2020. Determining the variability of its wood density within and between trees and understanding the influence of tree diameter on the wood density will allow for the improvement of the species growth parameters and wood physico-mechanical characteristics through appropriate silvicultural treatments. The main objective of this study is to identify patterns and drivers of wood density variation in A. auriculiformis grown in plantations in South Benin. More specifically it aims to (i) determine the relationship between the diameter and wood density of A. auriculiformis; and (ii) determine the radial variation of the wood density of A. auriculiformis.

Study area
The study was conducted in Southern Benin around 6º22 'to 6º54'N latitude and 2º05 'to 2º8'E longitude ( Figure 1) and precisely in twelve state-owned plantations of A. auriculiformis. These plantations were located at Lama (on vertisol), Pahou (on ferruginous soil), Ouedo (on ferralitic soil) and Sèmè-kpodji (on sandy soil). The climate is similar across the study sites (Amoussou et al. 2016). The average annual rainfall is 1100 mm and the average annual temperature 27 °C.

Data collection
The data comes from twelve state-owned plantations of A. auriculiformis (Table 1, Figure 2). A total of 255 cores of 5 mm diameter were sampled, at 1,30 m height from 255 tree individuals (1 core per tree), using a Pressler auger. The transverse surface of the cores was sanded with sandpaper (fine grits) to obtain a flat and smooth surface for the measurements. The cores moisture was stabilized at 12%. The near infrared spectrometry (NIRS) method was used to determine the wood density on each core sample at 1 cm interval ( Figure 3) and the radial variation of the wood density of A. auriculiformis was described. Near infrared spectra were obtained with a Bruker Vector 22/N spectrometer run by OPUS 200 software version 5.5.  On each core, the number of measures in the heartwood was ≤ 20 (20 th radial position, Figure 3 and Figure  6).
After removing broken and poorly preserved cores from the samples and after removing outliers, 225 cores translating into 2869 measurements (430 on sapwood and 2439 on heartwood) were validated (Table 1). However, the wood density of A. auriculiformis was predicted using only the 2439 measurements on heartwood because wood density is always higher in heartwood than in sapwood (Githiomi and Kariuki 2010). This is due to the high proportions of carbon, lignin and extractives in the heartwood (de Aza et al. 2011, Bertaud andHolmbom 2004). In addition, heartwood is the most interesting part of the tree for use as timber.
For the prediction of wood density, we used a pre-established NIRS model of the basic density of A. auriculiformis in South Benin (Tonouéwa et al. 2020). The model had a root-mean-square error (RMSE) of 50,33 kg/m 3 (R 2 = 0,75) for the prediction model and 45,88 kg/m 3 (R 2 = 0,79) for the calibrated model. The Unscrambler software, version 9.7 CAMO (The Unscrambler 2007) was used to estimate the basic density and the standard deviation for each measured point. The value of the basic density at a given point on a wood core is an average of 16 measurements with the spectrometer at this point. The standard deviation of the 16 measurements at each point was ≥ 60 kg/m 3 .

Figure 3: (a)
A. auriculiformis wood core packed within the field with codes indicating the location, the tree and tree diameter (b); a wood core marked for measurements (c) and the spectrometer used to make the measurements.
The basic density of A. auriculiformis trees was evaluated as a function of the radial position in the tree and as the ratio between the dry mass of a sample and its saturated volume (Rybníček et al. 2012, Diesel et al. 2014).

Statistical analysis
A first exploratory analysis of the predicted wood density of A. auriculiformis on cores was done. Samples with standard deviations greater than or equal to 200 kg/m 3 (i.e. 1,5 times the interquartile range above the third quartile or below the first quartile; Crawley 2007) were considered as outliers and excluded from the batch for the subsequent analyses.
To assess the relationship between the wood density and tree diameter, several Linear and Non-Linear Mixed Effects Models (NLME) were tested in R.3.5.2 (R Core Team 2018) with the nlme package (Pinheiro et al. 2018). The random effects were: plots nested within zone of data collection and the fixed effect was tree diameter. Based on the inspection of the scatterplots and models previously used for explaining the relation between tree diameter or tree age and wood density, a linear (Silva et al. 2019) and four nonlinear functions (Table 3) were assumed to potentially fit well the data. The nonlinear functions include the second-degree polynomial function (Githiomi and Kariuki 2010), the first exponential function (Oddi et al. 2019), the Michaelis-Menten asymptotic function (Oddi et al. 2019) and the second exponential function (Oddi et al. 2019).
The appropriate model was selected based on the Akaike Information Criterion (AIC) (Akaike 1973) and the random effect. The best model is the one that minimizes the AIC value (Chave et al. 2005) and shows a high random effect (i.e. variance in the wood density explained by the random effect). The general equation of the NLME model developed in R.3.5.2 is showed below:  (Table 2); WD data: the database containing the dependant (wood density) and the explanatory variables; a + b + c ~ 1: the parameters of the function (Table 2) used for the fixed effect of the model; a ~ 1 | zone / plot: the random effect; u, v, w: the list of initial estimates for the values of a, b, and c respectively.
When the function has two parameters (a, b), the fixed effect takes the form a + b ~ 1.
Regarding the type of linear or nonlinear relationship, parameters a, b and c were calculated with an adjustment in R (R.3.5.2).
Concerning the linear function, parameters a and b were determined by solving in R the following matrix Equation 1: Considering the second-degree polynomial function, parameters a, b, and c were calculated by solving in R the following matrix Equation 2: 2 2 2 1 1 1 1 2 *C 2 2 1 Regarding the first exponential Equation 3, a and b were calculated as follow: For the Michaelis-Menten asymptotic function, a and b were calculated using the SSmicmen function of the package stats.
For the second exponential Equation 4, a and b were calculated as follow: After the selection of the best model, normality quantile, modelling variance, correlation structure, residuals wood density as function of tree diameter, and a plot of the predicted vs observed wood density were analysed to evaluate the model assumptions.
In addition, the relations between the wood density and the age of the plantation, and the radial position in the tree were determined using a mixed effect model in R.3.5.2 (R Core Team 2018) with the lmerTest package.
The average values of the wood density were eventually regressed against the radial position for each age of plantation.

Variation in wood density of A. auriculiformis in relation to tree diameter
Among the models tested (Table 2) for expressing the wood density as a function of tree diameter, the linear mixed effect model was the most suitable for A. auriculiformis (low AIC, high random effect). This model validity is restricted to A. auriculiformis trees with at least 10 cm diameter at breast height and growing in conditions similar to those of south Benin. The model is in the form of: WD=a*D+b, with D = tree diameter, WD = wood density, a =1,2335; b= 537,6931 from solving Equation 1. With a Root-Mean-Square Error (RMSE) of 51,79 kg/m 3 and a Bias of 0,2%, the quality of the model is suitable. Results from the five linear and nonlinear models tested for the prediction of A. auriculiformis wood density (WD) in kilograms per cubic meter (kg/m 3 ) with tree diameter (D) in centimetre (cm) as the predictor. WD = wood density; a, b and c are the parameters of the function used for the fixed effect of each model (see Table 2); AIC = Akaike Information Criterion; ∆AIC = difference between the AIC of the best model (smallest AIC) and each of the alternate models, for ease of comparison.
The characteristics of the linear model obtained indicate a distribution of the data close to normal ( Figure  4a), a homogeneity of the variance (Figure 4b), a weak autocorrelation structure (Figure 4c), and a coherent and uniform distribution of wood density residues as a function of the diameter of the trees (Figure 4d). The scatter plot between the real data and those predicted is not perfect (Figure 4e), however we observe that the predicted values are averages of the real values. In general, wood density of A. auriculiformis increased with the diameter ( Figure 5). There is also a significant and positive correlation between tree diameter and wood density of A. auriculiformis (r = 0,23; p-value = 0,0006**).

Intra-species and intra-tree variations in the wood density of A. auriculiformis
Wood density varies from one tree to another (Table 3), and the random effect of this parameter explains 25,7% of the variation of A. auriculiformis wood density in the study plantations. Table 3: Results of the mixed effect model predicting wood density as a function of the plantation age and the radial position of the wood in the tree.
In general, the relation between the wood density of A. auriculiformis and the radial position of the wood in a tree was not significant (Table 3, Figure 6). The radial pattern of the wood density of the species did not show the demarcation between juvenile and mature wood. Still, we noted a sawtooth radial variability of wood density, an increase in the density of the wood outwards until a wood density peak is obtained, and a decrease in the wood density towards the ends of the tree. On the contrary, the age of the plantation has a significant and positive effect on wood density (Table 3).

Discussion
The best model for predicting the wood density of A. auriculiformis as a function of diameter is a linear function, and wood density increased with tree diameter within the range of diameters considered for the sample trees in this study (10-35 cm diameter at 1,30 cm). Linear models have been widely applied for the estimation of wood density in various settings and for various species. For example, an estimation of the wood density of Cerrado species (e.g. Luehea paniculata, Terminalia fagifolia) was obtained in Brazil with a lineal mixed model (Silva et al. 2019) and for several species in Madagascar (Ramananantoandro et al. 2016). Similarly, a linear mixed-effect model was used to estimate the wood density of Quercus petraea as a function of growth parameters and site quality (Guilley et al. 2004). Wood density increased with diameter. Forestry focused on accelerating the growth of A. auriculiformis trees is generally recommended for the rapid obtaining of good wood quality and large diameters. As such, regular thinning could be effective in increasing the value of A. auriculiformis plantations as shown elsewhere (Huong et al. 2020, Wiersum andRamlan 1982). However, climate and soil conditions can alter trees response to thinning and post-thinning diameter growth. Thus, further experiments are needed to evaluate the response of the species to frequent thinning practices in the specific conditions of South Benin.
The correlation between the diameter of the trees and wood density, although significant, was moderate in this study and suggests that the diameter of the tree alone does not explain entirely the variation in wood density of A. auriculiformis. Indeed, the relationship between wood density and growth rate in a species is generally influenced by environmental, silvicultural and genetic factors (Zobel andvan Buijtenen 1989, Zhang andMorgenstern 1995). Consequently, contrasting relations between tree growth and wood density are found in the literature. For example, in Madagascar, Ramananantoandro et al. (2016) found that tree diameter did not significantly affect wood density for native hardwood species. Similarly, a lack of correlation between tree growth and wood density was observed for Eucalyptus globulus in Portugal (Quilhó and Pereira 2001) and for black spruce (Picea mariana) in Canada (Hall 1984), while DeBell et al. (2001 found a negligible influence of growth rate on wood density for Eucalyptus saligna in Hawai. In contrast, Roque and Fo (2007) and Boyle et al. (1988) reported negative correlations between wood density and growth traits, respectively for Gmelina arborea in Costa Rica and for black spruce (Picea mariana) in Canada. In the present study, the moderate positive correlation between A. auriculiformis wood density and tree diameter suggests that diameter growth can be improved with a small gain in the species wood density. This is interesting as most wood mechanical properties are closely related to wood density.
In addition, wood density varies from one tree to another within same plot. This variability of the wood density can find an explanation in the silvicultural practices in Benin. A. auriculiformis plantations in Benin are set up from seeds from mother plants chosen mostly randomly, or based on the availability and accessibility of the trees (survey in South Benin). The probability of a large genetic variability between trees on the same plot is thus high. This stress the importance of genetic selection, as the structural characteristics of A. auriculiformis wood, such as the wood density, are heritable. The selection of good quality parent material are particularly critical for improving the properties of new plantations (Hai et al. 2010, Chowdhury et al. 2012, Nabais et al. 2018.
Regarding the intra-tree variation of wood density, we found no significant relation between the radial positions of the wood and the wood density for A. auriculiformis. Wood density being the main technological parameter of wood, its variation within trees and the magnitude of the variation provide information on the quality of the logs produced (Guilley et al. 2004). As such, our results indicate that the characteristics of A. auriculiformis logs are heterogeneous. Bouriaud et al. (2005) linked the variability of the radial density of wood to the differences in radial growth of trees. The latter is influenced by climatic variations, thinning and soil fertility (Mäkinen and Hynynen 2012, Hietz et al. 2013, Miranda and Pereira 2015, Nabais et al. 2018. For A. auriculiformis these site-specific constraints could relate to climatic conditions and tree spacing. Although the intra-tree variation of wood density was not significant in this study, the following patterns could be drawn from the data: (i) a sawtooth radial variability of wood density that possibly reflect the succession of rainy and dry seasons at the study sites; (ii) an increase in the density of the wood outwards until a wood density peak is obtained, suggesting that the wood formed during the last years of the tree's life is of higher density; (iii) a decrease in the wood density from pith to bark, which is potentially linked to the presence of sapwood. Similar variations of radial characteristics were also recorded on A. auriculiformis produced in Asia (Chowdhury et al. 2012) as well as for other timber species (Hietz et al. 2013).
The low radial variability in the wood density indicates that for estimation of wood biomass of A. auriculiformis and carbon content in the wood, the samples wood can be taken at any radial position in the tree (Chave et al. 2006, Hietz et al. 2013. This low radial variability in the wood density also makes it possible to predict low constraints growing of the tree (Curran et al. 2008, Nock et al. 2009, Nabais et al. 2018 predicting good ecological and biological conditions of growing and better quality of the log.

CONCLUSIONS
In this study, the best model for predicting the wood density of A. auriculiformis as a function of diameter is a linear function, and wood density increased with tree diameter. The moderate positive correlation between A. auriculiformis wood density and tree diameter suggests that diameter growth can be improved with a small gain in the species wood density. The suggested opportunities for improvement include the selection of good quality parent and the practice of frequent and regular thinning to reach desirable diameters and produce high-density timber. However, further experiments should evaluate the response of the species to frequent thinning in the specific climate and soil conditions of A. auriculiformis grown in South Benin. The study also highlights the need for reducing the intra-tree variability in wood quality, which could also be achieved through improved tree breeding.

ACKNOWLEDGMENTS
The first author received support from the International Foundation for Science (FIS; Grant I-1-D-6154-1), L'Oréal UNESCO (Sub-saharan Africa young Talents program 2019; grant For Women in Science), and IDEA Wild (field equipment). The authors extend their thanks to the French Agricultural Research Centre for International Development (CIRAD-Montpellier, France) for making it possible for the first author to carry out wood samples analyses within its UR BioWooEB laboratory.