Modelling variation in wood density within and among trees in stands of New Zealand-grown radiata pine
© Kimberley et al. 2015
Received: 31 August 2015
Accepted: 14 October 2015
Published: 12 November 2015
Density is an important wood property due to its correlation with other wood properties such as stiffness and pulp yield, as well as being central to the accounting of carbon sequestration in forests. It is influenced by site, silviculture, and genetics, and models that predict the variation in wood density within and among trees are required by forest managers so that they can develop strategies to achieve certain wood density targets. The aim of the study presented here was to develop a wood density model for radiata pine (Pinus radiata D. Don) growing in New Zealand.
The model was developed using an extensive historical dataset containing wood density values from increment cores and stem discs that were obtained from almost 10,000 trees at over 300 sites. The model consists of two sub-models: (1) a sub-model for predicting the radial variation in breast-height wood density and (2) a sub-model for predicting the distribution of density vertically within the stem.
The radial variation in breast-height wood density was predicted as a function of either ring number or both ring number and ring width, with the latter model better accounting for the effects of stand spacing. Additional model components were also developed in order to convert from annual ring density values to a whole-disc density, predict log density from disc densities, and account for the variation in wood density among individual trees within in a stand. The model can be used to predict the density of discs or logs cut from any position within a tree and can utilise measured outerwood density values to predict the density by log height for a particular stand. It can be used in conjunction with outerwood density to predict wood density distributions by logs for stands of any specified geographic location and management regime and is designed to be able to incorporate genetic adjustments at a later stage.
The analysis has confirmed and quantified much of the previous knowledge on the factors that affect the variation in wood density in radiata pine, particularly the influences of site factors and silviculture. It has also quantified the extent and patterns of variation in wood density within and among trees.
Density is an important wood property that affects the performance of solid wood products, pulp and paper, and some panel products (Kibblewhite 1984; Panshin and de Zeeuw 1980; Xu et al. 2004). It is also an important determinant of carbon sequestration in forests. Radiata pine (Pinus radiata D. Don) is the main commercial forestry species in New Zealand and is grown on a wide range of soil types and under differing climatic conditions, particularly with respect to temperature and rainfall. Past research in radiata pine growing in New Zealand established that there are significant regional trends in wood density, related to environmental factors such as mean annual temperature and soil nutrition (Beets et al. 2001; Beets et al. 2007; Cown 1999; Cown et al. 1991; Harris 1965; Palmer et al. 2013). In common with many other conifer species, radiata pine also exhibits a marked radial pattern whereby wood density increases from pith to bark (Cown 1980). In the vertical direction, whole-disc average wood density decreases with height up the stem largely because the number of rings decreases with height, meaning that proportionately more wood is contained within the lower density inner rings (Cown 1999).
Previous research has also investigated the effects of forest management practices, such as thinning, pruning and rotation age, and genetic differences on wood density (Burdon and Harris 1973; Burdon and Low 1992; Cown 1973, 1974, 1999; Cown and McConchie 1981, 1982; Cown et al. 1992). These studies have reported a positive correlation between wood density and mean annual temperature and a weak negative correlation between growth rate and wood density. Silvicultural treatments have a lesser impact unless stands are suddenly released from intense competition by severe thinning or a nutritional deficiency is corrected by fertiliser application. In these cases, a noticeable drop in density can occur for a few years immediately after treatment (Cown 1973). However, forest management is still expected to have an effect on wood density by varying the proportion of corewood within a tree (Cown 1992).
Forest managers commonly use growth and yield models to predict the impact of different combinations of site, genetics, and silviculture on volume and log product outturn (Weiskittel et al. 2011). There is also a demand to be able to predict the impacts of these factors on wood density as some log grades have a density requirement, often as a proxy for wood stiffness. For example, forest managers want to be able to determine what genetic stock and silvicultural regime (i.e., combination of spacing, thinning, and rotation length) are needed to achieve a particular wood density target for a given site. There are a number of examples of modelling systems that have been developed to link forest growth and timber quality in a range of species (Gardiner et al. 2011; Houllier et al. 1995; Peng and Stewart 2013), but a comprehensive modelling system does not exist for radiata pine wood properties. In New Zealand, an empirical model called STANDQUA was developed in the mid-1990s that enabled within-tree patterns of radiata pine wood density to be estimated from breast-height core samples and the future log-level wood density to be predicted (Tian and Cown 1995; Tian et al. 1995). More recently, a model was developed by Beets et al. (2007) to predict the density of annual growth sheaths in order to estimate carbon sequestration.
Both of these previous radiata pine wood density models were developed using various subsets of the extensive data that have been collected in numerous published and unpublished studies over many years. More comprehensive analyses of these data are required along with the development of models that enable forest managers to predict how different combinations of site, silviculture, and genetics affect wood density. Such analyses and new model development has been undertaken in three phases: (1) the development of a model to predict the spatial variation in breast-height outerwood density (i.e., basic density of the outer five growth rings or outer 50 mm); (2) the development of a model to predict the variation in wood density within a tree and among trees within a stand given a measured or predicted value of breast-height outerwood density; and (3) the incorporation of the effects of genetic gain for wood density into the model.
The results from the first phase of the analysis were presented in Palmer et al. (2013). They developed the concept of a wood density index, which is somewhat analogous to site index in growth and yield analysis as it uses a common base age to account for the known variation in wood density with age. The wood density index is defined as the breast-height outerwood density of 20-year-old radiata pine trees with silvicultural and genetic characteristics typical of stands planted in the 1990s. Across New Zealand, this wood density index was shown to be positively associated with mean annual air temperature, with higher values of wood density found in the warmer northern latitudes (Palmer et al. 2013). In this paper, we present analyses of both the intra-stem variation in wood density and the variation in density among trees within a stand. These analyses were used to develop a model that can be linked to the site-level model developed by Palmer et al. (2013) and also to growth and yield modelling systems (West et al. 2013). This enables investigation of the effects that factors such as rotation age and tree spacing have on within-tree patterns of wood density and the resulting whole-stem average density. Genetic effects can also be included in the modelling system using adjustments to the wood density index. The derivation of these genetic adjustments is described in a separate paper (Kimberley, MO, Moore, JR, & Dungey, HS (in review). Modelling the effects of genetic improvement on radiata pine wood density. New Zealand Journal of Forestry Science).
Description of datasets used in the analyses
Summary of the different wood density datasets that were used to develop the various models
Five-ring density samples at breast-height
Disc-level data collected on felled trees
Ring-level densitometry data at breast-height
Number of sites
Number of trees
Number of sites
Number of trees
Number of sites
Number of trees
Total tree height was generally not measured in these studies, which has presented some problems in previous analyses (e.g., Moore et al. 2014; Watt and Zoric 2010). However, it was possible to predict the total height of trees in many studies using the relationship between disc diameter and height up the stem at which the disc was sampled. For each tree, separate quadratic regression models were fitted to predict disc diameter as a function of height up the stem, and total tree height was then predicted by extrapolating these models to a diameter of zero. To ensure this procedure provided reliable predictions of tree height, the models were only fitted using discs cut at greater than 5-m height, as above this height, stem taper was found to be adequately approximated by a quadratic model. Furthermore, predictions were only made when the diameter of the uppermost disc was less than 200 mm and where the uppermost disc was sampled from at least 70 % of the predicted total tree height. This procedure made it possible to estimate total tree height at 150 of the 219 sites where disc samples had been collected at multiple heights up the stem. Relative height of each disc sample was then calculated as disc height divided by predicted total tree height.
Various component models were developed from this extensive database as described below. In most cases, a nonlinear mixed modelling approach was used with models fitted using the NLMIXED procedure in Version 9.3 of the SAS software (SAS Institute Inc. 2011).
Breast-height density by ring number
where D BH is the basic density of a five-ring group at breast-height, Ring is the midpoint ring number from the pith for this five-ring group, and a, b, c, d, and f are model parameters estimated from the data. Because wood density varies considerably between sites (Palmer et al. 2013), a normally distributed site-level random term with a mean of zero, L, was included in the model to account for local site effects. When the model is applied to predict wood density for a particular site it is calibrated using this local parameter L. This parameter can be obtained using either the wood density index map (Palmer et al. 2013) or a wood density measurement from a sample of trees of known age (see Appendix 1 for details).
Breast-height density by ring number and ring width
where D BH is the basic density of a given annual ring (Ring) at breast-height, Rwidth is the width of the annual ring (mm), a, b, c, d, and f are model parameters estimated from the data, and L is a normally distributed site-level random term with mean zero.
Disc density by height in the stem
where D disc is the whole-disc average density, H is the relative height of the disc up the stem, and a, b, c, and d are model parameters estimated from the data. As with the radial density models, this model is calibrated for a particular site using a local parameter L.
Conversion between outerwood basic density and whole-disc average density
where D disc is the whole-disc average density, D ow is the outerwood basic density, age is the stand age (years), and a, b, and c are model parameters.
Variation in outerwood density among individual trees in a stand
In order to quantify the tree-to-tree variation in outerwood basic density, we used data from 82 stands which were sampled using two or more cores per tree. With these data, it was possible to separate out the small-scale variability of cores within a tree from the general variation between trees using variance component analysis.
The first step in this analysis was to examine the form of the statistical distribution of outerwood density between trees. Secondly, the existence of any potential relationships between easily predicted tree characteristics and wood density were examined. More specifically, the potential relationship between DBH and outerwood density was investigated by calculating correlation coefficients between these two variables for each stand. Following this, between- and within-tree variance components were estimated for each stand. Stands were classified on the basis of mean basic density into the following classes: 300–350, 351–400, 401–450, 451–500, and 501–550 kg m−3, and the variance components were averaged across stands in each class. Variance components were expressed as coefficients of variation (i.e., standard deviation as a percentage of the mean).
Application of the model
Characteristics of the four sites selected to demonstrate the utility of the models
Wood density index
(m3 ha−1 yr−1)
Central North Island
Modelling radial variation in wood density at breast-height
Modelling vertical variation in whole-disc average density along a tree stem
Converting outerwood density to whole-disc average density
Variation in outerwood density among individual trees within a stand
Application of the model
The models described in this paper represent a comprehensive analysis of the data collected for radiata pine over the past 50 years. While the general within- and among-stem trends in radiata pine wood density are generally well-known (Cown 1973, 1974; Cown and McConchie 1981, 1982; Cown et al. 2002; Palmer et al. 2013), this is the first time that a complete model linking tree growth and wood density has been developed for the species. This modelling system will allow the relative effects of environmental, silvicultural, and genetic effects on radiata pine wood density to be accurately quantified. The breast-height radial density model linked to the height-within-stem density model can predict densities of logs cut from any position within a stem and at any age. When linked to a growth modelling system capable of predicting ring widths at any height, it is also possible to use these models to estimate density by annual ring and height within stem. This can be achieved by estimating the disc densities annually, and using the predicted ring width at any height, to derive the density of each ring. Finally, the distribution of individual logs cut from different stems in a stand is modelled on the assumption that they are normally distributed with a fixed coefficient of variation. Model implementation details are explained in Appendix 1 and Appendix 2.
The purpose of the analysis reported here was to investigate the variation in wood density within and among trees within a stand. However, analysis of the breast-height five-ring and the whole-disc datasets showed that approximately 45 % of the variation in these datasets was due to differences between sites. These site effects are incorporated into the model through a local parameter, which can be estimated from density samples collected from trees or based on the location of the stand, from the national wood density index map described by Palmer et al. (2013). Differences in wood density among sites have been shown to be due to factors such as temperature, rainfall, and soil fertility (Beets et al. 2001; Beets et al. 2007; Cown et al. 1991; Harris 1965; Palmer et al. 2013). While it is conceivable that the effect of these factors on wood density might be explained by ring width as they are known to also affect productivity (Watt et al. 2010), our analysis showed that even after accounting for ring width, there was still a large amount of unexplained site-level variation (Fig. 4). Therefore, the wood density model given by Eq. (2) that included ring width as an independent variable also requires a local parameter to account for site differences.
The negative relationship between ring width and wood density, after accounting for ring number, is consistent with findings in studies on other species (e.g., Gardiner et al. 2011; Jozsa and Middleton 1994; Jyske et al. 2008; Kantavichai et al. 2010; Zhang 1998). This apparent relationship between wood density and ring width has been the subject of some controversy in the scientific literature (e.g., Sutton and Harris 1974; Wimmer and Downes 2003) where, in some cases, the negative correlation between ring number and ring width has not been accounted for. Our results showed that ring width can be used to explain the effect of growth differences on wood density among stands growing at the same site but not differences among sites. In fact, the negative relationship between ring width and wood density would suggest that lower density wood would be found on those sites where radial growth rate (all other factors being equal) is higher. However, for the same silvicultural regime both wood density and ring width are higher on warmer northern sites than on cooler southern sites (Palmer et al. 2013; Watt et al. 2010). A previous study by Cown and Ball (2001) showed that latewood percentage was the main factor associated with regional variation in wood density. More detailed investigation is required in order to better understand the relationship between ring width and wood density, particularly how within-ring density components (i.e., earlywood density, latewood density, and latewood percentage) are affected by ring width. Studies in Norway spruce (Picea abies Karst.) have shown that the partial correlation between ring width and density, after controlling for latewood percentage, is much lower than the simple correlation (Jyske et al. 2008; Wimmer and Downes 2003). Furthermore, the correlation between ring width and wood density fluctuates between years depending on climatic and silvicultural factors (Wimmer and Downes 2003).
This level of variation in wood density among trees within a stand confirms the results from previous studies (Cown 1999; Cown et al. 1991). Overall, there was no evidence of a correlation between wood density and diameter at breast-height. However, in a few of the stands there was a weak negative correlation between these traits. A closer examination of the few stands that showed a significant association between DBH and density indicated that this occurred only in older, highly stocked stands, containing small suppressed trees. Such trees tended to be of higher than average density producing a weak negative correlation between density and DBH in these stands. It is important to note that this result applies to individual trees within a stand, not to stands growing at different stand densities at the same site, where mean wood density is related to mean ring width. While this study found that there was generally no phenotypic correlation between wood density and diameter at breast-height, most studies in radiata pine have found that there is a negative genetic correlation between these two traits (Wu et al. 2008). The wood density model is able to assist tree breeders who want to be able to predict the implications of early selections on later age wood properties and whole-log density. At present, tree breeders rely on knowledge of age-age correlations to assist with this (Kumar and Lee 2002; Li and Wu 2005).
The radial and vertical trends in wood density were broadly similar to those observed in other studies (Burdon et al. 2004; Cown et al. 1991). Previous research has suggested that the gradients of wood properties found in radiata pine are underpinned by differences in the rate of cambial cell division, differences in the rate and duration of tracheid wall thickening, and differences in gene expression (Cato et al. 2006). In the radial direction, wood density increased rapidly with increasing ring number from the pith before reaching a quasi-asymptotic value such that little change in density occurred after approximately ring 20. This typical radial pattern has frequently been used to determine the extent of the corewood zone, which is defined as the region in which the radial rate of change in wood properties is greatest (Lachenbruch et al. 2011; Zobel and Sprague 1998). In radiata pine, corewood has typically been defined as the innermost ten growth rings from the pith (Burdon et al. 2004; Cown 1992), although a threshold density of 400 kg m−3 has also been proposed (Cown 1992). The results from the current study show that wood density is still increasing rapidly with cambial age at ten rings from the pith, suggesting that the arbitrary ten ring definition may be inadequate. However, other properties, such as microfibril angle, also need to be considered when determining the age of transition from corewood to outerwood (Mansfield et al. 2009). The models developed in this study can be used to further investigate the extent of the corewood zone, particularly if defined based on a wood density threshold, and how this is affected by different factors, such as environment and silviculture.
An extensive database of radiata pine wood density data collected over 50 years of research has enabled models to be generated to predict within-tree, within-stand, and among-stand variation in wood density. These models can be linked to growth and yield models so that forest managers can predict the impacts of factors such as site, silvicultural regime, and genetics on wood density. The research here has confirmed and quantified much of the previous knowledge on the factors that affect the variation in wood density in radiata pine.
Funding for the analysis of these data was provided by Future Forests Research Ltd. We would like to thank numerous current and former colleagues who collected density samples over many years.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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