Dynamics and variability of response variables
The data on growth and properties show a considerable variability of different origin. This is illustrated in Fig. 3 with means for growth ring width plotted versus cambial age with data from 24 trees: From each site, 6 trees of a slow-growing family and 6 of a fast-growing family. The dynamic variation related to age is evident. There are clear differences between the two families (related to genetics and the suitability of the families to perform on the sampled sites). Also, clear site differences were observed caused by factors such as local climate and soil fertility. However, there are also very large differences among individual trees of the same family and same site, reflecting large variation not related to age or site, but to individual environmental conditions of each tree.
Figure 3 also illustrates effects of the differences among the trees in longitudinal growth mentioned above, resulting in different cambial ages of the last ring formed inside the bark at the time of sampling. Frequency distributions for cambial age at breast height of all the sampled trees are shown in Fig. 4 for both sites. At sampling age (21 years) the number of annual rings at breast height ranged from 6 to 18, a considerable variability among trees planted the same year, meaning that the ages at which the trees reached breast height ranged from 3 to 15 years. Thus, wood of rings with the same cambial age has been formed during different growth seasons with different weather. The trees of Trial 1147 Erikstorp generally reached breast height earlier than those of Trial 1146 Höreda. More than 90% of the trees reached breast height at ages from 4 to 8 years, with the highest frequency for age 5 and 6 years, resulting in 14 and 15 annual rings, respectively.
The fact that trees with slower height growth are not represented at the higher cambial ages makes cambial age not necessarily the best independent variable for modelling age and weather effects, in particular if the trees are young, showing rapid changes with age. To elucidate this, the trees were classified based on the year when they reached breast height. Averages were calculated for all cambial ages within each tree class and plotted versus both cambial age (CA) and total tree age (TA) for comparison. The results show clearly different patterns depending on the use of cambial age or tree age. In Fig. 5a, this is illustrated with plots of the average widths of rings and their EW, TW and LW bands for the five most frequent classes of trees reaching breast height 1994 to 1998, respectively, presented with colours in the following order: magenta (1994), blue, green, yellow green, brown (1998). In its upper part, the averages are plotted versus cambial age, separately for the two trials. In its lower part, the same data are plotted versus the year of wood formation which equals the tree age, if the year of planting (1990) is subtracted. It should be noted that the latewood widths are shown in 10-fold scale of the y-axis.
Several distinct patterns were observed, related to influences of intrinsic or extrinsic control of growth traits. A first pattern is that the year-to-year variations of the ring width curves as expected synchronise obviously better when plotted against tree age (Fig. 5a lower plots) compared to cambial age (Fig. 5a upper plots), for which the wood of the tree classes was formed under different years and weather conditions. This extrinsic effect is also consistent for the different parts of the tree ring and on both sites. A second pattern, less expected, is the good agreement between the developments of widths versus total tree age among the tree classes, from the extremely juvenile wood towards maturity. The average ring widths for the tree classes decreased from 5 to 6 mm close to the pith of trees reaching breast height around age 5 years to 2–3 mm at age 20, in relative terms equalling 50–60%. The curves representing trees reaching breast height later successively lined up. This means that trees with slow height growth, reaching breast height late, will not only fall behind in competition for light and resources. They will also miss the opportunity to form the widest rings close to the pith and start with narrower rings, decreasing outwards. The trees with higher longitudinal growth are thus prone to also have higher radial growth, which is expressed by a positive correlation of R2 = 0.67 between family averages of diameter at breast height and tree height at age 7 years on both sites. Very similar patterns were observed for cell numbers in radial direction in the rings and their parts.
The corresponding plots for radial tracheid width in Fig. 5b show a third pattern differing from that for the tree ring widths. When plotted versus cambial age, the curves for the development of ring and EW means representing the different tree classes followed each other closely up to cambial age of 8 years (upper graphs), a very dynamic phase, indicating cambial age control. Thereafter, the average curves of the different tree classes successively entered a more moderate phase. These shifts seem related to the total tree age according to the lower graphs. This indicates that, on average, the trees which grew faster in height and also radially will experience more years of initial increase before entering the more moderate phase, forming wider tracheids in radial direction at higher tree ages than those of slower grown trees. This is in line with observations from old trees of Norway spruce (Lundqvist et al. 2005a; Franchescini et al. 2012). The results thus indicate a stronger intrinsic control of tracheid width during the most dynamic phase, combined with control related to tree age of the time when the more moderate phase is entered. The compartments show a very clear cambial age control of radial tracheid width in EW, less so for TW, and radial fibre widths in LW, which seems more related to total age (and annual weather), and further, little influence from annual weather variations on the radial cell expansion in EW, some in LW, but strong influence in TW. The overall effect on the total ring level indicates that the year-to-year variations during the early years are dominated by cambial control, while during the following period of moderate change they become dominated by weather effects and are strongly related to the variations in TW, and with differentiated controlled by growth rate and total age.
For tangential fibre width (not shown), the variations showed a similar character as for radial width, with the exception that the differences were smaller between EW, TW and LW, and so were the annual variations. This is expected as the fibres are organised in files, and their widths cannot vary freely.
Figure 5c shows the corresponding graphs for tracheid coarseness, allocated biomass per length unit of the tracheids, indicating stronger cambial control age than that of total tree age. The graphs representing the average developments with age of the different tree classes line up well when plotted versus cambial age, expect for disturbances from extreme weather conditions during 2004, which occur at different cambial ages. Adversely, the graphs plotted versus tree age are well synchronised regarding the annual variations, while showing bias between the tree classes, reflecting the stronger cambial control. The radial development of coarseness was still in a more dynamic phase at the time of sampling, indicating a slower maturation of the biomass allocation process than for the radial tracheid expansion process.
Capabilities of the models and contributions from age and weather-related factors
Against the backdrop of the idiosyncratic patterns described above, models were developed from combining total tree age or cambial age, respectively, with temperature sum across growth season (GDD) and precipitation sums for the four quarters of the growth seasons. Table 1 presents the degrees of determination R2 of models for means of rings and their parts. The first two data columns to the left show this for models with age only in their fixed parts, age expressed with cambial age and total tree age, respectively, the following two columns illustrate the same for models including also the temperature and precipitation parts, showing the change in R2 when adding weather variables to the age factors in absolute terms. Values in bold indicate if a specific age variable provided a substantially higher degree of determination than the other for the trait (R2 difference ≥ 0.01). The two next columns show the gains in R2 when adding the weather factors, in relative terms. Models benefitting more than 4%, and then reaching R2 values > 0.15, are indicated in italics. To the far left, the baseline (intercept) values of the models are presented.
To facilitate comparisons, the R2 values of model estimation the traits representing the three fundamental processes of wood formation are shown graphically in Fig. 6. Each set of four bars shows the two CA-based models to the left with dashed contours and the two TA-based models to the right with solid contours, models based on age only with white bars and those using also weather input in grey. It should be mentioned that this study focuses on the ages of most dynamic change. At higher ages with smaller age-related changes, the differences between the residuals when using CA or TA are expected to be smaller, and the effects of genetics and environmental factors larger in a relative but not necessarily in an absolute sense.
Cell divisions: Number of radial tracheids
The best models of all were obtained for the number of tracheids formed per year in radial direction. Using total tree age alone gave an R2 value as high as 0.49, as mentioned before, reflecting the large relative decrease in the intensity of cell division across this very dynamic phase in the life of trees. When adding the weather-related parts, R2 increased for 7% to 0.53, indicating substantial influences from the temperature sum and the precipitation sums. It should be pointed out here that these sums reflect not only the levels of temperature and precipitation, but also the lengths of the seasons. Use of tree age combined with the weather parts gave the best degrees of determination also for the radial numbers of tracheids in the ring compartments: high for EW (0.41 → 0.48) and TW (0.29 → 0.35), but very low for LW (0.03 → 0.07) with its small overall variation.
Thus, the R2 values for the compartments were lower than that for the ring level, but their relative improvements when adding the weather factors were larger for the compartments than on the ring level: 18% for EW, 20% for TW, and as high as 155% for LW.
This can be understood as follows: While each cell division is solely governed by the current and previous weather, the final identity of the tracheid as part of EW, TW or LW is also influenced by the weather during the time of cell expansion and biomass allocation/wall thickening to follow, which will eventually affect if a tracheid will grow to a EW or TW tracheid and, if later formed, to a TW or LW tracheid. From this perspective, it is expected that the influences of weather are relatively stronger on the parts of the rings than on the total ring, as well as the substantial increase in R2 for radial number of tracheids in TW when adding weather factors, as TW is defined to capture the most weather-dependent part of the wood.
Cell expansion: Radial and tangential tracheid widths
The model with the second highest R2 value was obtained for tracheid widths in for EW (R2 = 0.44) based on cambial age, which was reached already with use of the age factor only. For all models estimating tracheid widths, cambial age provided higher R2 values than tree age. The marginal gain in degree of determination for EW from adding the weather factors may reflect that the expansion of these tracheids first formed is mainly influenced by conditions during the initial phase of the vegetation period, to a large extent predetermined by factors such as the reserve state of the tree, which is in turn largely determined by previous growth periods. In contrast, the R2 values obtained for TW and LW were low, but with large relative increases when adding the weather factors: for TW 0.06 → 0.16 and for LW with its very small overall variation 0.02 → 0.10. The LW band contained on average only 11 tracheids, less than 10% of the average number for rings. As EW and TW thus stand for more than 90% of the tracheids, it is reasonable that the capability of the model for average tracheid width of the full ring was in between those of EW and TW, rising from 0.17 to 0.23 on adding the weather-related part.
For the tangential widths of tracheids, the models for means of rings and their EW and TW all showed R2 values of about 0.35 and 0.25 for LW. The gains when adding the weather parts were small, most likely reflecting that the tracheids are arranged in radial files, leaving limited freedom for variation in tangential tracheid width.
Widths of rings and their parts
The relative capabilities of the models for widths of rings and their parts are similar to those for number of tracheids formed in radial direction. The obvious explanation is that the ring width is a product of the number and the width of tracheids radially, combined with the fact that the relative variation of the numbers is much larger than that of the widths. This also implies that total tree age provides better models than cambial age, and also a similar particularly large relative increase in R2 for TW models when the weather part is added (also for LW but at much lower levels of R2). However, the degrees of determination are generally lower than for the number of tracheids radially, most likely since the widths of rings and their parts are products of two variables, both influences by many factors, meaning that its variability has a more complex background.
Biomass allocation: Coarseness and wall thickness of tracheids
For the allocation of biomass at cell level, measured as tracheid coarseness, the cambial age-related part of the model explained 0.39 of the overall variances from all sources for the average coarseness of rings, just above 0.30 for EW and TW and 0.21 for LW. When adding the weather-related parts, these R2 values increased to 0.42, 0.34, 0.37 and 0.30, respectively, again remarkable increases for TW and LW.
The wall thickness of a tracheid is related to its coarseness and its radial and tangential tracheid widths (also of the tracheid wall density, but this shows little variation). Wall thickness is thus another complex property under multiple influences. Therefore, it is reasonable that its models show lower R2 values than those for coarseness.
Developments with age and effects of temperature and precipitation
Influences presented with spline functions and differences between cambial and total age
The developments with age and weather factors are described with spline functions showing changes across the span of variation of each factor in relation to baseline values, given in Table 1. These baseline values differ among traits and also among the averages for rings, EW, TW and LW. Generally, these values are close to the calculated averages for the trait across all trees and rings and the spline function is a model for the average development related to each trait across all trees of the two sites. This is illustrated in Fig. 7 for influences of age on number of tracheids formed annually (left) and their mean coarseness on ring level (right). The plots superimpose the spline functions of the models based on tree age (TA, black curves) and cambial age (CA, red dotted curves) together, shifted in time for the best match of curves.
Shifted like that, the TA and the CA splines become very similar at the lower end of the age span, but they differ considerably at the higher end. This is obviously related to the differences in height growth of the trees. With use of TA, the models are based on more trees with increasing age, in fact all trees for the last 6 annual rings, see Fig. 4. But with use of CA, the models at the highest cambial ages will be based solely on the trees with the fastest longitudinal growth. The negative but decreasing slope of the TA spline function for number of tracheids, combined with the upturn of the CA splines at high ages, and the adverse developments for coarseness, suggests that with age: (1) fewer tracheids were formed but that these had higher coarseness, on average across all trees, and that (2) the more fast-grown trees had more tracheids with somewhat lower coarseness compared to the averages at these ages. The fact that only trees with a fast height growth are represented at higher CA values is the reason of the upturn of cell numbers with the higher cambial age and the downturn for coarseness. Similar effects are seen also for radial tracheid width, where the more fast-grown trees have wider than average tracheids as noticed from Fig. 5b. Such differences in relation to the averages will be studied in later steps of these investigations.
Thus, the comparison of models based on TA and CA, respectively, shows that for CA, the model for a trait may be distorted at high cambial ages due to an over-representation of trees with faster height growth, with the consequence that it will not reflect the average development of the trait. This is, however, not the case for models based on TA. Therefore, the choice was made to present spline functions only for models based on tree age. The splines for influences of weather factors were however as expected similar on use of both age types.
Models based on age and weather
Figure 8 illustrates the full sets of spline functions for all the traits modelled and presented in this article: Influences of age to the left, then of GDD, and to the right of that the four precipitation sums of quarters of the vegetation period. Splines are provided for effects on the ring level (solid black) and for EW, TW and LW (dashed curves in green, red and blue), all along a common zero line representing their baseline values provided in Table 1. The absolute value of each estimation is thus the sum of the specific baseline value and the contributions from age, GGD and the precipitation sums.
The splines showed three major patterns: an increase, a decrease or a humpback shape pattern with a maximum. In all plots of spline functions related to weather effects, three vertical lines have been introduced. The middle vertical line indicates the median annual weather in the data set, the outer ones the 10% and 90% quantiles. Effects indicated outside these lines should only be interpreted with care. In the following sections, temperature and precipitation sums inside but close to the outer lines will be referred to as low and high, and values closer to the median as on the low or high side. For all weather-related factors, the splines indicate that the influences of the median values of the factors were close to zero, meaning that median weather would result in spline values close to the baseline.
Numbers of cell divisions at cambium across the years and of tracheids in EW, TW and LW
Part a of Fig. 8 presents the models obtained for number of tracheids formed in radial direction across the year, together with the numbers of tracheids in EW, TW and LW. The baseline numbers for rings, EW, TW and LW were 120, 60, 47 and 11 (cf. last column of Table 1). According to the age-related graphs, these base values occur at a total tree age of about 12 years, where the curve crosses the zero line. The ring level model tells that the trees having reached breast height at age 5 years had formed on average 125 tracheids more than this average, thus 245 in total. The radial number of cells then decreased linearly down to on average about 30 above the average at age 10 years. At age 15, a level of about 40 cells below the baseline was reached, meaning on average 80 tracheids formed radially per year. The models indicate that the radial number of tracheids in EW continues to decrease at all investigated ages, while for TW the decrease stops at about age 14. This would entail an increasing proportion of TW tracheids during the last years investigated.
The model indicates a positive GDD effect from about − 15 to + 15 tracheids across the span of GDDs observed, the 10% most extreme events at both ends excluded. At low GDD, the decrease in tracheid numbers was divided about equally between EW and TW, but at high GDD, the increase was mostly reflected in the TW. Further, the splines for precipitation sums indicate similar positive influence of high precipitation during the second quarter of the vegetation period (Q2 = major parts of June and July), also here mostly reflected in TW, while dry conditions during this period impacted negatively. The precipitation sum during Q3 did not affect the annual radial number of tracheids much, but in dry weather conditions, more of them got EW character and equally less TW character. A similar but weaker antagonistic behaviour was expressed at median precipitation sum during Q1.
Widths of tracheids in rings and parts, and comparison of models based on cambial and tree age
Part b of Fig. 8 illustrates the corresponding effects on the radial tracheid widths in rings, EW, TW and LW, in relation to their baseline widths of 29, 32, 27 and 20 µm, respectively. The modelled radial tracheid widths of trees which had reached breast height at age 5 years were on average 5 µm slimmer than the baseline value, while those formed at age 14 were 1.2 µm broader than the baseline value of 29 µm. At higher ages, the estimated age effect on ring means started to decrease slightly. The age effects on the tracheids in the EW were larger than this, but smaller for those in the TW. The radial widths of the radially slim LW tracheids increased only slightly in absolute terms across the ages.
Radial extension (widening) of tracheids is according to the models for ring means favoured by low GDD (small effect), precipitation on the high side during Q1, high during Q2 and Q4, but low during Q3. Just as for the influences from age, several of these weather conditions affects the number and size of the tracheids adversely. For tracheids in TW, the weather splines indicate that high precipitation during the 2nd and on high side in the 3rd quarters favours larger widths of TW tracheids, which makes them in this respect more similar to those in EW.
In Fig. 8c, the influences on tangential cell widths are illustrated. The baseline values in Table 1 show that the average widths are quite similar for ring, EW, TW and LW, and the dynamics with age are so, too. The variations related to the weather variables are also small. This strengthens the assumption that their freedom of variation is limited due to the organisation of the tracheids in radial cell files.
Widths of rings and their parts
Part d of Fig. 8 illustrates the average effects on widths of rings and their parts, in relation to the baseline values for the ring 3.4 mm, EW 1.9 mm, TW 1.3 mm and LW 0.2 mm. All spline functions are very similar to those for number of tracheids radially.
The trees which have reached breast height at age 5 years had then on average about 2.7 mm broader rings than baseline, resulting in an average ring width of 6.1 mm. Following a close to linear slope, the rings were at age 10 years on average only about 0.5 mm broader than the baseline value, 3.9 mm, and at age 15 years after continued but retarding decline they were about 1 mm thinner than this value, 2.4 mm. Further, the model indicates that the average age effects on EW and TW first are on average rather similar, but that the proportion of TW increases toward the end of the age range investigated. The width of the LW band is very thin, and the changes due to age are barely visible in the figure.
Continuing to weather-related effects, the model results indicate that low GDD is negative for ring width, decreasing its average with up to about 0.5 mm, while at high GDD about 0.4 mm of radial increment is added, extremes excluded. The graphs indicate that both thinner EW and TW bands are the cause of the narrower ring widths at low GDD, with the strongest effect from EW, possibly reflecting a late start of the growth season. The same pattern reveals broader bands of EW and TW at higher GDDs, contributing to the broader rings. The influences from the weather factors on ring widths were generally quite similar to those observed on radial number of tracheids. According to the models, the effects on radial growth of the variations in GDD and in precipitation during Q2 corresponded to ± 0.3 to ± 0.4 mm per year, each.
The results also suggest that widths of EW and TW often show a certain competitive behaviour. As commented after the description of the definition of TW: Fibres at the interphase between the two compartments may end up in either of the classes, depending on how the weather a certain year influences the expansion of the cells.
Tracheid coarseness and wall thickness
Part e of Fig. 8 shows the corresponding spline functions for tracheid coarseness. The baseline values for averages of the ring, EW, TW and LW were 318, 274, 358 and 428 µg/m, respectively (Table 1). The modelled average age-related developments were rather similar for ring, EW, TW and LW, starting in the innermost rings from coarseness values 80–120 µg/m below their respective baselines, with LW and TW at the lower end, then converging almost linearly to reach the baseline at the same tree age of 12 years. Above this age, the spline functions start to diverge: the spline for EW tracheids levels off at values about 20 µg/m above the baseline, the LW spline continues to add biomass, reaching the double at tree age 19, while the splines for ring and TW averages develop in between. These increases in coarseness will be linked with increasing thickness of the tracheid walls, and as the perimeters of the tracheids in TW are smaller than those of EW, and even more so in LW, the increase in wall thickness with age will be largest in LW, smallest in EW, and with TW and ring averages in between (Fig. 8f).
The weather factors showed smaller influences than age in this age span. The average influence of GDD shows the same development for means of rings, EW and TW: for coarseness a linear decrease from + 15 µg/m at low GDD to − 15 µg/m at high GDD, and a similar development for wall thickness. At higher temperature sums, the biomass is thus distributed to more tracheids (Fig. 8a) with smaller radial width (Fig. 8b), lower coarseness (Fig. 8e) and thinner walls (Fig. 8f). The most evident precipitation effects are indicated for the LW, for which the coarseness and wall thickness splines show reducing values on increasing precipitation during Q2 and Q3.
Example: Combined weather effects of ring width
The use of GAMMs makes it possible to simply add up the influences of different variables. A simulation was done to exemplify the effects of different scenarios of annual weather, including extreme scenarios for radial growth. For this, we used different combinations of medium, low and high GDD and precipitation sums, defined by the median and 10% and 90% quantile values of the weather variables. The effects of these different levels of the weather variables were assumed to be the values of the respective spline functions at these levels in Fig. 8d. In Table 2, all individual effects of the five weather factors are compiled and added to estimate the full annual effect of each scenario.
With a baseline value of 3.4 mm and age effects of about + 2.0 at age 7 and − 1.0 at 19 years, an average tree would according to the simulations on ideal weather show a decrease in ring width from age 7 to age 19 years of 6.1 to 4.1 mm and of 3.1 to 1.1 mm on worst weather conditions.
The residuals were checked for influences related to the different independent variables. In Fig. 9, the results are illustrated for the model of ring width against tree age, and the outcomes are similar for the other properties modelled. Figure 9a shows the original data for all tree ages from 5 to 19 years including the trees from both sites based on a box plot. The central lines of each box plot indicate the median values, and the vertical widths of the boxes the 0.25 and 0.75 quantiles of the distributions. In Fig. 9b, the residuals are shown in the same manner. Subtraction of the modelled age- and weather-related variation resulted in a substantial reduction of the variance. Some systematic deviations may however be observed in the residual plot, such as a sequence of positive residuals (under-estimation) at ages 9–12 coinciding with a period of four warmer than average years on both sites, and negative residuals (over-estimation) at ages 5 and 7 coinciding with two cold years.