New insights into estimating the age of old Scots pine from increment cores with stem rot

Trunk inner rot is a common phenomenon in some old-growth pine dominated forests, making it impossible to determine tree age by counting annual rings. We compared the efficiency of five methods to estimate the age of hollow pine trees (Pinus sylvestris L.). Our main aims were to select the best-performing method and to test whether the age of the tree or the proportion of rot influences the accuracy of estimation. We used full increment cores (reaching the pith or within 1 cm of it) from 100 trees (54–562 years old) collected in northern Sweden and simulated rotten centres of three different sizes in order to test the methods. The lowest error rates were obtained when less than a third of the sample was missing (down to 5.0 % error rate), and by using a method based on the growth pattern of a set of healthy trees. Using linear extrapolation of the mean radial growth led to large overestimates (up to three times the number of absent rings) with error rates up to 27.3 %. We also found that the performance of all methods was reduced in cores from older trees. Our main conclusion is that non-linear methods should be preferred for age estimation of hollow pines. We also argue that more precision in the age estimation could be gained already in the field by collecting multiple cores from rotten trees or by developing alternative coring methods.     

Tree age estimates in Fagus sylvatica and Quercus robur: testing previous and improved methods

The accuracy of direct (based on increment cores) and indirect (based on age-size relationships) methods of tree age estimation in Fagus sylvatica and Quercus robur was tested. This was done through increment cores and stem discs taken in an old-growth forest of Northern Spain. It was found that cross-dating was more precise than ring counting by up to 7 years per tree. Furthermore, cross-dating permitted the estimation of the age of trees with floating ring-width series, which were 7% of cored F. sylvatica and 40% of Q. robur ones. In partial cores with the arcs of the inner rings, the length of the missing radius was estimated with both a geometric method, based on the curvature of the arcs, and a new graphical method, based on the convergence of xylem rays at the pith. The graphical method was more accurate when the radial growth was eccentric, as happens in Q. robur, while both methods showed a similar accuracy for F. sylvatica, whose growth is relatively concentric. Empirical models of initial radial growth (IRG), built to estimate the number of missing rings, reduced the errors associated with other methods that assume constant growth rates. Age estimates obtained from the graphical method combined with the IRG models were within 4% of the actual age. This combination ensured age estimates with a mean accuracy of 8 years for 98% of the F. sylvatica trees, and 4 years for 89% of the Q. robur. In partial cores without the arcs of the inner rings, the length of the missing radius was estimated as the distance to the geometric centre of the tree. In that case, age estimates obtained by extrapolating the mean growth rate of the 20 innermost rings in the cores were from 10 to 20% of actual age, which coincided with results obtained in other tree species with this method. Finally, the age-diameter equations of the different cohorts produced better age estimates (from 8 to 14% of actual age) than equations of the population as a whole (from 20 to 40% of actual age). These results proved that the errors derived from doubtful assumptions, such as concentric radial growth, constant growth and recruitment rates, or the absence of anomalous rings, could be reduced by applying more realistic methods of tree age estimation.     

IncrementR: Analysing height growth of trees and shrubs in R

Dendrochronology mostly deals with secondary (radial) growth and attention to primary (height) growth has so far been limited. However, tree-ring widths might not adequately represent stem volume increments, net primary productivity and the size of the tree stem carbon sink. The main reason for the prevailing focus on radial growth is that establishing height growth chronologies requires time-consuming and destructive methods. However, for certain ecological applications, less laboriously acquired data on height growth averaged over several successive years are satisfactory. Here we present an R package that contains a set of tools for the analysis of height growth. The tools have been developed for input data of tree-ring widths extracted from series of successive stem height levels. Tree-ring widths ideally represent four directions in each cross section to capture potential changes in stem eccentricity between various height levels. The main computed parameters provided by the package include height growth along the stem, changes of stem eccentricity and stem taper. Accurate determination of average height growth depends on the correct estimation of the number of tree rings at different stem height levels, which might be complicated by missing rings in off-pith cores. The presented package therefore also contains functions implementing common procedures for the estimation of the number of missing tree rings near to the pith. Most outputs can be visualized graphically. The package is useful for estimating height growth in ecological and dendrogeomorphological studies, especially in situations where both primary and secondary growth is influenced by different environmental factors. It is also useful for analysing tree-ring chronologies assembled using serial sectioning, which typically applies to shrubs.     

The Zurich method for sapwood estimation

We present a new predictor for the estimation of the number of missing sapwood rings in oak. It circumvents a number of problems with predictors used in traditional sapwood estimation procedures such as mean ring width or tree age. Instead, we use the mean ring width of the last 9 heartwood rings and the first sapwood ring, which mirrors the growth level during sapwood formation. We present a model to produce a 95 % prediction interval for the felling year. Our method accounts for the skewed distribution of the number of sapwood rings towards higher values.     

Variation of cellulose microfibril angles in softwoods and hardwoods-a possible strategy of mechanical optimization

Position-resolved small-angle X-ray scattering was used to investigate the nanostructure of the wood cell wall in two softwood species (Norwegian spruce and Scots pine) and two hardwood species (pedunculate oak and copper beech). The tilt angle of the cellulose fibrils in the wood cell wall versus the longitudinal cell axis (microfibril angle) was systematically studied over a wide range of annual rings in each tree. The measured angles were correlated with the distance from the pith and the results were compared. The microfibril angle was found to decrease from pith to bark in all four trees, but was generally higher in the softwood than in the hardwood. In Norwegian spruce, the microfibril angles were higher in late wood than in early wood; in Scots pine the opposite was observed. In pedunculate oak and copper beech, low angles were found in the major part of the stem, except for the very first annual rings in pedunculate oak. The results are interpreted in terms of mechanical optimization. An attempt was made to give a quantitative estimation for the mechanical constraints imposed on a tree of given dimensions and to establish a model that could explain the general decrease of microfibril angles from pith to bark.     

The effect of missing rings on stand-age estimation of even-aged forests in northern Hokkaido,Japan

The effectiveness of estimating stand age from increment core samples taken at stump height (20 cm above ground) was tested in an even-aged stand ofBetula ermanii that had regenerated after a forest fire in 1945 in Hokkaido, Japan. Careful cross-dating revealed that annual rings were missing in 11 cores out of a total of 42 cores sampled, and that all these missing rings occurred in the outermost part of the core. These facts indicate that precaution has to be taken in selecting trees from which cores are to be sampled. The present work also revealed that those trees with missing rings have a characteristic appearance, with a thinner stem and less crown foliage than normal trees with complete rings. It was also found that even if this appearance test failed, the possibility of missing rings could be detected from a declining growth pattern, with extremely narrow rings on the increment core which normal trees did not show.     

Collateral missing value imputation: a new robust missing value estimation algorithm for microarray data

MOTIVATION: Microarray data are used in a range of application areas in biology, although often it contains considerable numbers of missing values. These missing values can significantly affect subsequent statistical analysis and machine learning algorithms so there is a strong motivation to estimate these values as accurately as possible before using these algorithms. While many imputation algorithms have been proposed, more robust techniques need to be developed so that further analysis of biological data can be accurately undertaken. In this paper, an innovative missing value imputation algorithm called collateral missing value estimation (CMVE) is presented which uses multiple covariance-based imputation matrices for the final prediction of missing values. The matrices are computed and optimized using least square regression and linear programming methods. RESULTS: The new CMVE algorithm has been compared with existing estimation techniques including Bayesian principal component analysis imputation (BPCA), least square impute (LSImpute) and K-nearest neighbour (KNN). All these methods were rigorously tested to estimate missing values in three separate non-time series (ovarian cancer based) and one time series (yeast sporulation) dataset. Each method was quantitatively analyzed using the normalized root mean square (NRMS) error measure, covering a wide range of randomly introduced missing value probabilities from 0.01 to 0.2. Experiments were also undertaken on the yeast dataset, which comprised 1.7% actual missing values, to test the hypothesis that CMVE performed better not only for randomly occurring but also for a real distribution of missing values. The results confirmed that CMVE consistently demonstrated superior and robust estimation capability of missing values compared with other methods for both series types of data, for the same order of computational complexity. A concise theoretical framework has also been formulated to validate the improved performance of the CMVE algorithm. AVAILABILITY: The CMVE software is available upon request from the authors.     

Assessing the utility of direct and indirect methods for estimating tropical tree age in the Western Ghats, India

The knowledge of tree age is important for understanding tree growth and forest dynamics. It may be estimated by ‘direct’ methods involving growth ring counts, or by ‘indirect’ methods involving field measurements of growth rates. Direct methods are considered more accurate, but it is not clear if they are appropriate for all species, notably from the humid tropics. In this paper we assess the occurrence of annual growth rings and their utility for age estimation in three tropical tree species, Acrocarpus fraxinifolius, Dalbergia latifolia (Fabaceae) and Syzygium cumini (Myrtaceae), growing in traditional shade coffee plantations of the southern Western Ghats, India. These species previously were described as having “indistinct or absent” growth rings. We used anatomical studies, field measurements and computational methods to characterise growth rings and assess similarities between directly and indirectly estimated tree ages. Our study revealed that annual growth rings were characterised by different sets of anatomical features per species and were most distinct in the fast-growing deciduous A. fraxinifolius. Growth rates measured in the field showed annual periodicity in all three species, and reflected annual rainfall-drought cycles in D. latifolia and S. cumini. Direct age estimates were most similar to indirect estimates in D. latifolia, and least so in S. cumini. The results of direct age estimation by counting rings are consistent with them being annual in nature in tropical species with distinct and reliable annual growth ring formation. However, for species with poorly defined growth rings, indirect age estimation methods might be more useful.     

Growth forms and age estimation of treeline species

The correct evaluation of the age of small tree individuals is of great importance in ecological studies, and can be performed if growth units are identifiable even under strong environmental constraints. We aimed to assess the reliability of age evaluation of small individuals of four species commonly occurring at the treeline in the Alps and the Apennines (N Italy), Picea abies, Pinus cembra, Larix decidua and Fagus sylvatica. A total of 224 individuals were sampled along an altitudinal gradient up to the treeline. For each species, we assessed the growth architecture and the appearance of annual growth units; for each individual, age and evaluation uncertainty were estimated. To verify the estimation a core or a cross-section was obtained. The estimated age was compared with the tree-ring age through linear regression and reduced chi square test, and the estimation accuracy was evaluated as function of tree age, dimension and environmental parameters. A good estimation was possible for all species, even when loss of vertical growth occurred. The highest error occurred for Larix, the lowest for Pinus; the error was generally correlated with tree age and dimension, and was affected by altitude and geomorphology. Good reduced chi square values were reached considering only the youngest individuals for Fagus and Picea and the smallest for Fagus and Larix; the uncertainty was generally underestimated for Pinus. Even though reliable age estimation could be obtained, a realistic and species-specific evaluation of the estimation uncertainties is necessary to assess estimation accuracy for ecological studies.     

Estimating missing sapwood rings in three European gymnosperm species by the heartwood age rule

Precise dating of the year of felling is one intended outcome of dendrochronology. However, occasionally some or all sapwood rings might be missing, either due to deterioration or because they were carved off, or for some other reason. Consequently, while heartwood is preserved, sapwood might be fully or partially missing. In such cases, the year of felling must be estimated by adding a suitable number of sapwood rings. A heartwood age rule (HAR) has been advocated for Scots pine and adapted to European larch and Cembra pine, implying a linear relationship between sapwood ring count and the square root of heartwood ring count, largely irrespective of position in the stem. The same rule applied to all observations of a species, irrespective of silviculture, location or fertility of the growth site. Scots pine had twice or thrice as many sapwood rings as Cembra pine, which had 10% more rings than larch. The magnitude of model residuals was proportional to estimated sapwood ring count. Relative residuals were roughly normally distributed. To be applicable in Bayesian modelling in dendrochronology analyses, detailed information on model errors has been provided.     

Comparing two methods for aging trees with suppressed,diffuse-porous rings (Betula pubescens ssp. czerepanovii)

The annual growth rings of diffuse porous species such as mountain birch are often difficult to distinguish when samples are collected from trees that grow at treeline or in other harsh environments. In this study we document the differences in seedling and sapling ring counts obtained from two methods of analysis: a traditional analysis based on reflected light and low-power microscopy and one based on transmitted light with higher power magnification that uses thin-sections of the samples. Rings are easier to resolve using the more labor-intensive transmitted light method. Small rings are often missed when using the reflected light method, resulting in an underestimation of tree age. The dates estimated by the standard method agreed with those determined using the thin-sectioning method in 9.6% of the cases. Most commonly, the standard method gave a younger age than did thin-sectioning (72.4% of the trees). In only 18.03% of the cases did the standard method result in a greater age than did thin-sectioning. The reflected light method produced age estimations that were on average 1.37 years younger than those determined using the transmitted light method. The difference between the two methods was positively correlated with age and negatively correlated with mean ring-width. Age-class histograms based on the two methods show little difference at coarser aggregation levels (decades and pentads), but annualized age-class histograms have less agreement between the two methods. Therefore, we suggest using the more labor-intensive thin-sectioning method when annualized age counts are necessary in suppressed seedlings and saplings, for example, comparing tree establishment with annual climate conditions at treeline.     

Ancient juniper trees growing on cliffs: toward a long Mediterranean tree-ring chronology

Juniperus phoenicea is a tree that can grow on vertical cliff faces in dry and warm Mediterranean climate conditions. These trees are adapted to extreme growing conditions where the main constraints are verticality, compact hard limestone, and low water supply. They respond to these constraints via various specific features and high longevity. The objective of this study is to confirm whether or not their tree-rings are annual in order to specify growth strategies and accurately date these trees. Trunk morphology, anatomical wood anomalies and radial growth were analyzed on 53 trees in the Ardèche canyon. Crossdating of the ring widths using traditional dendrochronological techniques was unsuccessful, so radiocarbon dating of tree pith was used to assess tree age, and wiggle-match dating was used to test for differences between number of rings counted and radiocarbon dates. Radiocarbon dates span the period 2520–685 BP. Minimal difference between radiocarbon dates and ring counts was apparently small—missing rings occur, but not in large numbers. Tree-ring formation is annual and radial growth is low, which creates stunted old trees. Such old living trees are uncommon in the Mediterranean basin, especially at low elevation. They can provide long tree-ring chronologies back to 792–524 cal BC. Results from the radiocarbon dating indicate that accurate annual dating of these rings may be possible by crossdating. J. phoenicea growing on cliffs offer a valuable model to better understand cliff population ecology and the functional responses of trees that can live in harsh environmental conditions.     

不同去趋势方法对树轮气候信号识别的影响

树木生长受到气候因子、随年龄增长的内在生长趋势、环境干扰和其他扰动信号的影响。目前存在不同的去趋势方法对树木年轮进行去趋势以识别树木生长中的气候信号。以往的研究多基于单个方法识别树轮气候信号,而不同去趋势方法识别的树轮气候信号可能会有一定的差别。为了对比不同去趋势方法对树轮气候信号识别的影响,我们基于国际年轮数据库网站获取中国西部地区68个点的树轮宽度数据,采用最常用的"signal-free"方法（SsfCrn）、线性和负指数函数法（std）、67%样条函数法（spline）、firedman方法、以及基于经验模式分解去趋势方法（EEMD）5种去趋势方法分别建立树轮年表,并对比分析同一地点的不同年表对气候响应的异同。结果表明：不同去趋势方法得到的年表对温度、降水以及相对湿度等气候因素的响应具有明显差异。其中,SsfCrn去趋势方法建立的年表对温度（月平均温、月最低温、月平均最低温）响应中相关最高的样点在所有样点中占比最高;EEMD去趋势方法建立的年表对降水量、相对湿度和月最高温响应中相关最高的样点在所有样点中占比最高;firedman去趋势方法建立的年表对月平均最高温响应中相关最高的样点在所有样点中占比最高。研究结果表明SsfCrn,EEMD和firedman方法在识别树轮气候信号方法具有一定的优势。在不同研究区域中,不同去趋势方法建立的年表对不同气候条件响应有差异,因此选择不同的去趋势方法识别树木生长趋势,分析哪种方法可以更好的反应气候变化对树木生长的影响显得尤为重要。     

Variations in pith eccentricity and ring width in teak (Tectona grandis L. F.)

Summary Wood samples were collected from a teak (Tectona grandis) plantation established in Gambari Forest Reserve (Dry Forest) near Ibadan in south-western Nigeria. Values of percentage pith eccentricity (PPE) of bole cross-sections were computed using appropriate geometrical methods. Also the growth rings of the cross-sections were identified and their widths measured. Pith eccentricity and ring width did not vary significantly between plots on the site. Variations in pith eccentricity and ring width between trees on plots were very highly significant (at 0.1% probability level). Pith eccentricity and ring width varied along tree boles: the effect of height above the ground was very highly significant in each case. On average, pith eccentricity was highest at the base and top of the merchantable bole. The magnitudes of variations in both pith eccentricity and ring width along the bole differed between the plots: plots x levels interaction effect was very highly significant in each case. A decrease in ring width corresponded with an increase in the age of the vascular cambium. Only small proportions of the variation in pith eccentricity could be estimated from concomitant variations in radial growth rate (ring width), bole form factor and crown depth; the values of r ² were 11%, 10% and 11% respectively.     

Age and growth determinations in the catfish, Chrysichthys nigrodigitatus (Lacépède) by use of the dorsal spine

Annual rings on the first dorsal spine were used to determine the age and growth of the catfish, Chrysichthys nigrodigitatus (Lacépède), in the Lagos Lagoon, Nigeria. From back-calculations, it was found that the mean total length ofthe species when the first annulus was formed was 18.5 cm, 32.6 cm for second annulus, 43.5 cm for the third annulus and 53.9 cm for the fourth annulus. It was shown that this species in the Lagos Lagoon attained four years of age and that the fastest growth in length was achieved during the first year of life. Thereafter, increase in length gradually decreased with age. The relationship between the body length and dorsal spine radius was shown to be linear and highly correlated.     

Ontogenetic wood anatomy of tree and subtree species of Nepalese Rhododendron (Ericaceae) and characterization of shrub species

Ontogenetic trends in the wood structure of Nepalese Rhododendron were studied in 15 specimens of two tree and four subtree species. Average growth ring width was constant from pith to bark in spite of occurrences of extremely narrow, false, or discontinuous rings. Vessel density, vessel area, vessel element length, and multiseriate ray height generally had an initial increase or decrease to 1.5 cm radius and near plateau or slight decrease or increase outward. Multiseriate ray density and area percentage were variable between specimens without a clear pattern. Ontogenetic trends from pith to fully mature wood in trees plus subtrees were inferred by treating the measurements in the present study with those of mature individuals in a previous study. Comparison of trends in trees plus subtrees and those in shrubs lead to ecological or systematic groupings. Vessel features showed that alpine shrub species have distinctly small, numerous vessels composed of short vessel elements. Multiseriate ray features indicated a systematic difference between the trees plus subtrees of subgenus Hymenanthes and the shrubs of subgenus Rhododendron. Vessel features of alpine shrubs may be an adaptation against frequent freeze-thaw cycles or the result of growth stress imposed by the severe alpine environment.     

The record of daily growth in otoliths of Atlantic silversides, Menidia menidia, from field and laboratory

Otoliths were removed from field-collected silversides of age less than 3 months. Otolith diameter was highly correlated with total length of the fish. Daily growth ring counts for this species are known to be a function of age rather than size, so widths for the daily growth rings provide a record of daily increases in length of the fish. Measurement of ring widths showed that weekly specific growth rate was greater than 70% at age 1 week, but declined to about 30% at age 1 month and about 15% at age 2 months. A laboratory experiment in which temperature was changed on a weekly basis demonstrated that environmental variables can affect the width of rings. Nevertheless, the growth rate of field-collected fish, as calculated from otolith ring widths, was more highly correlated with size of fish, as measured by otolith radius, than with the environmental variables of temperature, salinity and plankton abundance. Back-calculation of growth rates from otolith ring widths of five fish collected at the end of the growing season yielded the same age-growth curves as were obtained from 203 fish collected biweekly during the season.     

Assessing bias in diameter at breast height estimated from tree rings and its effects on basal area increment and biomass

Above-ground forest productivity can be reliably estimated from tree-ring width measurements. In doing so, annual growth is linked to the tree’s basal area increment (BAI), which is the change in cross-sectional area associated with each annual ring. When BAI is estimated from ring-width series, a value for the diameter of the tree is required. This diameter is ideally measured in the field, but can also be estimated as the sum of the annual ring widths. Tree biomass can also be estimated directly from the diameter estimates derived from tree-rings. Summing the ring widths, however, typically underestimates the tree’s true diameter. To evaluate this potential bias in diameter, we compared field-measured diameter and diameter estimated from the sum of the ring widths using tree-ring chronologies for seven common species in the eastern United States. We then evaluated the impacts of using the biased diameter estimates on derived BAI and biomass values. To simulate field-sampling error (i.e., failure to reach the pith when obtaining a core sample), we re-calculated BAI and biomass after removing a portion of the innermost rings from each tree. Comparisons of these various methods quantify the substantial and consistent underestimations in forest productivity estimates. To reduce the bias in diameter when using ring widths, we developed a regression model to adjust the diameter using core samples. This model is predicated on having some field-measured diameter values available at a site to calibrate and validate the model, but it can then be used to produce estimates at similar sites with similar species where no field-measured diameter values are available. Values of BAI and biomass derived from model-estimated diameter were more accurate at representing absolute growth than values produced by using the sum of the ring widths. Assessing the interannual variations in tree-growth is dependent on having metrics that accurately reflect the area and mass of wood produced. Our results suggest that published estimates of BAI and biomass using the sum of the ring widths to estimate diameter have substantially underestimated these productivity metrics. Our new procedure allows for more reliable estimates of productivity metrics that use diameter-at-breast height derived from tree rings.     

Xylem cell length under drought and its value for predicting radial growth of SRF poplar cultivars (Populus spp.)

Xylem cell length of juvenile tree rings was investigated in poplars in order to check the hypotheses that fiber length or vessel element length are indicative of drought tolerance and have predictive value for final stem base diameter at the end of rotation. The radial increment in the drought year 2003 served as the reference indicator for quantifying drought tolerance. All nine investigated cultivars suffered severely. In terms of their moderately decreased radial increment in 2003, the two aspen cultivars were clearly less drought susceptible than the seven hybrid poplar cultivars. The variance components of xylem cell length data explained by the two genetic factors ‘cultivar’ and ‘botanic section’ as well as the ‘tree ring’ (of the years 2002 and 2003) were compared by means of ANOVAs. The cultivar effects were superior to the effects of the critical precipitation status in 2003 and the botanic section. Fiber and vessel element length were found to be less sensitive to the drought compared with radial increment. They did neither correlate with radial increment in the drought year 2003 nor in 2002. Therefore, higher xylem cell length cannot indicate drought tolerance in poplars. However, a linear relationship between fiber length of both juvenile tree rings and the stem base diameter proved to be highly significant to a linear mixed effect model. Higher fiber length of a juvenile tree ring was considered to be predictive of larger stem base diameter at the end of rotation.