Among many other attributes, big monumental trees are of great symbolic and cultural significance, mainly in reference to their longevity. Their age is not always easy to establish, and the degree of accuracy of tree-age estimates can vary depending upon the previous available data on each tree species and upon the methods used. Some examples are the age estimates of the trees named General Sherman (Sequoiadendron giganteum (Lindl.) Buchholz) and Tule Tree (Taxodium mucronatum Ten.). The General Sherman is considered to be the tree with the largest amount of biomass on earth (83.8 m high and 31 m perimeter). Since the initial attempts, estimations of its age have varied: 3500 years (Douglass, 1946) or 2500 years (Hartesveldt et al., 1975); the most recent calculation places it between 1900 and 2400 years old (Stephenson, 2000). As for the Tule Tree, which has the longest trunk diameter in the world (14 m), estimates of its age have varied from 3000 years old, established in a study conducted in 1892, to the most recent estimates, which indicate an age of between 1400 and 1600 years old (Debreczy &Rácz, 1997). In the Mediterranean region, the olive tree (Olea europaea L.) have traditionally been considered a particularly long-lived species, in which millenarian trees are not uncommon. However, recent studies in the NE of Spain and in the Garden of Gethsemane (Jerusalem), have determined maximum ages between 700 and 900 years, respectively, for monumental trees of more than 8 m perimeter (Arnan et al., 2012; Bernabei, 2015).

In many species forming annual tree rings, the best tree-age estimate is based on the exact correspondence between each ring and the calendar year in which it was formed (Stokes & Smiley, 1968). Disks taken from dead monumental trees provide a complete tree-ring series if the wood is in good condition (Génova et al., 2017), but this technique does not usually apply to living trees, especially if them are valuable or protected specimens growing in parks and natural reserves (Rozas, 2003). The most habitual sampling technique therefore involves extracting increment cores and analyzing these by means of dendrochronological methods, because well-replicated chronologies perfectly estimate tree age (Stokes & Smiley, 1968; Fritts, 1976). Furthermore, evidence has shown that tree coring hardly affects conifer species (Grissino-Mayer, 2003).

Nevertheless, tree-age estimation based on dendrochronological analysis of increment cores presents limitations because the cores are frequently incomplete, and the number of missing rings is unknown. In many large trees, for example, the inner part is missing because the wood has rotted. However, even in cases where the central zone of the tree (the oldest wood) has disappeared or is poorly conserved, the age of an individual can be established with a certain degree of accuracy by means of the analysis of known tree-ring series (Norton et al., 1987; Stephenson, 2000; Rozas, 2003; Clark & Hallgren, 2004). These methods of estimation generally involve extrapolating the mean ring width (or the mean increment of the basal area) in order to estimate the number of rings missing as far as the pith (Norton et al., 1987), or using regression techniques to estimate the age based upon the diameter at breast height (DBH) (Rozas, 2003; Arnan et al., 2012). Both approaches present drawbacks that can give rise to lower accuracy in age estimation. For example, the use of mean values implies a hypothetical concentric radial tree-growth and the regression does not take into account the variability of individual growth patterns (Clark & Hallgren, 2004). Furthermore, tree-ring series from long-lived trees provide extensive records of information , which can be very useful because their annual resolution can enable reconstruction of past events (Arnan et al., 2012).

Juniperus thurifera L. (Spanish juniper) is a long-lived conifer species, endemic to the western Mediterranean region and growing under continental and cold climatic conditions; it is more abundant in North Central Spain and the High Atlas Mountains in Morocco (Costa et al., 1997;Gauquelin et al., 1999). Dendrochronological studies on Spanish juniper began in Spain with Alcalde & Génova (2006), Olano et al. (2008) and Rozas et al. (2008), and in recent years have multiplied and extended (Esper et al., 2015; Olano & Rozas, 2015). The oldest estimated age of a specimen in Morocco exceeds 500 (DeSoto et al., 2014); this age is lower in Spain (ca. 400 years old, DeSoto et al., 2012).

The Dehesa de Carrillo (Calatañazor, Soria, Spain) houses a unique forest of Juniperus thurifera traditionally used for grazing; in the year 2000 it was declared the “Sabinar de Calatañazor” Nature Reserve by the Castilla y León Regional Goverment. It is located at 1,000 m a.s.l. on mesozoic sands and conglomerates, and cretaceous limestones; it is characterized by a Mediterranean climate with a high degree of continentality. Amongst its most noteworthy values are monumental trees with perimeters that exceed 4 m and heights of up to 25 m (Alcalde & Génova, 2006).

The present research provides technical age-data to support Spanish juniper management and conservation measures in this Nature Reserve, in order to advance and consolidate previous efforts in this sense. To this end, we employed more better-quality increment cores and applied different methods to estimate tree ages. In addition, the discussion on the constraints and accuracy of each of the methods used can be of great use in future studies on the ages of many monumental trees. Lastly, establishing a well replicated local chronology, along with other long chronologies developed in the western Mediterranean, could be useful in reconstruction studies referring to management, past events and climate change (Olano et al., 2008; Camarero et al., 2014; DeSoto et al., 2014; Esper et al., 2015).

Field sampling and tree-ring data analysis

We selected 25 J. thurifera trees growing in the Dehesa de Carrillo (Calatañazor, Soria, Central Spain) with a large perimeter, a straight trunk without bifurcation and a healthy appearance, with the aim of obtaining dendrochronological samples that were as long as possible. All these trees were growing under similar ecological conditions and it is assumed that they were all traditionally pruned to provide young branches for cattle fodder. Two to four cores per tree at a height of 1.3 m were collected with a standard Pressler increment borer (40 cm) during the fieldwork in April 2004 and in July-October 2012 (Fig. 1). In each tree, the perimeter was measured at the same height at which the samples were taken. The cores were air dried and cut in transverse section until tree rings became clearly visible. Tree-ring widths were measuredat an accuracy of 1/100 mm with a LINTAB™ measuring device (Rinntech, Heidelberg, Germany). We measured 8,925 tree-ring widths from 65 tree-ring series.

The series of tree-ring widths measured were crossdated with the use of TSAPWin software and the COFECHA program facilities. Crossdating is a technique that ensures that each individual tree-ring is assigned its exact year of formation. TSAPWin software enables the treering series to be verified; it detects false, incomplete, or missing rings and eliminates possible errors in order to pinpoint the correct dated position in time (Rinn, 2003). COFECHA is a quality-control program for checking the crossdating and overall quality of tree-ring chronologies (Holmes, 1999). We employed these crossdating techniques to synchronize the tree-ring width series and elaborate a chronology for each tree.

Lastly, tree-ring widths were converted into indices by standardizing and detrending the raw data for each tree with the program ARSTAN (Cook & Holmes, 1996) to obtain a representative local chronology. Detrending enabled tree-ring widths to be transformed into dimensionless growth indexes by dividing measured ring-widthvalues by fitted values. Tree-ring width series were double-detrended, a negative exponential function was fitted, followed by a 30-year long spline, and a biweight robust mean was computed. To assess the reliable period of the chronology, we used the Expressed Population Signal (EPS); EPS values above 0.85 are a threshold widely used in dendrochronological analysis (Wigley et al., 1984).

Despite their healthy external appearance, numerous trees presented internal decay, and the samples obtained were therefore incomplete; in addition, some trees had a radius greater than the standard borer used (Table 1). Consequently, to establish tree ages we needed to estimate the tree-ring number in the missing portion. To this end, we used different statistical methods that are explained in the following section.

Tree-age estimation

Tree-age was calculated based on the estimated radius (ER), according to the perimeter value. Due to internal decay and a large perimeter in some trees, manycores were incomplete and there was therefore a missing tree-radius portion (MR) of variable length in each tree (Table 1). Consequently, we calculated tree-age (number of estimated tree-rings, ETR) by adding the maximum number of tree rings measured (TR) to the estimated number of missing tree-rings (MTR) in MR. As the length of the MR increases, there is a logical decrease in the accuracy of the age estimation (Norton et al., 1987; Ro-zas, 2003; Altman et al., 2016). In each tree, we evaluated the percentage of uncertainty presented by the samples obtained in relation to the estimated radius (ER), by means of:

In order to check the ETR calculation accuracy, we employed four different methods to estimate MTR, ta-king into account sample length (SL), TR and tree-ring width (TRW).

Method 1

Habitually, when estimating the number of missing rings in long-lived trees, the radial increment (TRW) or the increment of the basal area (BAI) are considered to be constant in each tree throughout time (Norton et al., 1987; Biondi & Qeadam, 2008). However, the tree-growth tendencies do not generally respond to this pattern, so that direct estimation based upon any of the-se hypotheses will generally give rise to bias in the estimations. Extrapolation of the TRW tends to overestimate the number of missing rings, whereas application of the constant BAI generally involves underestimation. To balance this over- and underestimation, which result from the common decrease in TRW and the increase in BAI as tree age increases, Altman et al. (2016) propose averaging the number of rings estimated with these two techniques. Besides they point out that the maximum error is less when this average TRW-BAI value is used than when using either of the two estimators separately. We emplo-yed this proposal, calculating MTR as the mean of these two estimates:

And, analogously, MTRBAI was obtained as the quotient between the Missing Basal Area (MBA) and the Mean Basal Area Increase (MBAI). MBAI represents the average of the increments in the basal area based on the tree rings present in the sample, i.e. the quotient between the estimated area of the section, presuming a shape of a circular crown, and the number of rings that it contains:

Method 2

In this method, we introduce a new way of estimating MTRTRW and TRWBAI, so far original, which consists of simultaneously obtaining, through an iterative process, the values of the number of missing rings and the ring widths that make up the series most similar to the actual data. In each step of the process, we considered one of the MTR possibilities (MTR= 1, 2, 3, etc.), and the tree-ring width value associated with each possibility, under the hypothesis of constant annual width increment:

This growth model was compared with the data referring to ring width (TRWk, ring width generated in the year k according to the previous hypothesis) by means of the sum of the squares of the differences between the corresponding TRW and TRWk values, i.e. based on the quadratic deviation (QD) between the model values and the measured values:

The value of MTR that minimises the sum of the squares was the estimation of the number of missing rings (MTRTRW).

Analogously, MTR was calculated under the hypothesis of constant annual increment of basal area. For each possible MTR value the corresponding BAI was obtained:

This value was used to calculate the TRWIk by means of the following expression:

Rk being the radius of the section in the year k.The estimation of MTRBAI was the value that minimises the sum of the squares (quadratic deviation):

All these estimation processes were made by algorithms designed with the mathematics software MAPLE (Maple, 2018).Finally, and following the same criterion as in method 1, the number of missing rings was calculated by means of:

Method 3

To calculate the tree-age, regression models are also used which relate the age to certain easy-to-measure da-sometric variables. These models are particularly useful when the tree cannot be sampled or the cores do not reach the pith or the internal wood is rotten (Clark & Hallgren, 2004). Among the most habitually used models are those that relate age with DBH (Rozas, 2003; Clark & Hall-gren, 2004; Arnan et al., 2012; Altman et al., 2016) with the available information, we fitted TR and SL data to a simple linear regression model. We used a regression line without intercept as recommended by some authors (Stephenson & Demetry, 1995; Rozas, 2003), in order for the model to ensure that a 0 radius corresponds to the 0 age. To estimate the model, we discarded all tree-ringseries exhibiting an anomalous growth pattern (outliers). We subsequently adapted the equation obtained to deter-mine the MTR in each tree based upon MR. The model was applied to the variable MR, and not to ER, in order to obtain the most reliable estimates, especially in the thicker trees.

Method 4

The tree-growth pattern usually presents two clearly differentiated stages: a juvenile one, in which the growth rate decreases linearly with age, and a mature period, more adjusted with the environment, and in which the growth rate is constant over time (Cook, 1985). This general pattern is the source of inspiration to propose a new estimation method, which consists of estimating the relationship (λ) between the average of the tree-ring width in the juvenile stage (MTRWJ) and in the mature stage (MTRWM), i.e.:

In our case study, λ was calculated as the average values in trees that provide sufficient information, without rot and that clearly show these two growth stages. λ was obtained, in each tree, as the maximum reached by the function f(x). This function has defined as the quotient between MTRW until reaching x (the ring-width average of the sample from the pith to x) and MTRW after x (the ring-width average of the sample from x to the bark), be-ing x the radius at the possible time of stage change. RCH (Radius at the time of growth CHange) corresponds to the value of x that maximizes relationship (the point at which the function f(x) reaches its maximum).

Having calculated RCH and λ for the population (as the mean of the individual values), we estimated MTR. MTRJ was the number of missing rings estima-ted for the juvenile stage (before the radius reaches RCH) and MTRM was the number of missing rings esti-mated for the mature stage (after the radius has reached RCH). MTR was estimated according to two possible situations (see Fig. 2):

a) Trees in which MR>RCH:

b) Trees in which :

Chronology of J. thurifera of the “Sabinar de Calatañazor” Nature Reserve

Most tree-ring width series were crossdated and synchronized, once determined an average of 0.02% mis-sing rings. However, depending on the intercorrelation values of the individual chronologies, we selected those that overcome the critical correlation (99% confidence level, 0.3281; see table 1) to elaborate a local chronology of the “Sabinar de Calatañazor”. This chronology ranges from 1738 to 2012 (275 years, Fig. 3) and the time span in that EPS>0.85 extends 1880-2000. It is the second longest Spanish juniper chronology on the Iberian Peninsula, being the first one from southeast Iberian System, ranged 1681 to 2010 and with EPS values exceeding 0.81 from the mid-eighteenth century (Esper et al., 2015).

Estimated tree-age

The percentage of uncertainty, which assesses the degree of lack of knowledge of the length of the missing radius, ranged from a minimum of 6.12% and a maximum of 77.43% for the samples analysed. It was greater than 20% in over three-quarters of the trees, and very close to or over 50% in more than half the trees (Table 1).

Table 2 shows the estimates furnished by means of the four methods used. Estimations of the number of missing rings by means of methods 1, 2 and 4 provided similar results. In both method 1 and method 2, the number of mis-sing tree rings estimated under the hypothesis of constant radial increment (MTRTRW) exceeds the number of mis-sing tree rings estimated under the hypothesis of constant basal area (MTRBAI), i.e. TA . The effect of calculating the mean of both estimates is shown in Fig. 4. The average estimate corresponds to another model, in which the raw data are located, in general, among tho-se corresponding to the models of constant TRW or BAI. This may not be the case when a tree shows abrupt changes in the growth trend (see Fig. 4-B).

In method 3, we have fitted a regression line relating age and radius to the available data, obtaining T SL= and adapting it to T = . The fitted model could likely be reliable, given its high coefficient of determination (R2=98.31%). However, the number of years estimated by this method generally exceeded that obtained by other methods (table 2), and it increased as MR becomes longer. As exception, the number of yearsestimated had lower than that estimated with other methods when the average ring-width was very narrow, as it happened with the outlier tree-ring series that were discarded for the estimation of the model (see Fig. 5). Fig. 5 and Table 3 show the confidence intervals for the prediction or for the mean of the age of each tree. Some predictions were based on values that lie outside the range of SL (8.130.7 cm), thus increasing the uncertainty of that results (see table 1).

The estimations of RCH and λ (method 4) were obtained from the samples providing sufficient information on the two growth stages considered (juvenile and mature), and in which the time of change from one phase to the other can clearly be determined. In our case study, only the ones displaying no rot meet these requirements (Table 1). Nevertheless, the ring series of trees 1377 (whichdoes not show a decrease in tree-ring width over time), 2367 (comparatively young), and 844 and 1623 (in which the value of RCH cannot be clearly calculated), could not be used; thus the dataset was limited to four trees (2257, 1318, 477, 1944, see Fig. 6). Both RCH and λ were estimated for each of the tree-ring series selected; results are shown in Table 4. In the calculation of individual RCH we did not consider values of x at the start or the end of the series when they generate maxima in the function f(x) that do not correspond with the radius at the time of growth change (see Fig. 6).

Taking as a reference the average of the tree-age estimates (Table 2), it can be said with great certainty that all the specimens are over 200 years old (except for specimen 2367). Almost half the trees are over 300 years old and another 25% are close to this age. Furthermore, 3 trees(1048, 1246 and 590) might be older than 400 years and one of them (1246) very likely exceeds 500 years; they all possess an estimated radius (ER) of over 35 cm. Many other trees, however, present an ER over 35 cm, with average ages estimated at between 275 and 381 years. It becomes increasingly speculative to establish age as the ER gets bigger, and the percentage of uncertainty approaches or surpasses 50%, but in general terms, trees with an ER over 30 cm can live up to, or around, 300 years in the study area.

Tree-age estimation according to the constant growth hypothesis

The hypotheses of constant TRW or BAI give rise to different models that attempt to resemble the raw data as closely as possible, each one from its approach. Calculating the mean of both values involves balancing, at least partially, the inaccuracy occurring in age estimation based upon the TRW (overestimation) or BAI (underestimation) methods. The accuracy of the estimate with the TRW-BAI method decreases with the increase in the longitude of the missing radius in a similar manner to that of the TRW and BAI methods, but the errors (both absolute and percentage) are clearly lower (Altman et al., 2016). Even when the missing radius represents over 50% of the radius (as in more than half the trees, our case study, Table 1), this averaged method appears to be recommendable because it compensates the estimations by excess and by defect.

As opposed to using partial increments in the estimation (TRW and BAI of the 5, 10, 20 or 50 innermost rings) employed by different authors (Norton et al., 1987; Rozas, 2003; Altman et al., 2016), we have used all the available width-data for each tree, in accordance with the recommendation proposed by Altman et al. (2016). Whenthe missing radius represents a very high percentage of the total radius, the innermost rings provide very partial information.

Estimations of the number of missing rings by means of methods 1 and 2 provided very similar results. However, the latter method proved to be more versatile. Whilst in the former method MTR is deduced from MTRW or from MBAI, in method 2 MTR and TRW act as a bi-dimensional value and are estimated jointly. Moreover, the least squares estimation endows the raw data with a more influential role in comparison with their mean values. Method 2 could even be conveniently adapted to incorporate other hypotheses (e.g., assuming a negative exponential growth model) and to contrast different results. An improvement of both methods would be obtained by using estimates based upon the weighted average of the MTRTRW and MTRBAI estimators, with different weights adapted to this or other species.

Tree-age estimation according to regression model

Stephenson (2000) successfully used regression models to estimate the number of missing rings in monumental Sequoiadendron giganteum, although this study was based upon a large set of complete samples of stumps of dated age. Moreover, Fraver et al. (2011) estimatedthe age by expressing the number of rings according to sampling height and to the width rate of the innermost rings. The relationship between age and size varies greatly according to the age of the tree and its environmental conditions, especially when the trees are bigger and older (Rozas 2003; Altman et al., 2013). For this reason, Rozas (2003) proposed the use of multiple predictive regression models if the age structure is discontinuous. The above-mentioned studies show that the performance of the regression models was enhanced when a relatively large number of tree-ring series reached or almost reached the pith and when other variables were included in the models. In our case study, we had samples of 25 monumental trees, even though only 20% of them approaching to the pith. However, further samples could not be obtained, be-cause the study area lies within a protected natural space. In addition, trees are part of a population subjected throughout its history to multiple managements. These conditions are far from the criteria that advise using regression models in estimating age. The increased uncertainty that this method implies makes the estimates obtained less re-liable. To improve this regression analysis for future studies, there is a need for further samples, as well as for data referring to other variables from nearby sites.

Tree-age estimation according to two growth stages

As only four trees are suitable with regard to developing the growth model in two stages, we analysed how this small sample size would affect to the values of RCH and λ in the estimation of ETR. Using the tree-ring series of the four trees selected, we calculated the value of λ corresponding to values of RCH between 90 and 250mm. These values are the minimum and the maximum selected as possible RCH for the four trees. We employed a step-size of 10 mm. For each RCH value, we established the rings before and after this RCH in each of the four trees. We calculated the average of the tree-ring width in these two groups and the quotient between the two averages. Finally, λ was obtained as the mean of the four values obtained for the quotient. On varying RCH the variation of λis determined to be less than 1 for the RCH range previously indicated and less than 0.2 when RCH varies between 90 and 150 mm (a more reasonable range of values for change in growth stage; see Fig. 7). In conclusion, modifications in the estimation of RCH have little effect on the estimation of λ.

However, the influence of RCH in the estimation of MTR can be relevant. We chose two cases presenting different values of RCH but with a similar value for their corresponding λ (RCH=90 mm and λ=2.2986; RCH=150 mm and λ=2.3015).

Both cases provide quite a different estimation of ETR in some trees; however, this is not very relevant on estimating the minimum age (see Table 5).

Application and reliability of the different methods

We employed different methods for estimating J. thurifera age, attempting to be as accurate as possible and evaluating the efficiency of each one. All the estimates were based on the geometric radius. Although we are aware that this assumption is inaccurate, this is less relevant than the uncertainties relating to the internal rot or the large perimeter of most of the monumental trees studied (Table 1).

The first two methods, which take into account the constant growth hypothesis, only require information on individual tree-ring series to estimate the age of the trees. They are easy to use and the estimates obtained provide relatively reliable tree ages, although we agree that the TRW-BAI averaged estimator is the most suitable for tree-age estimation (Altman et al., 2016). As additional advantages, method 1 requires little calculation, and method 2 could be adapted to other models, such as the negative exponential model.

The regression method (Method 3) uses the combined information on all the tree-ring series in order to makeestimations. This method requires many samples that are suitable for the conditions in which the tree-age estimation is to be conducted, and these are sometimes difficult or impossible to obtain. This requirement is mostly necessary for monumental trees; and when available samples are relatively scarce, as in our case study, this method proves to be the least reliable of them all.

The fourth method, based on tree growth stages, combines the previous two approaches: estimation of RCH and λ is conducted with the joint information that can be extracted from all the trees sampled, and this is applied to the individual information to estimate the age of each tree. In practice, it is the most difficult method to apply, because it also requires many and suitable samples (although not as many as in the regression method), as well as a greater number of calculations. However, this model is the one that best reflects the radial growth of the trees. The choice of λ as the maximum value of the quotient between mean tree-ring width before and after change in growth stages, makes this method more reliable with regard to estimating the age of the more long-lived or monumental trees. We think that this method would enable particularly reliable estimates to be made if the sampling were conducted in managed populations presenting homogeneous growth.

Many Spanish juniper trees in the “Sabinar de Calatañazor” Nature Reserve are estimated to be several hundred years old; almost half of the trees are over 300 years old and three of them might be older than 400 years. These estimations surpass the ages estimated in Alcalde & Génova (2006), but are more reliable due to the increase of the number of samples and the complexity and quality of the analysis carried out. Such long-lived J. thurifera trees have only previously known in three Spanish sites: Sigueruelo (Segovia), where DeSoto et al. (2012) indicate a maximum age of 413 years in a tree presenting a perimeter of 85.3 cm; Cabrejas del Pinar (Soria), where Olano et al. (2008) establish a maximum age of 350 years; andRoyuela (Teruel), whose chronology ranges from 1681 to 2010 (329 years) according to Esper et al., (2015). Howe-ver, in the other Spanish sites sampled this species does not surpass 200 years.

We provide dendrochronological data and tree-age estimates to support management and conservation mea-sures of Juniperus thurifera in the “Sabinar de Calatañazor” Nature Reserve. We have developed a new chrono-logy, with some of the longest-lived trees of this species in the centre of the Iberian Peninsula, ranging from 1738 to 2012.

We employed different methods to estimate tree age, attempting to overcome the main disadvantage arising from the unavailability of data: many trees presented high percentages of missing rings (over 50% of the tree radial growth) as a result of rot or of a large perimeter. Methods based on the mean of the estimations under the classical hypotheses of constant radial increment or constant basalarea, balance the bias of the estimations based on each of the hypotheses separately, thus giving rise to more reliable estimates. We have introduced a new estimation method, based upon the determination of two growth stages (juvenile and mature), an approach more coherent with the biological behaviour of tree growth. Its application in our case study has led to the detection of small differences with respect to the two previous methods. On the other hand, regression model has not been very reliable and it would have been necessary to have much more data to obtain more accurate results.

Our better estimates indicate that the J. thurifera trees in this Nature Reserve with radii greater than 30 cm are mostly over 300 years old; we also established the age of some trees as being over 400 years.

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