Many ways to die – partitioning tree mortality dynamics in a near-natural mixed deciduous forest


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  1. Partitioning of tree mortality into different modes of death allows the tracing and mechanistic modelling of individual key processes of forest dynamics each varying depending on site, species and individual risk factors. This, in turn, may improve long-term predictions of the development of old-growth forests.
  2. Six different individual tree mortality modes (uprooted and snapped (both with or without rot as a predisposing factor), standing dead and crushed by other trees) were analysed, and statistical models were derived for three tree species (European beech Fagus sylvatica, hornbeam Carpinus betulus and common ash Fraxinus excelsior) based on a repeated inventory of more than 13 000 trees in a 28 ha near-natural deciduous forest in Central Germany.
  3. The frequently described U-shaped curve of size-dependent mortality was observed in beech and hornbeam (but not ash) and could be explained by the joint operation of processes related to the six distinct mortality modes. The results for beech, the most abundant species, suggest that each mortality mode is prevalent in different life-history stages: small trees died mostly standing or being crushed, medium-sized trees had the highest chance of survival, and very large trees experienced increased rates of mortality, mainly by uprooting or snapping. Reduced growth as a predictor also played a role but only for standing dead, all other mortality modes showed no relationship to tree growth.
  4. Synthesis. Tree mortality can be partitioned into distinct processes, and species tend to differ in their susceptibility to one or more of them. This forms a fundamental basis for the understanding of forest dynamics in natural forests, and any mechanistic modelling of mortality in vegetation models could be improved by correctly addressing and formulating the various mortality processes.


Tree mortality is one of the key processes in forest dynamics (Franklin, Shugart & Harmon 1987; Runkle 2000; Chao et al. 2009). In unmanaged forests, it influences successional pathways and the composition of forest communities (Shugart 1987), creates gaps, the precondition for regeneration (Franklin, Shugart & Harmon 1987; Canham, Papaik & Latty 2001) and is an important driver of carbon cycling. This is because tree longevity determines the residence time of carbon and as a result the size of the carbon pool in forest biomass (Wirth & Lichstein 2009). Understanding and predicting tree mortality are therefore indispensable for modelling the dynamics, diversity and biogeochemistry of forest ecosystems (Purves & Pacala 2008). However, in contrast to tree growth, it is less well understood. There are a multitude of processes operating simultaneously that cause tree death, a fact that is reflected by the diversity of formulations in forest dynamic models (Hawkes 2000; Keane et al. 2001; Porté & Bartelink 2002; Hickler et al. 2012). The question of when and why trees eventually die is largely unsolved. Tree mortality appears to be context dependent and species specific, it is highly stochastic and one of the greatest challenges of forest ecology (Watkinson 1992; Hurst et al. 2011). Processes leading to a tree's death comprise of lethal damage through disturbances or infestations and gradual decline in vigour by accumulated stress (Franklin, Shugart & Harmon 1987). Understanding and quantifying these various processes are important to attribute correctly causes of tree mortality and are expected to improve vegetation models significantly (Keane et al. 2001). Old-tree mortality is usually modelled simplistically in forest dynamic models, its rate being derived from reported maximum ages without any mechanistic considerations (Hawkes 2000; Keane et al. 2001; Porté & Bartelink 2002; Lutz & Halpern 2006).

A comprehensive mechanistic understanding of individual tree mortality needs to first disentangle and categorize the different causes or modes of mortality (Larson & Franklin 2010). Among exogenous causes are wind-throw (Canham, Papaik & Latty 2001), crushing by other trees (Larson & Franklin 2010), fire (Franklin, Shugart & Harmon 1987) and biotic attacks on trees (Cherubini et al. 2002). Many studies address stress due to competition or water deficiency, which reduces tree vitality and thus results in a critical lack of resources (Peet & Christensen 1987; Wunder et al. 2007; Allen et al. 2010). It is debated whether trees lose vitality with age (Franklin, Shugart & Harmon 1987; Watkinson 1992; Lanner 2002; reviews: Petit & Hampe 2006; Kutsch et al. 2009). Whilst the concept of senescence (understood as an endogenously controlled process, sensu Watkinson 1992) does not apply to the longest-living tree species (Pinus longaeva D. K. Bailey, Lanner & Connor 2001), it is not clear whether, and to what degree, it applies to other shorter-lived tree species (Schweingruber & Wirth 2009). Researchers generally agree that the age of a tree is not a good predictor of mortality, because the meristem remains young (Franklin, Shugart & Harmon 1987; Mencuccini et al. 2005) and deleterious mutation rates are very low in trees (Peñuelas 2005; Petit & Hampe 2006). Instead, with increasing tree size, transport problems through the increasing complexity of the vascular transport system may arise (hydraulic limitation hypothesis) (Ryan, Phillips & Bond 2006), and the risk of wind-related damages rapidly increases as does the chance of infection by destabilizing or potentially lethal pathogens through the breakage of large, long branches and hence the accumulation of wounds (Franklin, Shugart & Harmon 1987; Canham, Papaik & Latty 2001; Dhôte 2005; Schulze et al. 2009; Larson & Franklin 2010).

Recent studies that have modelled the general patterns of mortality for different temperate tree species in different regions and sites confirmed the general assumptions that survival rates are higher with increased growth, reduced competition and increased size (e.g. Fridman & Ståhl 2001; Bigler & Bugmann 2003; Wunder et al. 2007; Das et al. 2008; Lines, Coomes & Purves 2010). However, survival rates have been shown to decline again in very large trees (Monserud & Sterba 1999; Yao, Titus & MacDonald 2001; Lines, Coomes & Purves 2010), which hints at different underlying mortality causes for larger trees when compared with smaller trees. To explicitly model the process of old-tree mortality, very large inventories are needed that include larger trees and also a sufficient number of mortality events in this size class. Moreover, it is necessary to record the circumstances of death for each tree, even though determining the cause might entail a great degree of uncertainty (Fridman & Ståhl 2001; de Toledo et al. 2012). Because of this, as an observable surrogate the mode of mortality, which can ‘indicate the most probable agent of mortality’ (de Toledo et al. 2012), is frequently used to get a hold on the different mortality processes (Chao et al. 2009; Larson & Franklin 2010). In contrast, a precise attribution of a proximate cause needs thorough observations and short inventory periods, which are rarely achieved (Lutz & Halpern 2006; van Mantgem & Stephenson 2007).

In this study, we analysed a large data set of deciduous trees (90% beech) in a near-natural stand, covering a large range of sizes and including several very large trees with a diameter at breast height (d.b.h.) of up to 126 cm. Mortality modes were assessed, and we used this information to (i) model different modes of tree mortality embracing the whole life history of trees from sapling to gapmaker, (ii) provide a mechanistic interpretation helping to improve mortality algorithms in forest succession models and (iii) compare species survival rates across gradients of tree size to infer aspects of life-history strategies. Moreover, we present a solution for dealing with different measurement methods for live and dead trees, and with negative growth measurements, which present a notorious problem in all inventory-based studies. Unlike other studies that either kept (Yao, Titus & MacDonald 2001) or even omitted negative values from the data set (Wunder et al. 2007, 2008), we estimated and included measurement errors in the model framework.

The objective of this study was to partition mortality patterns of three deciduous tree species into different proximate (observable) processes and to assess the implications of this on mechanistic modelling efforts. We thus addressed the following questions: (i) How do individual tree characteristics explain the mortality of the different modes? (ii) how and to what degree can overall mortality be partitioned into by the different mortality modes? (iii) how do the mortality rates of the different species compare to each other and what specific demographic traits can be inferred from the patterns? and (iv) can we derive estimates of longevity or any other practical measure from survival scenarios based on mortality models that could be useful for mechanistic models of forest dynamics?

Materials and methods

Study Site and Inventory Data

The study was conducted in a 28.5 ha plot of mature deciduous forest (‘Weberstedter Holz’; trees aged 1–> 250 years), located in the Hainich National Park (51°06′ N, 10°31′ E), Thuringia, Germany. The National Park is part of Germany's largest continuous deciduous forest (Hainich) and is listed as a UNESCO World Heritage site. The climate is suboceanic/subcontinental, long-term annual means are as follows: 7.5–8 °C air temperature and 750–800 mm precipitation (Knohl et al. 2003). Altitude is approximately 350 m a.s.l. with a gentle north facing slope (inclination 2–3°). The soil type at the study plot is a Luvisol developed from loess over limestone. The stand was managed as coppice-with-standards until about 1900, after which it was gradually transformed into a beech selection forest. Harvesting was reduced again in 1965, when it became part of a military training ground and ceased completely in 1997, when it was included in the core zone of the National Park (Mund 2004; Butler-Manning 2007). The main tree species in the plot were beech (Fagus sylvatica L.), ash (Fraxinus excelsior L.), hornbeam (Carpinus betulus L.), sycamore (Acer pseudoplatanus L.) and wych elm (Ulmus glabra Huds.) (Table 1).

Table 1. Inventory data of the plot (total area 28.5 ha) in 1999, in 2007 and of trees that died in this period: number of stems, basal area per hectare (BA). Respective percentages in parentheses
TreesBA (m2 ha−1)TreesBA (m2 ha−1)TreesBA (m2 ha−1)
Ash564 (4)6.1 (17)528 (4)6.6 (18)39 (2)0.26 (14))
Beech13297 (90)24.3 (68)12197 (90)25.5 (69)1535 (92)1.02 (55)
Wych Elm70 (0)0.6 (2)39 (0)0.3 (1)35 (2)0.33 (18)
Hornbeam391 (3)1.6 (5)361 (3)1.6 (4)30 (2)0.10 (5)
Sycamore322 (2)2.6 (7)345 (3)2.7 (7)14 (1)0.08 (4)
Other82 (1)0.6 (2)82 (1)0.6 (2)10 (1)0.06 (3)
Total14726 (100)35.9 (100)13552 (100)37.2 (100)1663 (100)1.85 (100)

All trees on the plot with a diameter at breast height (d.b.h.) ≥ 1 cm were recorded in the summer of 1999. The tree parameters measured were as follows: coordinates of the trunk base, species, d.b.h. and status (live or dead) (Table 1). Trees were resampled in the summer 2007. Later inspection of the inventory data revealed that 27 trees were missing without any idea of their status. We assumed them to be missing at random with respect to mortality. Dead trees were defined as being physiologically dead or likely to die within a few months because of being uprooted completely or because the crown had been completely destroyed (Table S2-1,S2-2 in Supporting Information). Mortality modes were recorded (Table S1), as either: standing dead and fallen dead further distinguished into: uprooted, snapped and crushed by other trees. Where for uprooting and snapping, wood or root rot as predisposing factor (Larson & Franklin 2010) was also recorded, when the wood at the breaking point was degraded and the break was not in splinters but rather an even brittle fracture and also fruiting bodies [typically tinder fungus, Fomes fomentarius (L.) Kickx, red banded polypore, Fomitopsis pinicola (Sw.) P. Karst.] were present. The differentiation and respective identification followed Kahl (2008). Trees that disappeared were identified as dead but with an unknown mode of mortality. Clear evidence of insect attacks could not be obtained, and therefore, the importance of insects as a proximate cause of mortality remains unknown. Also, for a random subsample of dead trees (n = 620, 37% of all dead trees), wood cores (sample dimensions ca. 4 × 5–25 mm) were taken during the inventory of 2007 with an increment puncher (Table S3).

To estimate the longevity of beech and the relationship between d.b.h. and tree age, we used 90 stem discs (d.b.h.: 0.6–107 cm, age: 5–285 years; D. Hessenmöller and E.-D. Schulze, unpubl. data; Mund 2004; contributing 45 stem discs each). These trees came from stands in the vicinity of the plot that were managed as selection forests or not managed at all.

Mortality Model

We modelled annual mortality probabilities (pannual) for each mortality mode (i), except unknown mortality, using logistic regression (eqn 1):

display math(eqn 1)

where X is the design matrix of the linear predictors and β the respective parameter vector. The annual probability was scaled to the inventory interval of 8 years (eqn 2).

display math(eqn 2)

The scaled probability (p) was used as predictor for the observations (eqn 3).

display math(eqn 3)

The different mortality modes are mutually exclusive, and hence, the modelled respective probabilities should add up to a total mortality probability. Accordingly, we also modelled total mortality with the summed probabilities (eqn 4)

display math(eqn 4)

where i = 1…n indicates the different mortality modes. This ensures coherence and acts as a surrogate to a multinomial distribution, which we could not use because of missing values contained in the data (known mortality but unknown mode).

We fitted the logistic regression models combined in one model frame and independently for each of the three most abundant species. As explanatory variables, we used d.b.h. as proxy for tree size. As a proxy for tree growth, we estimated diameter increment (dincest, see below) and relative diameter increment (reldincest). Also, log-transformations (with varying additive constants to allow for different curvatures) of the variables and interactions between the explanatory variables were tested. We did not use basal area increment or relative basal area increment (such as Wunder et al. 2008), because the first would be strongly correlated to d.b.h. and the latter to reldincest, both for purely mathematical reasons. Only one growth variable (either dinc or reldinc) was used in the models. If the relationship between mortality and d.b.h. indicated a U-shape, we split eqn (eqn 1) into two models (labelled ‘early’ if decreasing with d.b.h. and ‘late’ if increasing with size) and added the resulting probabilities. To plot mortality estimates against d.b.h., where growth was also a predictor, we applied a simple model to estimate dincest with d.b.h. (see eqn S12 in Appendix S1).

We estimated total mortality by combining all the models representing the separate modes. We used plots of observed mortality versus the predictors to set up candidate models and then the Deviance Information Criterion (DIC) as selection criterion. We simultaneously modelled the uncertainty of the measurements (d.b.h. and dincobs), imputed the missing values and estimated dincest with a sub model (eqns 5 and 6, see below). As goodness of fit, we calculated the area under the curve of the receiver operating characteristic (AUC). Values of 0.6–0.7 are commonly regarded as average, between 0.7 and 0.8 as good and above 0.8 as excellent (Hurst et al. 2011).

To assess the influence of modelling different mortality modes on the estimate of total mortality, we contrasted our approach with a simple ‘no-modes’ model that allowed for a similar curvature and used the same predictors (d.b.h. (transformed or untransformed) and growth).

Estimation and Errors of Tree Growth

Tree growth measurements in this study came from two different sources: repeated d.b.h. measurements for live trees and sampling of dead trees with an increment puncher. Additionally, growth of nonsampled dead trees was imputed with auxiliary data. To make these values commensurable and to incorporate the respective uncertainties, we estimated growth (dincest) independently for each species with eqns 5 and 6:

display math(eqn 5)
display math(eqn 6)

where dincobs is the observed diameter increment (dinc) in both live and dead trees, dincest is the estimated true dinc and the measurement error is σN, which could either be the measurement error of live or dead trees, or zero for trees with missing increment measurements. In eqn (eqn 6), the mean (dincpred) and variance (math formula) were derived from predictive models, which, together with the respective errors (σN), are further explained in Appendix S1. An additive constant (a) was introduced to set a threshold at half the minimum observed growth of wood cores from this study (0.05 mm a−1). To assess the usefulness of this approach, we also tested a simplified mortality model for beech, here referred to as the ‘simple-growth model’. In this model, we used the original growth values (dincobs) without considering the measurement errors and missing values were imputed with an ordinary linear model (see Appendix S1).

Longevity and Lifetime Mortality of Beech

To derive general estimates of beech longevity, we needed to relate mortality rates to tree age. To estimate tree age from the d.b.h. values for beech, we modelled the relationship between d.b.h. and age with eqn (eqn 7) using the free parameters α1–α4 (data points, fitted curve, parameter estimates and additional information in Fig. S1)

display math(eqn 7)

(eqn 7) was chosen to find a form that fitted the data well and that could also be extrapolated to ages greater than those observed with reasonable estimates. We used the estimates (including the uncertainties) of d.b.h. and the simultaneously available annual growth estimations (dinc) per age as input for the mortality model of beech. We then ran survival scenarios (as cumulative products of the annual survival rates) with different combinations of mortality modes and thus derived estimations of tree longevity under various circumstances, starting with trees with a d.b.h. of 0 (height = 1.30 m). We contrasted our results for beech with mortality processes in the model of Wirth & Lichstein (2009), referred to as ‘W&L’, as well as with whole-patch mortality in the vegetation model LPJ–GUESS (Smith, Prentice & Sykes 2001; Hickler et al. 2012). In W&L, self-thinning is related to biomass production and whole-patch mortality to longevity and remains constant over the lifetime, whilst whole-patch mortality in LPJ–GUESS is also derived from longevity but increases with age.

For the first approach, we modelled a height to age relationship using data from Mund (2004). However, to make it comparable with our study, we allowed mortality to start at an age of 15 years, at which age we assume that saplings have reached a height of 1.30 m. Longevity is defined in both approaches as the age at which 1% of the initial population survived and we followed this definition here. In both approaches, we fixed longevity at 300 years (Felbermeier & Mosandl 2002; this study).

We used WinBUGS (Gilks, Thomas & Spiegelhalter 1994), the R-Program (R Development Core Team 2011) and the R packages ‘R2WinBUGS’ (Sturtz, Ligges & Gelman 2005) and ‘ROCR’ (Sing et al. 2009) for Bayesian and conventional analysis. Simulations in WinBUGS were run with two chains until convergence, which we assumed when the Gelman–Rubin statistic was below 1.1 for all estimated nodes. To speed up convergence and reduce correlations of parameter estimates, variables used as predictors in the Bayesian analysis were rescaled to a mean of 0 and a variance of 1, where possible. For all stochastic nodes, we used uninformative (flat) priors if not stated otherwise. When additive constants for a log-transformation needed to be estimated, they were set to a fixed value in the final model, so as not to add to the uncertainty of the parameter estimates.


In the period of 8 years between the two inventories, at least 1663 trees died, with 27 trees of unknown status (Table 1). This translates into an annualized mortality rate of 1.5% in absolute numbers and 0.66% of the basal area. The majority of trees died standing (61% of all trees), they were generally small but also included larger trees up to a d.b.h. of 90 cm. Uprooting and snapping, with and without rot, affected only few and mainly large and very large trees. Crushing was a common cause of mortality for smaller trees (165 trees), but also a few large trees were crushed. Unknown mortality, that is, trees that had disappeared, was most common in smaller trees. In terms of the basal area, standing dead accounted for 36% of the dead trees basal area, uprooting with rot and without rot for 8% and 23%, respectively, snapping with rot and without rot for 17% and 7%, respectively (Table S2-1 and Fig. S2).

With respect to growth, trees that died standing grew somewhat slower than trees that survived and no obvious difference was found between crushed and surviving trees. Growth of trees that were uprooted or snapped, irrespective of predisposing rot, was generally higher than that of surviving trees, which was mainly a size effect. The different distributions of the predictors (Fig. S2) corroborate the usage of separate models for each mortality mode.

Modelling of Mortality

According to the lowest DIC (summed up for all mortality submodels) and parameter significance, we chose the models in Table 2 for further consideration and reported the respective parameter estimates and model fits (AUC). Details of all candidate models are reported in Table S4.

Table 2. AUC, deviance information criterion (DIC) and mean parameter estimates (standard error, SE) from posterior distributions for best mortality models and, as a contrast, for ‘no-modes’ models. Parameter estimates refer to predictors on the original scale (no normalization); int. = intercept; additive constants c1 to c5 were assigned constant values: 1, 8, 16, 20 and 40 (cm), respectively
Model AUCDICExplanatory variablesParameter estimates: median (95% CI)



Total         Early



int., log(d.b.h. + c 2 ), dinc est

int., d.b.h.

1.8 (1.2, 2.5) −2.1 (−2.4, −1.9) −1.4 (−2.4, −0.45)

−8.9 (−10.0, −7.8) 0.052 (0.035, 0.072)


Standing   Early



int., log(d.b.h. + c 3 ), dinc est

int., log(d.b.h. + c 5 )

5.9 (5.1, 6.7) −3.2 (−3.5, −2.9) −1.8 (−2.7, −1.0)

−42 (−57, −21) 7.3 (2.9, 11)

Uprooted0.89450.0 int., log(d.b.h. + c 4 ) −17 (−20, −14) 2.4 (1.7, 3.1)
Uprooted and rot0.68161.0int., d.b.h.−9.9 (−11, −9.0) 0.029 (0.0044, 0.051)
Snapped0.81168.0int., d.b.h.−10 (−11, −9.2) 0.039 (0.018, 0.059)
Snapped and rot0.75208.7int., d.b.h.−11 (−12, −10) 0.062 (0.047, 0.079)
Crushed0.691665.9 int., log(d.b.h. + c 1 ) −3.7 (−4.1, −3.2) −1.2 (−1.4, −1.0)
AshTotal0.71241.2 int., log(d.b.h.) 1.3 (−0.20, 2.8) −1.6 (−2.0, −1.2)
AshStanding0.8492.7 int., log(d.b.h.) 3.1 (1.7, 4.5) −2.4 (−3.0, −2.0)
Uprooted58.8int.−6.8 (−7.7, −6.1)
Uprooted and rot77.2int.−6.5 (−7.3, −5.8)
Snapped39.3int.−7.3 (−8.7, −6.4)
Snapped and rot49.5int.−7.0 (−8.2, −6.2)
Crushed16.3int.−8.6 (−11, −7.1)
HornbeamTotal0.66208.4int., d.b.h.−0.083 (−3.3, 2.9) −1.2 (−1.9, −0.37)
HornbeamStanding0.82119.6int., d.b.h.4.0 (0.71, 7.0) −2.4 (−3.3, −1.5)
Uprooted0.7752.4 int., log(d.b.h.) −11 (−16, −6.7) 0.10 (0.0081, 0.21)
Uprooted and rot15.5int.−8.3 (−11, −6.8)
Snapped15.5int.−8.3 (−11, −6.7)
Snapped and rot37.0int.−7.1 (−8.5, −6.1)
Crushed37.2int.−7.0 (−8.8, −6.1)


For all mortality modes, d.b.h. proved to be a valid predictor, whilst standing dead trees were also affected by growth rates. For uprooting and snapping, we predicted a strong increase in susceptibility with tree size, whilst uprooting remained constantly important and snapping with rot became the most important mode at d.b.h. > 80 cm (Fig. 1, Table 2). The risk of being crushed by other trees decreased considerably with increasing size. Standing dead was estimated to be the most prevalent mode in small trees and to rapidly decrease with size but also to increase again for very large trees (Fig. 1). Standing dead trees showed, as the only mode, a relationship with reduced growth (Fig. 2). Absolute growth (dincest) proved to be a slightly better predictor than relative growth (reldincest). No significant interaction between size and growth was found (Fig. 2, Table S4). The contrasting ‘simple-growth’ model, which did not estimate dincest but used the unaltered values and did not account for measurement errors, had an equally good fit (Table S4). The effect size for dincobs, however, was slightly smaller and less certain than for dincest (parameter means: −1.8 versus −1.4, Table S4).

Figure 1.

Modelled annual mortality logits and probabilities over d.b.h. (cm) for beech. Thick lines: median estimates, thin lines and shaded area: 95% credible interval. For standing and total mortality, a modelled growth for the respective d.b.h. was assumed (dincest ~ d.b.h., cf. eqn S12)

Figure 2.

Modelled annual standing dead probabilities [iso-lines, (%)] overlaying modelled annual growth (dincest) (cm a−1) over d.b.h. (cm), both axes on log-scale. Symbols mark individual trees with black open triangles: dead (standing mortality) and grey dots: live or other mortality modes. Light grey dashed line: simple fit of dincest over d.b.h. (eqn S12).

Total mortality assumed the form of the well-known U-shaped curve (Fig. 1): very small trees had a high risk of mortality, which would also be increased by lesser growth (Fig. 2). Trees of intermediate size (d.b.h. 30–50 cm) had the least risk of dying, whilst very large trees with a d.b.h. > 60 cm had an increased mortality risk, with all mortality modes except crushing being relevant here. The simple ‘no-modes’ model, that lumped together all mortality modes and allowed for a flexible curvature, rendered a similar curve, with a slightly worse model fit (AUC 0.72 versus 0.73, Table 2). However, it had a higher prediction uncertainty across the whole range of d.b.h., especially for very large trees (Fig. S3), and a weaker and less certain parameter estimate for growth (Table 2).

Other Species

The small sample size of ash and hornbeam restricted model complexity. Only d.b.h. was found to be a significant predictor of standing and total mortality (Table 2 and Fig. 3). Growth did not show any sign of having an effect on the mortality risk (Table 2). For hornbeam, a significant influence of d.b.h. on uprooting was found. The standing mortality rates of ash and hornbeam were estimated to be relatively high, even at the intermediate d.b.h. range (30–50 cm). Only above this range, they were as low as or lower than beech. Other than that, uprooting and snapping only played minor roles and crushing was nearly irrelevant (Table 2). The picture changed slightly for total mortality rates. Here, ash maintained low mortality rates at larger d.b.h. ranges (> 60 cm), whilst for beech and hornbeam, a significant rise with increasing d.b.h. was found.

Figure 3.

Modelled annual total mortality logits and probabilities over d.b.h. (cm) for three species. For beech, a modelled growth for the respective d.b.h. was assumed (cf. eqn S12). Thick lines: median estimates, thin lines and shaded area: 95% credible interval.

Longevity and Lifetime Mortality of Beech

The age to d.b.h. relationship and the respective model are displayed in Fig. S1. The extrapolation appears reasonable and was thus considered usable for further analysis. Although, because we did not have additional data of comparable stands to support the extrapolation beyond the maximum observed age of 285 years, any inference should be treated with caution.

Depending on the mortality mode, different survival curves (Fig. 4) and thus different estimates of longevity were obtained from the survival scenarios. The early occurring tree deaths (crushing and early part of standing dead) would not suffice to kill a population (no estimated longevity). The later occurring mortality (uprooting, snapping and the later part of standing dead) resulted in an estimated longevity of 405 (95% CI: 337–500) years. For total mortality, a longevity of 379 (319–464) years was estimated. Longevities derived from the modelling approaches were much lower (Fig. 4). However, this is rather trivial because of the predefined input parameter (longevity = 300 years). With regard to the form of the survival curves, applying the self-thinning mortality of Wirth & Lichstein (2009) lead to a similar curve as the early mortality in our model. Whole-patch mortality as compared to late mortality of our model showed a quicker and stronger onset, whilst it was weaker in later stages. LPJ–GUESS whole-patch mortality closely mimicked the modelled curvature of late mortality (Fig. 4).

Figure 4.

Survival proportions with different scenarios for beech. Assumed 100% at a height of 1.30 m, which is equivalent to a d.b.h. of 0 cm. The scenarios referring to results from this study are as follows: late (uprooting, snapping and the later part of standing dead), early (crushing and early part of standing dead) and total. Proportion of the population surviving at a given age when applying different or all mortality modes (scenarios) and for three approaches: data-driven models of this study and two mechanistic models (see text). Thick lines: median estimates, thin lines and shaded area: 95% credible interval. The y-axis is root transformed. The 1% level, which serves as a threshold to define longevity, is marked with a horizontal line. Bold ticks at the bottom mark median estimates of longevity, thin lines the respective 95% credible interval.


In our study, we were able to disentangle the frequently described U-form of the size (and also age) dependency of mortality, often just taken for granted (Rüger et al. 2011), as the joint product of different mechanisms related to six distinct mortality modes. As our results for beech indicated, the modes occurred at different life-history stages of the trees. Standing mortality and crushing were important mainly in young and small trees, whereas uprooting and snapping, and to some degree also standing mortality, occurred in late and very late stages. We have demonstrated clearly that mechanistic modelling of mortality across all life stages of a tree very much relies on knowledge of the mode of each mortality event, to which the proximate cause is closely linked (van Mantgem & Stephenson 2007; Larson & Franklin 2010), and that the assumption of constant mortality rates, which is often applied in forest dynamic models (Keane et al. 2001), is too simplistic. Nonetheless, the absolute rates of mortality and the relative importance of the modes are highly species and site specific and may also be shifted by singular events (such as the heat wave in 2003).

We found that tree size (diameter at breast height, d.b.h.) explained a large part of the mortality patterns observed. Growth was a significant predictor of standing dead in beech trees, which suggests that mortality in these trees was caused, inter alia, by stress, be it induced by competition or pathogens, which are hard to disentangle because of the strong interdependence (van Mantgem & Stephenson 2007; Larson & Franklin 2010). We assume that growth was also important for the other species, but the data were too sparse and the uncertainty of the growth estimates too large, to detect an effect. Lowest growth rates were observed in small and presumably shaded trees that may struggle to maintain a positive carbon balance. This contributes to the high mortality observed in small trees. Major sources of uncertainty relating to the influence of growth on mortality were the measuring methods and the estimation of a large proportion of data, as explained in the 'Materials and methods' section, and the averaging of growth over 8 years. This period might be too long and dilute any signal of stress as it may take < 8 years for a tree to die from stress (Bigler & Bugmann 2003). The effect size of growth on standing mortality was to some extent larger and also less uncertain when compared to the ‘simple-growth’ model, which is less informative because of not accounting for the different methods of measurement and for errors. However, we admit a more refined and less uncertain information on growth could be hoped for.

Partitioning Total Mortality

In the case of beech and hornbeam, the total mortality rate assumed a U-shaped curve against d.b.h. and we could trace back this emergent pattern to six distinct and presumably differently caused mortality modes. This shape was already found by Monserud & Sterba (1999, for Norway spruce) and others (Yao, Titus & MacDonald 2001; Smith, Rizzo & North 2005; Temesgen & Mitchell 2005; Lines, Coomes & Purves 2010; Hurst et al. 2011) and hypothesized by Franklin, Shugart & Harmon (1987). However, these studies could not relate the shape of the curve to different mortality causes or modes, and in some species, mortality rates may level off with increasing size (Petit & Hampe 2006). The use of mortality causes or modes in detailed and mechanistic approaches has been extensively discussed (e.g. Franklin, Shugart & Harmon 1987; Fridman & Ståhl 2001) and more recently been applied (e.g. van Mantgem & Stephenson 2007; Chao et al. 2009; Larson & Franklin 2010). However, there is an apparent lack of ascribing the lifetime mortality regime (the U-shape) to various underlying processes, which we attempted with this study. Although the mortality modes used here are rather descriptive, they certainly point to different proximate causes (Larson & Franklin 2010).

Total mortality dynamics could be modelled with the ‘no-modes’ model without strongly reducing the model fit, this being just a matter of curve fitting. However, we got less certain parameter estimates, mainly for the influence of growth, which was relevant only for one mortality mode in the full model. We also acknowledge potential errors in the attribution of the mortality modes. Of all variables, this is arguably the most subjective and relies on the experience and diligence of the surveyors. In this study, we could not quantify or incorporate the degree of uncertainty of this parameter but recommend that it be considered during the inventory and analysis of future studies and that census intervals be as short as possible to better identify modes or proximate causes of death.

Possible underlying processes of the modes could be an interrelated network of competition, lethal and nonlethal pathogens for standing dead, mainly wind for uprooting and snapping without signs of rot, lethal pathogens (rot fungi) in combination with wind, for uprooting and snapping with rot, whilst the incidence of lethal pathogens can be preceded by competition and other pathogenic stress. Crushing by other trees can be seen as mode and proximate cause at the same time.

How Do Species Compare

Considering tree size as a proxy for tree age, we compare total and standing mortality rates across the life history of the three modelled species. Total mortality rates were similar at the lower d.b.h. ranges for ash and hornbeam and higher than that of beech. This pattern changed in large and very large trees: mortality rates increased in beech and hornbeam, whilst it remained low with no apparent increase in ash.

We expect that, at some point, the mortality rates for ash would increase with size, as their susceptibility to pathogens and wind-throw naturally increases. However, with the available data, we could not identify an increase and conclude that it is small in the observed range of d.b.h. and only is significant at larger d.b.h.. Susceptibility to wind-throw depends a great deal on tree size (height, crown exposed area), tree species, site characteristics (rooting depth, exposition) and canopy roughness (Canham, Papaik & Latty 2001; Dhôte 2005; Albrecht et al. 2012). In the stand, beech and ash were the tallest trees with maximum heights of 40 m and above and hornbeam the shortest, reaching around 33 m (Butler-Manning 2007). In winter, beech has a denser crown compared to ash (they have larger leaves; Corner's rule). Its wood is less flexible, and its rooting patterns may be shallower than ash (Felbermeier & Mosandl 2002; Roloff & Pietzarka 1997). Yet, these facts do not wholly explain that only beech and hornbeam had increasing mortality rates with increasing size. Of all the tree species, mortality with predisposing rot was only relevant in beech. Fuentes Perivancich (2010) found that fungal fruiting bodies were more common in larger beech trees (d.b.h. > 40 cm) and of infected trees about three quarters died in a period of 10 years. Although fungal pathogens, which are potentially lethal for all the three species, were present in the stand, beech suffered the most. Tinder fungus (F. fomentarius), an important mortality agent, commonly prefers beech over the other species as a host (Kreisel, Dörfelt & Benkert 1980). The sheer density of beech and thus tinder fungi may help facilitate infections, whilst the lower densities of other species might impair infection of host-specific pathogens.

At smaller d.b.h., ash and hornbeam exhibited substantially higher mortality rates than beech (Fig. 3). This suggests that these species have a problem establishing in the stand. Beech is known to cast a lot of shade and to be very shade tolerant. Of the other species, ash is the least tolerant and hornbeam is intermediately tolerant (Niinemets & Valladares 2006). Comparing the aforementioned species with beech, Collet et al. (2008) observed reduced growth and Petritan, von Lüpke & Petritan (2007) higher mortality rates of saplings at low-light conditions.

If, as we assume, the observed species differences are not just ephemeral phenomena and the differing mortality rates reflect fundamental demographic traits of these species, the differences in life-history mortality rates may help to explain abundance patterns. The actual species composition is a combined result of the historical coppice-with-standards management, which fostered the nonbeech species, a gradual change into a beech selection forest and natural regeneration. Whilst the lower mortality rates in small and young beech trees may have led to a general dominance of beech, the low mortality rates of larger ash trees, due to less susceptibility to lethal pathogens and wind damage, may have allowed these species to coexist and develop large and fecund old trees. Hornbeam, with its high mortality rate as a small tree and also higher mortality rate than the other species as a large tree, appears to be decreasing in abundance. With the complete lack of saplings surviving to heights of 1.30 m in the study period, it appears to be a relic species in the stand without any potential to persist. Another important factor for the regeneration pattern is roe deer browsing, which selectively disadvantages the nonbeech species (Kenderes, Mihók & Standovár 2008; Boulanger et al. 2009; Guse 2009).

Estimates of Longevity

Longevity, as defined by many forest dynamic models (review: Bugmann 2001), of beech could be estimated from demographic processes alone in a survival scenario. This estimate, however, is uncertain, because of extrapolating the data to ages higher than observed and no strict relationship between age and d.b.h. (Trotsiuk, Hobi & Commarmot 2012; this study). It corresponds only roughly to previous estimates. Piovesan et al. (2003) reported on beech trees aged more than 500 years old on a high-elevation site and estimated the maximum life span for beech to be more than 700 years. However, longevity as a parameter required by models might be very different from sheer age records (such as a reported 900 years, Felbermeier & Mosandl 2002). Because data on this parameter are rare, it remains a relevant source of uncertainty in the models.

In our study, the beech population suffers from mortality in two phases: up to the age of c. 50 years, crushing and standing dead are the prevailing modes of death, then, after a calm phase, starting from c. 150 years and speeding up with age, the other modes, including standing dead, quickly reduce the population. This pattern could be summarized in the sequence self-thinning, stability and decline, which Hurst et al. (2011) attribute to ‘asymmetric competition’ killing small trees and ‘exogenous disturbance’ killing large trees. This underlines the importance of having a good understanding of mortality in the late stages of tree life for modelling long-term forest dynamics. The common assumption of constant lifetime mortality rates for the random component of mortality applied by Wirth & Lichstein (2009, there called ‘whole-patch mortality’) and many other forest dynamic models (e.g. Pacala et al. 1996; reviews: Hawkes 2000; Keane et al. 2001; there called ‘intrinsic mortality’) leads to an exponential decrease in population size and misses the phase of relatively low mortality. A similar dynamic may be reached if growth dependent mortality not only acts on young trees but increases again in larger and old trees (e.g. Botkin, Janak & Wallis 1972). However, it is by no means clear that very large trees necessarily grow slower. There are many examples where annual diameter increment does not strongly decrease in large trees (e.g. Mountford et al. 1999; Jaworski & Paluch 2002; Piovesan et al. 2005; Mund et al. 2010; this study) and decreased growth might in fact be a subsequent effect of pathogens. In contrast, modelling of mortality rates that increase with age, as in LPJ–GUESS, is in accordance with the pattern that we found. Again, our study hints that mortality in large trees is by no means intrinsic but rather a complex of exogenous mortality events partly mechanical (uprooting and snapping without the influence of pathogens) and partly stress-related or biotic.


Mortality dynamics, especially of large and old trees, are an important field of study. First, in the context of carbon sequestration because they contain a lot of biomass and continue to grow up to late ages (Wirth 2009) and also in the context of biodiversity research because large trees that die function as gapmakers for regeneration (McCarthy 2001; Hurst et al. 2011). Mechanistic and predictive models of forest dynamics have to account for the mechanisms of individual tree mortality and need the appropriate mechanical understanding, as well as empirical parameter estimates, preferably on a species level (Purves & Pacala 2008). We conclude that knowledge of the various mortality modes or proximate causes and their respective dynamics is an essential component for a better understanding of old-growth forest dynamics and mechanistic modelling approaches.


We thank Jürgen Huss for establishing the large-scale inventory site ‘Weberstedter Holz’ in 1999 in the course of the European Nat-Man project and David Butler-Manning, Osama Mustafa, Susann Willnecker and Ulrich Zählsdorf for their help during the second inventory in 2007. We are grateful to Manfred Grossmann for the permission to work in the core area of the National Park and for substantial support during the 2007 inventory. Ernst-Detlef Schulze, Dominik Hessenmöller and Martina Mund for kindly provided valuable data. Nadja Rüger gave helpful comments on the statistical modelling and Peter Otto insight into fungal tree pathogens. We thank Sophia Ratcliffe for proofreading. The work has been funded by the Max-Planck-Society and the DFG Priority Program 1374 ‘Infrastructure-Biodiversity-Exploratories’ (WI 2045/7-1). Fieldwork permits were issued by the responsible state environmental office of Thüringen (according to § 72 BbgNatSchG). C.W. acknowledges the Max-Planck-Society for funding the second inventory. We thank four anonymous referees for highly useful comments and suggestions on the manuscript.