A general integrative framework for modelling woody biomass production and carbon sequestration rates in forests


Correspondence author. Email: dac18@cam.ac.uk


1. Forests are an important, yet poorly understood, component of the global carbon cycle. We develop a general integrative framework for modelling the influences of stand age, environmental conditions, climate change and disturbance on woody biomass production and carbon sequestration. We use this framework to explore drivers of carbon cycling in New Zealand mountain beech forests, using a 30-year sequence of data from 246 permanent inventory plots.

2. A series of disturbance events (wind, snow storms, earthquakes and beetle outbreaks) had major effects on carbon fluxes: by killing large trees, they removed significant quantities of carbon from the woody biomass pool, and by creating canopy gaps, they reduced the crown area index (CAI) of stands (i.e. canopy area per unit ground area) and woody biomass production. A patch-dynamics model, which we parameterized using permanent plot data, predicts that episodic disturbance events can create long-term (c. 100-year) oscillations in carbon stocks at the regional scale.

3. Productivity declined with stand age, as shown in many other studies, but the effect was hard to detect because of canopy disturbance. Individual trees can increase productivity by adjusting the positioning, nutrient content and angle of leaves within canopies. We show that such optimization is most effective when trees are large and suggest it reduces the impact of water and nutrient limitation in old stands.

4. We found no evidence that forests were responding to changing climatic conditions, although strong altitudinal trends in biomass production indicate that global warming could alter carbon fluxes in future.

5.Synthesis.Our study emphasizes the critical role of disturbance in driving forest carbon fluxes. Losses of biomass arising from tree death (particularly in older stands) exceeded gains arising from growth for most of the 30-year study, moving 0.3 Mg C ha−1 year−1 from biomass to detritus and atmospheric pools. Large-scale disturbance events are prevalent in many forests world-wide, and these events are likely to be a driving factor in determining forest carbon sequestration patterns over the next century.


Forests are an important, yet poorly understood, component of the global carbon cycle (Houghton 2007). Deforestation and other forms of land-use change released about 2.1 Pg C year−1 of CO2 into the atmosphere in the 1980s and 1990s (Houghton 2007), and ongoing disturbances (human-induced and natural) reduced forest cover by 0.6% year−1 during 2000–2005 (Hansen, Stehman & Potapov 2010). Yet young forests arising from reforestation and afforestation, as well as some old-growth forests, are carbon sinks (Pacala et al. 2001; Piao et al. 2005, 2009a; Ciais et al. 2008; Luyssaert et al. 2010), and the CO2 absorbed by terrestrial systems was greater than losses by about 1.1 Pg C year−1 in the 1990s, offsetting about 15% of emissions arising from burning of fossil fuels in that period (Le Quere et al. 2009). Forest management could make a cost-effective contribution to stabilizing atmospheric CO2 concentration at 550 p.p.m. by 2050 (Pacala & Socolow 2004), and implementing a carbon-credit system to reduce emissions from tropical deforestation and degradation is a United Nations priority (Gibbs et al. 2007).

The rate of carbon sequestration in woody biomass is controlled by two fundamentally different processes – growth and death – both of which need to be understood to predict carbon dynamics at regional and global scales (Dixon et al. 1994; Houghton 2007; Bonan 2008; Purves & Pacala 2008). Growth requires an understanding of how photosynthetic and autotrophic respiratory processes are influenced by light, temperature, nutrients and carbon dioxide (e.g. Zaehle, Friedlingstein & Friend 2010). The equivalent of about 45% of all atmospheric CO2 diffuses into leaves each year, of which about a third is transformed into sugar via photosynthesis. About 40% of this sugar returns to the atmosphere within weeks as a result of autotrophic respiration. Much of the remaining organic carbon is used to produce leaves and fine roots that last a few months or years before dying and are then utilized in heterotrophic respiration, while just a small fraction ends up as polyphenolic compounds in wood and soil that persist for hundreds of years (Jansson et al. 2010). Given that environmental changes can affect any one, or all, of these processes, predicting their effects on carbon sequestration is difficult and much debated (e.g. Lewis, Phillips & Baker 2006). Losses require an understanding of how competitive processes, disturbances and changes in land management affect tree death (e.g. Caspersen et al. 2000). Relative to biomass carbon gains, disturbance-induced loss of carbon to the atmosphere may be rapid, aptly characterized by Körner (2003) as ‘slow in, rapid out’. Biomass loss events may be hard to predict; for instance, chestnut blight killed up to three billion Castanea dentata trees within a few decades of its introduction into North America (Lovett et al. 2006), and the rapidity with which carbon returns to the atmosphere depends greatly on disturbance agent (e.g. more rapidly after fire than after wind storms, because the latter produces deadwood that takes time to decompose). Research on demographic processes, such as tree death, has often proceeded independently of that ecophysiologically based research into carbon gain processes (Houghton 2007).

This paper seeks to develop a general integrative theory of forest growth and carbon sequestration rate, taking into account the effects of both disturbance and competition on growth, mortality and recruitment processes. Our premise is that forest landscapes are comprised of a shifting mosaic of patches of different ages (development phases), as explained in Fig. 1. Understanding how biomass production, loss and net sequestration vary during stand development is essential for accurate modelling of landscape-level carbon sequestration. We take the metabolic scaling theory of forests (MSTF) as a baseline physiological model to do this (West, Brown & Enquist 1999; Enquist et al. 2003; Enquist, West & Brown 2009; West, Enquist & Brown 2009). We chose MSTF because of the elegant way that it unifies knowledge of physiological and scaling processes to derive metabolic rules applicable to whole organisms and ecosystems, including the prediction that net primary production (NPP) remains constant during stand development. However, MSTF was deliberately kept simple, and particular core assumptions lead to notable inaccuracies in its predictions (Coomes et al. 2003; Muller-Landau et al. 2006; Coomes & Allen 2007a,b; Coomes, Lines & Allen 2011). With this in mind, we develop five extensions to MSTF which introduce extra details that may be important for carbon dynamics, and test the biological significance of those extensions using field data.

Figure 1.

 (a) We develop a general integrative theory of forest growth and carbon sequestration, based on the premise that a forest is comprised of shifting mosaic of populations (=patches) that establish as a result of asynchronous disturbance events and function as if even-aged. Each population goes through a series of developmental phases: there is a seedling recruitment phase, followed by a phase in which the canopy is closed and competitive thinning takes place. Later, the stands become mature and disturbance plays an increasingly important role in killing trees; minor disturbances create gaps that refill by lateral branch spread, but major disturbances cannot be refilled and provide opportunities for seedling regeneration, whence the cycle starts again. Carbon storage is determined by the proportion of stands at each development stage and the amount of carbon stored within them. (b) We test five hypotheses about biomass production (ProdM, blue lines), loss (LossM, red lines) and net sequestration (SeqM, orange lines) trends during stand development. Metabolic scaling theory of forests (H0) predicts ProdM is invariant of stand age because resistivity of the hydraulic transport systems is size invariant. The water/nutrient limitation hypothesis (H1) predicts ProdM declines because large trees are incapable of delivering sufficient resources to maintain productivity. The crown optimization hypothesis (H2) suggests older trees organize leaves to maximize carbon gain resulting in increased ProdM with stand age. The increased packing hypothesis (H3) suggests that leaf area index of three-dimensional canopies increases with stand age, leading to increased ProdM. These hypotheses all assume stands are at maximum density and that competition is the only driver of tree death; for this reason, LossM is directly proportional to ProdM and net sequestration is always positive. The last hypothesis (H4) is that disturbances kill trees, particularly in old stand, and so LossM becomes increasingly negative during stand development; disturbance also creates canopy gaps that are slow to refill, resulting in lower ProdM. The final hypothesis (H5, not shown) concerns the effects of climate change.

We evaluate our general integrative theory by using it to explore carbon cycling in one of the world’s simplest forests: the mountain beech (Nothofagus solandri var. cliffortioides) forest of New Zealand’s Southern Alps. These are naturally monospecific and respond to major disturbances by producing cohort-like pulses of regeneration and so are well suited to modelling patch dynamics and stand development. Inventory data have been collected from 246 permanent plots in these forests since 1974. There is also a long history of ecophysiological research on this species. We test the MSTF model of stand development and the five extensions and develop a simulation model to explore how landscape-scale carbon sequestration – in biomass and coarse woody debris – is affected by disturbance, altitudinal variation in temperature and climate change over 30 years.

Carbon sequestration in above-ground biomass during stand development: a theoretical framework

MSTF is ground breaking in providing ‘a quantitative, predictive framework for understanding the structure and dynamics of an average idealized forest’ (West, Enquist & Brown 2009), but its core assumptions are simple, meaning that the processes envisioned to occur within ‘idealized forests’ differ from those occurring in reality. Specifically, MSTF assumes the following (i) all leaves in a canopy capture equal amounts of light and transpire at equal rates, irrespective of whether they are located in the shaded understory or the upper branches (implicit in the ‘energy equivalence’ assumption); (ii) competitive processes affect tree survival but not growth; (iii) competition is the only determinant of tree death, and disturbances have no effect on forest structure; and (iv) crown architecture is rigidly determined by biomechanical and hydraulic constraints. The key question is whether creating more mechanistically accurate models is necessary for predicting carbon sequestration rates; it could well be that the simple model captures the primary processes well enough.

We explore whether adding more realistic details improves the predictive power of MSTF by developing five extensions (summarized graphically in Fig. 1). The first allows NPP to decline during stand development, recognizing that supply of water and/or nutrients to leaves diminishes with tree size, with direct and indirect consequences for growth (Ryan & Yoder 1997; Magnani, Grace & Borghetti 2002). The second explores the hypothesis that individual plant canopies develop in ways that maximize their productivity (Monsi & Saeki 1953; Hirose & Werger 1987; Hollinger 1989), leading to increased NPP during stand development, if competitive interactions among trees are reduced. Our third extension explores how crown form and tree packing might determine production and sequestration, via demographically based self-thinning rules (Weller 1987a,b; Westoby 1984). The fourth extension investigates how the creation and filling of canopy gaps affect carbon storage, by exploring recruitment, death and competitive processes within forest stands. Our final extension explores how systematic changes in productivity as a result of climate change interact with stand-development processes. Each of these extensions provides predictions about variation in wood production, biomass loss rate and carbon sequestration rate with size, which can be tested against data. The extensions are now explained in more detail; for clarity’s sake, some of our terminology departs from that used in MSTF.

H0: The baseline model predicts sequestration rate is size-invariant

MSTF makes predictions about size-dependent growth and death processes, and energy flux through ecosystems, by starting from first principles. The fundamental basis of MSTF is that the resistivity to sap flow within plant vascular systems is invariant of pathway length (West, Brown & Enquist 1999). The bulk transport system of plants comprises narrow interconnected ‘pipes’ formed out of tracheids and vessels. Hydraulic resistivity is defined as resistance per unit leaf area within this transport pathway. If the pipes were of equal diameter throughout the transport network, there would be a crippling increase in resistivity with plant size, impeding the flow of sap and leading to stomatal closure and loss of photosynthetic capacity. However, the pipes are actually narrower in outer branches than in the main stem, and this ‘tapering’ reduces resistivity. If tapering follows a particular scaling rule, fractal modelling of transport systems suggests that resistivity is completely independent of path length (West, Brown & Enquist 1999), or is nearly so (Savage et al. 2010).

MSTF predicts that, for an idealized tree in an idealized forest, the gross primary production of an individual tree (GPPi) is directly proportional to its total leaf area (AL) and proportional to the square of its stem diameter (D2). Implicitly, this depends on all leaves having an equal supply of water and light, leading to an equal photosynthetic rate irrespective of tree size, and also on the tapering of pipes making resistivity invariant of path length. MSTF also predicts that AL scales isometrically with stem basal area and that above-ground biomass (M) scales as M3/4 = γ1AL = γ2D2 where γ1 and γ2 are constants. The assumptions behind these predictions are that the branching network is a volume-filling fractal with area-preserving branching and that the length of each branch is constrained by biomechanics. If it is additionally assumed that respiratory losses are directly proportional to GPPi, then the net primary productivity of an individual tree (NPPi) is related to its size as follows:

image(eqn 1)

where β1 is a constant of proportionality. The NPP of a stand is then the NPPi values summed for all trees within a specified area. MSTF assumes that leaf area index (LAI = leaf area per unit area on the ground) remains constant during stand development in an idealized forest which has a constantly closed canopy. The maximum number of stems (Nmax) that can pack into a unit area is given by inline image, where inline image is the mean leaf area of a tree (this is a ‘self-thinning’ rule, as discussed in H4). It follows that the maximum NPP of a population is

image(eqn 2)

Hence, MSTF predicts that NPP remains constant during stand development: it is invariant of mean tree size and of the population size distribution. Most NPP is rapidly expended on producing fine roots, leaves and fruit or feeding the microbial community in the rhizosphere (e.g. 70–80% for tropical forests; Malhi 2012). Assuming that an invariant fraction (f) of NPP is invested in above-ground wood biomass, then the production rate of above-ground biomass is

image(eqn 3)

and, from eqn 1, the above-ground growth of an individual tree is dM/dt = fβ1M3/41.

To calculate biomass sequestration rates at the stand level, we must subtract losses arising from tree death (LossMH0). MSTF assumes that competitive processes alone are responsible for tree death, and relatively small trees are killed by competitive starvation. We model this by assuming that trees starve to death during stand development if their biomass, relative to the mean biomass of trees in the stand (inline image), drops to some fixed fraction C (i.e. inline image, where C < 1). This mortality process is different to that given in the study of West, Enquist & Brown (2009), where forests are assumed to be in dynamic equilibrium, but similar to that used in the simulation approach described in Enquist & Niklas (2001). We quantify the rate of loss of biomass (LossMH0) by differentiating the self-thinning equation (inline image) to obtain a rate of stem loss (inline image) and multiplying this by the mean biomass of trees at the point of death (inline image) to give the biomass loss:

image(eqn 4)

Equation 4 can be expressed in terms of mean tree mass (inline image ) by converting mean leaf area inline image to mean tree mass inline image using the allometric relationship between these terms (inline image), giving us inline image. We can remove above-ground biomass growth from the expression because inline image and inline image, to obtain:

image(eqn 5)

Carbon sequestration rate in above-ground biomass (SeqMH0) is ProdMH0 − LossMH0, so we obtain

image(eqn 6)

Under MSTF assumptions, NPP and ProdMH0 are invariant of plant size in populations that have reached their maximum leaf area (the invariant ‘total energy flux’ assertion in Enquist, West & Brown 2009). Our analysis of MSTF also predicted that LossMH0 and SeqMH0 are invariant of plant size on the proviso that inline image is constant.

H1: Photosynthetic rate declines during stand development

It is well established that NPP often reaches a peak (approximately at the time of canopy closure) and then declines as forests mature (Gower, McMurtrie & Murty 1996; Ryan et al. 2004). The hydraulic limitation hypothesis provides one explanation for ‘age-related’ declines in productivity. The hypothesis is that tall trees are unable to supply adequate water to the top of their canopies, because it has to be carried against gravity and through a high-resistance conduit system, leading to stomatal closure and reduced photosynthesis per unit leaf area (Ryan & Yoder 1997; McDowell et al. 2002a,b; Mencuccini 2003; Koch et al. 2004). Trees adjust to dwindling supplies by increasing the ratio of sapwood to leaf area and by investing in fine roots, but diverting resources away from photosynthetically active tissue reduces growth (Magnani, Mencuccini & Grace 2000; McDowell et al. 2002a; Zaehle 2005). Even though tapering of pipes is effective in reducing the path-length dependency of resistivity, it does not overcome it completely (Du et al. 2008; Petit et al. 2010).

The nutrient limitation hypothesis is that immobilization of soil-derived nutrients in aggrading woody biomass during stand development leads to a reduction in the available nutrient pools (e.g. Johnson & Todd 1990; Binkley, Smith & Son 1995). Increasing nitrogen (N) limitation may lead to a reduction in foliar area or photosynthetic capacity (Luo et al. 2004). Support for the nutrient limitation hypothesis comes from temperate forests where a large response to N fertilization occurs in the mature stages of forest development (e.g. Tamm 1991; Miller, Cooper & Miller 1992; Binkley & Hogberg 1997). Productivity also would decline during stand development if increases in whole-plant respiration outstrip increases in photosynthesis, but there is little evidence that this is the case (see Ryan et al. 2004). The latest studies show that respiration of seedlings and trees (anything larger than 100 g) scales approximately as M0.80, which is close to the MSTF-predicted scaling of root and leaf mass with (M0.75), indicating that most respiration occurs in resource-absorbing tissues rather than in stems (Mori et al. 2010).

One way to model decline in growth is to fit the following mass growth function (Pretzsch & Biber 2010):

image(eqn 7)

If a plant is able to supply its leaves with sufficient water and nutrients as it grows (as MSTF assumes), then parameter τ4 = 0 and the function follows a power law, but growth peaks and then declines when τ4 > 0. If all else remains unchanged, then


and therefore,

image(eqn 8)

Other factors may be responsible for declines in growth with tree size, including self-pruning of branches. Trees direct resources towards branches positioned in sunshine and away from those positioned in shade, resulting in the eventual death of shaded branches (Sprugel 2002; Strigul et al. 2008). Thus, crown form is highly influenced by competition with neighbouring trees (Mäkelä & Valentine 2006). Branch death in dense stands leads to decreasing growth of individual trees with size, but no loss of productivity (see Supporting Information).

H2: Canopy optimization results in biomass production in older stands

Sun leaves at the top of canopies have very different form and function than shade leaves at the bottom (e.g. Niinemets, Kull & Tenhunen 1998), in contrast to the energy equivalence assumption of MSTF. Within-canopy organization of leaf inclination and N content can increase productivity (Hollinger 1989; Law, Cescatti & Baldocchi 2001) in accordance with optimality principles, suggesting that individual plant canopies develop in ways that maximize their productivity (Monsi & Saeki 1953; Hirose & Werger 1987). Having steeply inclined leaves at the top of the canopy reduces photo-inhibition and other detrimental effects of too much light, while horizontal leaves in the lower canopy are efficient at harvesting the limited supply of light (Duncan 1971; Niinemets, Portsmuth & Truus 2002; Demmig-Adams & Adams 2006). Allocation of N (a key determinant of maximum photosynthetic capacity) in response to within-canopy light levels also results in the optimization of canopy carbon uptake by reducing carboxylation limitation in high-light environments and respiratory costs in low-light environments (Hollinger 1996). Many single-stand studies have shown broad support for such optimal design of plant canopies, but there have been very few studies of changes in canopy structure with stand development, especially in relation to trends in ecosystem productivity (Day, Greenwood & White 2001).

We hypothesize that optimal organization of individual canopies is constrained by the local competitive environment. When trees are young, competition for light is intense (e.g. Coomes & Allen 2007b), and positioning horizontal leaves at the top of the canopy is an effective way of capturing light and disadvantaging neighbours. When trees are mature, competition is less intense, and organizing the crown to optimize whole-plant productivity is advantageous. Crown optimization would increase β1, with size (eqns 1 and 2) leading to increasing ProdM and SeqM during stand development.

H3: Canopy packing leads to increased productivity in older stands

Density-dependent regulation of crown packing has strong influences on forest structure and productivity (Strigul et al. 2008; Franklin, Aoki & Seidl 2009), but its governing rules are still debated. MSTF assumes that LAI of a forest stays constant during the stand development in ‘idealized’ stands at maximum stem density (Fig. 1) and that an individual’s leaf area is proportional to its ‘Euclidean’ crown volume (West, Enquist & Brown 2009). Thus, if the mean crown volume of trees within a stand is inline image, then inline image, from which we obtain inline image. Now, MSTF assumes that the ‘Euclidean’ crown volume scales with D2 because volume is proportion to area × height, and horizontally projected area of a crown Ac scales with D4/3, while height scales with D2/3. This gives rise to the prediction of the MSTF invariant self-thinning rule inline image (Enquist & Niklas 2001). It also gives rise to the prediction that CAI (the sum of Ac of all trees within a unit ground area) falls during stand development (inline image): tree crowns overlap when small and have gaps between them when large (see H0 in Fig. 1; West, Enquist & Brown 2009).

Classical self-thinning theory is subtly different: it also assumes that LAI remains constant during stand development but differs from MSTF in assuming that a tree’s leaf area is directly proportional to Ac and that both scale as D2. Under these assumptions, maintaining constant LAI during stand development is equivalent to maintaining constant CAI: crowns fill horizontal space without overlapping or leaving gaps (Westoby 1984; Weller 1987a; Strigul et al. 2008). It follows that inline image and accordingly that inline image. So, the same thinning relationship between Nmax and inline image is predicted, but the underlying assumptions are slightly different.

Our new hypothesis is that CAI remains constant during stand development (i.e. the traditional viewpoint), but that leaves are distributed throughout the crown’s volume (i.e. the MSTF viewpoint). Under this scenario, the LAI of a stand increases during development as inline image, and if all other assumptions remain unchanged, we predict an increasing wood production rate:

image(eqn 9)

H4: Gap filling takes longer in older stands, reducing productivity and sequestration

Understanding the process of gap creation and filling is essential to predicting carbon cycling (Clark 1992; Körner 2003; Seidl et al. 2011). The baseline model assumes that competition for resources is the sole cause of tree death, but in reality, disturbance and senescence are important elements in forest dynamics (e.g. see Coomes et al. 2003). In dense young stands, small gaps are filled quickly by the lateral spread of neighbouring canopies, but in older stands, the death of large trees creates holes that can take much longer to fill (Runkle & Yetter 1987; Zeide 2005). Gap creation reduces carbon sequestration in biomass by reducing canopy area (i.e. lower ProdM) and transferring carbon from biomass to necromass (i.e. greater LossM). The baseline model predicts that sequestration is always positive, because trees die from competitive starvation (i.e. C < 1 in eqn 6), but sequestration can be negative if C > 1, which occurs when, for instance, a windstorm knocks over the bigger trees within a stand. If we assume that ProdM is positively correlated with the total area of tree crowns within a stand (i.e. the CAI), then the gaps created by disturbance events will reduce CAI and thereby reduce ProdM. Our hypothesis is that C increases over the course of stand development (reflecting the fact that competition drives death in young stands but disturbance is important in older stands) and that CAI falls (because large gaps take longer to fill), both of which decrease carbon sequestration.

H5: Climate change drives temporal patterns of productivity

Productivity of forest stands may respond to rising CO2 concentrations in the atmosphere (Lewis et al. 2009), global warming (Clark et al. 2003) or increased N deposition (Thomas et al. 2010), potentially obscuring age-related changes in productivity. Temperature strongly influences metabolic processes (Allen, Gillooly & Brown 2005; Anderson et al. 2006) and is rising in many parts of the world as a consequence of increased greenhouse gas concentrations in the atmosphere. The MSTF assumes that all metabolic processes are controlled by the Arrhenius equation, which describes the temperature dependence of chemical reaction rates, such that

image(eqn 10)

where T is the absolute temperature (Kelvins), k is the Boltzmann constant and Ea is the activation energy (c. 0.6) (Anderson et al. 2006). Following this logic through, we would expect LossM and SeqM to respond similarly. A key assumption here is that photosynthesis and respiration respond identically to temperature, which might be reasonable in cool temperate ecosystems when photosynthesis is temperature limited. However, in the hot tropics, forests may switch from being carbon sinks to sources with rising temperature if photosynthesis is unable to respond while respiration continues to rise (Clark et al. 2003; Lewis et al. 2006). CO2 fertilization of glasshouse-grown plants often leads to spectacular increases in growth, and enrichment of atmospheric CO2 within forests (FACE experiments) results in growth and productivity gains (Ainsworth & Long 2005). CO2 fertilization is also the leading explanation for tropical forests being a net carbon sink (Lewis et al. 2009), but this effect is probably transient, as mineral nutrients limitation is likely to saturate the photosynthetic response to CO2 (Lewis 2006).

Regional-scale carbon sequestration

Major disturbances often produce a shifting mosaic of patches of varying age at the landscape scale (Bormann & Likens 1979; Shugart 1984) and have enduring influences on regional carbon stocks and fluxes (Bradford et al. 2008; Pan et al. 2011). However, few studies have explored the effects of the temporal pattern of major disturbance (Uriarte et al. 2009). We predict that infrequent large-scale disturbance events would be capable of perturbing carbon fluxes over several decades. We define disturbances as ‘major’ when they kill enough trees to initiate a new cohort of young trees and restart the stand-development process, distinguishing them from ‘minor’ disturbances, which create gaps that are filled by the growth of neighbouring trees (see Fig. 1).

It is important to include coarse woody debris in regional-scale estimation of carbon sequestration. Tree death takes carbon from the living biomass pool (i.e. LossM) into a persistent detrital pool. For example, coarse woody debris from dead tree trunks can persist for tens of years, depending on wood properties and climatic conditions favourable for wood decay (Richardson et al. 2009). The decay products of wood, as well as senesced leaves and fine roots, could be incorporated into soil organic matter, the most recalcitrant forms of which have residency times of thousands of years (much longer than the life span of most trees). Nevertheless, on average, long-term storage of C in soils may be close to steady state as the amount of carbon moving into long-term soil C pools (c. 0.5% of annual NPP) is similar to losses of C to rivers and oceans and release of CO2 from oceans to the atmosphere (Chapin et al. 2006). For that reason, we focus our attention on the dynamics of living biomass and coarse wood debris (CWD) in this paper.

Materials and methods

The integrative framework consists of a baseline model and series of five extensions that may (or, equally, may not) be necessary for modelling carbon fluxes. We now illustrate the utility of this approach for modelling carbon fluxes in a simple low-diversity forest. We show how each hypothesis can be tested with empirical data and develop a simulation model to predict changes in carbon stocks over hundreds of years, thereby illustrating how disturbance might interact with the endogenous forest processes to determine carbon balances.

Overview of data sets

We used data collected in mountain beech [N. solandri var. cliffortioides (Hook. F.) Poole] forests within the Craigieburn study area of New Zealand’s Southern Alps (43°15′ S, 171°35′ E). Soils are acidic and low in N and cation availability (Allen, Clinton & Davis 1997; Clinton, Allen & Davis 2002). Forest occurs between valley bottoms and the tree line (650–1400 m a.s.l.) and consists exclusively of natural monospecific stands of mountain beech (Allen, Clinton & Davis 1997), which is an evergreen species. This species is widely recognized as light-demanding, requiring large canopy gaps to regenerate successfully and producing cohort-like populations (Wardle 1984) following wind-throw (Harcombe et al. 1998; Martin & Ogden 2006) and earthquake (Allen, Bellingham & Wiser 1999) events. Windstorms and snowstorms in 1968 and 1973 caused extensive damage to the forests, which had previously consisted largely of mature stands, and populations of pinhole beetles built up on the woody debris before attacking live trees, resulting in ongoing mortality through associated pathogens (Wardle & Allen 1983; Harcombe et al. 1998). Further damage was caused by an earthquake in 1994 (Allen et al. 1999). Consequently, the probability and size dependence of tree death varied greatly among the three decades encompassing this study (Hurst et al. 2012).

Five projects in the mountain beech forests, described in detail below, contribute to the results we present: (i) a large-scale forest dynamics project comprising a distributed network of 246 permanent sample plots, established in 1974 and remeasured about every 5 year since then; (ii) investigations into the scaling of crown diameter, height and above-ground biomass with stem diameter; (iii) a stand-development study established in 1991, exploring patterns of carbon sequestration and nutrient dynamics among even-aged stands of different ages; (iv) a fertilizer addition experiment examining the relationships between N availability and productivity during stand development; and (v) ecophysiological studies evaluating the hydraulic limitation hypothesis using gas exchange and isotopic discrimination measurements. We now demonstrate how each hypothesis was tested using the available data.

H0: Testing the baseline model

To test the baseline hypothesis that biomass production and carbon sequestration were invariant of stand age, we used data from two sets of permanently marked plots. The stand-development sequence samples even-aged stands which were about 10, 25 and 120 years of age at the time of plot establishment in 1991. Three stands were initially selected in each age class, all at c. 1050 m altitude and on north-facing slopes (Allen, Clinton & Davis 1997; Davis, Allen & Clinton 2003); an extra stand was added in 1998 (Davis, Allen & Clinton 2004). Stem diameters in these plots were remeasured in 2008, and all new recruits were tagged and deaths recorded. The second source of data came from 246 plots within the distributed network, which provide a systematic sample of forests encompassing around 9000 ha (see Supporting Information). Each plot was 0.04 ha (20 × 20 m), and in the austral summer of 1974, all tree stems within the plots >30 mm diameter at breast height (1.35 m) were tagged and diameters recorded. The diameters of all tagged trees were remeasured in 1978, 1983, 1987, 1993, 1999 and 2004, and all recruits were tagged and deaths recorded in these censuses. Soil chemistry data are available from 1992: eight samples (c. 60 mm diameter) were systematically collected from the top 100 mm of mineral soil in each plot and composited to form a single sample. Composites were air dried and sieved (<2 mm), and a subsample was finely ground and had their N and C concentrations (%) determined using a CNS elemental analyser (model NA 1500; Carlo Erba Instruments, Milan, Italy).

To calculate ProdM, LossM and SeqM for plots in the stand-development sequence and distributed plot network, we first calculated the above-ground biomass (M in kg C) of each tree in every plot and census, using the following empirical relationship developed for mountain beech (Harcombe et al. 1998):

image(eqn 11)

where D is stem diameter at breast height (cm) and H is stem height (m). Height was estimated for each tree using the following equation developed for mountain beech:

image(eqn 12)

where ALT is scaled altitude, calculated as inline image (see Supporting Information). Given data from two censuses, ProdM was calculated as the biomass growth of all stems present in both censuses, RecM was biomass gained through new recruits, LossM was the biomass lost in dead trees, and SeqM was the net gain. We slightly underestimate ProdM because our calculations do not include the growth of trees that died between one census and the next. We performed the same calculations for each of six periods between 1974 and 2004 in the distributed network, giving temporal trends in these processes.

We tested whether ProdM, LossM and SeqM depended on age in the stand-development sequence using analyses of variance. For the distributed plots, we examined factors affecting productivity using linear mixed-effects models (the lme function in R) with plot included as a random effect, because the six measurements of productivity per plot were not statistically independent. These analyses focused on the 76% of stands that were ‘thinning’, within which there was a net loss of individuals and an increase in mean tree size over time (see Coomes & Allen 2007a). Some of these thinning stands were growing at maximum stem density (i.e. were directly analogous to the stand-development plots), but many others had large trees dying in them, creating gaps that were slowly refilled by lateral ingrowth. The thinning plots were quite distinct from ‘disturbed’ plots, in which extensive tree death occurred, resulting in a pulse of regeneration and a reinitiation of the stand-development sequence (see Coomes & Allen 2007a). We did not know the age of stands in the distributed plot network, so we used mean tree biomass as a proxy for age (cf. Bradford et al. 2008) and tested whether ProdM varied with mean biomass (inline image). We conducted analyses with inline image as the only explanatory variable, as well as multivariate analyses in which the following variables were included: altitude, soil N-to-C ratio, CAI and census interval (a factor allowing productivity to vary over our six time steps).

H1: Testing resource limitation hypotheses

To test the hydraulic limitation hypothesis, McDowell et al. (in press) measured the gas exchange characteristics, as well as foliar and wood δ13C, of small (4.3 m tall) and large (11.2 m tall) mountain beech growing at 1300 m elevation in the Craigieburn study area. If the supply of water to the leaves of older trees is more limited, then leaf water potential and/or stomatal conductance should fall and the photosynthetic rate should decrease. In addition, the 13C-to-12C ratio of leaf tissues should increase; carbon isotope ratios provide a temporally integrated signal of foliar photosynthesis and stomatal conductance because 13C uptake by the leaf is less discriminated against (relative to 12C) when CO2 supply is reduced by stomatal closure or when the demand for CO2 at the sites of photosynthesis is low (McDowell et al. in press).

The nutrient limitation hypothesis was tested by Davis, Allen & Clinton (2004) using 25-year-old sapling and 125-year-old pole stands to which N was applied in two dressings (early winter and spring) in the form of urea at 200 kg N/ha each. Measurements of tree responses included foliage chemistry and litter fall measured over three successive years, as well as stem diameter, soil chemistry and bulk density. Three new ‘tests’ of the resource limitation hypothesis are made by observing whether productivity declines with size (see section H0) whether individual tree growth slows down with size (see section H4) and whether the height–diameter relationship is best described by a power law or by an asymptotic function. All three of these ‘tests’ are based on observational data and thus provide inconclusive evidence.

H2: Testing the size-dependent optimization hypothesis

The hypothesis that larger trees reorganize their canopies to increase productivity, once competition from neighbours is reduced, was tested using detailed canopy structure data from stands in the development sequence. For each stage of the sequence, LAI values were obtained by estimating the leaf area of each tree, using allometric relationships calibrated from the destructive sampling of 87 trees (Holdaway et al. 2008). Percentage light interception was calculated from above and below canopy measurements of photosynthetically active radiation, assessed with paired quantum sensors on uniformly overcast days in March 2008. Leaf angle profiles were sampled during January–March 2008. Branches in different height tiers were felled, and a total of 10 400 leaf inclination angles measured using a protractor and hanging weight. A selection of leaves was removed, pooled among branches within each height tier and analysed for N and phosphorus (P) concentrations (see Holdaway 2009). To facilitate comparison between stands, we calculated ‘relative height’, defined as the mid-point of each height tier divided by total canopy height.

We developed a simple physiological model to explore how changes in leaf properties affect whole-canopy photosynthesis. We divided the canopy into height tiers and calculated the amount of light intercepted by each height tier based on measured leaf angles and LAIs. We then estimated carbon uptake in each tier using leaf-level photosynthetic response curves, which was light- and nitrogen-dependent (see Supporting Information for a fuller explanation). Finally, we summed carbon uptake across height tiers to estimate whole-stand productivity. It should be noted that our whole-canopy photosynthesis model provides the potential rate of carbon uptake when water is not limiting and may overestimate productivity of old trees if hydraulic limitation becomes important.

H3: Testing the self-thinning hypothesis

We tested whether crown area (Ac) scaled with D2 (self-thinning theory) or with D4/3 (MSTF) and whether crown volume (V) scaled with D2 (MSTF), by fitting allometric relationships. We measured the stem diameter at breast height (D), crown width (W) and depth (B) of 201 mountain beech stems within Craigieburn study area (see Supporting Information). For each tree crown, we calculated the surface area in a horizontal plane (Ac = πW2/4) and V by assuming the crown to be half a spheroid (= 2/3πW2B). We used standardized major axis (SMA) line fitting to estimate the slope and intercept of the allometric relationship between Ac and D, and V and D, and compared exponents with theoretical values using line.cis in the smatr package in R (Warton et al. 2006).

The new crown-packing hypothesis was tested by seeing whether Volume Index (VI) increased during stand development and whether Crown Area Index (CAI) stayed constant. We derived a relationship between W and D for the 201 trees using nonlinear least-squares regression (see Supporting Information) and used it to predict Ac for each tree present in the distributed plot network in 1974 and 1993. We used the same approach to derive a regression relationship between V and D, enabling us to predict V for every tree. We then calculated CAI and VI by summing all the Ac and As values, respectively, within each plot. We then tested whether CAI and VI varied during stand development by using linear regression with inline image as the explanatory variable. We also calculated inline image and inline image for each plot and tested whether inline image or inline image by fitting upper boundary relationships to log–log transformed data, using quantile regression (the quantreg package in R). Zeide (2005) recommends fitting functions of the form inline image instead of the traditional log–log relationship; this function produces a convex curve when plotted on log–log axes, which Zeide (2005) argues is necessary because the death of large trees create gaps that are slow to fill. We tested Zeide’s hypothesis using nonlinear quantile regression (setting τ = 0.95).

H4: Exploring the role of forest dynamics

The mixed-effects modelling of ProdM, described in section H0, provides a test of whether disturbance influences productivity, because we included CAI in the model; we predict that plots with low CAI have been recently disturbed and should have low productivity. Gaining a greater understanding of the effects of disturbance and competition on the carbon cycle is challenging, as tractable maths is not feasible when nonlinear relationships operate in size-structured populations (Strigul et al. 2008). Fortunately, competition and disturbance can be quantified from plot data (e.g. Canham & Pacala 1995; Busby et al. 2009; Uriarte et al. 2009) and simulators used to investigate the role of tree mortality, gap filling and canopy dynamics in patterns in ProdM, LossM and SeqM. We used tree performance data from the distributed plot network (1974–1993 records) to develop individual-based models of tree growth, mortality and recruitment. We created a simulator that tracked cohorts over time, predicting growth and mortality at each time step as a function of CAIh, the sum of crown areas of trees taller than those in a particular cohort (Caspersen et al. in review). Our simulator assumed that trees within a cohort were completely flexible in the positioning of crowns when competing for space (the ‘Perfect Plasticity Approximation’ or PPA of Strigul et al. (2008) and Purves et al. (2008)) and that all trees in a cohort had identical growth rates. These approximations speed up simulations and arrive at similar predictions to complex spatially explicit individual-based models (Strigul et al. 2008).

We parameterized our model using data from 208 ‘thinning’ plots within which there was a net loss of individuals and an increase in mean tree size (see Coomes & Allen 2007a). An adaptive MCMC Metropolis algorithm (Houghton 2007) was used to fit parameters and credible intervals (CIs) to models of individual annual growth and annual probability of mortality, and Akaike Information Criterion (AIC) was used to compare alternative models (see Supporting Information). Annual growth was modelled using a modified power function:

image(eqn 13)

where ρ2, ρ3, ρ4, ρ5 and ρ6 are estimated parameters and CAIh is the sum of crown area of all trees taller than the target tree in 1974. Potential growth rate is described by a power-law growth curve (inline image), which is reduced by ‘age-related decline’ (accommodated by the inline image multiplier) and competition with taller neighbours (the denominator; see Coomes & Allen (2007b). To quantitatively define taller neighbours, we defined the parameter z as the altitude of a horizontal plane at which CAIh was calculated. Imagine a point on the stem of a target tree that is some fraction z of the way down the canopy (z = 0 and z = 1 representing the uppermost and lowermost heights where foliage is present, respectively), and imagine a horizontal plane cutting through that point and extending across the whole 20 × 20 m plot. CAIh is the sum of the crown areas of all trees within that plane, assuming crowns have cylindrical geometry. We fitted alternative models that varied in the z value used to calculate CAIh and allowed parameters ρ2, ρ3, ρ4, ρ5 and ρ6 to vary with altitude.

Annual probability of mortality was modelled as a size-, altitude- and competition-dependent function (adapted from Lines, Coomes & Purves (2010) using a logistic transformation:

image(eqn 14)

where ρ7, ρ8, ρ9 and ρ10 are estimated parameters. This function produces U-shaped mortality curves, consistent with competition killing small trees and disturbance killing large trees, with trees of intermediate size being relatively unlikely to die (Lines, Coomes & Purves 2010). Again, we fitted alternative models that varied in the z value used to calculate CAIh and allowed parameters ρ7, ρ8, ρ9 and ρ10 to vary with altitude.

Annual recruitment (I) was modelled for thinning stands (= 208) as a decreasing function of the total CAI of a stand:

image(eqn 15)

where the parameters a and v were estimated using nonlinear least squares.

Details of the PPA simulator are described in Supporting Information. We modelled changes over time for each of the 208 thinning plots by initializing the PPA simulation using observed data from 1974 and implementing growth, mortality and recruitment on an annual basis. We ran 100 simulations per plot and compared mean predicted values for 1993 with observed values to see whether the PPA model as formulated was able to recreate the observed patterns in ProdM, LossM and SeqM. We set aside a random sample of 10% of the plots (= 20) as a validation data set and fitted growth, mortality and recruitment parameters on the remaining 178 plots. All analyses and simulations were performed in the R statistical framework (R Foundation 2011; http://www.r-project.org/), except that the analysis of growth and mortality was performed using algorithms written in C language.

H5: Climate change drives productivity changes

The mixed-effects model, described in section H0, provides predictions of ProdM within densely packed stands (i.e. when CAI = 1) for each of the six measurement periods represented in the 30-year data set. To test whether climate change or CO2 fertilization was responsible for change in ProdM among these periods, we compared our predictions with those obtained from a process-based model which calculates daily carbon uptake by mountain beech stands as a function of solar irradiance, minimum and maximum air temperatures, precipitation and atmospheric CO2 concentrations (Richardson et al. 2005). The model, based on the 3-PG model (Landsberg et al. 2001; Whitehead et al. 2002), calculates photosynthesis from maximum carboxylation and electron-transfer rates measured on mountain beech trees, using the methods of Farquhar, Caemmerer & Berry (1980) and includes the effects of stomatal conductance (Leuning 1995; Davis, Allen & Clinton 2004) and temperature (Bernacchi et al. (2001). We summed carbon uptake estimates for all days in each census period and compared the physiological model’s predictions with wood production rates values using correlation tests.

Regional-scale modelling of carbon sequestration

We extended our PPA stand-development model into a patch-dynamics model to explore the effects of major disturbance (Pickett & White 1985; Bugmann 2001; Scheller & Mladenoff 2007). Our approach is similar to that used by Coomes & Allen (2007a) to investigate size structure dynamics. Each stand in the simulation was initially devoid of trees, but at each yearly time step, it gained new recruits (eqn 15), making the reasonable assumption that seed limitation does not occur in these single-species forests. Simulations were initialized with 100 empty stands and run for 1000 years. The simulator kept track of the number of trees, and the mean size of those trees, in each cohort in each of the 100 stands. For each iteration, trees grew and died according to the statistical rules derived from data (i.e. eqns 13 and 14). At the end of each yearly time step, a percentage of the stands were destroyed, killing all trees with D > 5 cm in the stand (the next paragraph describes the process in more detail). This simulator was allowed to run for 800 years, by which stage the biomass and age structure of each stand was independent of starting conditions, and we report what happened in the next 200 years.

Destroyed stands were chosen by random draws from a probability density function that depended upon stand biomass. The percentage of plots destroyed each year was simulated by drawing random deviates from a beta-binomial distribution (using the rbetabinom function in R), with a constant long-term probability of disturbance of 0.6% (Coomes & Allen 2007a) and an over-dispersion factor (theta) of 20. This resulted in significant variation in frequency of major disturbance among years, with no disturbances at all occurring in >80% of the years. Since older stands are more prone to some types of disturbance than younger stands (see Coomes & Allen 2007a), we used weighted probabilities based on stand-level carbon stocks to select the plots in which disturbance would occur (using the sample function in R).

The long-term simulator kept track of the decomposition of dead trees, thereby modelling long-term dynamics of both biomass and necromass pools. When a tree died, it entered the CWD pool, and the simulator kept track of how much CWD was produced at each time step. Following the method of Beets et al. (2008), we modelled decay of CWD using an exponential function, the decay coefficient of which was estimated from mean stand-level CWD in seedling, sapling and pole stages of the stand-development sequence (Clinton, Allen & Davis 2002). The fitted model took the following form:

image(eqn 16)

where Mt0 is the mass of the tree at time of death and t is the number of years since time of death. MCWD = mass of CWD at time period of interest. Our exponent of 0.028 is similar to the value of 0.024 reported for another common beech species (Nothofagus menzeisii) by Beets et al. (2008).


H0: The baseline model

The above-ground wood production rate (ProdM) of 120-year-old stands was 39% lower than that of 25-year-old stands in the stand-development sequence (Table 1), contrary to the baseline model prediction of size-invariant production rate. Age-related decline was also observed in thinning stands within the distributed plot network. In these stands, ProdM was related to altitude (ALT), soil N-to-C ratio (NC), CAI and mean tree biomass (inline image) as follows:

image(eqn 17)

where MPE is an intercept term that varies among the six measurement periods in the 30-year data set (see H5 section below). All terms in this model were statistically significant (standard errors for ALT, NC, CAI and inline image parameter values were 0.013, 2.2, 0.044 and 0.00040 respectively). We entered the mean biomasses of trees in the 25- and 120-year-old stand-development plots (inline image = 3.46 and 73.7 kg, respectively) into eqn 17 to predict changes in productivity with age (setting ALT = 4, NC = 0.04 and CAI = 1). This approach indicated a 15% drop in productivity from young to old stands. The effect of inline image is very weak; for instance, there is no detectable relationship between ProdM and inline image in the 1974–1993 time interval when analysed by univariate regression (Fig. 2a, F1,206 = 1.2, = 0.27), but a negative response is observed when other factors are included in a multiple regression analysis.

Table 1.   Carbon stock and fluxes in young and old stands of Nothofagus solandri var. cliffortioides (mountain beech) growing under similar conditions at 1000–1100 m elevation and in ‘thinning’ and ‘disturbed’ stands within a distributed network of 246 plots
 Stand developmentDistributed plot network
25 years old125 years old‘Thinning’‘Disturbed’
  1. CWD, coarse wood debris.

  2. *Modified from the study of Davis, Allen & Clinton (2003) using a multiplier of 1.4 from Benecke & Nordmeyer (1982).

  3. †Estimated as 0.338 M0.9256, taken from the global analysis of Cairns et al. (1997).

  4. ‡Taken from the studies of Davis, Allen & Clinton (2003, 2004), based on trends over 8 years.

  5. §Modified from the study of Clinton, Allen & Davis (2002).

Stocks (Mg C ha−1)
 Above-ground biomass21.4 ± 5.7*119.1 ± 2.5*94.1 ± 1.4565.5 ± 1.89
 Root biomass5.7 ± 1.2†28.2 ± 0.47†  
 Coarse woody debris51.4‡13.0‡  
 Litter and humus layers21.4‡35.9‡  
 Mineral soil32.033.4  
 Ecosystem total131.9229.6  
Fluxes (Mg C ha−1 year−1)
 Above-ground biomass
  Growth (ProdM)2.09 ± 0.23§1.28 ± 0.16§1.17 ± 0.0271.08 ± 0.037
  Recruitment (RecM)0.11 ± 0.027§0.012 ± 0.067§0.039 ± 0.0160.032 ± 0.004
  Loss through death (LossM)0.20 ± 0.041§0.90 ± 0.067§1.46 ± 0.0621.74 ± 0.061
  Net sequestration (SeqM)2.00 ± 0.23§0.39 ± 0.22§−0.24 ± 0.057−0.76 ± 0.107
 Other components
  Leaf litter fall1.151.60  
  Root turnoverUnknownUnknown  
  Seed + flowers production0.030.03  
  Shed of branches/twigs0.501.05  
  Decomposition of CWD−0.64−0.04  
  Decomposition of litter and humus−0.05‡−0.75‡  
  Net flux from mineral soil0.0‡0.0‡  
Figure 2.

 Measured above-ground wood production, loss and net sequestration (ProdM, LossM and SeqM in Mg C ha−1 year−1) in relation to mean tree biomass (inline image; kg C) in 208 ‘thinning’ stands (1974–1993 data). Univariate analysis suggests that ProdM does not depend on tree biomass (the slope of the dotted line is not significantly different from zero), but a weak negative effect is observed once altitude, soil N-to-C ratio and CAI are included in a multivariate analysis. Significant declines were observed for LossM and SeqM, consistent with H4 shown in Fig. 1. Fitted lines are inline image; inline image.

Sequestration rate (SeqM) declined greatly with stand age (an 80% reduction between 25- and 120-year-old stands) because the older stands lost more biomass through death each year than did the young stand (Table 1). Similarly, in the distributed plot network, we observed increased loss rates with tree size (F1,206 = 17.1, < 0.001), resulting in a drop in sequestration rate (F1,206 = 19.1, < 0.001), as shown in Fig. 2. These trends are consistent with the fourth hypothesis (Fig. 1) and do not lend support to our baseline assumption that asymmetric competition is the only process that kills trees, such that C values (inline image) are always less than one. In fact, only 63% of thinning stands had < 1, suggesting that disturbance has a strong influence in many stands.

H1: Resource limitation

Mountain beech trees have tapering vessels within their vascular transport systems, which reduce the size dependence of hydraulic resistivity (Coomes, Jenkins & Cole 2007). Nevertheless, hydraulic limitation may contribute to age-related decline in these forests. McDowell et al. (in press) showed that larger trees had lower rates of photosynthesis and stomatal conductance (when vapour pressure deficits exceeded 0.8 kPa) and discriminated less against 13C compared with short trees, all consistent with hydraulic limitation. Similar isotope discrimination patterns were found in comparisons of 25- and 120-year-old stands in the stand-development study (Davis, Allen & Clinton 2004).

Nutrient limitation does not appear to contribute to age-related decline in NPP. Addition of N fertilizer to 25- and 120-year-old stands led to greater seed and fine root production, with the strongest increases in the older stands (Davis, Allen & Clinton 2004), but had no detectable effect on wood production. Pools of soil cations and available N decline with stand age (Allen, Clinton & Davis 1997; Clinton, Allen & Davis 2002) while pools of N in wood biomass increase greatly (Clinton, Allen & Davis 2002). The amounts of N and P held in foliage were higher in the intermediate-aged stands than in youngest and oldest stands, consistent with their comparatively high LAI (see Supporting Information and Holdaway 2009). It seems that trees allocate N and P differently in older stands: they had higher canopy-average leaf N and P concentrations (Fig. 3e,f), and their total canopy nutrient content remained high despite a significant reduction in LAI (Holdaway et al. 2008). It also seems that having greater reserves of in planta N provides trees with the flexibility to meet the nutritional demands of reproduction (Smaill et al. 2011).

Figure 3.

 Within-canopy profiles of mean leaf angle (a), leaf N concentration (b) and leaf P concentration (c) plotted against relative height in canopy for small saplings (• and solid line), large saplings (bsl00066 and dashed lines) and pole stands (× and dotted lines) and associated age-related changes in mean leaf angle (d), mean leaf N (e), mean leaf P (f), modelled CO2 uptake (g), leaf area efficiency (h) and light-use efficiency (i). Error bars are ±1 SEM and letters reflect significant Tukey HSD groupings.

Analyses of individual tree growth in the distributed plots also indicates age-related decline. The best-supported model of diameter growth for trees was

image(eqn 18)

when trees have no taller competitors and are growing at 640 m elevation (see eqn 23 in section H4). This function predicts similar diameter growth to a power function when trees are small (D < 25 cm) but much lower growth rates for larger trees (e.g. 40% less when D = 50 cm; Fig. S3). Heights reach an asymptote with increasing stem diameter (see eqn 12), which also provides indirect evidence of hydraulic limitation (Bond & Ryan 2000).

H2: Size-dependent canopy optimization

The organization of leaves within individual canopies was consistent with trees optimizing productivity. We found that, irrespective of stand-development stage, leaf angles were steeper, and leaves had higher N and P concentrations, towards the top of the canopy (Fig. 3a–c): having steep leaves increases productivity by reducing the risk of photo-inhibition of upper-canopy leaves and allows light to penetrate to lower-canopy layers, while allocating N to upper leaves increases Rubisco concentrations and rates of carboxylation (Horn 1971).

Systematic increases were observed in the proportion of LAI located towards the top of the canopy during stand development (Holdaway et al. 2008), resulting in steeper canopy-average leaf angles (Fig. 3d), consistent with the observed decrease in canopy-level light interception during stand development (94.1 ± 0.58% in 120-year-old stands compared with 98.1 ± 0.14 and 97.4 ± 0.41 for the 10- and 25-year-old stands, respectively). There was also an increase in canopy-average leaf N and P concentrations during stand development (Fig. 3e,f). These changes in canopy structure resulted in the 120-year-old stands having the highest modelled average light levels per unit leaf area (301 ± 6.9 μmol m−2 compared with 275 ± 8.4 and 243 ± 10.6 for the 10- and 25-year-old stands, respectively). Modelled instantaneous rates of net stand CO2 uptake varied significantly with developmental stage, with 10-year-old stands having significantly lower rates than 25- and 120-year-old stands (Fig. 3g), and both light-use efficiency and leaf area efficiency increased with stand age (Fig. 3h,i), reflecting the optimization of canopy architecture for increased productivity. Age-class averages of modelled CO2 uptake rates were well correlated with the measured growth (ProdM) across the stand-development sequence (Pearson’s correlation = 0.80, = 0.003).

H3: Self-thinning theory

Neither VI nor CAI was invariant among thinning stands in the distributed plot network, indicating that neither MSTF nor traditional ‘packing rules’ applied. CAI decreased with increasing mean tree mass (Fig. 4a, based; inline image, r2 = 0.45, F2,206 = 82, < 0.0001), as did VI (inline image, r2 = 0.78, F2,206 = 361, < 0.0001). However, VI was much less variable among plots than CAI (9% vs. 17% drop from 25- to 120-year-old stands, respectively), so MSTF was the better-supported of the two models. The temporal relationship between log(inline image) and log(stem density) would need to have a slope of −1 to maintain constant CAI as stands grow, but the mean slope of the lines shown in Fig. 4c is −1.57 ± 0.22, indicating that CAI fell over time; VI also fell over time. We emphasize that many of the thinning stands were not at maximum density and were affected by disturbance as time progressed, so these analyses do not provide a strong test of self-thinning theories, which only apply at Nmax.

Figure 4.

 Changes in (a) crown area index (CAI) with mean tree biomass (inline image; kg C); and (b) wood production vs. CAI, assessed using data collected in 1974 from 208 ‘thinning’ mountain beech plots, (c) changes in stem density vs. mean crown area over time (1974–1993, plotted as arrows on log–log axes); (d) stem density vs. mean crown area based on data from all censuses, with upper boundary relationships fitted using quantile regression. Open triangles and black arrows show data from low altitudes (640–800 m), red circles and arrows from mid-altitudes and blue squares and arrows from high altitudes (1100–1400 m). Predictions for low, mid- and high altitudes are shown (black line = 700 m, red line = 1000 m, blue line = 1400 m).

Focussing on the upper boundary of the log–log relationship between plant size and stem density provides a stronger test of theory than fitting lines through the centre of data (Westoby 1984; Weller 1987a,b). When mean crown area is plotted against mean stem density using data from all seven measurement years, the upper boundary appears to curve (Fig. 4d). Zeide (2005) argues that we should not expect self-thinning relationship to be straight lines on log–log axes, because deaths of trees in older stands create large gaps that are slow to refill. We fitted his suggested alternative function to the upper boundary of the mountain beech data, using nonlinear quantile regression (nlrq in the quantreg package of R with τ = 0.95), and obtained the following:

image(eqn 19)

with standard errors of 0.62, 0.021, 0.044, 0.0066, respectively. The last term in this function acts to reduce stem density in old stands below that predicted by classic self-thinning theory (Zeide 2005); however, the parameter value was not significantly different from zero (= 0.08). This function predicts that CAI falls by 51% between 25- to 120-year-old stands. The equivalent formula for crown volume is

image(eqn 20)

with standard errors of 5.3, 0.014, 0.019 and 0.0001, respectively, which predicts that VI rises by 7% between 25- and 120-year-old stands. Thus, VI varies much less than CAI during self-thinning, suggesting support for the MSTF prediction of constant VI.

While the MSTF ‘packing rule’ is better supported than traditional theories, its allometric scaling predictions are not. The allometric relationship between Ac and D had an exponent of 2.16 (SMA line fitting, 95% CI of 2.01–2.32), which differs substantial from the MSTF prediction of 4/3 but is slightly greater than the ‘traditional’ geometric theoretical value of 2 (see Fig. S5). Similarly, the relationship between V and D had an exponent of 2.97 (SMA line fitting, 95% CI of 2.76–2.21), departing from the MSTF prediction of 2 but similar to the geometric expectation of 3 (see Fig. S5).

H4: Forest dynamics

Storms, insect outbreaks and earthquakes had major effects on forest dynamics. For most of the 30-year period, losses of carbon through tree death and gains through wood production, resulted in a net loss of biomass (Fig. 5a). The opening up of canopies, almost certainly as a result of the disturbances, had profound effects on ProdM (Fig. 4d). For example, least-squares regression of the 1974–1993 data set using standardized explanatory variables (i.e. transformed to have a mean of zero and standard deviation of one) gives

image(eqn 21)

with standard error estimates of 0.019, 0.023, 0.023, 0.021, and 0.025, respectively. The coefficient estimates associated with standardized variables indicate their relative influence on ProdM; they indicate that variation in CAI is 3.1 times more influential than altitude on ProdM, while tree size is the least influential variable. Even though there is covariance between CAI and ALT (correlation coefficient = 0.48), including both terms is strongly supported (ΔAIC = 9.0).

Figure 5.

 (a) Changes in mean carbon stocks in above-ground biomass (Mg C ha−1) of 246 mountain beech stands (±1 SEM) monitored over 30 years; (b) rate of carbon sequestration in above-ground biomass (SeqM = bsl00001), which is the sum of the biomass production rate (ProdM = •), biomass gain through recruitment (RecM = □) and biomass loss arising from tree death (LossM = ○). Stars show the ProdM of young, closed-canopy, low-altitude forest growing on nutrient-rich soils, predicted by mixed-effects modelling.

The best-supported model for diameter growth (cm year−1) took the following form:

image(eqn 22)

where CAIh was calculated with = 0.25 (95% CIs are given in Supporting Information). The model predicts a 44% decline in growth rate from the lowest- to the highest-altitude plots and that competition from taller trees has strong effects on the growth of individuals (Fig. 6). The interaction term on the denominator suggests that the effect of CAIh on growth was more pronounced at higher altitudes.

Figure 6.

 Growth and mortality predictions in relation to stem diameter for varying values of crown area index of taller trees (CAIh) and altitudes (low and high values for CAIh and altitude represent 2 standard deviations either side of the mean).

The best-supported model for annual probability of mortality (p) took the following form:

image(eqn 23)

where CAIh was calculated with = 0. Mortality was U-shaped with respect to stem diameter and greater at high CAIh values and high altitudes (Fig. 6; 95% CIs are given in Supporting Information). The annual recruitment rate was I = 0.83 exp(−1.438 CAI). This function underestimates recruitment in plots where significant recruitment had occurred after part of (rather than all of) the plot area was cleared of trees by disturbance (Fig. S8). However, this was not important for our data set owing to the minimal role that recruitment had in carbon sequestration over the studied time-scales. The PPA model predicts the declining relationship between mean tree size and LossM and SeqM (Fig. 7), as well as the subtle decline in ProdM with size. The simulations predicted ProdM of 1.32 ± 0.03 Mg C ha−1 year−1, LossM of −1.50 ± 0.04 Mg C ha−1 year−1, and SeqM of −0.19 ± 0.05 Mg C ha−1 year−1. In the cases of LossM and SeqM, the predicted values were not significantly different to observed values (paired t-test, > 0.05), but the simulator over-predicts ProdM by 13% (< 0.01).

Figure 7.

 Above-ground wood production, loss and sequestration (ProdM, LossM and SeqM in Mg C ha−1 year−1) predicted by a PPA simulator in relation to initial mean tree mass (inline image; kg C). The model was calibrated using permanent plot data collected in 208 thinning stands in 1974 and 1993, and each point represents an average of 100 simulations per stand. Fitted lines show significant relationships (P < 0.001 in all cases); inline image, inline image and inline image.

H5: The influences of climate change

ProdM varied greatly over the 30-year study, rising during the first 15 years and then falling in the latter period (Fig. 5b). Estimates of time period effects (MPE in eqn 17) were used to predict ProdM under the best conditions available for growth in the study area (i.e. when ALT = 0, CAI = 1, inline image, NC = 0.06). These estimates, plotted in Fig. 5, indicate that ProdM varied by up to 40% between time intervals. It seems unlikely that climate change is responsible for such strong variation: Richardson’s process-based model (Richardson et al. 2005) predicted near-constant carbon uptake across the six time periods (coefficient of variation = 0.029 compared with 0.27 for the MPE values), and model predictions were uncorrelated with MPE values (> 0.40). Instead, it seems likely that disturbance damage created the temporal patterns: many crowns were broken in heavy snow storms of 1968 and 1973 (Wardle & Allen 1983), and we speculate that it took about 10 years for damaged trees to recover; more damage was caused by an earthquake in 1994, and this may be responsible for declining growth rates in the last two census periods.

Forest structure and function varied along the 5.3 °C temperature gradient represented within the plot network (Harcombe et al. 1998; Coomes, Jenkins & Cole 2007). Trees at high elevation are shorter and narrower crowned (Figs S2 and S5) and lower CAI (Fig. 4); they grow more slowly and die less frequently (eqns 22 and 23). Previous work indicates that elevation has important effects on the NPP and structure of mountain beech forests (e.g. Benecke & Nordmeyer 1982; Harcombe et al. 1998; Coomes & Allen 2007a). The optimal summer temperature for photosynthesis is c. 17 °C at 890 m, considerably above the typical temperatures at that elevation (8.0 °C). As a consequence, air temperatures limit net photosynthesis, particularly at higher elevations (Benecke & Nordmeyer 1982). Using eqn 17, we predict that ProdM falls from 1.74 Mg C ha−1 year−1 at 640 m altitude to 0.68 Mg C ha−1 year−1 near the tree line at 1400 m.

Given these strong altitudinal effects, it seems likely that mountain beech will respond to global warming. However, climate records from the study area show no long-term trend in either mean annual temperature or growing-season temperature, although winter temperatures do show a significant upward trend (see Supporting Information). Interannual variation in growth arising from temperature variation may have occurred, but we did not detect any pattern because our growth measurements were averaged over c. 5-year periods.

Regional-scale modelling of carbon sequestration

In the stand-development sequence, biomass represented 16% and 52% of the total carbon stored in the ecosystem in 25- and 120-year-old stands, respectively (Table 1). The younger stands still contained large amounts of coarse woody debris arising from tree deaths during the major disturbance that created the regenerating stands; much of this CWD had decomposed after 120 years. In contrast, carbon stocks increased in the litter, fermentation and humus layers over time. Of course, wood production is only a small fraction of total production, amounting to roughly 31% and 22% of all known production in the two respective stands, assuming that root production is similar to litter production and omitting several factors for lack of data (e.g. volatile production, losses to herbivores and root exudation and respiration). The process-based model of Richardson et al. (2005) estimated NPP as 14.2 ± 0.2 Mg C ha−1 at 1050 m elevation (virtually identical to the mean altitude of plots in the network), which is similar to field estimates of Benecke & Nordmeyer (1982). If this estimate is representative of NPP across the distributed network, it suggests that the fluxes in Table 1 represent less than half of all carbon fixed by the forests.

Simulated regional-scale mean stand biomass patterns were relatively constant over a 200-year period when competition and minor disturbance were the only mortality processes. The predicted mean above-ground biomass (99 ± 0.04 Mg C ha−1, Fig. 8a) was similar to observed values for thinning stands (94 Mg C ha−1, Table 1). However, when major disturbance was also included (at a mean frequency of 0.6% of plots disturbed per year), the mean stand biomass was significantly lower (65 ± 0.93 Mg C ha−1) and highly variable (ranging from 38 to 86 Mg C ha−1). This variability in above-ground biomass was noticeably lower when CWD was included as a carbon pool (Fig. 8b). Increasing the frequency of the disturbance among years, while holding the long-term mean constant, resulted in even stronger variation in standing biomass over time (results not shown). The simulations indicate that regional-scale biomass stocks may increase, decrease or stay approximately constant depending on disturbance history.

Figure 8.

 Simulated mean stand biomass patterns over a 200-year period based on (a) modelled individual tree-level mortality (driven by competition and ‘minor’ disturbances) only and (b) including plot-level disturbance equivalent to 0.6% of plots disturbed per year. Black line is live stem biomass; red dashed line is total above-ground biomass including coarse wood debris (CWD). Data are averaged across 100 plots. Note the lower temporal variation in mean carbon stocks when CWD pool is included.


Declines in productivity and sequestration during stand development

Many forests are ageing because they were planted or regenerated recently, particularly in the northern hemisphere, so understanding how productivity varies with stand age is essential to predicting future carbon sequestration rates (Caspersen et al. 2000; Zaehle et al. 2006; Piao et al. 2009a,b; Luyssaert et al. 2010; Wang et al. 2011a). Declines in productivity have been observed in virtually every stand-development study ever conducted (Ryan et al. 2004, 2010; cf. Sillett et al. 2010), including the one conducted in mountain beech forests (Table 1). These studies were designed to examine age effects while minimizing all other sources of variation among stands and were typically conducted in stands growing at near-maximum stem density. In contrast, size-related decline was hardly detectable in the distributed network of mountain beech plots (Fig. 2), because disturbance, temperature and soil nutrients varied greatly among these stands and strongly influenced productivity, almost drowning out the size effect signal. Only when multivariate analyses and simulation modelling (Fig. 7) were used did size-related decline become apparent.

Various adjustments by plants may prevent a strong decline in wood production with stand age (Magnani, Mencuccini & Grace 2000). Mountain beech trees exhibit vessel tapering (Coomes, Jenkins & Cole 2007), a vascular design that reduces the size dependence of resistivity (West, Brown & Enquist 1999; Petit et al. 2010). Older mountain beech stands have reduced LAI (Holdaway et al. 2008), a feature widely reported in other species (Ryan & Yoder 1997; Nock, Caspersen & Thomas 2008), and this reduces demand for water (Magnani, Grace & Borghetti 2002). Soil nutrient availability dwindles with stand age, but this does not impact on foliar nutrient concentrations (Fig. 3) and N addition did not have a detectable effect on stem-wood production (Davis, Allen & Clinton 2004). High foliar nutrient concentrations in older stands could promote increased water-use efficiency (e.g. Ripullone et al. 2004), as well as high potential rates of photosynthesis, perhaps offsetting some of the losses arising from hydraulic limitation (Fig. 3). Plant allocation patterns tend to maximize plant fitness within the limits imposed by the environment and functional traits (Magnani, Grace & Borghetti 2002). These limits include competition with neighbouring trees (Holdaway 2009), risk of embolism in vascular systems under arid conditions (Magnani, Mencuccini & Grace 2000), costs of constructing transport systems (Mencuccini et al. 2007) and imbalances in the supply of resources (Chapin et al. 1987). MSTF emphasizes the importance of minimizing the energy required to distribute water from roots to leaves (West, Brown & Enquist 1997; Enquist et al. 1999; West, Enquist & Brown 2009) with little consideration of how environmental constraints may vary during stand development.

Size-dependent canopy optimization

Mountain beech had steeper leaf angles and higher nutrient concentrations in leaves located in the high-light environments found in the top of the canopy, as shown in other studies (e.g. Duncan 1971; Hollinger 1989, 1996; Law, Cescatti & Baldocchi 2001, Walcroft et al. 2005). Additionally, older stands tended to have a greater proportion of total stand LAI located near the top of the canopy, steeper average leaf angles and higher leaf nutrient concentrations. This resulted in older stands having increased light penetration (per unit leaf area) through the canopy, reducing photo-inhibition in the upper canopy and increasing assimilation rate in the lower strata. We argue that the optimization process is dependent upon the intensity of asymmetric competition for light, which diminishes as trees grow larger (Coomes & Allen 2007a). However, the extent of productivity gains arising from this mechanism remains unclear, because our simple productivity model ignores potential N-independent variation in stomatal conductance and hydraulic resistance within the canopy (Farquhar, Caemmerer & Berry 1980; Ryan et al. 2010), the effects of night-time leaf respiration, and carbon investment associated with the construction of fine roots and maintenance of soil mycorrhizae (Hendricks, Nadelhoffer & Aber 1993). More research on this topic is required.

The size-dependent optimization hypothesis is the direct opposite of that put forward by Binkley et al. (2002), in which increased dominance during stand development causes a decline in gross above-ground productivity owing to an increase in the portion of total LAI contained in subordinate tree canopies. Binkley et al. (2002) focus on the decline in efficiency of the subordinate individuals and argue that the resource-use efficiency (in terms of growth) of dominant individuals declines as the spacing between trees increases (Binkley, Stape & Ryan 2004, Ryan et al. 2004). We speculate that the hypothesis of Binkley et al. (2002) does not apply to mountain beech forests because they are light-demanding single-cohort stands (Wardle 1984). Subordinate stems thus account for a low portion of the total canopy leaf area, especially in the 120-year-old stands. In contrast, competition between shade-tolerant species might slow growth of subordinates without killing them (or reducing their leaf area), potentially resulting in the predicted declines in stand-level resource-use efficiency (Binkley et al. 2002; Binkley, Stape & Ryan 2004).

Crown packing theories

There was absolutely no evidence that increased packing of canopies enabled productivity to rise with stand age, but our analyses shed new light on the ‘packing rules’ governing mortality in high-density stands. Self-thinning is one of the most debated topics in plant ecology, yielding an extraordinary number of empirical tests of whether allometric relationships between mean biomass and stem density have slopes of −3/2 (Weller 1987a,b; Westoby 1984) or −4/3 (Enquist, Brown & West 1998) or idiosyncratic values dependent on crown architecture (Weller 1987a; Osawa & Allen 1993; Strigul et al. 2008). A common idea running through these self-thinning theories is that either CAI or LAI stays constant during stand development and that differences in assumptions about the allometric scaling of Ac or AL with tree size (either M and D) give rise to different exponents (e.g. Osawa & Allen 1993). Our work challenges the fundamental ‘packing rule’ as well as how the rule is translated through allometric functions: we found that LAI of mountain beech stands rises when they are very young, peaks and then falls as the stand ages, so the assumption of constant LAI is not supported (Holdaway et al. 2008, in agreement with Ryan & Yoder 1997); we also found that CAI falls as the stand ages (even at maximum density). Intriguingly, we found that canopy volume changed little during stand development (for stands at maximum stem density), much as predicted by MSTF. We believe ours is the first test of the MSTF prediction of constant canopy volume, and it would be fascinating to test it out with other data sets. It is important to recognize, however, that few stands were functioning as classic self-thinning stands, because disturbances were killing large trees and creating canopy gaps that took time to refill (Zeide 2005; Hurst et al. in press).

Disturbance and the slow filling of canopy gaps

Disturbance by wind and snow storms, earthquakes and beetle outbreaks had very strong influences on carbon cycling: by killing trees, it moved large quantities of carbon from biomass into necromass (LossM in Figs 2 and 5), by creating canopy gaps, it reduced wood production (ProdM in Fig. 5b), and by damaging individual tree crowns, it reduced tree growth (the most parsimonious explanation for MPEs, see results section H5). In addition, multiple tree deaths arising from disturbance create opportunities for regeneration from seed. Disturbance events capable of reinitializing stand development in this way occur infrequently, and our simulation models suggest that the rare events result in long-term oscillations in carbon stocks at the landscape scale (Fig. 8). The U-shaped nature of the size-dependent mortality curve (Fig. 6) demonstrates that trees become increasingly prone to disturbance as they age (Runkle 1982; Lorimer, Dahir & Nordheim 2001; Coomes et al. 2003). Low CAI in older stands (as well as some young stands) is primarily the result of disturbances killing trees and creating canopy gaps (Fig. 4). The death of old trees creates large gaps that can take many years to refill, depending on forest type (Zeide 2005), and this leads to a prolonged decrease in CAI and a concomitant loss of productivity. The MSTF and extensions H1–H3 (Fig. 1) all assume that competition is the only process driving morality in forests; this clearly is not the case in mountain beech forests, so the models make inaccurate predictions regarding growth and sequestration.

Wood production was far more influenced by CAI than by altitude, nutrient availability or mean tree size (eqn 20 and Fig. 4b). Because of the central importance of CAI as a signature of disturbance and a predictor of productivity, we recommend that researchers who measure stem diameters in permanently marked plots should also routinely measure crown area relationships. For relatively little effort, it allows the calculation of two important metrics: the crown area of taller neighbours (CAIh) and the total crown area of all stems in the stand (CAI). These metrics have several advantages over basal area, the most widely used metric of competitive crowding. First, CAIh and CAI make better sense to non-specialists than traditional metrics such as the cross-sectional area of stems. Secondly, CAIh is an important determinant of individual growth and mortality (Fig. 6), and CAI strongly predicts productivity (Fig. 4b). Finally, growth and mortality functions based on CAI and CAIh can be used in computationally efficient PPA simulation models (Strigul et al. 2008). It would be interesting to explore whether CAI could also be used alongside LAI to ground-truth remotely sensed imagery (e.g. Wang et al. 2007).

Forest response to changing climatic conditions

Wood production of mountain beech was observed to rise and fall over 30 years, but these changes appear unrelated to climate change and were probably driven by disturbance damage. Physiological models predict that mountain beech responds only modestly to rising atmospheric CO2 concentrations (Richardson et al. 2005), whereas we found no evidence of a growth response. While temperature has strong influences on growth and carbon storage, mean annual temperature in New Zealand’s Southern Alps has not trended upwards over the last 40 years (Fig. S12), so we did not observe any global warming effects on wood production. Approaches developed in this paper allow climate change effects to be distinguished from other processes; it would be interesting to see these methods applied to other forest types.

Our study emphasizes the need to closely integrate physiological process models for predicting responses to anthropogenic change with information on disturbance frequencies and intensities (Friend, Shugart & Running 1993). For example, while researchers are becoming more and more confident in their understanding of how various metabolic processes vary with temperature and water supply (e.g. Peng et al. 2009; Piao et al. 2009b; Ryan et al. 2010; Wang et al. 2011b), they require a much clearer understanding of how mortality changes in response to extreme temperatures and droughts in order to predict forest responses to climate change (Van Mantgem & Stephenson 2007; Phillips et al. 2009; Van Mantgem et al. 2009; Allen et al. 2010). Similarly, it is increasingly clear that N deposition in Europe and the USA has enhanced forest growth (Solberg et al. 2009; Thomas et al. 2010) and probably contributed towards accelerating carbon sequestration rates in European forests (from 0.18 kg C m−2 year−1 in the 1950s to 0.29 kg C m−2 year−1 in 2007; Ciais et al. 2008). Physiological modelling of N responses is well advanced (e.g. Whitehead et al. 2002; Zaehle, Friedlingstein & Friend 2010). However, the long-term impacts of N deposition on mortality are poorly understood yet could have important effects on competitive processes (e.g. Baribault & Kobe 2011).

Regional-scale modelling of carbon sequestration in the context of anthropogenic global change

Major disturbances have long-term influences on regional-scale carbon sequestration. Over a period of 30 years, the mountain beech forests were hit by a series of disturbance events that caused above-ground biomass to fall by 0.3 Mg C ha−1 year−1. If similar losses had occurred throughout the 2.9 million ha of Nothofagus forests in New Zealand (Wardle 1984), an estimated 870 Pg C year−1 would have moved from living biomass to detrital and atmospheric pools, equivalent to about 11% of New Zealand’s annual fossil fuel emissions (based on per capita consumption of 2 Mg C year−1). The simulation models suggest that, under realistic disturbance scenarios, above-ground carbon storage may fall by as much as 40% over a 40-year period and take equally long to recover (Fig. 8). Similar transformations are occurring in other regions. An outbreak of mountain pine beetle (Dendroctonus ponderosae) in British Columbia, Canada, is greater in extent and severity than any previously recorded, killing trees across 0.374 million km2 of forest and releasing an estimated 0.27 Gt C into the atmosphere over 20 years (equivalent to 0.36 Mg C ha−1 year−1) as a result of decomposition of dead wood and reduced productivity (Kurz et al. 2008). In Amazonia, widespread low-intensity tree mortality in 2005 and 2010 – probably in response to severe droughts – is estimated to have decreased carbon storage by 1.6 and 2.2 Pg C, respectively (Phillips et al. 2009; Lewis et al. 2011). In summary, natural forests are non-equilibrium systems in which major disturbances drive long-term dynamics (Sprugel 1991), and disturbance history, especially of a large-scale nature, has profound influences on carbon sequestration (e.g. Caspersen et al. 2000; Allen et al. 2010).

Of particular concern is the possibility of a positive feedback between climate and movement of CO2 into the atmosphere, mediated through increased forest disturbance (Dale et al. 2001). In North American boreal forests, the area of forest burned and frequency of larger fires doubled from the 1960s/1970s to the 1980s/1990s (Kasischke & Turetsky 2006) and are projected to increase further (Kurz et al. 2008). Through a series of model simulations, Kurz et al. (2008) concluded that unrealistically high growth enhancements (without commensurate increases in decomposition rates) would be required to offset carbon released to the atmosphere through increased fire. At the same time, owing to a more favourable climate, mountain pine beetle has extensively expanded its range in western North America, resulting in the largest outbreak ever recorded. Many other tree species in Europe and North America are now threatened by introduced pathogens and diseases (Lovett et al. 2006), which could lead to the release of large quantities of CO2. The modelling framework described in this paper provides a method for exploring climate change effects in the context of disturbance and age-related productivity decline.

Building disturbance history into regional-scale forest carbon models will require detailed information on present and past anthropogenic impacts (Clark 2007). In mid-northern latitudes, forests increased in cover during the 20th century and are rapidly sequestering carbon: 0.30–0.58 Pg C year−1 in the USA (Pacala et al. 2001), 0.8–2.0 Pg C year−1 in China (Piao et al. 2009a,b) and 0.14–0.21 Pg C year−1 in Europe (Ciais et al. 2008). These forests are net carbon sinks because they are young and growing, resulting from abandonment of agricultural land in the 19th century in eastern USA (Foster 2002), abandonment of coppicing in southern Europe (Ciais et al. 2008), post-war plantations in northern Europe (Ciais et al. 2008) and ambitious Chinese afforestation and reforestation programmes in the 1980s (Wang et al. 2011a,b). There is mounting evidence that forests in tropical regions are also carbon sinks, uptaking about 1.3 Pg C year−1 in the 1980s and 1990s (Lewis et al. 2009). The reason why they act as sinks remains unresolved (Clark 2002; Lewis, Phillips & Baker 2006). While CO2 fertilization appears the most likely explanation based on available evidence (Lewis et al. 2009), Clark (2007) argues that ‘there is now abundant reason to think that all extant tropical forests are likely to have been affected by significant past disturbances’ and that ‘without first identifying such legacies, we cannot judge their potential contribution to current forest processes’. We predict that disturbance events will have less effect on the productivity of lowland tropical forests than they do in mountain beech forest, because multilayered canopies and rapid growth rates (Anderson et al. 2006) ensure that canopy gaps are rapidly refilled with leaves, but disturbance could nevertheless have strong effects on LossM and SeqM. Tropical forest cover only 7–10% of the world’s land surface but process six times as much carbon per year as humans emit by burning fossil fuels (Lewis et al. 2009), so understanding the contribution of disturbance to their carbon cycle is urgently required.

At regional and local scales, the particular disturbance regime critically determines the rate at which carbon originating from tree mortality returns to the atmosphere. Intense crown fires represent the quickest release to the atmosphere of biomass carbon. Based on a chronosequence study from a dry tropical forest in Mexico, total ecosystem biomass and carbon required 70 and 50 years after fire, respectively, to recover values similar to mature forests (Vargas et al. 2007). Tree mortality via wind disturbance or insect outbreaks typically results in slower return of carbon to the atmosphere, with actual rates depending on both the decay resistance of the woody debris (e.g. Grove, Stamm & Wardlaw 2011) and local climate. For example, C. dentata (American chestnut) canopy trees were eradicated from eastern US forests in the 1930s owing to chestnut blight but still comprises a substantial component of the coarse woody debris in these forests (Lovett et al. 2006). As a result of slow decomposition rates in this cool, nutrient-poor system (Zhang et al. 2008; Weedon et al. 2009), there is a substantial lag between tree mortality and the return of carbon to the atmosphere.

Disturbance is inherently unpredictable and spatially patchy (Runkle 1982, 1990; Pickett & White 1985; Clark 1992; Oliver & Larson 1996; Allen, Bellingham & Wiser 1999), adding considerable uncertainty to carbon-sink predictions. We have developed an integrative framework for understanding long-term carbon fluxes in the context of disturbance and have used it to investigate processes in a simple forest type that was ideal for gap-phase modelling: mountain beech is a light-demanding species, which regenerates in cohorts following major disturbance events and forms naturally monospecific stands. Nevertheless, the PPA simulation models developed here can be applied to complex multispecies forests (Purves et al. 2008) and provide a powerful approach for predictive modelling of forest dynamics (Purves & Pacala 2008). As we enter a new era in which the governments of developing countries will be paid to manage carbon sequestration in forests (Pacala & Socolow 2004; Gibbs et al. 2007), we need to develop a much better understanding of the risks associated with such management, in the face of uncertain disturbance events. PPA modelling is a promising approach for quantifying uncertainty around carbon-sink estimates.


We are grateful to Drew Purves for inspiring us to work on this topic and to John Caspersen and Mark Vanderwel for generously sharing an unpublished manuscript describing PPA modelling of Canadian forests. Andrew Friend and Nikée Groot provided insightful comments. We thank the many researchers who have contributed towards data collection at the Craigieburn study site, particularly John Wardle for setting up the distributed plot network in the 1970s and Murray Davis and Peter Clinton for helping establish the stand-development sequence. This work was partly funded in New Zealand by MSI Contract No. C09X0308 and the MAF Sustainable Land Management and Climate Change fund (contract C04X1002 administered by the Ministry for Science and Innovation) and in Britain by the Natural Environment Research Council.