Age-related decline in stand productivity: the role of structural acclimation under hydraulic constraints


Correspondence: F. Magnani c/o Istituto Miglioramento Genetico delle Piante Forestali, CNR, via A. Vannucci 13, I-50134, Firenze, Italy. Tel.: +39 55 461453; Fax: +39 55 486604; E-mail:


The decline in above-ground net primary productivity (Pa) that is usually observed in forest stands has been variously attributed to respiration, nutrient or hydraulic limitations. A novel model is proposed to explain the phenomenon and the co-occurring changes in the balance between foliage, conducting sapwood and fine roots. The model is based on the hypothesis that a functional homeostasis in water transport is maintained irrespective of age: hydraulic resistances through the plant must be finely tuned to transpiration rates so as to avoid extremely negative water potentials that could result in diffuse xylem embolism and foliage dieback, in agreement with experimental evidence. As the plant grows taller, allocation is predicted to shift from foliage to transport tissues, most notably to fine roots. Higher respiration and fine root turnover would result in the observed decline in Pa. The predictions of the model have been compared with experimental data from a chronosequence of Pinus sylvestris stands. The observed reduction in Pa is conveniently explained by concurrent modifications in leaf area index and plant structure. Changes in allometry and shoot hydraulic conductance with age are successfully predicted by the principle of functional homeostasis.


The decline with age in above-ground forest stand productivity (Pa) has long been known to forest ecologists ( Kira & Shidei 1967; Gower, McMurtrie & Murty 1996). This process is only partly explained by the often observed decline in leaf area index and light interception: productivity per unit foliage biomass is also reduced ( Ryan, Binkley & Fownes 1997).

Because of prolonged meristematic activity and of a continuous tissue turnover, the detrimental effects of cell ageing do not appear to play the same role in polycarpic plants as they do in animals ( Nooden 1988). Rather, the explanation seems to be found in the shifting balance between photosynthesis, respiration and tissue turnover.

Kira & Shidei (1967) first hypothesized that the decline in net primary production with stand age was due to the continuous increase in respiring tissues. Direct observations, however, have recently demonstrated that increasing sapwood respiration accounts for only a small proportion of the Pa decline ( Ryan & Waring 1992; Ryan et al. 1995 ).

An increased below-ground allocation has also been proposed as a possible explanation, as a consequence of the reduced availability of nutrients that are increasingly immobilized in litter during stand development ( Murty, McMurtrie & Ryan 1996). A greater fine root-to-foliage biomass ratio with age has indeed been often observed ( Grier et al. 1981 ; Santantonio 1989; Ryan & Waring 1992; Usol’tsev & Vanclay 1995; Vanninen et al. 1996 ).

The photosynthetic rates of young and old trees have also been observed to differ ( Kull & Koppel 1987; Grulke & Miller 1994; Schoettle 1994; Yoder et al. 1994 ). The decline in photosynthesis per leaf area observed in ageing stands has been attributed either to a reduced foliar nitrogen concentration ( Field & Mooney 1986), as a result of nutrient limitations, or to the increased hydraulic resistance of longer stems and branches in mature trees: in order to avoid extreme leaf water potentials and diffuse xylem cavitation, stomatal conductance and gas exchange would have to be reduced so as to maintain a functional homeostasis ( Yoder et al. 1994 ; Saliendra, Sperry & Comstock 1995). However Sperry et al. (1993) reported that, following the artificial reduction of xylem hydraulic conductance, diffuse xylem embolism and foliage dieback could be prevented only temporarily by stomatal closure, but an increased production of xylem was required in the longer term.

Also over the lifetime of the stand, structural changes contribute to the maintenance of a functional homeostasis in water transport: not only by the already mentioned increase in fine root-to-foliage ratio, but also through an altered balance between the area of conductive sapwood and transpiring foliage ( Albrektson 1984; van Hees & Bartelink 1993; Vanninen et al. 1996 ) that partly counterbalances the effects of increasing height on shoot hydrau-lic resistance ( Mencuccini & Grace 1996a). As a result, hydraulic conductance per unit leaf area is remarkably constant with age. A shift of resource allocation from leaves to conductive structures in the stem and in the roots, reducing photosynthesis and increasing both respiration and turnover, could help explain the observed reduction in Pa.

Above-ground productivity has often been assumed as an indirect criterion of plant fitness, in particular in forest species that are strongly limited by competition for light ( Bloom, Chapin & Mooney 1985; Parker & Maynard Smith 1990). One could then expect plants to have evolved a strategy of optimal growth under hydraulic constraints, whereby hydraulic safety is achieved through the minimum possible investment in sapwood and fine roots, so as to allocate as many resources as possible to the production of assimilating leaves and maximize Pa.

Two questions were therefore addressed in the present analysis. First, can the decline in above-ground net primary production observed in a chronosequence of Scots pine (Pinus sylvestris L.) be explained by changes in the functional and allometric structure of the stand, even without a reduction in gas exchange and light use efficiency? Second, can the observed structural changes be explained by a strategy of optimal plant growth under the hydraulic limitations imposed by the risk of diffuse xylem embolism? A new mathematical model was developed to answer these questions.


Implications of structural developmental changes

The effects of structural changes on stand Pa and growth can be explored by a simple carbon balance analysis. Above-ground net primary production Pa can be expressed as:


where A is stand assimilation, Rm is maintenance respiration, rg is specific growth respiration and Pb is stand below-ground net primary productivity. All variables and parameters are defined in Appendix 1.

Stand assimilation can be assumed to be proportional to the cumulated photosynthetic active radiation intercepted by the foliage over the growing season ( McMurtrie et al. 1994 ):


where ɛ0 is stand gross light utilization coefficient, I is incoming photosynthetically active radiation, σ is specific leaf area, Wf is stand foliage biomass and k is a light extinction coefficient for the canopy.

A simple formulation can be used for both respiration and turnover of tree compartments ( Thornley & Johnson 1990). Maintenance respiration of each plant compartment is assumed to be proportional to its biomass:


where Ws is sapwood biomass (inclusive of coarse roots > 5 mm diameter), Wr is fine root biomass (< 5 mm diameter) and the specific respiration rates rim are a function of tissue nitrogen content Ni and annual average temperature and variability ( Ryan 1990, 1991).

Stand below-ground net primary production is the sum of root turnover Tr (equal to root mortality) plus any changes in fine root biomass taking place over the year (ΔWr). Because of the high turnover rate of fine roots ( Schoettle & Fahey 1994; Eissenstat & Yanai 1997), ΔWr can be assumed to be negligible in comparison with root mortality and Pb can be therefore expressed as:


where root mortality has been expressed as the ratio between fine root biomass and longevity.

An age-related decline in Pa can be partly explained by the decline in leaf area index and light interception that is commonly observed in ageing stands ( Gholz, Linder & McMurtrie 1994). However, stand growth efficiency (Eg; stand Pa per unit foliage biomass; Waring 1983) is also reported to decline concurrently ( Ryan, Binkley & Fownes 1997). When Eqns 1–4 are combined, Eg can be expressed as the sum of carbon gain and costs per unit foliage biomass:


Assimilation per unit leaf biomass (i.e. the unit carbon gain term) may even increase in old stands, because of reduced self-shading of foliage. A decline in growth efficiency, on the contrary, could result from changes in the balance between photosynthetizing foliage, conducting sapwood and fine roots with stand development, resulting in greater unit respiratory and below-ground costs.

Such a structural acclimation, often reported in the literature ( Persson 1983; Albrektson 1984; Usol’tsev & Vanclay 1995; Vanninen et al. 1996 ), could result from the need to maintain a functional homeostasis in water transport and prevent the negative effects of extreme water potentials.

The hydraulic constraint

The movement of water from the soil through the plant is customarily described in analogy to Ohm’s law ( Slatyer 1967). At equilibrium, the water potential of the leaves will exceed in absolute terms the water potential of the soil Ψsoil by a gravitational component (Ψgrav) that is a linear function of tree height H. Transpiration will induce an additional loss of water potential, as water has to overcome in its movement through the plant an hydraulic resistance Rtot, consisting of a root (Rroot) and a shoot component (Rshoot) arranged in series. If any differences in transpiration and hydraulic resistance among leaves within the canopy are neglected, all fluxes and resistances can be expressed on a ground area basis and the minimum water potential experienced by the foliage (Ψleaf) can then be represented as:


where Es is maximum stand transpiration over the year, H is tree height and ρw and g are water density and acceleration due to gravity, respectively.

Both stand transpiration and hydraulic resistances are to a large extent a function of stand structure. Scots pine canopies are generally open and aerodynamically well-coupled to the atmosphere ( Jarvis, James & Landsberg 1976) and environmental gradients through the canopy are consequently small; vertical gradients in stomatal conductance, transpiration and photosynthesis per unit foliage biomass are also reasonably small ( Kellomäki & Hari 1980; Troeng 1981). Transpiration can be therefore assumed to be linearly proportional to stand foliage biomass Wf:


where σ is specific leaf area and Eun is maximum transpiration per unit leaf area, assumed to be a constant function of site environmental conditions. The implications of this assumption and of alternative formulations of stand transpiration will be discussed in detail in the Results section.

The hydraulic resistance of the root system is mainly determined by the radial resistance of fine roots ( Weatherley 1982; Magnani, Centritto & Grace 1996) and is therefore inversely related to the surface and, in first instance, to the biomass of feeder roots:


where kr is fine root hydraulic conductance per unit biomass.

The hydraulic resistance of the shoot can be expressed as a function of plant height H and sapwood area As ( Whitehead, Edwards & Jarvis 1984; Whitehead, Jarvis & Waring 1984). If the simple assumption is introduced that the cumulative cross-sectional area of the sapwood in stem and branches is constant all along the plant ( Shinozaki et al. 1964 ; Makela 1986), then shoot resistance can be expressed as:


where ks and ρs are sapwood specific hydraulic conductivity and density, respectively.

As already mentioned, the minimum water potential experienced by the leaf is rather conservative for any species, changing little with plant age and site conditions (as reviewed in the Discussion section). This minimum appears to correspond to the critical value for the onset of xylem embolism ( Tyree & Sperry 1988; Sperry & Pockman 1993):


This functional homeostasis has profound implications for the hydraulic architecture of the plant, as it requires that hydraulic resistance per unit leaf area does not exceed a limit given by ( Eqns 6–7):


When shoot and root resistances are expressed as a function of plant allometry ( Eqns 8–9), the principle of functional homeostasis results in a general hydraulic constraint on plant structure:


Optimality theory ( Bloom, Chapin & Mooney 1985) requires that Rtotu not only does not exceed, but exactly matches the limit imposed by Eqn 12: if higher values would result in extensive cavitation and foliage dieback, lower values on the other hand could only be achieved if a lower leaf area were produced than can be safely sustained, so limiting light interception and photosynthesis and ultimately plant growth and fitness.

But for the minor effects of gravitational potential, Eqn 12 therefore predicts an age-independent value of hydraulic resistance per unit foliage area in the soil-plant continuum. Experimental evidence (reviewed in the Discussion section) seems to suggest that Rtotu is indeed rather conservative over the lifetime of the plant, despite major changes in plant dimensions.

Optimal allometry under hydraulic constraints

According to Eqn 12, when new transpiring foliage is produced, the plant will support its needs with enough absorbing roots and conducting sapwood to keep the minimum water potential within a safety range. Optimality, moreover, requires that a reduction in hydraulic resistance is achieved at the lowest possible cost, so as to reserve as many resources as possible for foliage growth and maximize plant fitness ( Parker & Maynard Smith 1990).

In order to decrease hydraulic resistance, the investment of carbon in fine roots or sapwood yields to the plant very different returns, both because of different hydraulic conductivities and because of the strong impact of plant height on shoot resistance. On the other hand, fine roots and sapwood have markedly different longevities and the cost of production, discounted for turnover, will differ accordingly.

Optimal growth under hydraulic constraints requires that the ratio of marginal hydraulic returns to marginal annual cost for carbon investment in either roots or sapwood be the same ( Bloom, Chapin & Mooney 1985; Case & Fair 1989), i.e.


where ls is sapwood longevity, assumed to be constant. From Eqns 8–9, this corresponds to:


from which the allometric constraints can be derived:




Equation 16 predicts a constant ratio, under any environmental conditions, between conductive sapwood and absorbing roots, suggesting the existence of a functional balance in water transport. Such a constant balance, though, would not extend to foliage. When Eqn 15 is combined with the hydraulic constraint of Eqn 12, the allometric relationship between sapwood area and foliage biomass can be expressed as:


According to Eqn 18, the ratio between sapwood and foliage biomass is not constant, as suggested by the pipe model theory, but increases with height. The relationship would be linear, were it not for the effects of gravitational potential on Rtotu. It is interesting to note that the first term in brackets is the allometric ratio that would be expected if all the hydraulic resistance were located in the shoot, as assumed in the hydraulic model of Whitehead et al. (1984) . Because of a positive root resistance, however, the optimality model predicts a rather large sapwood-to-foliage ratio even in small seedlings (second term in brackets in Eqn 18).

The ratio of fine root-to-foliage biomass will also increase with stand height:


The first term in brackets in Eqn 19 represents the constant allometric ratio that would be expected if all the hydraulic resistance were located in fine roots, as predicted for herbaceous plants by Givnish (1986). In the case of trees, however, because of the longitudinal resistance in the shoot, optimization theory requires an almost linear shift in the root-leaf balance as tree height increases.

A result of the allometric changes of Eqn 19 is the progressive decline of fine root hydraulic resistance per unit foliage area over the lifetime of the stand. However, this reduction will be matched by a parallel increase with height of the shoot component, so as to maintain an almost constant value of total resistance per unit foliage area, as predicted by Eqn 12:


As height increases, this shoot component will approach asymptotically the maximum value of plant hydraulic resistance per unit leaf imposed by the threat of foliage dieback.


Site description

The predictions of the model were tested against a chronosequence of P. sylvestris stands, part of an extensive plantation in Thetford Forest, East Anglia, U.K. ( Mencuccini & Grace 1996a, 1996b). Average summer precipitation is 170 mm and average July temperature is 17 °C. Despite local differences, soil nutrition is not considered to be a limiting factor for tree growth at the site ( Corbett 1973). The forest has been thoroughly studied over the years so that most of the parameters required by the model could be attributed species- as well as site-specific values (Appendix 1).

Nine study sites were selected in even-aged stands of Scots pine, with tree age ranging from 7 to 59 years and densities comprised between 3285 and 398 trees per hectare ( Table 1). Stands were selected according to origin so as to minimize genetic variability. No thinning had been performed over the last 10 years and stands less than 33-year-old had never been thinned.

Table 1.  Summary of stand density, diameter at breast height (D) and top height (H) of the chronosequence of P. sylvestris stands
(years)(trees ha−1) (cm)(m)
  1. 59

  2. 398

  3. 34·8

  4. 21·7

73285 6·9 2·2
14313312·8 7·7
18388310 9·9

Leaf and xylem characteristics

At each site, three dominant trees were felled. Tree sapwood area and biomass, leaf biomass and area were determined by stratified sampling, as described by Mencuccini & Grace (1996b). Tree above-ground hydraulic resistance per unit foliage area (Rshootu) was derived from direct measurements in the laboratory, as described by Mencuccini & Grace (1996a). All measurements were conveniently scaled-up to the stand level, based on observed empirical relationships with sapwood area and tree diameter ( Mencuccini & Grace 1996b).

Stand Pa

Shoot biomass growth (above- plus below-ground, excluding fine roots below 5 mm) was computed for the felled trees and scaled-up to the stand level as described in Mencuccini & Grace (1996b). Stand above-ground net primary production was computed as the sum of shoot growth and annual litterfall, assumed to be a constant fraction of foliage biomass ( Jalkanen et al. 1994 ).

Fine root biomass

Fine root biomass was not directly measured, but derived from the empirical model proposed for Scots pine by Usol’tsev & Vanclay (1995), relating tree fine root biomass to plant age, diameter and height. The model fitted very well the experimental data reported by Vanninen et al. (1996) for Finnish stands and by Ovington (1957) for Thetford Forest itself (R2 = 0·96 and 0·99, respectively). Site-specific parameter values were therefore used to estimate the root biomass (< 5 mm) of felled trees, that was then scaled-up to the stand level on a basal area basis.

Fine root characteristics

A value for fine root longevity in P. sylvestris was derived from Persson (1980); the highest of the two figures reported (lr = 0·55 and 0·65) was chosen, as the study referred to finer roots (< 2 mm diameter) than considered here. Similar values have been reported in the literature for several pine species ( Santantonio 1989; Schoettle & Fahey 1994).

The hydraulic conductance per unit biomass of fine roots could not be directly determined, but was derived from the literature. Roberts (1977) measured by the tree-cutting technique the hydraulic conductance of entire root systems of P. sylvestris trees growing in Thetford. The fine root length of the same stand was measured by Roberts (1976) and was translated into an appropriate figure for fine root biomass assuming a specific root length of 25 m g−1 ( George et al. 1997 ). A value for the specific hydraulic conductance of fine roots could then be derived from Eqn 8. The estimated figure was in rather good agreement with the value of 3·5 × 10−7 m3 s−1 MPa−1 kg−1 that can be inferred for pine seedlings from experimental data in Sands et al. (1982) and Smit-Spinks et al. (1984) .

Values for all other parameters in the model were either directly measured or derived from the literature, as specified in Appendix 1.

Sensitivity and uncertainty analysis

Some of the parameters used in the model could not be directly measured, but had to be computed with a certain degree of uncertainty. Moreover, a few of them are known to change to some extent over the lifetime of the plant, whilst a constant value has been assumed in the model. To evaluate the effects of individual parameters on model predictions, a sensitivity analysis has been carried out following Miller (1974). A random change in each input parameter has been imposed, assuming a normal distribution with coefficient of variation V = 10% around the baseline value reported in Appendix 1. Allometric ratios and hydraulic resistances have been simulated for each value of the input parameter (n = 20) and the corresponding coefficient of variation V computed separately for each point in the chronosequence.

Model uncertainty has been assessed by the Monte Carlo random sampling method described by Jansen et al. (1994) . Sensitive parameters have been jointly varied (n = 100), assuming they are independently distributed with V = 25%. Confidence limits for model predictions have been based on the standard error of the resulting output.


Plant functional structure

A rather clear picture of P. sylvestris stand dynamics emerges from the chronosequence of homogeneous plots ( Fig. 1). Stand height is still increasing at an age of almost 60 years, albeit at a reduced pace. As a consequence, sapwood biomass per unit surface is also increasing (data not shown), despite the concurrent decline in sapwood basal area. The estimated biomass of fine roots, on the contrary, is almost constant after a maximum value of about 0·7 kg m−2 has been reached at an age of 30. A marked decline in leaf area index is observed after a maximum is reached at polestage; light interception is therefore lower in older stands ( Mencuccini & Grace 1996b). Similar results have often been reported for P. sylvestris ( Ovington 1957; Albrektson 1984; Vanninen et al. 1996 ) and several other species ( Margolis et al. 1995 ; Ryan, Binkley & Fownes 1997).

Figure 1.

Developmental changes in top height (H), leaf area index (LAI), estimated fine root biomass (Wr) and sapwood area (As) in a chronosequence of P. sylvestris stands.

The different dynamics of plant compartments translate into marked changes in the functional structure of the stand.

The ratio between sapwood cross-sectional area at breast height and foliage biomass (As/Wf) is not constant, as often assumed ( Makela 1986; Margolis et al. 1995 ), but increases with stand height. This pattern is well explained by the hypothesis of optimal growth under hydraulic constraints ( Fig. 2), as expressed in Eqn 18.

Figure 2.

Height-related changes in sapwood area-to-foliage biomass ratio (As/Wf). Experimental data are compared with model predictions ( Eqn 18). Dotted lines correspond to 95% confidence intervals, as determined by uncertainty analysis. A constant ratio would be expected from the pipe model theory.

A re-analysis of published data-sets confirms this finding for Scots pine ( Albrektson 1984; van Hees & Bartelink 1993; Vanninen et al. 1996 ) as well as for P. taeda ( Shelburne, Hedden & Allen 1993) and P. contorta ( Thompson 1989). The opposite pattern has been reported on the contrary for Abies balsamea ( Coyea & Margolis 1992).

A possible explanation for this different pattern lies in different dynamics of xylem anatomy and hydraulic characteristics. Juvenile wood is known to be characterized in conifers by smaller tracheid length, diameter and, ultimately, lower specific hydraulic conductivity ( Pothier, Margolis & Waring 1989; Pothier et al. 1989 ). A continuous increase in tracheid dimensions and sapwood conductivity was observed in A. balsamea until the age of 70 ( Coyea & Margolis 1992), whilst in Scots pine wood maturation had already been completed by the age of 15, before the onset of the Pa decline ( Mencuccini, Grace & Fioravanti 1997). The assumption in Eqn 9 of a constant value of sapwood hydraulic conductivity seems therefore appropriate. If ks were assumed to increase markedly with age, on the contrary, the model would indeed predict a decline in the sapwood-to-foliage area ratio with stand development (data not shown). This result highlights the relevance of cell maturation and xylem anatomy not only for wood quality ( Zobel & van Buijtenen 1989), but also for forest function and productivity.

It is perhaps worth noting that a much larger change in the sapwood-to-foliage area ratio would be predicted by the model of Whitehead et al. (1984) , which neglects the contribution of fine roots to total plant hydraulic resistance, since the effects of height would have to be entirely counterbalanced by the larger sapwood area. A constant shoot hydraulic resistance per unit foliage biomass is assumed by Whitehead et al. (1984) ; direct measurements, on the contrary, support the view that Rshootu increases with height, despite the greater conductive sapwood area ( Fig. 3), as predicted by the hypothesis of functional balance and cavitation avoidance ( Eqn 20).

Figure 3.

Height-related changes in shoot hydraulic resistance per unit foliage area (Rshootu). Experimental data are compared with model predictions ( Eqn 20). Dotted lines correspond to 95% confidence intervals, as determined by uncertainty analysis. A constant value would be expected from the model of Whitehead, Jarvis & Waring (1984).

The hydraulic resistance per unit foliage area in the soil-plant continuuum, however, does not seem to be affected by plant dimensions, as demonstrated by a review of literature data for seedlings and mature P. sylvestris trees ( Table 2). To draw a comparison, a 20-fold difference in Rshootu would be expected between a seedling 70 cm tall and a tree of 15 m based on the pipe model theory, if all resistance were assumed to be located in the shoot, or a 10-fold difference if the additional assumptions were introduced that 50% of total plant resistance is below-ground and that the ratio between feeder roots and foliage is constant.

Table 2.  Comparison of published values of hydraulic resistance per unit foliage biomass (Rtotu) in P. sylvestris plants of different dimensions, growing under similar climatic conditions (Scotland, UK). The large variability in tree height does not reflect in different values of minimum needle water potential or hydraulic resistance in the soil-plant continuum
HLAIMinimum ΨRtotu
(m)(MPa)(MPa s/m)
  1. seedling

  2. – 1·8

  3. 1·84

  4. 1 Whitehead et al. (1984) , 2Jackson et al. (1995b) , 3Jackson et al. (1995a) , 4Peña & Grace (1986).

15 2·4– 1·83·21
15 3·1– 1·51·81
10 2·59– 1·54·92
seedling– 1·2 1·63

As a consequence, the minimum water potential experienced by the needles under a wide range of conditions is almost constant at a value close to the threshold for xylem cavitation (– 2 MPa), as determined experimentally for Scots pine by Cochard (1992). It is worth noting that the value of total plant resistance per unit foliage area estimated from Eqn 11 for the environmental conditions at Thetford Forest (3·0 × 107 MPa s/m for H = 24 m) is not far from the one derived from measurements by Jarvis (1976) for the same site (2·6 × 107 MPa s/m for H = 16·5 m).

This functional homeostasis could be obtained by a concurrent shift in the balance between transpiring foliage and absorbing roots ( Eqn 12), as suggested for Thetford Forest by the estimates reported in Fig. 4. This appears to be mainly the result of the marked decline in stand leaf area index, in the face of a constant fine root biomass ( Fig. 1). Although not based on direct root measurements, these figures are consistent with the report by Ovington (1957), Persson (1983), Usol’tsev & Vanclay (1995) and Vanninen et al. (1996) of an increased allocation to fine roots in ageing P. sylvestris stands. The same pattern has been reported for several other species ( Santantonio 1989; Gholz, Linder & McMurtrie 1994).

Figure 4.

Height-related changes in fine root-to-foliage biomass ratio (Wr/Wf). Experimental data are compared with model predictions ( Eqn 19). Dotted lines correspond to 95% confidence intervals, as determined by uncertainty analysis. A constant ratio would be expected from the functional balance model proposed by Givnish (1986).

This picture would appear in contrast with the common assumption of a root-shoot functional balance ( Wilson 1988; Makela 1990; Cannell & Dewar 1994), whereby foliage and fine root biomass and activity should be matched so as to provide a constant pool of carbon, water and nutrients for growth. It should be noted, on the other hand, that fine root activity in nutrient absorption could be lower in ageing stands. Gower et al. (1996) suggested that nutrient immobilization in soil organic matter could reduce the effectiveness of fine roots in ion uptake, thus requiring a greater below-ground allocation and a lower leaf area index. This would be consistent with the observation of a rather constant foliar nitrogen concentration in the P. sylvestris chronosequence analysed ( Mencuccini & Grace 1996b). Homeostasis in both water transport and nutrient content would therefore appear to be achieved at the same time.

For the sake of simplicity, only a coarse representation of plant hydraulic architecture and transpiration has been included in the model. It is therefore important to discuss some of the simplifying assumptions introduced.

Several features of plant hydraulic architecture have been neglected in the model. Sapwood area is assumed to be constant along stem and branches and above-ground hydraulic resistances are lumped together, as if the xylem were indeed just a bundle of uniform conducting pipes. Experimental data, however, suggest that this does not result in significant errors. In P. sylvestris the effect of greater branch length in the lower portion of the crown appears to be largely compensated by the reduced leaf area supported and by the lower internode resistance ( Mencuccini & Grace 1996a). Moreover, when the simple model of Eqn 9 with fixed parameters is compared with detailed measurements of above-ground hydraulic resistance ( Mencuccini & Grace 1996a) a rather good fit is observed (R2 = 0·78, with a slope of 0·99; Fig. 3).

Xylem conductivity and longevity, however, have but a minor impact on model predictions ( Table 3), which are more sensitive to the estimated value of root hydraulic conductivity. Imposed transpiration rates and the water potential for cavitation, on the other hand, appear to be the most critical parameters.

Table 3.  Sensitivity of predicted functional structure to input parameters. A random change in input parameters has been imposed, assuming a normal distribution with coefficient of variation V = 10% around the baseline value reported in Appendix 1. Output variables have been simulated for each value of the input parameter (n = 20) and the corresponding coefficient of variation V computed separately for each point in the chronosequence. For each input parameter, the average value of V over the chronosequence is presented
 V (%)
  1. 17·7

  2. 17·7

  3. 15·6

kr 3·6 9·2 3·5
ks 7·5 1·9 3·6
lr 3·6 1·9 3·5
ls 3·5 1·9 3·6

Transpiration is assumed in Eqn 7 to be directly proportional to stand foliage biomass, rather than to the amount of available energy. However, a very similar developmental pattern of sapwood- and root-to-foliage ratio is predicted by the model if the alternative assumption is introduced that transpiration scales with intercepted radiation, in analogy with assimilation ( Eqn 2), rather than with foliage biomass ( Fig. 5).

Figure 5.

Effects of alternative formulations of stand transpiration: estimated values of sapwood area-to-foliage biomass (As/Wf) and fine root-to-foliage biomass ratio (Wr/Wf) are compared with model predictions when transpiration is assumed to scale directly with foliage biomass (●; R2 = 0·92 and 0·45, respectively) or with absorbed radiation (○; R2 = 0·58 and 0·89).

The combination of height and small leaf dimensions ensures that coniferous forests are well coupled to the atmosphere, so that transpiration is well approximated by imposed transpiration ( Jarvis & McNaughton 1986). It is therefore little affected by available energy, but strongly depends upon stomatal and canopy conductance. According to Schulze et al. (1994) , canopy conductance is almost proportional to leaf area index up to a value of 6, as confirmed even for broadleaf species by experimental results in Rauner (1976) and Lindroth (1993). Additional support for this view comes from the experiment of Whitehead et al. (1984) , who manipulated the transpiration of a Scots pine stand by thinning. Leaf area index and transpiration rates of the thinned stand were 80% and 70% of the control, respectively. Even if a value as low as 0·42 is assumed for the extinction coefficient of net radiation ( Jarvis, James & Landsberg 1976), a reduction in available energy of no more than 13% would be predicted. It seems therefore reasonable to assume that transpiration is more closely linked to foliage biomass than to available energy in open forest stands.

Above-ground net primary production

The increased allocation to fine roots would appear to contribute a large proportion of the observed decline in above-ground net primary production. Stand Pa dropped from 1·78 to 0·50 kg m−2 years−1 from age 14–18 to age 58–59 ( Fig. 6). Similar values and dynamics have been reported for other species, both coniferous and broadleaf ( Ryan, Binkley & Fownes 1997). The decline in Pa is well explained by concurrent changes in foliage biomass and functional structure, as predicted by the carbon balance model of Eqn 1 ( Fig. 7). Reduced leaf area index and light interception accounted for 45% of the observed change ( Table 4), but most of the drop in Pa stemmed from a shift in the functional balance between foliage, sapwood and fine roots. The pattern is still rather clear even if a ± 25% error in fine root estimation is assumed. In the absence of structural changes (i.e. with constant sapwood area-to-foliage biomass and fine root-to-foliage biomass ratios) the carbon balance model suggests on the contrary that the observed drop in foliage biomass and light interception would have been largely compensated by reduced respiration and root turnover ( Fig. 6).

Figure 6.

Developmental changes in stand Pa. Estimated values (●) are compared with predictions of the equilibrium model ( Eqn 1) when structural changes are either accounted for (○) or neglected (◊). Dotted lines correspond to model predictions when a ± 25% error in fine root estimation is assumed.

Figure 7.

Developmental changes in stand Pa. Estimated values are compared with predictions of the equilibrium model ( Eqn 1) when structural changes are duly accounted for (R2 = 0·89, b = 0·99).

Table 4.  Reduction in above-ground net primary productivity between age 14–18 and age 58–59 in P. sylvestris stands. Absolute values and percentage change are reported. Observed changes are partitioned among co-occurring processes, based on the model of Eqn 1: assimilation A, maintenance respiration Rm and root turnover Tr. Both A and Rm estimates have already been discounted for growth respiration ( Eqn 1)
 Age% of Pa
 14–1858–59change explained
  1. Tr

  2. 0·51

  3. 1·13

  4. – 43

Pa1·780·50 (– 72%)
A2·612·01– 45
Rm0·410·48– 12

It has been suggested that the risk of diffuse xylem embolism could be prevented by stomatal closure ( Yoder et al. 1994 ; Williams et al. 1996 ), resulting in reduced radiation use efficiency ( Landsberg & Waring 1997). This possibility can not be ruled out. However, the value of maximum transpiration per unit leaf area derived from the literature for mature trees at Thetford ( Stewart 1988; Jackson, Irvine & Grace 1995b) is in close agreement with that reported elsewhere for P. sylvestris seedlings ( Peña & Grace 1986). Such indirect evidence suggests that stomatal mechanisms did not play a major role in maintaining a functional homeostasis in Scots pine.

The decline in stand productivity was partly explained by the development of Eg with age. Stand growth efficiency declined by more than 55% from canopy closure at age 14–18 to age 58–59 ( Fig. 8a). A decline in Eg with age had already been reported by Ovington (1957) for Thetford Forest and by Albrektson & Valinger (1985) for P. sylvestris in central Sweden, although with much slower dynamics in the latter case. In the present study, light interception and estimated photosynthesis per unit foliage biomass (i.e. unit carbon gain; Eqn 5) decreased quickly with canopy closure, but recovered to a large extent as self-shading declined in ageing stands. Because of changes in plant allometry, on the contrary, unit respiratory and below-ground costs increased in ageing stands and more than offset the recovery in carbon gain ( Fig. 8b). The increase in maintenance respiration determined by the greater sapwood and fine root biomass accounted for 12% only of the change in Pa, in good agreement with estimates by Gower et al. (1996) for P. contorta, using the G’DAY model. Estimated fine root turnover and the resulting increase in below-ground allocation, on the contrary, appear to play a key role in the reduction both of Pa and of Eg ( Tables 4 & 5). Santantonio (1989) suggested that an increased below-ground allocation and the resulting carbon loss through fine root turnover could largely explain the lower productivity of stands either ageing or on poor sites, a hypothesis supported by a growing body of experimental evidence ( Gholz, Linder & McMurtrie 1994; Beets & Whitehead 1996). Despite all the uncertainties in the evaluation of model parameters and flux components, the results presented seem to confirm this view, shedding new light on causes and implications of the commonly observed change in plant functional structure with age.

Figure 8.

Height-related changes in stand growth efficiency (Eg). (a) Comparison of estimated values (●) and predictions of the equilibrium model of Eqn 6. (b) Concurrent changes in unit carbon gain (●), unit respiratory costs (▴) and unit below-ground costs (○), as estimated from Eqn 5.

Table 5.  Reduction in foliage biomass Wf and growth efficiency Eg between age 14–18 and age 58–59 in P. sylvestris stands. Absolute values and percentage changes are reported. Observed changes in Eg are also partitioned among co-occurring processes, based on the model of Eqn 5
 AgeEg change
 14–1858–59explained (%)
  1. unit below-ground costs

  2. 0·57

  3. 1·94

  4. – 102

Wf0·80·51 (– 37%)
Eg1·910·85 (– 55%)
unit C gain2·863·44+ 47
unit respiratory costs0·450·82– 45


Several hypotheses have been put forward over the last few years to explain the age-related decline in stand productivity. The implications of the risk of diffuse embolism have been recognized, but the focus has been on the effects of hydraulic limitations on gas exchange only ( Sperry & Pockman 1993; Yoder et al. 1994 ; Williams et al. 1996 ; Landsberg & Waring 1997). On the other hand, the role of increasing below-ground allocation and carbon loss through root turnover has been stressed in relation to the acquisition of nutrients ( Gower, McMurtrie & Murty 1996; Murty, McMurtrie & Ryan 1996; Ryan, Binkley & Fownes 1997).

The new hypothesis presented, on the contrary, highlights the role of hydraulic limitations and structural acclimation in Pa reduction. The observed reduction in stand productivity appears indeed to be accounted for by allometric changes over the life-time of the stand. Moreover, the principle of optimal growth under hydraulic constraints seems to explain conveniently most of this structural acclimation: not only in the balance between foliage and fine roots, that could be explained also by the hypothesis of nutrient limitation ( Gower, McMurtrie & Murty 1996), but also in the foliage-to-sapwood area ratio, often assumed to be constant. Only one of these components, on the contrary, had been accounted for in previous models of plant structure under hydraulic constraints ( Whitehead, Jarvis & Waring 1984; Givnish 1986; Friend 1993).

That the increasing length of the hydraulic pathway in the stem of ageing trees should result not only in a larger sapwood area, but also in greater allocation to fine roots could seem counter-intuitive. Apart from being expected from optimality theory, however, such a complementarity in water transport is a good example of the integrated behaviour that is typical of complex systems.

The new perspective should be viewed as complementary rather than alternative to existing hypotheses of Pa reduction in ageing stands, as several mechanisms are likely to superimpose to a various extent under different environments. Further research is required to explore the interactions between water and nutrients in driving structural acclimation and between structural and stomatal responses in preventing the onset of diffuse embolism and tissue damage. Additional efforts are under way on the same P. sylvestris chronosequence to address some of these stimulating questions, as well as to test in greater detail the predictions of the optimality model.


We thank Prof. M. Borghetti (University of Basilicata, Italy), Prof. R.H. Waring (Oregon State University, U.S.A.), Prof. P. Hari and Dr F. Berninger (University of Helsinki, Finland) for helpful comments on the manuscript. The work was supported by the EU LTEEF-2 Project (Long-Term Regional Effects of Climate Change on European Forests: Impact Assessment and Consequences for Carbon Budgets) and by the Italian MURST IMPAFOR Project (Impact of Climate Change on Forests and Wood Production).



  1. 1Stewart (1988), 2Jackson et al. (1995b) , 3Page & Lebens (1986), 4Mencuccini & Grace (1996b), 5Roberts (1976), 6Roberts (1977), 7Mencuccini & Grace (1995), 8Persson (1980), 9Helmisaari & Siltala (1989), 10Mencuccini, unpublished, 11Braekke (1995), 12Chung & Barnes (1977), 13McMurtrie et al. (1994) , 14Cochard (1992).

Astand assimilationkg m−2 years−1
Assapwood basal area
Egstand growth efficiency (= Pa/Wf) years−1
Esstand transpirationm s−1
Euntranspiration per unit foliage aream s−14·2 × 10−81, 2
gacceleration due to gravitym s−29·8
Hstand heightm
Iincoming PAR over the growing season (mid April – mid October)MJ m−2 years−125543
klight extinction coefficient0·3–0·534
krspecific hydraulic conductance of fine rootsm3 s−1 MPa−1 kg−12·3 × 10−75, 6
ksspecific hydraulic conductivity of the sapwoodm2 MPa−1 s−11·3 × 10−37
lrfine root longevityyears0·658
lssapwood longevityyears3910
Nfnitrogen concentration in foliagekg N kg −10·0154
Nrnitrogen concentration in fine rootskg N kg−10·00759
Nsnitrogen concentration in sapwoodkg N kg−10·000511
Pnet primary production (subscript: a, above-ground; b, below-ground)kg m−2 years−1
rggrowth respiration coefficient0·2812
rmspecific maintenance respiration (subscript: f, foliage; r, fine roots; s, sapwood)years−1
Rmmaintenance respirationkg m−2 years−1
Rhydraulic resistance (superscript: u, per unit projected leaf area;MPa sm−1
 subscript: root, shoot, total)
Trfine root turnover ratekg m−2 years−1
Wstand biomass (subscript: f, foliage; r, fine roots; s, sapwood)kg m−2
ɛ0gross light utilization coefficientkg MJ−11·7 × 10−313
ρssapwood densitykg m−34404
ρwdensity of waterkg m−31000
σspecific leaf aream2 kg−14·57
Ψwater potential (subscript: leaf, foliage; grav, gravitational)Mpa
Ψsoilminimum soil water potentialMPa– 0·52
¯Ψcritical leaf water potentialMPa– 2·014