Summary It has previously been shown that lack of magne-sium, potassium or manganese depresses allocation of new mass to roots in trees, and that these elements often occur in low amounts in declining forest stands. A model for tree growth and nutrient uptake was used to examine the effect of allocation pattern of new plant mass on growth and development in soils with low nutrient concentrations. Growth parameters and em-pirical allocation functions from steady-state experiments with birch (Betula pendula Roth.) and Norway spruce (Picea abies (L.) Karst.) limited by N or Mg were used in the simulations. The simulation results show that plant nutrient concentration is sensitive to decreases in soil Mg concentration and is not counteracted by an increased allocation of plant mass to roots. A 50% reduction in the optimal soil Mg concentration de-creased the plant Mg concentration to the threshold of survival, whereas a 50% reduction of soil N had much less effect. Birch was more sensitive to low soil Mg concentration than Norway spruce. We conclude that, in the discussion of forest decline, it may be important to consider the decreased allocation of mass to roots when Mg (or K or Mn) is in short supply.
Keywords: forest decline, model, nutrient productivity.
Introduction
Nutrient deficiency causing needle yellowing has been ob-served in declining forests and has been proposed as one of the causes of decline (Huettl 1989, and references in Schulze 1989). According to Schulze (1989), this hypothesis is unlikely to provide a general explanation because of the large number of nutrient deficiencies known to induce needle yellowing: Mg on acid soils, Mn on dolomite, and K or Fe on limestone. Deficiencies of K, Mg and Mn decrease the allocation of plant mass to roots, in contrast to deficiencies of N and P that normally limit tree growth (Ericsson 1991). The lower the plant nitrogen concentration, the larger the root fraction and the higher relative uptake capacity. This negative feedback between nitrogen concentration and root allocation is strong and greatly enhances tree survival. However, when the feed-back is positive, as for Mg (Ericsson and Kähr 1995), Mn (Göransson 1994) and K (Ericsson and Kähr 1993), an increas-ing deficiency decreases biomass allocation to roots and hence uptake capacity, leading to even lower nutrient concentrations
in the tree. Ericsson (1991) suggested that, in the field, such a situation may give rise to a continuous decrease in tissue magnesium concentration culminating in tree death. To test this hypothesis, a simple model of tree growth was modified to include an allocation function.
The model
Plant growth
The model is described in detail in Wikström (1994). Briefly, the growth formulation follows the nutrient productivity con-cept (Ågren 1985, 1988, Ingestad and Ågren 1988, 1992). The nutrient productivity is the slope of the linear relationship between the relative growth rate and the plant concentration of the growth-limiting nutrient. In terms of absolute growth rate, the formula is
dW
dt = Pnn − Cn,min W ,
(1)
where W is plant mass, n is the amount of the growth-limiting nutrient in the plant, Pn is the productivity of that nutrient, and Cn,min is the extrapolated nutrient concentration at zero growth
rate. Theoretically, Cn,min is the lowest plant nutrient
concen-tration at which growth occurs, but in reality, plants die before this concentration is reached. The formula is valid for plant nutrient concentrations below Cn,opt , which is the minimum
plant nutrient concentration at which maximal relative growth rate (Rg,max ) is achieved. Although the nutrient productivity
does not include variations in light and water conditions, it has been shown to agree well with both experimental and field data (Ågren 1985). The formula has also been used in the NAP model to study the interaction between N and Mg in acidified forests (van Oene 1992).
Nutrient uptake
The nutrient uptake rate (dn/dt) is proportional to root growth (dWr/dt) and the soil nutrient concentration (Cn,soil ), and can be
expressed as:
dn
dt = dWr
dt Vd Cn,soil,
(2)
Allocation of mass in trees subject to nitrogen and magnesium
limitation
FREDRIK WIKSTRÖM and TOM ERICSSON
Swedish University of Agricultural Sciences, Department of Ecology and Environmental Research, P.O. Box 7072, S-750 07 Uppsala, Sweden
Received October 6, 1994
where Vd is the volume of growth substrate that is depleted of
nutrients by one unit of new root (cf. root absorbing power formulated by Nye 1966). The value of Cn,soil is assumed to be
constant during a simulation.
The formulation of nutrient uptake in Equation 2 has no upper limit for the uptake rate because dn/dt can be made arbitrarily large by increasing Cn,soil . We have chosen to keep
the model as simple as possible and the relative uptake rate, Ru,
is limited only by
Ru≤ Ru,max= Rg,max, (3)
ignoring the uptake capacity above the capacity needed for maximal growth.
Allocation of growth
The allocation of mass varies depending on the nutrient limit-ing growth. The patterns in Figure 1 for birch (Betula pendula Roth.) fall into two main categories: increased (N, P and S) and decreased (Mn, Mg and K) root fraction with increasing nutri-ent deficiency. Dry matter partitioning in Norway spruce (Picea abies (L.) Karst.) is less well documented than in birch, but there are some data for N and Mg (Figure 2). Although the data are from small seedlings, there is no reason to expect that larger trees differ in qualitative response even though they will differ in quantitative response.
We have examined the responses of birch and Norway spruce to low soil availability of N and Mg. The chosen nutrients may also represent the allocation response to low soil P and S, or Mn and K, respectively.
Linear regressions of data in Figure 1 give the allocation functions for birch:
fr= 0.49 −0.27
CN
CN,opt
r2= 0.85 (4a)
fr= 0.22
CMg
CMg,opt
r2= 0.97, (4b)
where fr is the root fraction (Wr/W). The allocation functions
for Norway spruce are (Figure 2):
fr= 0.79 − 0.51 CN
CN,opt
r2=0.92 (5a)
fr= 0.23 − 0.054 CMg
CMg,opt
r2= 0.35. (5b)
The relationships are valid if the nutrient in the equation limits growth and the concentration of the nutrient is below Cn,opt .
Concentrations above Cn,opt are not permitted in the
simula-tion. The allocation data for Norway spruce with low Mg deviate from linearity, but there are too few data to consider other approximations.
Simulation method
The initial values are for seedlings of 1 g dry mass at Cn,opt . The
simulation sequence is as follows. First, the plant nutrient concentration is inserted in Equation 4 or 5 to give the steady-state value of fr (the calculated fr differs from the actual root
fraction unless the plant is in steady-state). Second, whole-plant growth rate is calculated according to Equation 1, and the new mass is distributed to give the calculated root fraction. If it is not possible to reach the calculated root fraction, for example, if the plant concentration of N declines rapidly, all
Figure 1. Root fraction (of total plant dry weight) as a function of the concentration of the growth-limiting nutrient in birch seedlings. The nutrient concentrations are normalized relative to Cn,opt for each nutri-ent. The data are for steady-state growth (constant internal concentra-tion). Data from Ingestad and McDonald (1989) (N), Ericsson and Ingestad (1988) (P), Ericsson and Kähr (unpublished data) (S), Ericsson and Kähr (1993) (K), Ericsson and Kähr (1995) (Mg), and Göransson (1994) (Mn).
growth can be allocated to the root. The resulting root growth is used in Equation 2 to calculate the nutrient uptake. The simulation period was 200 days, and the time step was de-creased until changes in results were practically zero.
Parameters
The data used in the simulations are given in Table 1. The volume of Vd was set arbitrarily to 1 (see Wikström 1994),
because it is the product VdCn,soil that is of interest in these
simulations. The minimum value of Cn,soil giving steady-state
growth at maximal relative growth rate, hereafter called the optimum value, was found by trial and error. Thereafter, Cn,soil
was reduced by 0, 20 or 50% of its optimum value in the simulations. A reduction of exchangeable base cation pools by up to 74% has been measured in southern Sweden during the years 1949--1984 (Falkengren-Grerup et al. 1989) and 1927--1984 (Hallbäcken 1992). Although a comparison between field data and Cn,soil in absolute terms is difficult, the data
indicate that the magnitudes of reduction in the simulations can occur in the field.
Results
The simulated plant mass development in response to a 0, 20 or 50% reduction in the soil N or Mg concentration required
for maximal growth is shown for birch and Norway spruce in Figures 3a and 3d, respectively. The corresponding relative plant nutrient concentrations, expressed as Cn/Cn,opt , are
pre-sented in Figures 3b and 3e, and the resulting root fractions in Figures 3c and 3f. The results for the soil Mg reductions of 20 and 50% for birch are so similar that the differences cannot be distinguished in Figure 3.
The figures illustrate that an increased allocation of plant mass to roots can partly compensate for a lower soil nutrient availability. A 50% reduction in soil N concentration from the optimum resulted in a reduction in plant N concentration of 26% in Norway spruce and 30% in birch at the end of the simulations (Figures 3b and 3e). The same reduction in soil Mg concentration gave a reduction in plant Mg concentration of 57% in Norway spruce and 80% in birch. The N-limited plants were hence better able to compensate for low soil nutrient availability than the Mg-limited plants by increasing their biomass allocation to roots. Values of Cn/Cn,opt in the most
Mg-limited plants were close to, or below, the concentrations at which plants can be kept alive under otherwise optimal laboratory conditions (indicated by dotted lines in Figures 3b and 3e). The survival limits are not exact but are estimated from experiments. The limits are similar for N and Mg when expressed relative to the optimum concentration. The re-sponses of birch and Norway spruce plants were similar for N
Table 1. Parameters used in simulations. Abbreviations: S = Norway spruce, B = birch.
Symbol Description Unit Value Reference
Cn Mass of nutrient per unit dry mass of tissue g g−1
Cn,min Minimum Cn for growth to occur g g−1 S: 0.00585 (N) Ingestad and Kähr 1985
0.0000907 (Mg) Ericsson, Kähr and Arveby, unpublished data
B: 0.0023 (N) Ingestad and McDonald 1989 0.000277 (Mg) Ericsson and Kähr 1995
Cn,opt Minimum Cn for maximal growth g g−1 S: 0.0184 (N) Ingestad and Kähr 1985
0.000636 (Mg) Ericsson, Kähr and Arveby, unpublished data
B: 0.042 (N) Ingestad and McDonald 1989 0.00141 (Mg) Ericsson and Kähr 1995
Cn,soil Mass of nutrient per volume of growth medium g dm−3 S: 0.066 (N)
0.0023 (Mg) B: 0.195 (N)
0.00695 (Mg)
fr Root fraction
Pn Nutrient productivity g g−1 d−1 S: PN = 4.86 Ingestad and Kähr 1985
PMg = 112 Ericsson, Kähr and Arveby, unpublished data
B: PN = 6.24 Ingestad and McDonald 1989
PMg = 197 Ericsson and Kähr 1995
Rg,max Maximum relative growth rate g g−1 d−1 S: 0.061 Ingestad and Kähr 1985
B: 0.25 Ingestad and McDonald 1989
Ru Relative nutrient uptake rate g g−1 d−1
Ru,max Maximum relative nutrient uptake rate g g−1 d−1 = Rg,max
Vd Volume of growth medium that is depleted dm3 g−1 1
by 1 g of new root dry mass
W Plant dry mass g W(t = 0) = 1
but differed for Mg.
Plant Mg concentration in birch decreased rapidly as soon as CMg,soil was set below the optimum value, and growth ceased
after about 75 days. Birch differs from Norway spruce in decreasing biomass allocation to roots more sharply when plant Mg concentration decreases.
In Figure 4, the timescale is normalized to compensate for the species-specific differences in growth rate (days × Rg,max )
(see Ågren 1985), and the root fraction is normalized relative to its initial value, Wr/Wr(0). Expressed in this way, birch and
Norway spruce responded to N limitation almost identically, whereas birch had a lower root fraction at low Mg, which indicates that birch is more sensitive than Norway spruce to Mg shortage.
Discussion
The hypothesis tested was that biomass allocation to roots declines continuously as trees become growth limited by Mg. According to the model results, the hypothesis is true for birch, but not necessarily for Norway spruce, although Norway spruce is more sensitive to low soil Mg than to soil N.
But can we apply the model results to field conditions? Unfortunately not, because there are too many factors omitted in the model. We have to hypothesize how the simplified and neglected factors affect the model results.
Nutrient uptake in the model is only affected by the soil nutrient concentration. However, there is evidence that uptake of cations is reduced in acid soils by ammonium ions and aluminum (Roelofs et al. 1985, Boxman et al. 1986, Ulrich 1989, Godbold 1991, van Oene 1994). Cations are also lost by leaching in acid soils. These factors enhance the growth limit-ing consequences of Mg limitation found in the simulations.
Another important factor affecting nutrient acquisition un-der conditions of nutrient deficiency is the development of mycorrhizae. Ericsson, Kähr and Arveby (unpublished data) showed that mycorrhizal development in Norway spruce was greatly decreased in Mg-deficient plants. In contrast, mycor-rhizal development is almost unaffected by N deficiency (Ingestad et al. 1986). Reduced mycorrhizal development has also been observed in declining Norway spruce stands (Meyer et al. 1988). The amount and vitality of mycorrhizae affect root uptake capacity, expressed in the model through the parameter
Vd, which is also affected by root morphology. Birch seedlings
deficient in Mg have many short roots that provide a smaller uptake volume in soil and hence a smaller Vd compared to
N-limited plants that have fewer but longer roots (Monika Kähr, personal communication). A 25% decrease in Vd (Cn,soil
unchanged) gave the same result as a 25% reduction in Cn,soil ,
because uptake is proportional to the product VdCn,soil
(Equa-tion 2). A decrease in Vd in combination with a decrease in Cn,soil will therefore seriously affect uptake and plant health.
The mycorrhizal development on plants low in Mn and K is not known, but it is probably also negatively affected, because
Figure 3. The development of plant dry mass, W (a and d, logarithmic scale), plant nutrient concentration normalized to Cn/Cn,opt (b and e), and root fraction of plant dry mass (c and f) of birch and Norway spruce at varied soil nutrient concentrations. Figures show results for plants with optimum nutrient supply (0), or with 20 or 50% less than the optimum supply of N or Mg (N20, N50, Mg20 and Mg50). The dotted lines in b and e are the concentrations at which steady-state plants are on the threshold for survival under otherwise optimal labo-ratory conditions. The lines coincide for birch but differ slightly for Norway spruce (large dashes for N, small dashes for Mg). Values are estimated from Ingestad and McDonald (1989), Ingestad and Kähr (1985), Ericsson and Kähr (1995), and Ericsson, Kähr and Arveby (unpublished data).
plants limited in these nutrients have reduced tissue carbohy-drate concentration (Ericsson and Kähr 1993, Göransson 1994).
Nitrogen taken up in excess of growth requirements is gen-erally stored in the form of amino acids, which act as a sink for carbohydrates (Näsholm and McDonald 1990, Näsholm 1991). A high plant nitrogen concentration, which is common in declining forests, depresses the allocation of mass to roots, especially in Mg-limited plants (Ericsson 1995).
All the factors mentioned so far, ammonium and aluminum, mycorrhizae and excess N, enhance the negative impact of Mg deficiency on nutrient uptake and growth, thereby increasing further the difference found in the simulations between N- and Mg-limited plants.
The effect of mass allocation on plant water status was not included in the model. Water deficits, which are known to increase allocation of plant mass to the root system (Cannell 1985, Bongarten and Teskey 1987), might counteract the allo-cation response to magnesium deficiency, but information about such an interaction is lacking.
The difference between Norway spruce and birch exposed to Mg shortage might be less in the field. Birch has a deeper root system, which can explore less acidified soil horizons for Mg. In addition, birch acidifies the soil less than Norway spruce, which means less leaching losses of cations and less release of soil aluminum, improving conditions for the uptake of Mg.
The model has only been run for N and Mg, but the alloca-tion patterns for K and Mn are so similar to that for Mg (Figure 1) that the results can be extended to low availabilities of K and Mn. Likewise, a simulation of low soil P should yield results similar to those of the N simulations. Differences in response to deficiencies of various nutrients are likely to be greater in the field where seasonal influences, environmental stresses and other factors not included in the model may be important (see discussion in Oren and Schulze 1989). How-ever, until we have a more detailed understanding of uptake mechanisms, a more complex model may not increase the precision of model predictions (van Oene and Ågren 1994).
We conclude from the model results that Norway spruce and birch are much more sensitive to nutrient deficiencies that limit root growth than to nutrient deficiencies, such as N deficiency, which increase biomass allocation to roots. An illustration of the consequences of a deficiency of the former kind is provided by Mg-limited plants. Such plants have no compensating biomass allocating mechanism, rather they decrease allocation to roots, thereby hastening plant decline. The simulation re-sults for Mg can also be applied to K and Mn. Factors not included in the simulations, such as mycorrhizal development and root morphology, will probably accentuate the negative impact of Mg deficiency, thereby enhancing the differences between N- and Mg-limited plants. We believe therefore that, in the discussion of forest decline, it is important to consider the impact of Mg, K and Mn deficiencies on biomass alloca-tion to roots.
Acknowledgments
We are grateful to Monika Kähr for drawing Figure 1 and for the supply of information, and to Göran Ågren for valuable comments on the manuscript. The work was supported by the Swedish Council for Forestry and Agricultural Research.
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