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Journal of Experimental Botany, Vol. 50, No. 330, pp. 15–28, January 1999 An ecophysiological approach to modelling resource fluxes in competing plants Gilles Lemaire1,3 and Peter Millard2 1 INRA Station d’Ecophysiologie, F-86600 Lusignan, France 2 The Macaulay Land Use Research Institute, Craigiebuckler, Aberdeen AB15 8QH, UK Received 10 May 1998; Accepted 17 August 1998 Abstract Introduction A conceptual model of resource acquisition and allocation within a generalized, individual plant growing vegetatively in competition with others is presented. The model considers C and N acquisition, synthesis of assimilates and their transport and partitioning, growth of new tissues, reserve formation and recycling, and losses due to root exudation and respiration. These processes are regulated by the relative size of the C and N substrate pools in shoot and roots, in relation to meristematic sink strength. Translocation and allocation patterns are represented according to the Minchin phloem transport model. The current model is used to consider the impact of competition on resource acquisition and allocation, first by considering a plant growing in isolation and its response to manipulation of light, CO and N supplies. Secondly, 2 competitive plants are introduced and the direct effects on plant responses in terms of resource depletion are considered separately from indirect effects such as potential changes in the quality of resources available (e.g. light quality or soil N sources). In the past, many studies of plant competition have not established the importance of these indirect effects because they have not established all the processes involved in competition. This model can be used to interpret responses of whole plants to their neighbours in terms of the relative importance of both the direct and indirect effects of competition. Competition can be defined as the interactions between individual plants induced by the necessity to share limited resources, leading to a reduction of the number of survivors and/or a diminution of their growth (Begon et al., 1986). To analyse the effect of plant competition on resource fluxes it is, therefore, necessary to (i) consider resource acquisition and use by individual plants in the absence of competition (isolated plant model ); (ii) use this model to analyse the response of individual plants to a restriction in the availability of resources, as induced by the presence of neighbouring plants; (iii) study how the modification of the spatial distribution of the different physical resources are governed by the presence of neighbouring plants, and how individual plants can perceive these changes and develop an integrated response; (iv) analyse the extent to which a plant can perceive the presence of neighbouring plants by signals other than the quantitative depletion of physical resources; and (v) integrate resource effects with non-resource effects in a more comprehensive model at the level of the plant stand. Such an ecophysiological approach deals with both intraspecific and inter-specific competition. In developing a conceptual model there is no reason to think that changing the neighbouring species should change anything in the model, if the intrinsic capacities of the given species in modifying the physical resources quantitatively and qualitatively are properly described and accounted for at the scale of the individual plant. The first section of this paper describes a mechanistic, conceptual model for C and N partitioning in an isolated plant and analyses how a plant develops integrated responses to modifications in the availability of these resources. The second section uses this isolated plant model to analyse the overall response of an individual Key words: C and N allocation, source-sink relations, conceptual model, whole-plant ecophysiology, competition. 3 To whom correspondence should be addressed. Fax: +33 5 49 55 60 68. © Oxford University Press 1999 16 Lemaire and Millard plant to competition from neighbouring plants, as observed in competition experiments. This paper will focus mainly on the links between below- and aboveground resource fluxes and restrict ourselves to considering only C and N for the sake of simplicity and clarity. C and N fluxes in an isolated plant and their regulation by the physical environment Figure 1 represents the C and N fluxes between an isolated plant and its environment and within the plant as a result of the regulation of the different metabolic processes leading to growth of the plant. These processes are considered to be (1) carbon and nitrogen uptake and assimilation, (2) transport and partitioning of assimilates, (3) respiration, (4) use of assimilates for new tissue formation, (5) storage of C and N, and (6) root exudation. For simplicity and clarity, water relations have not been mentioned explicitly because water is not considered as a resource used for plant growth, but as a resource which affects the acquisition and the partitioning of N and C by the plant. Therefore, the model assumes that the plant does not experience any restriction in water supply. Finally, only vegetative growth is considered, to avoid the introduction of detailed mechanisms of reproductive development, which could differ greatly between species. This simplification can be accepted if it is considered that competition for resources is directly linked to the vegetative development of plants, even in situations where the consequences of competition on reproductive development of plants is also an important feature of plant communities. C and N substrate The photoassimilates produced in leaves (sugars) constitute the C substrates, while the N substrate pool is provided by the soluble reduced N produced either in leaves or roots, depending on the chemical form of external N (NO−, NH+, dissolved organic N, or N 3 4 2 fixation) and the localization of the nitrate reductase activity ( leaf and/or roots). The substrate pool could be defined as the quantity of C and N soluble compounds which are readily available for any use, in any plant tissue, and located in the cytosol. Thus the soluble C and N compounds sequestrated in vacuoles or in organelles like amyloplasts or chloroplasts are not considered as part of the substrate pool. The estimation of the size of the C and N substrate pools at the scale of the entire plant is very difficult, but the relative concentration of these two substrates in the different plant tissues plays an important role in the transport and allocation of C and N from source organs to the different sinks. C and N substrates are transported in phloem from leaves to sink organs by mass flow according to the Münch hypothesis (Minchin et al., 1993; Sheehy et al., 1995), the driving force being the difference in concentration in C plus N substrates between the source and sink generating the difference in osmotic potential. Both C and N substrates are transported by the same mass flow, but at a rate which is proportional to their relative concentration in the source (Sheehy et al., 1996). Thus sucrose concentration in sources and sinks plays an important role in substrate partitioning, as postulated by Farrar and Gunn (1996). However, the local availability of C and N substrates resulting from activity of source leaves, and activity of different sinks along the transport path which consume C and N substrates in variable proportions, could also regulate partitioning. Thus the C:N ratio of the substrate pool changes with time and varies between the different organs of the plant. This may be an important signal for the overall regulation of plant metabolism. C substrates are generally not loaded into the xylem and translocated up to shoot, but root exudates can represent an important sink (Lambers, 1987) stimulating microbial Fig. 1. Schematic representation of C and N fluxes within a vegetative plant growing in isolation. The diagram represents the plant as being composed of three morphological components ( leaves, roots and stems). However, the model is not a compartmental representation of the plant. Instead, the plant is split in three conceptual entities corresponding to the major plant functions: (i) metabolically active tissues responsible for resource capture and assimilation of C and N substrate; (ii) supporting tissues allowing the plant to develop its architecture in relation to its environment. (iii) storage tissues where C and N compounds are stored in specialized organelles. (1) C and N substrates (Csub — Ω and Nsub --- Ω) represents, respectively, sucrose and reduced N circulating symplastically in the cytosol and transported from leaves to roots by the phloem massflow according to Münch hypothesis and the model of Minchin et al. (1993). N substrates move apoplastically in the xylem from the roots to the shoots. Csub is provided directly from photosynthesis. The use of C for maintenance respiration is not represented on the diagram. Nsub is provided by N uptake mechanisms (NO− and NH+ absorption and/or N fixation) and N assimilation processes either in roots or in leaves 3 4 2 depending on the main localization of the nitrate reductase activity. Nsub is constantly recirculating from roots to leaves through xylem water stream. (2) Meristems and plant growth. Nsub and Csub are used in the leaf, stem and root meristems for new plant tissue formation. The rate at which N and C are used in a meristem is under the control of its activity in terms of cell division rate, cell growth rate, and cell differentiation. A part of Csub is directly used for growth respiration processes associated with new tissue synthesis but is not represented in the diagram. The overall meristematic use of C and N can be represented by Michaelis-Menten equations according to Sheehy et al. (1996). The rate of C use in a meristem is considered as led by N supply, it being the specific effect of N on cell division rate which determines sink-strength for C. Nsub sequestrated as proteins in chloroplasts can be recycled and re-used as leaves age and senesce. (3) Reserve formation. Storage of proteins and starch or fructans are regulated by numerous enzymes and requires transport of substrate across a membrane. These mechanisms are considered as highly inducible by increased concentration of C and N substrates and for this reason their competition with meristematic sinks are considered as low. (4) Root exudation. Csub and Nsub can be exuded from roots and used by rhizospheric microorganisms. By this way plants can affect soil N availability. In the absence of any clear information on mechanisms involved in the control of exudation, only a positive feedback on Csub concentration in root on C exudation flow is considered. Modelling of resource fluxes 17 18 Lemaire and Millard activity in the rhizosphere (Grayston et al., 1996). N substrates can pass to the xylem and be transported up to shoot with the flow of nitrate and reduced N (Simpson et al., 1982; Oscarson and Larsson, 1986). C and N supply C substrates are produced by photosynthesis. The accumulation of sucrose in leaves represses the expression of several photosynthetic genes (Sheen, 1990). Therefore, the C supply of the plant is down-regulated by the accumulation of C substrates. The photosynthetic activity of the leaf is directly related to the amount of proteins involved in the photosynthetic machinery used for light harvesting and CO reduction. Rubisco is the most abund2 ant soluble protein in the leaves of C plants (Millard, 3 1988) and there is often a correlation between leaf photosynthesis in saturating light and the N or Rubisco concentration of leaves ( Evans, 1989). Maintenance respiration can be considered as an unavoidable consumption of C, being temperature dependent in shoots and roots and proportional to the mass of proteins due to the energy lost by protein turnover (Penning de Vries, 1975). Therefore, the quantity of C substrate which becomes available to the shoot and is used in shoot sinks or translocated to the roots is the difference between plant photosynthesis and shoot maintenance respiration. The quantity of C substrate used for growth in root sinks is equal to the daily flux of C substrate to root, minus the daily roots respiration and loss of C as exudates. The reduction of nitrate and assimilation of ammonium in roots requires the use of C substrates as energy and carbon skeletons. In leaves, a part of the energy can be provided directly by photosynthesis (Beevers and Hageman, 1980). The phloem translocation of amino acids to roots could act as a signal for the down-regulation of nitrate ( Tourraine et al., 1994), and also probably ammonium absorption, through a direct repression of specific ion transport. It has been shown that in trees the rate of N uptake by roots is inversely proportional to the concentrations of some amino acids in root phloem tissue (Gessler et al., 1998). The best fit was achieved for glutamic acid and glutamine while asparagine and other nitrogenous constituents of the phloem sap of spruce trees did not correlate with rates of N uptake. For N 2 fixation, the nitrogenase activity also seems to be downregulated by N substrates in the roots, through an effect on the O diffusion barrier of the nodule (Oti-Boateng 2 et al., 1994). In contrast, mineral N absorption or N 2 fixation seem to be up-regulated by the flow of current C assimilates in the roots, as shown by phloem girdling experiments on trees (Goutouly, 1995), defoliation of grasses (Clement et al., 1978) or lucerne ( Kim et al., 1991) and by manipulation of CO assimilation rates of 2 plants through variation in the light level or CO concen2 tration (Gastal and Saugier, 1989). N -fixation by legumes 2 also seems to be regulated by the level of C supply in both lucerne (Boller and Heichel, 1983; Vance et al., 1979) and in white clover (Ryle et al., 1986). So the C5N ratio of the substrate pool in roots appears to be a key signal which allows the plant to regulate N uptake in relation to the relative use of C and N substrates by the different sinks. C and N use in meristems The activity of each meristem in a plant can be considered as being regulated by factors such as apical dominance and dormancy which lead to ontogenic plant morphogenesis. Plant morphogenesis can be considered as the expansion of a plant in space, with a specific shape resulting from the initiation of meristems and their co-ordinated activity. From the large variation of morphology between species and individuals growing in the same environment it is obvious that plant morphogenesis is genetically programmed. Nevertheless, large phenotypic variations occur with environmental changes, indicating that environmental signals and/or physical resources can affect the expression of plant morphogenesis, perhaps due in part to modification of the C and N resources shared between the different meristematic sinks within the plant. The sink activity of a single meristem can be considered as resulting from production of new cells (cell division rate), cell growth (cell expansion rate) and cell differentiation. The two former mechanisms determine the expansion rate of plant tissues, while the latter determines the final weight per unit volume of the mature tissue produced by the meristem (e.g. weight of C and N per unit of volume). Thus, meristematic activity can be analysed as a sequential use of C and N substrates for, successively, cell division, expansion and differentiation mechanisms. The rate of respiration of the meristematic tissues are very high ( Zamski, 1996) because cell division requires replication of DNA and protein synthesis. The consumption of sucrose by respiration of meristems has been postulated to sustain the gradient between the phloem and the sink cells (Geiger and Fondy, 1980) and a positive relationship has been found between respiration rate and root growth ( Kallarackal and Milburn, 1985). According to Vertregt and Penning de Vries (1987), the energy costs of the synthesis of a plant tissue can be related to the C content of the tissue when mature, according to the biochemical nature of the synthesized compounds. So the estimation of the C requirement for the synthesis of a new volume of plant tissue (the C demand of the sink) can be estimated by the weight per unit volume of tissue in the mature organs (Durand et al., 1991). It is therefore possible to define the potential C demand of a given meristematic sink as the C flux necessary to support the rate of tissue expansion resulting from both the potential Modelling of resource fluxes cell division and cell expansion rates as determined by genotypic and environmental factors such as temperature. Farrar and Gunn (1996) suggested that sucrose concentrations in sinks positively affect the expression of genes involved in growth, but increased C substrate concentrations only turn on the relevant genes if other factors such as N and P supply or temperature are not limiting. Increasing the temperature of meristems should increase the potential for cell division, expansion and differentiation thereby increasing the potential rate of C flux necessary to meet the sink demand and allow the expression of genes involved in these processes. As a consequence of any increase in potential sink activity, the concentration of substrates in the cells tends to be depressed and the rate of phloem unloading is stimulated. In contrast, any decrease in sink activity will increase the substrate concentration and so will depress the import of C and N substrates. The role of sucrose in the determination of sink strength has often been emphasized because of its quantitative importance as a substrate for respiration and as the main contributor to osmotic regulation in phloem unloading. Little attention has been given to the specific role of N substrates in meristematic sink activity. Gastal and Nelson (1994) showed that in the basal, elongating zone of grass leaves, the rate of deposition of reduced N is mainly associated with cell division, while Schnyder and Nelson (1987) showed that deposition of C substrates is mainly associated with cell expansion and cell differentiation. Therefore, there is a spatial and temporal succession in N and C substrate use by leaf meristems. There is also a similar situation in growing root tips ( F Gastal, personal communication). Therefore, the rate of N substrate flux would first determine the rate at which DNA and proteins can be replicated for cell division which, in turn, determines the further C substrate demand for subsequent cell expansion and differentiation processes as a consequence of the number of divided cells. Thus, not only should the concentration of sucrose in the sink play an important role in regulating sink activity, but also the relative concentrations of C and N substrates. Because phloem unloading in meristematic sinks is considered exclusively to be a symplastic pathway ( Turgeon, 1987; Zamski, 1996), the C5N of substrate flux to a meristem sink is that found in the phloem. A decrease in N substrate concentration in the phloem, resulting from a low plant N nutrition, will decrease the sucrose consumption in the meristem as a consequence of a rapid decrease in the rate of cell division, with only small effects on cell expansion rate (Gastal and Nelson, 1994). This will lead to an increased concentration of sucrose which, in turn, will depress the phloem unloading rate. In contrast, an increased N concentration in the phloem will promote the rate of C use in meristematic sinks by increasing the number of growing cells. 19 It is necessary to analyse separately the use of N in photosynthetic tissues ( leaves) and in non-photosynthetic tissues (roots and stems) and the consequences upon C and N fluxes. The differentiation of photosynthetic cells in leaf parenchyma requires N compounds for the formation of chloroplasts. This differentiation and the associated synthesis of proteins is largely induced by light (Prioul et al., 1980). Gastal and Nelson (1994) showed that the start of Rubisco synthesis in grass leaves occurred after cell elongation was complete, with the maximum rate of synthesis occurring at the emergence of the leaf out of the sheath of the preceding leaf. These authors also showed Rubisco formation in a leaf segment occurred without new N deposition, suggesting that synthesis of photosynthetic proteins is supported by N already in the leaf, with an internal recycling of N compounds which have already been used for cell division and early cell elongation. Such recycling could occur during the differentiation of the different leaf tissues, from cells which differentiate into vascular and supporting tissues to those which differentiate into chlorophyllous parenchyma tissues. Thus Gastal and Nelson (1994) therefore showed that with optimum nutrition the N concentration in leaf tissues falls from about 8% in the zone of cell division to about 4.5% in the mature leaf, this decrease being totally explained by C accumulation with a constant pool of N. In contrast, in roots, Gastal (personal communication) showed that the N% in root tissues fell from a similar initial value of 8% in root tips (cell division) to 2% in mature root tissues. In this case, the accumulation of C cannot account for all the observed decrease in %N. Therefore N may be released and reused for further cell division at the root tip. In consequence, root growth appears less dependent than leaf growth on N supply. Storage Most plants store C and N. There are several possible ecological advantages of storage which are important in considering competition between plants. These are (1) allowing growth to occur when the external availability of N is low, which can be important for perennial species (Nambiar and Fife, 1991; Millard and Proe, 1993), particularly if there is a short growing season such as in tundra ecosystems (Bloom et al., 1985), (2) to enable more rapid recovery from catastrophic events such as defoliation ( Thornton et al., 1994) and (3) to support reproduction, for example, in species exhibiting monocarpic senescence (Millard, 1988). Furthermore, the efficient internal cycling of C and N within a plant through the processes of storage and remobilization minimizes the loss of resources from the individual (e.g. through leaf litter), which would then only be available again in competition with other plants and soil microbes. Storage occurs if N or C can be ‘remobilized from one 20 Lemaire and Millard tissue and subsequently used for the growth or maintenance of another’ (Millard, 1988). For the purpose of the model two kinds of storage are considered, recycling and reserve formation. Recycling occurs as a consequence of tissue development or turnover (e.g. as a consequence of protein turnover during senescence). Storage resulting in recycling of resources, therefore, usually involves pools which are metabolically active. An example of storage of N by recycling is the case of Rubisco as a storage protein (Millard, 1988). There are several ways in which N is recycled from Rubisco. First, N can be recycled in the canopy of both herbaceous and woody plants in relation to the level of irradiance upon the leaves (Field, 1983; Hirose et al., 1988; De Jong et al., 1989), thereby maximizing C assimilation. Secondly, N can be stored in coniferous trees as Rubisco and to a lesser extent chlorophyl binding protein during the winter, and remobilized during a flush of growth in spring to provide substrates for the developing needles (Camm, 1993). While such spring remobilization of N results in a decline in the photosynthetic capacity of mature needles (Camm, 1993), it is not intimately linked to leaf senescence because the needles may still function for a number of years (depending upon the species). Thirdly, N is remobilized from Rubisco as a consequence of leaf senescence in most species (Peeters and Van Laere, 1994; Millard, 1996). Recycling of N can also occur as a consequence of root turnover (e.g. after defoliation of grasses or as found in the spring in young trees). Reserve formation differs from recycling in that it involves N or C deposition in a discrete storage organelle, such as a vacuole (Raven, 1987) or amyloplast (Zamski, 1996). Alternatively, reserve formation can utilize discrete protein bodies as found in the seeds of many species ( Higgins, 1984) or the ray parenchyma cells of deciduous trees (Sauter and Neumann, 1994). Reserve formation, therefore, requires active transport of C or N across a membrane. Resource allocation to reserve formation in Fig. 1, therefore, will only occur when the other metabolic sinks (e.g. meristems and respiration) have been satisfied. This would explain why reserve formation tends to occur only at times when the growth rate of the plant is low (e.g. in the autumn) or when the external availability of N or C is high in relation to the demands for growth. In this way the plant can remove substrates from the cytosolic substrate pools and so avoid down-regulation of either C or N uptake and assimilation. Root exudates The final sink for N and C substrates in the plant to be considered is the secretion of root exudates. Rhizodeposition of compounds, due to both root turnover and release of organic compounds, constitutes a major input of carbon into the soil. Estimates of the amount of carbon entering soil through rhizodeposition vary, but can be as great as 40% of the C assimilated by the plant ( Van Veen et al., 1991), with annual plants releasing less of their fixed carbon than perennials. Despite being a small proportion of the total rhizodeposition, exudates are important in providing readily available substrates for the growth of soil microbes. The composition of root exudates has been well documented, and in addition to reducing sugars, phenolic and organic acids also include N-containing compounds such as amino acids and amides (Grayston et al., 1996). The release of these compounds from roots results in an enhanced microbial activity in the rhizosphere compared with the bulk soil (Lynch and Whipps, 1990). In turn, the soil microbes have a key role in regulating N availability to the plant through the processes of mineralization and nitrification. Exudation can be both an active secretion of compounds and a passive leakage along a concentration gradient (Grayston et al., 1996). Our model suggests that the rate of exudation would be controlled by the relative availability of C and N substrates in the root substrate pool ( Fig. 1). C-replete plants whose growth is N-limited have an increased allocation of C to roots and a greater rate of exudation of C substrates compared to plants grown with a C-limitation. This, in turn, will lead to an increase in the activity of soil microbes (which are themselves C-limited ) and so an increased potential for N uptake availability in the soil. Plant response to modification of its environment The conceptual model represented in Fig. 1 can be used for analysing the response of an individual plant to changes in the availability of resources resulting from the presence of competing plants. However, the effect of any modification of C and/or N resources needs to be analysed in terms of the requirement for both of these resources. The effect of a change in the supply of one resource first depends upon whether this resource is limiting or not for plant growth. Therefore, before analysing the response of plants to changes in the supply of resources, an examination will be made of how the plant acquires supplemental C and N resources or uses C and N reserves in response to changes in its growth as determined by temperature. C and N supply and partitioning as affected by temperature An increase in temperature leads, in general, to an increase in the activity of all meristems in a plant through a response in the rate of cell division (Francis and Barlow, 1988) and a co-ordinated response of cell expansion rate (Ben-Haj-Salah and Tardieu, 1995). The response of meristems to increasing temperature is under the control of N substrates, through their direct effect on cell division. Modelling of resource fluxes Therefore it is possible to describe the activity of a meristematic sink by the rate of utilization of N substrates using Michaelis–Menten kinetics, where the maximum rate of substrate N use is a function of temperature (Sheehy et al., 1996). The rate of C substrate use in a meristem should, therefore, be driven by temperature and N substrate concentration. So the C and N demand of the meristems is increased by an increase in temperature, creating greater competition among sinks within the plant because the photosynthesis of source leaves and the N uptake by roots does not respond to the same extent to the change in temperature. For example, leaf elongation rate of grasses can be increased 400% by an increase in temperature from 10 °C to 25 °C (Gastal et al., 1992), while leaf photosynthesis is only increased by 50% (Gastal and Sangier, 1986). Warming a single meristem leads to a rapid decrease in its cytosolic sucrose pool and so to an increase in import of C and N substrates from phloem, while cooling creates the reverse (Farrar and Gunn, 1996). As a consequence, source leaves accumulate carbohydrates within a few hours when roots are cooled ( Farrar, 1988). At the whole plant level, warming in the short term creates a rapid increase of consumption of substrates in both root and shoot meristems that is not accompanied by a similar increase in C supply, because of the less sensitive response of photosynthesis to temperature and the increase in maintenance respiration. As a consequence of this discrepancy between C supply and demand, the root meristems receive a decreasing proportion of the photoassimilates, due to the longer translocation pathway and the higher resistance to phloem flow, as predicted by the model of Minchin et al. (1993). This short-term effect of temperature on C partitioning between roots and shoot has been confirmed by experiments with 14C labelling (Preud’homme et al., 1993). This temperature effect gradually disappears in the long term because (i) increasing leaf growth allows for more light interception and so tends to restore the ratio between C supply/C demand to the value prevailing before the change in temperature, and (ii) some temporal modifications of the synthesis or hydrolysis of C reserves induced by changes in sucrose concentration, can buffer the shortterm effect of temperature change (Farrar and Gunn, 1996). Thus, in an environment where resources are not limited, an isolated plant tends to restore its ontogenic partitioning of C and N after any change in temperature, even if a short-term modification of C allocation can be observed as a consequence of a temporary discrepancy between C supply and demand. This view is supported by the fact that the accumulation of sucrose stimulates the formation of reserves through the expression of genes involved in starch and fructan synthesis (Farrar and Gunn, 1996). So decreasing the temperature leads to a higher proportion of C stored in reserves, through an 21 increase in concentration of sucrose as a consequence of a decreased meristematic activity. Modifications of C supply Any decrease of C supply leads to a rapid proportional decrease in the N uptake rate, whatever the form of N utilized. Inversely, an increase in C supply leads to a proportional increase in N uptake, but as shown by Gastal and Saugier (1989), this proportionality between C and N supplies cannot be maintained above a given threshold value of C supply rate. In such conditions of high C supply, the N uptake capacity of a plant is no longer limited by the C substrate concentration in roots, but by the negative feedback due to recycling of N substrates in the phloem. The main consequence of variations in the C supply to the plant is a modification of C partitioning. Any reduction in C supply, whatever the cause, leads to a higher proportion of assimilated C allocated to shoot growth at the expense to roots, with the reverse observed with increasing C supply (Ryle and Powell, 1976; Gastal and Saugier, 1986). These general observations can be analysed with the help of Fig. 1. According to the assimilate transport model of Minchin et al. (1993), it can be considered that the total resistance pathway from source to sink is less from leaf sources to shoot sinks than to root sinks, any reduction in C substrate concentration in source leaves should induce a greater proportion of C substrate flow in the lower resistance pathway. The reverse should also occur with increases in C substrate concentrations in the source leading to proportionally more C flow through the highest resistance pathway, i.e. to the roots. This explains why increasing the irradiance of a plant can result in a greater allocation of carbon to roots and an increased loss of C as exudates (Hodge et al., 1997). The higher resistance for phloem transport to root meristems compared to shoot meristems can be linked to the distance, but also to the existence of a greater number of anatomical connections between the different phloem sieve tubes. Therefore, the anatomical architecture of the phloem imposes a kind of priority rule for shoot meristems against root meristems for C allocation. This priority rule allows the plant to have a more rapid restoration of C supply by favouring a more rapid expansion of leaf area and light capture, allowing a subsequent increase of C allocation to roots, as the C economy of the plants improves. Figure 1 suggests that the effect of manipulation of C supply on shoot/root C allocation depends mainly on the level of C demand resulting from the total potential meristematic activity of the whole plant. If C supply exceeds demand, a reduction of C supply should not affect shoot/root growth, until a threshold value is reached where it equals C demand. Any further decrease in C 22 Lemaire and Millard supply will then lead to the expression of the ‘shoot priority’ and as a consequence to an increase in shoot5root ratio. Therefore, the effect of any manipulation in C supply on the shoot5root ratio has to be analysed in terms of C supply5C demand ratio, and not in terms of C supply only. In this way it is possible to explain many contradictions in the literature on the effect of elevated CO on shoot/root growth (Farrar and Gunn, 2 1996). The predictions of our model agree with the concept of a functional equilibrium between shoot and root developed by Brouwer (1963). The other way to examine C partitioning within the plant is to consider allocation to meristems versus reserve formation. Figure 1 shows that an increase in C substrate concentration in source leaves increases both C fluxes to meristems and to reserve formation. There is little evidence in the literature on the priority between these two fluxes. However, most observations of whole plants show that shoot meristem activity saturates before reserve formation increases, when the C supply is increased. Inversely, shoot growth remains unaffected when there is a paucity of C and demand exceeds the supply, because C reserves can be used directly to support meristematic activity. Therefore, the effects of manipulation of C supply on growth versus reserve C partitioning also has to be analysed in terms of C supply:C demand ratio and not in terms of the absolute C supply. Modifications of N supply N deficiency leads to an increase in C substrate concentration in source leaves which, according to the model of Fig. 1, results in an increasing proportion of C being allocated to root growth (Belanger et al., 1992). The effect of manipulation of N supply has to be analysed in relation to the ratio between C supply and demand. If the plant is in a situation of excess C supply relative to demand, any decrease in N supply will not affect C partitioning between root and shoot meristems, and any increase in N supply will not affect C partitioning either, until the C demand becomes higher than the C supply. One of the important responses of a plant to a restriction in N supply is the trade-off between leaf growth and leaf N concentration. With a limited N supply what is the optimum response for the plant in terms of C economy? Two options exist, either maximizing leaf meristematic activity, leaf extension rate and interception of light while minimizing leaf N concentration and photosynthetic capacity per unit leaf area, or the reverse. Grindlay (1997) suggested that not all species have the same balance between these two responses. Maximizing leaf growth should tend to give plants a greater competitive ability, but at the expense of a longer-term investment of C in leaf meristems, while maximizing leaf N concentration should give an immediate C gain. The optimum between these two responses should be dependent on the response of leaf photosynthesis to leaf N concentration and should, therefore, be different between C and C 3 4 species because the optimum leaf N concentration for photosynthesis is lower in C species. 4 C and N partitioning for balanced growth Co-ordination between root and shoot growth has been reported by many authors as a consequence of a ‘functional equilibrium’ (Brouwer, 1963; Davidson, 1969). This concept considers the plant as composed of only two functional compartments, shoot and roots, which are involved in C and N acquisition, respectively. The model in Fig. 1 allows the identification of four plant compartments: leaf and root tissues which are directly involved in C and N acquisition, the supporting tissues (e.g. stems) and storage tissues. All compartments in total result in the architecture of the plant as a whole and its adaptation to the constraints of its environment. Körner (1991) showed that for a large range of species of the same alpine habitat, the partitioning of dry matter between shoot and root was often resulting from the partitioning between stems and storage root and not between leaves and fine roots (Fig. 2). In the same way, Allirand et al. (1992) showed that the change in shoot5root ratio of lucerne plants with temperature was only the consequence of a change in stem5tap root ratio while the leaf5fine root ratio remained constant. Stem growth is mainly associated with structural tissue formation, while tap root growth contributes to reserve formation. Thus, the shoot5root ratio only reflects the functional equilibrium of young, annual plants with shoots composed mainly of photosynthetic leaf tissues and with predominantly fine roots. Even considering the leaf compartment alone, a greater proportion of supporting tissues was required in sorghum as the size of the leaf lamina increased (Lemaire and Gastal, 1997). The study of C and N partitioning within a plant has to move from a morphological point of view to a more functional viewpoint. As proposed by Caloin and Yu (1984) and developed further by Greenwood et al. (1991) herbaceous plants can be considered as having both metabolic and structural compartments. The metabolic compartment represents the plant mass directly associated with C and N acquisition ( leaves+fine roots) and directly associated with growth, while the structural compartment represents the plant mass not directly involved in plant growth processes, such as storage or supporting tissues. A similar approach has been taken in modelling C allocation of trees, using the pipe model theory of Shinozaki et al. (1964) to relate C allocation between organs with tree architecture (Beringer and Nikinmaa, 1997). Thus, the growth rate of a freestanding plant can be considered as proportional to the size of its metabolic compartment and, as shown by Modelling of resource fluxes 23 Fig. 3. Relationship between shoot plant N% and shoot plant mass ( W ) for individual plants of Sorghum bicolor growing in isolation (&) or in a dense crop (O, 6, %, corresponding to three successive dates of sampling). The continuous line represents the equation N%= 5.06( W )−0.11 for isolated plants. The dotted line represents the equation N%=7.79( W )−0.34 for the average plant of the dense crop (crop shoot mass divided by plant density) (after Lemaire and Gastal, 1997). C and N partitioning in plants in response to competition by neighbouring plants The consequences of competition by neighbouring plants for C and N partitioning can be studied at two levels of organization, either at the level of the plant stand, referring to the functioning of a hypothetical ‘average plant’, or at the level of each of the individual plants by considering the hierarchical relationship for light interception between individuals within the canopy. Fig. 2. The partitioning of dry matter in different plant species (redrawn ) from Körner, 1991). ( e ) leaves; ( % ) stems; ( & ) storage roots; ( fine roots. Caloin and Yu (1982) for Dactylis glomerata and by Lemaire and Gastal (1997) for Sorghum bicolor and Medicago sativa, the plant metabolic weight increases as (total plant weight)a with a value of a close to 0.80–0.85. This indicates that structural mass increases in a relatively higher proportion than total plant weight as the plant grows. As a consequence, if we consider that the ‘metabolic’ compartment of the plant consists primarily of the photosynthetic machinery (with a high N concentration), and that the ‘structural’ compartment consists mainly of cell walls and carbohydrate reserves, this allometry between these two plant compartments leads to a decrease in plant N% with increasing plant mass, as illustrated in Fig. 3. Therefore, the study of the allocation pattern of C and N within plants must account for size and stage of development of the plant size. The effects of similar environmental constraints on shoot5root or leaf5stem C or/and N allocation will not have the same effect when comparing plants of different sizes, whatever the cause of these differences. From an isolated plant to the average plant in dense stand The rapid decline in plant N% observed at canopy level when competition for light occurs seems to be mainly the consequence of a decline in leaf area ratio (LAR) of plants, resulting from a higher investment in structural and supporting tissues with low N content, at the expense of metabolic tissues with a high N concentration in leaves (Greenwood et al., 1990; Gastal and Lemaire, 1997). So as the size of the plant increases, a greater proportion of these non-metabolic tissues are necessary to support and connect an increasing quantity of metabolic tissues ( leaves and roots). Competition inside a dense canopy results in ‘isometric’ growth of the average plants. This leads to a greater investment in supporting tissues than for an isolated plant of the same size, allowing the leaves of the competing plant to be placed at the top layer of the canopy to reach light and so assimilate more C. Lemaire et al. (1992) showed in lucerne stands that the decline in leaf5stem ratio as the competition for light becomes more intense was the driving phenomenon leading to the decline in plant N%. As illustrated in Fig. 4, a straight line can be drawn between the N content in shoots and the LAI of a lucerne stand, despite that a progressively greater 24 Lemaire and Millard Fig. 4. Accumulation of N in leaves (6, +) and in shoots ( leaves+stems: O, Ω) in relation with LAI during regrowth of lucerne stand in spring (dark symbols) or in summer (open symbols). proportion of the shoot N is invested in stem tissues, thereby allowing the new leaves to emerge at the top of the canopy. It is not easy to take into account roots at the level of the plant stand. It can only be expected that, as for isolated plants, the growth of the metabolic root tissue and the allocation of the associated C and N should respond to changes in the environment in a way which is co-ordinated with leaf area development, according to the ‘functional equilibrium’. Therefore, as competition for light increases in a dense canopy, and the C supply to an average plant decreases, according to Fig. 1 a lower proportion of C should be allocated to roots, in a similar response to that of shading an isolated plant. Some authors have reported such a progressive increase in shoot5root ratio during canopy development of different crops ( Troughton, 1977; Hanson et al., 1991). However, for perennial species with storage tissues localized in either stems (trunk) or tap roots, a similar functional equilibrium response can lead to a different pattern of resource allocation in morphological terms. Therefore, the above-ground5below-ground or shoot5root ratios have to be used with caution because they may have little functional significance. From an average plant to the individual plant in dense stand Figure 3 shows that in dense stands, individual plants do not necessarily follow the usual relationship between %N and mass observed for the whole stand (or for an ‘average’ plant). When this relationship is observed for isolated plants, the differences in plant mass due to plant–plant variation at a given date, or the differences due to plant growth between dates, gives a similar pattern of decline in %N as discussed above, with smaller plants having higher %N. However, when plants of different size are compared in a dense canopy, the smaller plants which experience stronger competition for light have a much lower N% than predicted by their size, compared to the dominant plants which have a %N closer to that of isolated plants. Such observations have been confirmed on a lucerne stand by Avice et al. (1997), who showed that not only was the N concentration in the shoots of plants reduced owing to their size, but that the reserve formation of N in vegetative storage proteins was restricted. Therefore, the partitioning of N to shoots can be affected by the hierarchical position of plants inside the canopy, as a consequence of an increased investment in structural-supporting tissues, and the consequent reduced N uptake capacity of the plant resulting in less N reserve formation. These data can be interpreted using the model of Fig. 1. Smaller plants in a dense stand have a low C supply because they are shaded and have to support an increasing demand for C to maximize the growth of supporting shoot tissues. In addition, the lack of C substrate in roots could also restrict the ability of plants to take up nutrients from soil. Shading effect: light quantity and light quality The causes of the modification of plant morphology and of the associated C and N allocation pattern between metabolic and structural compartments resulting from competition for light are not well understood. The reason is that it is difficult to separate properly the direct effect of shading, linked to the decrease in light quantity and C supply, from the indirect effects due to the photomorphogenetic responses of plants to the changes in light quality, due to differential extinction of red and far red light within the canopy. One important adaptive feature to shade is the photosynthetic acclimation in response to a change in irradiance, which allows the plant to minimize the reduction of its C supply (Pearcy and Sims, 1994). Many studies (Aphalo and Ballaré, 1995) have demonstrated that most plants are able to change their morphology and their allocation pattern of C in response to changes in light quality by means of photoreceptors sensitive either to the red5far red ratio (phytochromes) or to blue light (cryptochromes). Two types of morphological adaptation can be considered according to the species. For some plants the change in light quality leads to shade tolerance responses, characterized by an increase in leaf area ratio and specific leaf area (Bourdot et al., 1984; Peace and Grubb, 1982). In other species, the perception of low red:far red ratios triggers several morphological responses, such as increased stem internode elongation, reduced leaf5stem dry weight ratio and increased shoot5root dry weight ratio (Ballaré et al., 1991; Aphalo and Letho, 1997) and can be considered as a shade avoidance response. Shade avoidance responses results in the plant allocating an increasing proportion of Modelling of resource fluxes 25 its C to support shoot tissues. Kasperbauer et al. (1984) showed that root growth of Glycine max (L.) was depressed by end-of-day far red treatment. Using similar treatments, Robin et al. (1992) showed that photomorphogenetic responses of white clover plants led to an increasing proportion of assimilated 14C being used for growth of petiole and stolon internodes, to the detriment of root growth. So the decrease in red5far red ratio associated with shading in a plant canopy should emphasize the direct effect of the diminution of C supply. Our model (Fig. 1) predicts that a reduced C supply should lead to a reduced proportion of C allocated to root growth. In clover, the photomorphogenetic response to a change in light quality will increase the proportion of C allocated to the growth of structural shoot tissues associated with ‘light foraging’ and so decrease the C available for root growth. Another important morphological response of plants to a decrease in red:far red ratio is a reduction in tillering or branching (Deregibus et al., 1985). If new tillers or branches are considered as a replication of the main morphological unit at a younger ontogenic stage, branching can be postulated as being an optimum way for the colonization of the horizontal space, by younger and, therefore, smaller morphological units with a high LAR. The inhibition of branching and tillering by shading, and the preferential allocation of C to the main shoot meristems corresponds to a change from a predominantly horizontal to a more vertical strategy of growth, leading to a rapid decrease in plant LAR. Gautier and VarletGrancher (1996) and Gautier et al. (1997), showed that the decrease in blue light associated with shading provokes morphological responses in white clover plants, allowing the leaves to be positioned higher in the canopy. Plants also perceive their neighbours through the horizontal reflection of far red light allowing a response to competition before the quantity of light intercepted by the plant is reduced (Ballaré et al., 1987). Part of the hierarchy developed between individual plants inside a stand of vegetation for light capture and, therefore, for acquisition of soil resources could be the result of the responses developed during the early stage of canopy development, and the sensitivity of their perception of the presence of neighbouring plants. Experiments with split root systems have demonstrated clearly that the uptake capacity per unit root length could be increased up to 3-, and sometimes 10-fold when a part of the roots were deprived of nutrients. Burns (1990) showed that the fraction of the root system experiencing nutrient deprivation influences the extent to which uptake rates increase elsewhere, so the uptake rate at the whole plant level could be maintained, as predicted by the overall control of N uptake by N and C substrate concentration in roots (see Section I ). Many authors have reported a high proliferation of roots in nutrient rich patches ( Fitter, 1994). This observation could be considered as contradictory to our model ( Fig. 1) where allocation of C to roots is considered to be restricted with increasing plant N nutrition. But, as described by Fitter (1994), the changes of root architecture by means of a local proliferation of fine root branching at the expense of elongation of a large diameter root axis, does not necessarily require any supplementary C. Moreover, Robinson (1994) pointed out that local proliferation of fine roots in nutrient rich patches is often accompanied by a restriction of root growth elsewhere. So plasticity of root architecture may be expressed only within the limit imposed by the allocation of C to root meristems, resulting from the control of partitioning at the level of the whole plant. Recently, Zhang and Forde (1998) have identified a gene involved in lateral root proliferation and shown gene expression to be triggered by nitrate. So local NO− concentration could be consid3 ered as a qualitative signal for plants in determining the plasticity of their root growth. The sensitivity of different species to such a signal could, therefore, explain the variation in response in root growth between species to nutrient patches as observed by Grime (1994). Since nitrate is a very mobile ion in soil solutions such root proliferation might not be very important in regulating nitrate uptake. However, such a response could have a large effect on the ability of a plant to take up less mobile ions such as phosphate (Robinson, 1996). Further studies are necessary to determine the extent to which nutrient patches could be created from and maintained by means of rhizosphere C flow and the subsequent effects on rhizosphere microorganisms (Stark, 1994). Responses to soil heterogeneity Conclusion The distribution of mineral resources in soils are very heterogeneous, at scales ranging from centimetres to metres. This heterogeneity can be experienced by the root system of individual plants (Stark, 1994; Caldwell, 1994). Heterogeneity of soil nutrient resources in soil can affect plant nutrient uptake in two ways: (i) a local modification of nutrient absorption rate per unit of root tissue, and/or (ii) a local modification of root growth and root architecture (Robinson, 1994). The conceptual model that has been developed here is based upon the representation of the plant as the sum of the three functional components: (i) the plant tissue involved directly in resource capture, (ii) structural plant tissue associated with plant architecture, and (iii) storage. The internal communication between these different components is by phloem transport of assimilates, which allows the allocation of C and N substrates from leaf sources to the different sinks. Down-regulation of C and 26 Lemaire and Millard N uptake and of the assimilation processes by the internal concentration of C and N in substrate pools plays an important role for the control of C and N acquisition by a whole plant. The role of reserve formation in controlling internal C/N concentration of substrate has been emphasized. The model of source/sink partitioning developed by Minchin et al. (1993) allows the prediction of a priority for C and N use by leaf meristems as C supply is reduced relatively to C demand, and the model predicts qualitatively many observed responses of plants to manipulations of C and N resources. Balanced C and N supply for plant growth has to be analysed according to the increasing proportion of structural tissue of low N content as the plant grows, leading to a decline of N requirement per unit of C gain. In a dense stand, competing plants have to increase their investment in structural tissues in order to reach light. 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