WIMOVAC Growth, Partitioning & Allocation Module

The level of organisation and form of a plant determines which of a number of different patterns of photosynthate utilisation governs its production and growth, its competitive abilities and its responses to environment specific constraints {Larcher, 1995 #2022}. Although there is a broad spectrum of plant strategies they are typically grouped into two types: i). The first classification is the investment type typified by annual plants which commonly have a high photosynthetic capacity and a high proportion of photosynthetically active tissue in the total plant mass. During the growth phase the carbon assimilated by an investment strategists is mainly used to produce leaves which then serve to increase carbon gains by the plant. During and after the flowering phase the distribution of photosynthate then switches to favour the reproductive organs whilst supplies to other parts of the plant are restricted to that needed for maintenance purposes only. Annual species are able to make full use of short periods of time in which conditions are favourable for growth but perform less well when conditions are poor, particularly if water and nitrogen are in short supply, since they must commit significant resources to root development which would otherwise have been available for shoot growth. ii). The second approach is the conservative strategy typified by biennial and perennial vegetation. Plants which adopt this strategy typically achieve a lower net rate of canopy carbon uptake and thus grow more slowly than the investment type of plant but are able to survive under unfavourable conditions of dry or cold environments, or where the soil is poor in nutrients because they maintain a significant structural root component. The development of conservative strategists is at first similar to the investment type but after their vegetative structures are formed they accumulate reserve supplies in a large storage root component before proceeding to flowering.

For vegetation models to be useful in the broadest manner, from annual crops to perennial grassland systems, they must encompass the essential elements of both investment and conservative plant strategies.

Partitioning & allocation of assimilates

A truly mechanistic understanding of partitioning which adequately predicts plant morphology in response to environment and growth strategy currently eludes us. A number of authors have attempted to construct empirical descriptions of allocation patterns based upon observed phenomena {Charles-Edwards, 1986 #2023}. Others have developed partitioning models based upon growth equations, such as the allometric growth formula, which implies that there is a fixed ratio between relative growth rate of the shoot and that of the root {Troughton, 1956 #2024}. However such approaches are not very useful for predictive purposes because they possess a limited suitability for extension beyond the range of experimental experience. A number of phenomenological models of partitioning based upon observed phenomena have been developed. These include the functional equilibrium hypothesis in which the partitioning of photosynthate and absorbed nutrients at the roots maintains a balanced functional economy throughout the plant as shown by Davidsons (1969) equation {Davidson, 1969 #2025}:

Root mass ^. rate_{(nutrient absorption) µ} Leaf mass ^. rate_{(photosynthesis)}

Reynolds and Thornley (1982) produced a partitioning model based upon this concept which has been described as teleonomic or ‘goal seeking’. The approach has however, been criticised for assuming constant root and shoot specific activities, aggregated whole plant carbon and nitrogen substrate values and a fixed C:N ratio as well as ignoring nitrogen allocation. The lack of a firm physiological basis means that these models have a limited use in predicting environmental effects on the partitioning process {Hilbert, 1990 #2026}. Mechanistic models of partitioning are being developed which attempt to simulate the processes that comprise partitioning, in the hope that if these processes are described realistically the experimentally observed behaviour of both investment and conservative strategists will be exhibited by the model. Mechanistic partitioning models typically incorporate sources and sinks within the plant, may involve the action of hormones and growth factors and both active and passive modes of transport in relation to processes of utilisation and transport {Thornley, 1990 #1882}. The usefulness and accuracy of such detailed models is also somewhat questionable while the current state of knowledge about the actual mechanism of partitioning is limited and there is no consensus of opinion about how nutrient transport occurs and is controlled within plants {Wilson, 1988 #2017}.

Wimovac uses a number of partitioning routines to simulate carbon allocation within the plant growth module. Whilst none of these options is ideal in all respects each one offers a trade off between mechanistic richness and ease of parameterisation. The partitioning model options are controlled by a numerical switch setting in the model parameter database and currently consist of the following choices:

i). No partitioning of assimilates is performed and although photosynthesis takes place it is uncoupled from any growth of plant structures. This option speeds up calculations slightly, when a growing plant system is not needed, and is incorporated for diagnostic purposes.

ii). All CO₂ assimilates arising from canopy photosynthesis are allocated to the plant leaf pool. This is a useful diagnostic option for generating the hypothetical potential for leaf area generation if there was either a fixed, or no requirement for supportive root and stem structures.

iii). A dynamic mechanistic model of carbon partitioning based upon work by Farrar (1993) is currently under development in Wimovac as the third option in the model parameter database. The model consists of 11 state variables and 16 rate equations which attempt to simulate the control, production and fluxes of sucrose through the plant (Figure 29). In this approach it is proposed that sucrose is not just a substrate but is intimately involved in the expression of genes seminal in the regulation of growth {Farrar, 1991 #1235}. As yet this hypothesis is incomplete but it is assumed that pools of sucrose, in the cytosol of source (leaf, Cc), and sink (root, Cr) control the capacity of synthetic metabolism by regulating the amount of metabolic machinery. There is a considerable body of evidence that the rate of photosynthesis by a leaf, for example, is influenced by the demand for assimilate imposed upon it {Neales, 1968 #2029}.

Early work led to the hypothesis that photosynthesis is in part controlled by the concentration of assimilate in the leaf such that if the sink demands for assimilate were low the resultant accumulation of sugars or starch in the leaf suppressed photosynthesis in a manner analogous to end-product inhibition of biochemical reactions. In the work reviewed by Neales (1968) reduced photosynthesis was associated with increased levels of sucrose and/or starch in the leaves. Many plants have been shown to exhibit an increase in leaf starch content on long-term (days to months) treatment with elevated CO₂, reviewed by {Farrar, 1991 #1235}, and the introduction of separate starch (Ct) and sugar phosphate (Cx) pools in the model allows exploration of starch and sucrose storage and availability feedback’s on photosynthesis. Such increases in leaf starch may be responsible for the increases in leaf specific weight often observed under conditions of enhanced CO₂ {Madden, 1980 #474; Madden, 1988 #1088; Yelle, 1989 #850} and should be taken into account by growth models which form leaf area on the basis of a leaf specific weight value.

Examination of results from experiments, in which lighting conditions were manipulated to explore the effect of leaf carbohydrate concentration upon net CO₂ assimilation, gave rise to speculation that the decline in photosynthesis observed at high carbohydrate concentrations, in some species, resulted from impaired functioning of the Calvin cycle {Azcon-Bieto, 1983 #38}. Further observations that carbohydrate accumulation also leads to reduced quantum yields implying diminished production or consumption of assimilatory power (NADPH+ATP) supports this interpretation and suggests that these effects may be mediated by the concentration of inorganic phosphate (P_i) within the chloroplast {Edwards, 1983 #1773}.

Triose phosphate (TP) is the immediate product of the Calvin cycle and is either recycled for the regeneration of RubP or leaves the cycle to become the precursor of either starch synthesis in the chloroplast or sucrose synthesis after export to the cytosol. This movement of TP is linked with a counter movement of P_i which is released by sucrose synthesis {Hay, 1987 #2028}.

The Farrar (1993) model used here assumes therefore that the accumulation of sucrose in the cytosol leads to feedback inhibition of further sucrose synthesis. This in turn leads to less P_i available to the chloroplasts and consequently to TP export slowing down causing a greater proportion of it to be diverted towards starch synthesis. At the same time the diminished supply of P_i lowers the [ATP]/[ADP] ratio which causes a fall in the rate of regeneration of RubP and consequently to lower rates of CO₂ fixation.

A central argument in whole-plant partitioning is whether the capacity of sinks to grow is sufficient to maintain elevated rates of photosynthesis. Rates of CO₂ fixation must be co-ordinated with rates of carbohydrate metabolism and export from a leaf in order to maintain a balance between assimilate production and utilisation. A full understanding of the processes of sucrose transport to the phloem, loading into and unloading from the sieve tubes is not yet complete, even under current ambient CO₂ and temperature conditions. Although there is wide agreement that elevated CO₂ concentrations both promote CO₂ fixation and increase leaf starch accumulation, few studies have attempted to measure assimilate export from a CO₂ enriched leaf. Co-ordinated studies are still required throughout the growth cycle of a single species on the effect of elevated CO₂ on both transport and utilisation of assimilate {Farrar, 1991 #1235}. This model therefore represents a unique opportunity to explore not only the effects CO₂ on source processes but also to quantitatively test the viability of various transport hypothesis on source-sink dynamics.

Equations from Farrar (1991, 1993 and 1996) and Long (unpublished).

The network of state and rate equations that make up this model (Table 15) is solved using a two phase numerical integration approach on a 1 minute time step {Cheney, 1985 #1989}. This represents a very different methodology to that adopted by most current partitioning models, which run on a once daily time step, and allows exploration of transient changes, on the scale of a few hours, in carbon fluxes and pool sizes within the model plant. An animated graphical display of all partitioning rate and state variable dynamics of this model is incorporated within the wimovac dialog and provides a very direct visual cue for possible interactions within the model.

Equations from Farrar (1991, 1993 and 1996) and Long (unpublished).

The Farrar model is designed to examine the processes which make up carbon partitioning in detail and this is both a strength of the model and also a potential weakness. On the one hand mechanistic richness is required if we are to make reasonably reliable predictions about how partitioning will respond to climate change and on the other we have a model which is relatively complex and difficult to parameterise, particularly for use in a general vegetation growth model. Further this model currently only supports a single source leaf and sink root. At a later date incorporation of carbon assimilate from more than one leaf class into the phloem and of more than one flow of carbon out of the phloem needs to be added to give the multiple source/sink model required for whole plant growth simulation.

Farrar (1991, 1993 and 1996) mechanistic partitioning model. Parameters and values as specified in appendices I & II and{Farrar, 1996 #2027} Equation 91 to Equation 111

iv). There is a strong historical background to describing the phasic development of plants, particularly cereal crops, by noting key morphological stages of plant development and the thermal time (° days), elapsed since germination, at which initiation of the stage occurs. The phenological calendar produced by such observations can then be used to co-ordinate a number of plant processes in computer models including partitioning. Wimovac uses such a phenological calendar approach in which the number of stages and their respective thermal duration may be set and modified in the model parameter database. This calendar is then used to drive a partitioning table of coefficients that describe the fraction of available carbon in a given time interval that should be allocated to each of the plant structural pools (leaf, stem, structural root, fine root, storage root and seed). The partitioning coefficients in the table typically change with phenological stage reflecting varying source/sink demands during plant development. Although there is little mechanistic justification for this approach its simplicity and ability to relate measurable partitioning coefficients, based upon experimentally determined dry weights, to identifiable morphological stages has led to its wide spread adoption {Reynolds, 1989 #1837;Hodges, 1985 #2031}.

The investment and conservative approaches to growth associated with annual and perennial vegetation types respectively, are represented in this model by varying the patterns of carbon allocation in the partitioning table to reflect the experimentally observed dynamics of dry matter accumulation in the structures of these plant types.

Initial root and leaf area development in the model is indicated by a negative partitioning coefficient (0 to -1) setting, for one or more of the plant structure pools during the germination or initiation phenological stage. This is interpreted as indicating that the specified fraction of the dry weight in that plant pool should be made available for growth of other structures according to the positive partitioning coefficients indicated for the other pools. For an annual plant for example this means that initial growth is produced by setting the germination stage seed partitioning coefficient to -1, leaf pool coefficient to 0.9, structural root to 0.1 and all other pools to 0. Similarly initial growth for a perennial plant occurs from storage root carbohydrate by setting the partitioning coefficient in the range >-1 and <0 for this pool and setting leaf, stem and structural root partitioning coefficients to positive values. Suitable partitioning coefficient profiles for an annual in the form of spring planted wheat {Schulze, 1982 #2032} and a herbaceous perennial (Caltha palustris, after Eber, 1991) {Eber, 1991 #2033} are included as defaults in the model parameter database.

A summary of the basic growth model phasic sequence for a typical annual plant is given in Figure 30. Soil conditions are initialised from the model parameter database at the start of the simulation run and the plant pools zeroed until the planting day (P_day) is reached where upon they are initialised with default settings from the model parameter database. The initiation and duration of subsequent growth phases is then determined by the elapsed thermal time since germination. For the annual plant type at the end of the growth cycle the above and below ground material is assumed to be harvested with a return to bare soil and zeroed plant pools. The soil water and nutrient status is assumed to be carried over to subsequent simulation years. For the perennial plant type the plant pools are not reset which allows both soil and plant conditions to be carried over several years of growth.

Growth model sequence for a typical annual crop plant. The number of phenological stages, planting day and germination day settings are initialised from the model parameter database (IMPD). The initiation day and duration of other phenological stages is determined by the elapsed thermal time since germination (ETTSG). Growth stage descriptions may be modified as a text entry in the model parameter database for any plant type.

It has been noted by a number of authors that plants possess the ability to reduce imbalances among the environmental resources required for growth through homeostatic response processes {Chapin, 1987 #2016}. Plant growth and allocation response tend to act to increase the efficiency with which limiting resources are used, by increasing relatively the mass of the plant component that can ameliorate the stress {Wilson, 1988 #2017}. In this manner a higher root:shoot ratio is often observed in plants which have a nutrient deficiency in the rooting medium {Rufty, 1984 #2018}. Low light causes a decrease in root:shoot ratio and water stress an increase. Consequently wimovac incorporates a simple empirical water stress response function which serves to moderate the basic outline of partitioning indicated by the growth stage and partitioning table information, in a manner which aims to maintain an appropriate balance of root:shoot ratio for the prevailing climate and soil conditions. This response function monitors the average daily plant water potential and when this drops below a threshold value modifies the value of the partitioning table coefficients to favour allocation of carbon to the structural root pool from resources otherwise due to be allocated to leaf, stem and storage pools. Carbon allocation to seeds is assumed to be unaffected by water stress. The magnitude of the shift in allocation pattern is determined by the plant water status and the gradient of the response function as shown in Figure 31.

Allocation modifier function. With threshold, gradient and maximum effect parameters.

The phenological calendar, partitioning table and empirical adjustments of canopy and source carbon determines how much dry weight is available for growth of plant structures. The actual amount of leaf area, stem and root length that may be developed from the available dry weight may then be determined in a number of ways. Wimovac contains essentially two methodologies: i). The simplest approach to take the allocated dry weight for a plant pool and transform into an area or length term using specific area or length coefficients. For example the new leaf area that may be formed from carbon allocated to the leaf pool is given by:

and similarly the new structural root length formed given by:

Fine root and stem length are increased in a similar manner using the appropriate specific length values from the model parameter database.

ii). The second approach uses the conversion efficiencies of glucose to plant tissue suggested by {Penning de Vries, 1982 #2034}. Assuming that the approximate tissue composition for each of the main plant structures is known it is possible to calculate how much plant tissue can be formed from a given amount of partitioned carbon using this approach. Penning de Vries et al., 1982 considered that plant tissues were made up of six important chemical components: carbohydrates (structure), protein, lipids (including oils and fats), lignin, organic acids and minerals. These categories are important because they are characterised by different energy costs. Although other types of molecule could be considered they are not included in this analysis because they are either not important quantitatively or can be included in one of the other six categories. Penning de Vries and co-workers produced a quantitative basis for the carbon equivalent energy required for biosynthesis of each of these categories which considered glucose loss due to growth respiration for various synthetic pathways, the glucose energy equivalent stored in the compounds due to changes in molecular structure in the tissue (condensation) and the transportation costs associated with movement of the molecules across membranes. A summary of the findings of this work and a table of the conversion efficiencies included in Wimovac is given in {Boote, 1992 #2035}. The advantage of this approach is that its predictions of dry weight gain are based upon the composition of the plant and therefore enables the growth model to quantitatively explore the energy requirement implications of any changes in plant composition that may be associated with climate change. Currently the growth model in wimovac assumes a constant specific leaf area and stem and root lengths. Whilst this is almost certainly an incorrect assumption for many species, in the absence of a mechanistic understanding of these properties this approach has the virtue of simplicity and clarity.

Once the amount of new leaf area, stem or root length formed in a given time interval has been determined it is necessary to distribute the newly formed structures within the plant canopy and root system. New leaf growth has to be associated with a position in the canopy and an increase in leaf area index (F_canopy). Similarly new stem growth is associated with an increase in canopy height and new root growth with an increase in root density at a specific soil depth. The distribution of structural material to canopy and root is handled by sub-processes within the growth model which are currently rather simple in nature but have been constructed to be expandable to include more mechanistically orientated approaches that may become evident. The canopy models for example maintain a record of canopy height based upon stem length but assume that all leaf elements are uniform with respect to vertical distribution through the canopy profile.

Several categories of root growth models currently exist. The simplest are empirical descriptions of root distribution {Borg, 1986 #2037} and predetermined patterns of root system growth {Goodwin, 1982 #2038}. This approach is epitomised by the first root growth option in wimovac in which a uniform distribution of root material through a specified and constant rooting depth is assumed. As new root material grows the overall density of roots increases but there is no change in the rooting distribution profile.

Plant growth models may also simulate downward growth of the root system assuming a predetermined rate {Hansen, 1975 #2039} or include the effects of ecological factors such as soil temperature {Porter, 1986 #2040} and soil water potential {Hoogenboom, 1986 #2041}. Wimovac’s second root development option uses an simplified version of the latter approach in which a maximum root depth parameter (Z _max) and number of soil layers (n_soil) are used to determine the depth of individual layers. Growth of root material starts in the topmost soil layer according to the carbon available from partitioning and the specific root length until either the maximum rooting density for the layer (set in the model parameter database) is reached or the daily average plant water potential (Y _l) drops below a specified threshold value. Growth through the layers is therefore sequential from topmost surface layers to deeper subsurface strata. The plant water potential model is based upon the multiple layer soil model described in section 2.325 and as roots penetrate to deeper soil layers with on average higher water contents, the stresses associated with low water potential are in part alleviated.

The role of nitrogen availability in growth

The availability of nitrogen is an important determinant in productivity and growth for most vegetation types (section 2.3223). The effective availability of nitrogen for new plant growth has three main components. i). The nitrogen already present in the canopy material which may become available via relocation during senescence. ii). Nitrogen available in the soil pools or supplied by the semi-symbiotic relationship between leguminous plants and nitrogen fixing bacteria found in some plant root nodules. iii). The potentially rate limiting step of nitrogen uptake from available soil pools. A successful model of plant growth in relation to nitrogen nutrition should incorporate all of these components. However few existing crop and vegetation models attempt to do this.

Wimovac includes simplified, largely empirical, versions of these processes in a manner compatible with the limited datasets available. Nitrogen from relocation is assumed to be determined by the C:N ratio of leaf material and the proportion of dry weight that is reallocated during senescence. The maximum amount of nitrogen available from the soil is determined by the size and turnover of the Century soil nitrogen pools (described in section 2.327) and upon the plant nitrogen uptake function. A number of modelling approaches to nitrogen uptake by plants have been formulated. These range from teleonomic growth driven models which demand nitrogen from a finite soil pool until all nitrogen is depleted and further growth is not possible to more dynamic models which include some element of recycling of plant material nitrogen through soil litter pools and which determine actual root nitrogen uptake as a complex function of sink demand and soil availability. Wimovac incorporates two simple approaches to modelling plant nitrogen uptake. i). The first is based upon the generalised global model proposed by Woodward, et al. (1995),{Woodward, 1995 #1974} in which nitrogen uptake N_p is related to a function of soil nitrogen concentration as given by Equation 123.

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