AI/^ = ZEE
Chapter 3: Resource Balance in TILLERTREE
1.2 The carbohydrate balance model
that correspond with each layer (Aloa,h,t)- By this means values can be obtained for the overlying cnopy area for each layer (the leaf area index LAI), which is the sum of all live and dead blade and sheath material in overlying layers. Blades and sheaths are flat and so depend on the mass-to-area ratio (awAoi), while internodes are cylindrical and so depend on density (pin;).
Alba,h,t ~ awllbi llba,h,t awAb i J 3.2
Alin a,h,t 2 n llin wlin
a,h,t
a,h,t
pirij n Uinahi 3.3
Daily photosynthesis follows a model by Coughenour (1984). Maximum hourly
7 1 *•»
photosynthetic rate per unit leaf area, Pmax; (g carbohydrate cm" h"), is the amount of carbon dioxide fixed per unit leaf area per hour. Photosynthetic rate is modified by the daily duration of sunlight (daylen), a constant 0.67 that accounts for the daily variation in light intensity (Coughenour 1984), light extinction in the overlying canopy (FP(LAI)), and nitrogen concentration in the organ (FP(N)). The constant 0.9 represents losses due to dark respiration (mg carbohydrate dm"2 h"1), which are generally about 10% of gross photosynthesis (Herrmann & Schachtel 2000),
CNetPsrj = 0.9 />max;- £ £ a h
Alo 100
*min[ f(T
ave); / ( * , ) ]
^ L FP {LAIh ) F (N) 0.67 daylen F {oangle;)
3.4
Fp(oanglej,a) calculates the integral of daily light intensity at the organ surface as the product of the organ angle and the angle of the sun (sunangle) as it crosses the sky.
Fp(oangleia) = \sin(sunangle) sin(\sunangle - oangle^) / \sin(sunangle) . 3.5 0 / 0
Daily duration of sunlight (daylen) varies with latitude and day of the Gregorian year (Gregday) (Chidley & Pike 1970).
daylen = 1 2 + 2 cos 2 it (GregDay + 9)
365 + 0.22. 3.6
Light extinction through the canopy is dependent on the extinction coefficient of the absorptive medium (Kj) in accordance with Beer's law (Goudriaan & Van Laar 1994).
Fp(LAIh) =e~K'*LAIh 3.7
LAIh in a particular height layer is the amount of light absorbing surface area in the canopy overlying that layer per unit area of ground surface (GSA), which consists of both live and dead blade and sheath material (Adoa,h,0 across all ramets in the modelled system.
LAIh =
GSA h+\
HTjHTl
Aloa,h,t +
Ad°a,h,t\
8 y p a
3.8
FP(N) is the effect of tissue protein content on photosynthetic rate (Leriche et al. 2001).
F <N) =0.4107 + 0.1964 Nstoreyt + AVNyJ
wltry t 3.9
Photosynthesis may be restricted if intracellular carbohydrate content is high (Stitt et al.
1990) but the evidence is not consistent (Farrar et al. 2000). This is not applied in the current model.
1.2.2 Maintenance
Maintenance respiration is the daily carbohydrate required to maintain existing cells in each plant organ. Maintenance respiration is represented as a fractional cost of organ live mass (Cmfrloi), where individual organ types have different maintenance costs per unit mass
(Penning de Vries et al. 1989). An additional transport cost of 5.3 % by mass is associated with all carbohydrate allocations.
CMaint^ =
I
J ] 1.053 Cmfrloj wloa.^r>ta
+1.053 Cmfrlrj wlrrj fiTave)- 3.10
1.2.3 Growth
Structural growth is a large sink for non-structural carbohydrates. Growth respiration is the cost of carbohydrate for plant growth of all organs. The total growth demand of the ramet (CDemGrow7,t,) is the sum of the growth demands of individual organs calculated from their growth rates and growth conversion efficiency (aCgOj) and the additional transportation cost (Penning de Vries et al. 1989).
CDemGroWyf = /_ Y.aCgOi l.^'VgwlOapyt la
+ aCgr; 1.053 *¥gwlryj 3.11
The estimated the cost of glucose for structural growth in rice crops is 1.326 g glucose (g DM)"1 for leaves, stems and roots and 1.462 g glucose (g DM)*1 for inflorescence and grain formation (Penning de Vries et al. 1989), which will be a sufficient approximation for the species under analysis.
1.2.4 Storage
Carbohydrate can be added to or removed from storage on any given day. Carbohydrate storage is a property of individual organs on individual phytomers. Daily storage movement across the ramet is the sum of movements within individual organs.
Storage movement is achieved in the model by utilising a gap-goal function where the actual value of carbon storage, Cstore0)t; aims for a daily ideal storage value. The level of QCstore0,t, responds to the photosynthetic production of plants relative to their demands. In other words when demands are high and photosynthetic production is low, nCstore0,t is low
to allow more carbohydrate to be extracted from storage to feed these demands. When demands are zero, QCstore0,t is at the maximum value.
QCstore0,
max Cstore,- min Cstore,-
if CDemGroWy t < 0
if NetPsyj-Cmaintyi < 0 ,
/ / NetPsr t - Cma int„ t
min Cstore: n + (max Cstore; n - min Cstore; n 1 '• — I LDemOroWyt otherwise.
3.12
The rate of starch decomposition may depend on the starch type. Amylopectin is a multi- branched structure and therefore capable of constructing or deconstructing exponentially, whereas amylose is a single chain structure, which if this may not be spliced into smaller segments during disassembly would decompose at a more absolute rate. However it is apparent that starch splicing enzymes do occur (Whistler et al. 1984), so it is likely that decay is exponential. Therefore in each iteration, carbohydrate is supplied from storage (CDemStoreo,0 at a rate proportional to its mass, RCstorej, to the AVC. After this amount is removed, a demand (CDemStore0jt) is passed from Cstore0;t, for carbohydrate storage, which is the minimum of two times the maximum transfer rate and the difference between actual storage and ideal storage. The net change in storage, ACstorey,t, is the summed difference between supply and demand across all organs.
CSupStore 0 t = RCstorej Cstore0 t . 3.13
CDemStore0 t = min (2 * CDemStore0 t ; | QCstore0 , wlo, - Cstore0 t \). 3.14
ACStoreyt =^^[CDemStoreat - CSupStoreat)+ \CDemStorert - CSupStorer t). 3.15 P a
-1 t.-l
Farrar & Williams (1991) measured starch breakdown rates of 1.4 - 2.0 mg (g DM) h" in the roots of young barley plants, where the total amount of starch and fructan was 35 - 50 mg glucose (g structural DM)"1. Assuming that the starch decay rate is exponential, then the initial breakdown rate above yields an exponential decay rate of 0.041 g (g CHO)"1 hr"1,
which means that up to 67 % of the stored carbohydrate may be mobilised in a day.
However for the model it is assumed that the daily maximum rate of carbohydrate release from storage (RCstore;) is assumed to be 0.1 times the amount of carbohydrate in storage.
1.2.5 Senescence
As individual organs senesce intra-cellular structures are decomposed, which provides carbohydrate and minerals for re-allocation. Penning de Vries et al. (1989) note that much of the protein-rich cytosolic components are re-absorbed as plant tissues die, but none of the carbohydrate structures such as the cell walls are broken down. They estimated that about half of the cellular biomass of leaves may be re-absorbed, although they give no empirical backing for this estimate. This seems very high and different organ types contain different levels of cytoplasmic material. Therefore the present model uses values of 0.1 by mass for blades and sheaths and 0.05 by mass for internodes, flowers and roots.
Csenescer t -///_, RCdiebackiM dwloapyt+RCdiebackio dwlrrt. 3.16 P a
1.2.6 Defoliation
Defoliation of organ structures has already been described. Defoliation also removes non- structural carbohydrates that are housed in these organs. AVC is a property of the ramet.
Therefore its depletion is calculated in direct proportion to the live mass of the ramet removed during the defoliation event relative to the total live mass of the ramet.
cAVCyt =AVCr>t