The TILLERTREE Model
Phase 1 Phase 2 Phase 3 Phase 4
3.4 Co-ordination of phytomer recruitment
Phytomer recruitment rate depends on species properties (e.g. Tainton & Booysen 1965;
Appendix Al) and environmental factors (Nemoto, Morita & Baba 1995). It has been shown that there is co-ordination of growth between successive phytomers (Skinner &
Nelson 1994). As sheath lengthening was completed on one phytomer, elongation of the associated axial bud began. At the same time the ligule was initiated on the next consecutive phytomer and blade lengthening began on the third phytomer in the sequence. Hence only two blades ever expanded at the same time. One direct consequence of this is that phytomer recruitment interval will lengthen or shorten in response to the blade length of the associated phytomer. Two main terms have been used to describe the interval between phytomer recruitments: the plastochron is defined as the interval between initiation of successive leaf primordia on the apical meristem, and the phyllochron is defined as the interval between consecutive similar visible developmental stages in phytomer growth (Wilhelm & McMaster 1995). In addition the environmental factors that have been shown to affect the phyllochron, notably temperature, daylength, nutrition, light intensity and humidity (see Nemoto et al. 1995) may be captured by their effects on growth of individual phytomer blades and sheaths.
The model uses this co-ordination property to determine phytomer recruitment. The model ignores the plastochron and cell division which directly follows phytomer initiation (Skinner & Nelson 1994), and concentrates on expansion events only in order to focus on linear growth behaviour as a matter of simplicity. Phytomer recruitment is defined in the following manner: once the potential blade growth on an existing phytomer has exceeded a certain fraction of the maximum potential growth (presently 90%), the next phytomer is recruited and begins blade expansion.
This phytomer co-ordination characteristic, if true for all grasses, means that the present model need only know the maximum blade expansion rates and the maximum length of organs of each phytomer of a grass species, as phytomer expansion interval will be determined by these properties.
4 ROOT GROWTH
Each ramet consists of a shoot and a root. Most research has focussed on the ontogenetic growth of above-ground plant parts, while the behaviour of root systems is not well understood because they are difficult to study. Usually all that is studied is root mass and the number of roots at any one time during the season (e.g. Tainton and Booysen 1965;
Coughenour, McNaughton and Wallace 1985). It is probable that plants aim to maintain a functional balance ratio between shoot mass and root mass that relates to the relative rate at which each component supplies resources to the plant (Poorter and Nagel 2000).
In the model, roots are modelled in terms of mass only. Root growth and dieback depend on the root mass adjusting itself to stay in correct proportion with the shoot mass of the ramet. There is a goal-gap formulation between ideal root-to-shoot ratio, Halrlsh, and actual root to shoot ratio (alrlsh, the ratio of root mass, wlrT,t, to shoot mass, wlshT,t, which is the sum of live masses of all shoot organs on the ramet), which bounds daily root growth.
Potential daily root growth OFgwlr^t) is also limited by the daily maximum root growth rate (maxgwlrY,t).
VgWtyt = mm max gwlryt wiry t_\\ Qalrlsh wlshyt_\
wlry,t-\ N
wlsh
r,t-\ j
2.12
The maximum potential daily root growth is scaled by the size of the existing live root system. At very small root sizes, daily root growth may equal existing total root mass due to the extension abilities of individual rootlets, if resources are available. However this relative growth rate of the root system rapidly declines as root mass increases. Therefore past a threshold root mass value of 0.1 g the maximum rate of root growth is fixed at a value of 0.05 g (g DM)"1 d"1 (based on shoot growth rates from Wieners & Morris (2000).
max gwlryj -
wlry ,_j
1 " 7^". ) \ V ~ m a x ^lri) $ wlrYS-\ < 0 1>
[0.1-wlryt^j 2.13 max gwlrj if wlrr t_\>0.\ .
Actual daily root growth (gwlrr>t) is determined by the resource availability.
gwlry t - min (1.053 aCgOj *¥gwlryt\ AllocatedAVC). 2.14
Root dieback depends on three things. Firstly, there is a background senescence rate that accounts for the natural turnover rate of live root material. Secondly, if defoliation causes the actual root-to-shoot ratio to exceed the Qalrlshj, roots will die back using the same value for maximum potential dieback as for maximum potential growth. Thirdly carbohydrate limitation may mean that there is insufficient carbohydrate for root maintenance. In this case, root dieback must increase up to maximum dieback rate to reduce the maintenance requirement and to free up carbohydrates to service the maintenance demand (described subsequently).
dwlry t = = max
0.002 wlryt_x ,
wlry t_i
max dwlry t wlry f_j if '- > alrlshj, wlshyt_\
max dwlry t w/r«,_] if Cma'm\yt not satisfied
2.15
COUNTER-TYPE STATE VARIABLES
In order to assess the structural behaviour it is necessary to keep summary records of live and dead objects at various levels in the system. These are termed counter variables. They are also state variables because they give the population sizes of live and dead objects on the clone on any given day.
Total live phytomer number (lat) depends on recruitment and death rates and also on defoliation by grazing or fire events. Deaths rates are directly linked to the recruitment rate, with phytomer objects moving out of the system in response to the growth variables described above. Phytomers are also removed if a defoliation height to which they are subject falls below the height of the base height of their internode organ.