The TILLERTREE Model
Chapter 2: Structural Growth in TILLERTREE
1 BUNCHGRASS MORPHOLOGY AND MODEL OBJECTS
The TILLERTREE model simulates the growth of individual bunchgrass clones. It considers plant objects defined at a number of hierarchical levels within a clone that have already been described in the Introduction (Figures 1.1 and 1.2), namely phytomers (a), tillers (/?), ramets (y), ramet groups (S), and the clone itself (Figure 2.1).
Usually individual phytomers include the following organs: blade, sheath, and internode (Etter 1951; Kurihara et al. 1978; Bell 1991). In the TILLERTREE model flowers are also included in the phytomer structure because in many grass species flowers are borne on a number of phytomers near the terminal end of the tiller (Gibbs-Russell et al. 1990).
Flowers are located on each phytomer at the distal end of each internode.
A tiller (JT) consists of a number of phytomers connected sequentially to one another, with an apical meristem at its distal end that recruits new phytomers until the growth axis is terminated by flowering. Ramets are formed when tillers root. Ramets, which are functional plants containing shoot material and root material, may consist of several tillers connected to a single root system via the oldest parent tiller in the group. The simplest ramet consists of a single rooted tiller (known as a single-tiller ramet).
All ramets that are physiologically connected (termed physiological integration) in a ramet group are able to share nutrient resources. When the physiological connection between adjacent ramets is broken, connected ramets on either side of the broken connection form separate ramet groups (Figure 1.2). It seems likely that in most cases of caespitose grasses, ramets remain connected to their parent ramets as long as both are still alive (Danckwerts and Gordon 1987; Danckwerts and Gordon 1990; Briske and Derner 1998).In the model it is assumed that inter-ramet connectedness is broken by death of a parent ramet only (Figure 1.2).
Growth of the individual clone is recorded in the model in terms of the growth of individual organs (given the generic notation "o"). Four organ types are associated with each phytomer, namely blades (b), sheaths (s), internodes (in) and flowers (fl). Roots (r) are treated as the fifth organ type and are associated with each ramet (Figure 2.1). A description
Figure 2.1 Object hierarchy of the architectural model of a bunchgrass clone as used by TILLERTREE. A phytomer is composed of the individual organs: blade, sheath, internode and flower. A tiller is composed of phytomers. A ramet is composed of a shoot system of connected tillers and a root system connected to the oldest parent tiller. A ramet group is composed of physiologically connected ramets. A clone consists of all disconnected ramets descended from an original seedling.
of how the growth of each organ type is simulated in TILLERTREE is provided in the sections that follow.
Subscript notation in the equations is designed to locate variables and parameters in the object hierarchy (a, /?, y, 5). In addition, i is used for parameters that may be species- specific. Time is represented by t in the usual manner. A further subscript, h, is used to denote height layer (described later). These subscripts locate the position and nature of each variable of each object in time and vertical space (variablej,a,pjY;5;t). All calculations are made using a daily time step.
2 TILLER GROWTH
2.1 Tiller phenophase
Tillers pass through several stages of development during their life-cycles, known as phenophases. In this model, four possible phenophase states of tiller development are recognised.
Phenophase 1 (Vegetative phase):
When a new tiller is initiated it enters Phenophase 1. The phenophase is characterised by leaf production, root production and marginal stem growth. A tiller will remain in Phenophase 1 until floral induction, unless it is prematurely apically decapitated, in which case it will enter Stasis (Phenophase 3).
Phenophase 2 (Sexual reproduction):
This phase is characterised by leaf growth, stem expansion and flower growth.
Floral induction is a species trait. It may depend on an environmental signal such as season (Opperman & Roberts 1978) or diurnal length (Blazquez & Weigel 2000).
Alternatively it may be determined by a fixed number of phytomers from emergence to flowering.
For the model, if a tiller shoot that is in Phenophase 1 and beyond a minimum age, enters the season of flowering, Phenophase 2 is induced. Floral induction is inhibited by the combination of low tiller mass and low resource reserves, which forces tillers into
Stasis (Phenophase 3). Alternatively, when flowering is complete, the tiller enters Stasis (Phenophase 3).
Phenophase 3 (Stasis):
When a tiller has completed flower growth or has had it apex removed by defoliation, it cannot proceed with further primary growth because it is no longer able to recruit any phytomers. If the tiller has dependent daughter tillers that do not have their own root system then the tiller is remains in Stasis in order to act as a resource conduit between these daughter tillers and the rest of the plant. The tiller will die back from the apex to the highest point along the stem at which a live daughter tiller is connected to it. As soon as the tiller has no live dependent secondary tillers, it is able to die back to its base and then dies itself, allowing it to proceed to Phenophase 4.
Phenophase 4 (Decay):
When a tiller dies, any live material is converted to dead material immediately and any remaining stored energy is also lost to the system. Decay proceeds on the dead tiller until all structural masses of the shoot have declined to zero, at which point the tiller ceases to exist as an entity in the system.
2.2 Tiller morphological types
Axillary bud development leads to quite different micro-environmental contexts for the initiated tillers and this in turn leads to the development of morphologically distinct tiller subtypes (Tainton & Booysen 1965). The TILLERTREE model recognises two basic morphological subtypes of grass tillers in tufted grass species, namely culm tillers and basal tillers. Culm tillers are initiated at axils of leaf nodes that are on that portion of the stem of the parent tiller that is expanded to elevate the flower head. As culm tillers are elevated substantially above the soil surface, they are unable to produce a root system and are unable to recruit secondary tillers.
Basal tillers are initiated at leaf nodes along the unexpanded portion of the parent tiller stem. Basal tillers have the potential to develop roots (but they may not do so) and are able to recruit secondary tillers.
3 PHYTOMER GROWTH (Refer to Figure 2.2)
3.1 Phytomer organ growth phases
Plant growth characteristics in the phytomer object can be divided into those relating to each organ type on the phytomer. All phytomer organs go through the following series of life phases:
Organ Phase 1 (Expansion):
Active growth following initiation of the organ. The organ may proceed with functional activities (e.g. photosynthesis) during this phase.
Organ Phase 2 (Plateau):
Plateau period after growth is completed when the organ proceeds with its function.
Organ Phase 3 (Senescence):
Dieback of the organ after the plateau phase is completed. Some functions may slow down as the organ approaches death. Dead material begins to decay.
Organ Phase 4 (Decay):
Decay of dead organ matter. When this is complete the organ ceases to exist as a physical entity and is deleted in a similar fashion to tillers.
3.2 General difference equations for phytomer dimensions
Growth of an individual bunchgrass clone is the sum of growth of individual organs (blade, sheath, internode, flower) on that clone. Both length (mm) and dry mass (g DM) dimensions are recorded, and records are kept for live and dead material. Total material is calculated by summing the live and dead components. The state variables of each phytomer organ are live length (lloa,t), live mass (wloa,t), dead length (ldoa;t) and dead mass (wdoa>t).
Changes to organ mass are used to calculate the resource requirement for growth. Some organs increment their mass every cycle as they expand their girths, so mass values cannot be accurately predicted from lengths alone. For simplicity blades and sheaths are assumed
m a x W b ja
01 c -a
— CD