Tiller development
Tiller population is described by two functions, according to increasing and senescence phases, respectively. The approach is based on the one proposed by Inman-Bamber (1991), with some improvements proposed by Singels et al. (2008).
This phase of tiller population is represented by a polynomial function of thermal time above a base temperature (defined by a ecotype parameter TTBASEPOP), valid in the first TT_POPGROWTH °C d:
where totmax (shoots m-2) is the potential tiller population (i.e., without limitations due to water stress or light competition), MAX_POP (shoots m-2) is a cultivar parameter representing the maximum number of tillers, TT_POPGROWTH (°C-day) is a cultivar parameter thermal time cumulated from tiller emergence to pick tiller population, and TTpop (°C-day) is the tiller population thermal time variable. In this phase row spacing and water stress impact the potential tiller population rate, through two multiplication factors: (i) 1.4/rowsp (whit rowsp being the planting row spacing in m), and (ii) SWDF30 (see Water Stress section). In this phase tillers emerge at each time-step in cohorts of maximum 1.1 shoots m-2. Each new cohort is thus represented by a certain number of tillers (called number of tillers represented, NTR) in turn characterized by common properties (e.g., number and dimension of leaves) during the entire simulation.
This phase occurs when the thermal time reaches TT_POPGROWTH °C-day:
where Δtotpop (shoots m-2 d-1) is tiller population decreasing rate, POPDECAY (°C-day-1) is a ecotype parameter representing the tiller senescence rate per unit of thermal time, ΔTTpop and is thermal time rate (°C-day d-1), totpopn-1 (shoots m-2) is the previous step of tiller population, and POPTT16 (shoots m-2) is a cultivar parameter defining the stable population value reached by the crop at harvest. The rate of senescent tillers is gradually subtracted to the cohorts starting from the last emitted ones, thus decreasing the number of tillers represented.
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