# Biomass partitioning and re-translocation ## Biomass partitioning In the wheat module, wheat is divided into four components or parts: `Root`, `Heat`, `Leaf` and `Stem` (Fig. \@ref(fig:WheatClassStructure)), and is derived from a more generic plant module (meaning that it has some parts not used or has a terminology, better adapted to other crops). `Leaf` includes only leaf blades. `Stem` is defined in a functional rather than a morphological manner and includes plant stems, leaf sheaths and stem-like petioles (not applicable for wheat). `Head` is divided into `Grain` and `Pod` (which correspond to spike without the grain). Then grain are separated into `Meal` and `Oil` (not used). The structure of wheat parts is shown in Fig. \@ref(fig:WheatClassStructure). \begin{figure}[h] \begin{centering} \includegraphics[height=6cm]{figure/wdBiomassPartition} \par\end{centering} \caption{\label{fig:WheatClassStructure}} \end{figure} ```{r WheatClassStructure, fig.cap="The hierarchical structure of wheat parts. Texts in the parentheses are classes of parts. The gray box indicates a plant part not used in wheat."} knitr::include_graphics("figure/wdBiomassPartition.png") ``` On the day of emergence, biomass in plant parts (`Root`, `Head`, `Leaf`, `Stem`, `Pod`, `Meal` and `Oil`) are initialized by `root_dm_init` (set at 0.01 g plant\textsuperscript{-1} in the wheat.xml file), `leaf_dm_init` (0.003 g plant\textsuperscript{-1}), `stem_dm_init` (0.0016 g plant\textsuperscript{-1}), `pod_dm_init` (0 g plant\textsuperscript{-1}), `meal_dm_init` (0 g plant\textsuperscript{-1}), `oil_dm_init` (0 g plant\textsuperscript{-1}), respectively. Daily biomass production (Equation \@ref(eq:actualBiomassProduction)) is then partitioned to different plant parts in different ratios that vary with crop stage. Overall, Root biomass are calculated with a shoot:root ratio from the above-ground biomass ($\Delta Q$; Fig. \@ref(fig:BiomassPartition)). Then the above-ground biomass are partitioned into the different plant parts hierarchically, with biomass being attributed first to `Head`, then `Leaf` and finally `Stem`. This means that all parts might not have the biomass demand satisfied if the biomass production is limited. ```{r BiomassPartition, fig.cap="Biomass partition rules in the APSIM-Wheat module. Texts in the parentheses are partitioning methods of different organ types. The above-ground biomass is used to calculate Root biomass based on a shoot:root ratio, and is then partition to (1) Head based on the demand from Pod and Grain, and then (2) Leaf (proportion of the remaining biomass), and (3) Stem. Re-translocation occurs during grain filling, when the biomass accumulation doesn't satisfy Head demand. Biomass from Stem and Pod are then used to satisfy the Head demand (Pod and Grain)."} knitr::include_graphics("figure/wdBiomassPartitioning.png") ``` ## Biomass partitioning to `Root` Firstly, some biomass are allocated to the root as a ratio of daily available biomass ($\Delta Q$, Equation \@ref(eq:BiomassProduction)). The so-called 'magic' fraction of biomass going to `Root` is calculated from a stage-dependent function, but is independent on pedo-climatic factors (Fig. \@ref(fig:wdroothootRatio)). All biomass in the `Root` is considered as structural fraction, meaning that it cannot be re-translocated to other parts later on. \begin{equation} \Delta Q_{root}=\Delta Q\times R_{Root:Shoot} (\#eq:RootBiomass) \end{equation} where $\Delta Q_{root}$ is the daily increment in `Root` biomass; and $R_{Root:Shoot}$ is the ratio root:shoot biomass, which is defined by x_sta`x_stage_no_partition` and `y_ratio_root_shoot` in wheat.xml (Fig. \@ref(fig:wdroothootRatio)). \texttt{(}which is specified in wheat.xml ) ```{r wdroothootRatio,fig.cap='Relationship between ratio of root and shoot and growth stage.' } p <- wdVisXY(wheat_xml, "x_stage_no_partition", "y_ratio_root_shoot", xlab = "Stage", ylab = "Ratio of root and shoot") print(p) ``` ## Biomass partitioning to `Head` (`Pod`, \texttt{Meal and \texttt{Oil }(not applicable in this version))} Then all or part of available biomass ($\Delta Q$) are partitioned into `Heads` according to total demand of `Heads` (`Meal`, `Oil` and `Pod`). `Meal` and `Pod` demands are calculated by Equation \@ref(eq:MealDemand) and Equation \@ref(eq:GrainDemand). `Oil` demand always equals to zero in the current version of the APSIM-Wheat module. Biomass directly partitioned in `Pod` or `Grain` is considered as structural and cannot be re-translocated, however the biomass providing from re-translocation is accumulated as non-structural biomass. The `Pod` non-structural biomass can then be re-translocated into `Grain` (See Section @ref(Re-translocation)). \begin{equation} \begin{array}{c} \Delta Q_{head}=\min(\Delta Q,\,D_{grain}+D_{pod})\\ \Delta Q_{grain}=\frac{D_{g}}{D_{head}}\Delta A_{head}\\ \Delta Q_{pod}=\frac{D_{p}}{D_{head}}\Delta A_{head} \end{array} (\#eq:HeadBiomass) \end{equation} where $\Delta Q_{head}$ is the daily available biomass for `Head`, $D_{head}$, $D_{grain}$and $D_{pod}$ are demands for `Head`, `Grain` and `Pod`, respectively (see \autoref{sub:Grain-(meal)-demand} and Section @ref(Pod-demand)). $\Delta Q_{grain}$ and $\Delta Q_{pod}$ are biomass increment of `Grain` and `Pod`, respectively. ## Biomass partitioning to `Leaf` Then, the remaining biomass (after the partitioning to the `Heads`) are partitioned into `Leaf` based on a stage dependent function (Fig. \@ref(fig:wdFractionLeaf)). `Leaf` biomass is considered as structural and thus cannot be re-mobilised. \begin{equation} \Delta Q_{leaf}=(\Delta Q-\Delta Q_{head})\times F_{leaf} \end{equation} where $\Delta Q_{leaf}$ is the daily increment in `Leaf` biomass; and $F_{leaf}$ is the fraction of available biomass partitioned to the leaf, which is defined by `x_stage_no_partition` and `y_frac_leaf` in wheat.xml (Fig. \@ref(fig:wdFractionLeaf)). ```{r wdFractionLeaf,fig.cap='Relationship between fraction of leafLeaf and growth stage.' } p <- wdVisXY(wheat_xml, "x_stage_no_partition", "y_frac_leaf", xlab = "Stage", ylab = "Fraction of leaf") print(p) ``` ## Biomass partitioning to `Stem` Finally, the whole remaining biomass (if any) are partitioned into `Stem` (Fig. \@ref(fig:BiomassPartition)). Until the stage `start of grain filling`, 65\% of this biomass is distributed to structural biomass (Fig. \@ref(fig:wdStemGrowthStructuralFractionStage)), while remaining 35\% is allocated in un-structural biomass. Afterwards, all new biomass allocated to `Stem` is for non-structural biomass (which can re-mobilised). \begin{equation} \Delta Q_{stem}=\Delta Q-\Delta Q_{head}-\Delta Q_{leaf} \end{equation} \begin{equation} \Delta Q_{stem.\,structural}=\Delta Q_{stem}\times h_{structual} \end{equation} \begin{equation} \Delta Q_{stem.\,non-structural}=\Delta Q_{stem}\times(1-h_{structual}) (\#eq:StemNonStructural) \end{equation} where $\Delta Q_{stem}$ is the daily increment in `Stem` biomass; $\Delta Q_{stem.\,structural}$ is the structural biomass of `Stem`; $\Delta Q_{stem.\,non-structural}$ is the non-structural biomass of `Stem`; and $h_{structual}$ is the fraction of `Stem` biomass distributed to structural biomass which depends on the growth stage (S). $h_{structual}$ is specified by `stemGrowthStructuralFraction` and `stemGrowthStructuralFractionStage` in wheat.xml, with a default value of 0.65 before beginning of grain filling and 0 after. ```{r wdStemGrowthStructuralFractionStage,fig.cap='Relationship between fraction of structural and unstructural biomass in Stem.' } p <- wdStemGrowthStructuralFraction() print(p) ``` ## Re-translocation\label{subsec:Re-translocation} If the supply in assimilate (daily biomass increase) is insufficient to meet `Grain` demand, then re-translocation may occur to meet the shortfall (Fig. \@ref(fig:BiomassPartition)). The biomass re-translocation first occurs from the `Stem` non-structural biomass. From the start of grain filling, the wheat module allows a total re-translocation of up to 20\% of `Stem` biomass per day. If required, biomass can then be re-translocated from the `Pod` non-structural biomass. The re-translocated biomass is used to fulfill the `Grain` and `Pod` demands (\autoref{sub:Grain-(meal)-demand} and Section @ref(Pod-demand)) and is accumulated as non-structural biomass. \begin{equation} D_{diff,\,head}=(D_{grain}-\text{\ensuremath{\Delta}}Q_{grain})+(D_{pod}-\Delta Q_{pod}) \end{equation} where $D_{diff,\,head}$ is the unfulfilled demand from the plant, $D_{grain}$ and $D_{pod}$ are the demands from `Grain` and `Pod` (\autoref{sub:Grain-(meal)-demand} and Section @ref(Pod-demand)), and $\text{\ensuremath{\Delta}}Q_{grain}$ and $\Delta Q_{pod}$ are the daily increments in biomass accumulated to `Grain` and `Pod` (before re-translocation; Equation \@ref(eq:HeadBiomass)). \begin{equation} \Delta Q_{retrans,\,stem}=\min(D_{diff},\,Q_{stem.\,non-structural}\times20\%) \end{equation} where $\Delta Q_{retrans,\,stem}$ is the dry biomass re-translocated from `Stem`, and $Q_{stem.\,non-structural}$ is the non-structural part of the `Stem` biomass (Equation \@ref(eq:StemNonStructural)). \begin{equation} D_{diff,\,head}=D_{diff,\,head}-\Delta Q_{retrans} \end{equation} where $D_{dff,\,head}$ is updated value of the unfulfilled demand from the head. \begin{equation} \Delta Q_{retrans,\,pod}=\min(D_{diff,\,head},\,Q_{pod,\,non-structural}) \end{equation} where $\Delta Q_{retrans,\,pod}$ from pod is the dry biomass re-translocated from `Pod`, and $Q_{pod,\,non-structural}$ is the non-structural part of the `Pod` biomass. \begin{equation} D_{dff,\,head}=D_{diff,\,head}-\Delta Q_{retrans,\,pod} \end{equation} where $D_{dff,\,head}$ is updated value of the unfulfilled demand from the head. \begin{equation} \Delta Q_{retrans}=\Delta Q_{retrans,\,stem}+\Delta Q_{retrans,\,pod} \end{equation} where $\Delta Q_{retrans}$ is re-translocated biomass within the plant. \begin{equation} \Delta Q_{grain.\,non-structural=}\Delta Q_{retrans\,to\,grain}=\frac{D_{diff,\,grain}}{D_{diff,\,head}}\Delta Q_{retrans} \end{equation} \begin{equation} \Delta Q_{retrans\,to\,pod}=\frac{D_{diff,\,pod}}{D_{diff,\,head}}\Delta Q_{retrans} \end{equation} \begin{equation} \Delta Q_{pod.\,non-structural=}\Delta Q_{retrans\,to\,pod}-\Delta Q_{retrans,\,pod} \end{equation} where $\Delta Q_{grain.\,non-structural}$ and $\Delta Q_{pod.\,non-structural}$ are the daily increment in the non-structural part of `Grain` and `Pod` biomass; $\Delta Q_{retrans\,to\,grain}$ and $\Delta Q_{retrans\,to\,pod}$ to pod are the daily biomass re-translocated to `Grain` and `Pod`; $D_{diff,\,grain}$ and $D_{diff,\,pod}$ are the unfulfilled demand of `Grain` and `Pod`, which are calculated as ($D_{grain}-\Delta Q_{grain}$) and ($D_{pod}-\Delta Q_{pod}$), respectively.