Now more and more researchers are aware of the importance of the crop system
model. It can integrated information from different crop subsystems to help
us better understand the processes of responds of crop to environment and identity
the limiting factors to crop growth and yields (Guo et
al., 2006; El-Sharkawy, 2011).
In many plant model systems, the functional-structural plant models are a kind
of promising models (Yan et al., 2004; Godin
and Sinoquet, 2005). These models are based on the interaction of the plants
structure with the function and can be used to quantify processes of competition
of obtaining resources in the plant as well as the competition with other plants
and assess exploitation efficiency of soil resources etc. (Bidel
et al., 2000; Bionsini, 2001). Now, the models
have been successfully applied in the shoot system of plant (Allen
et al., 2005; Renton et al., 2005;
Guo et al., 2006). However, the relevant work
of root system for functional-structural models has not obtained enough development
because of complexity of root systems and the difficulties of observing and
sampling them in the soil. And furthermore no obvious morphological marks which
are used for discerning root growth unit (Zhang et al.,
Up to now, many models for root system have been developed and have been applied
to many aspects (Lynch et al., 1997; Pages
et al., 2004). However, these root system models can not integrate
with the shoot system in the same time scale and formation (Drouet
and Pages, 2003). So most of the works about interactions among plants and
environments can only considered the shoot system or the root system. These
have limited our understanding of plant-environment system from the entire aspect.
In order to integrate shoot parts and root parts of plant from an entire point,
we will carry out the study that develops a root functional-structural model
in an analogous way like the shoot model.
The objective of this study is to develop functional-structural model of root system based on the characteristics of root system and principle of plant model of Green Lab. and then, the processes of growth and development of two kinds of typical root system was simulated with the visual ways based on the parameters of the model from the literature data.
Topological structure: For the shoot system, the organ development was
relatively stable and the unit time was determined by the external morphology
(Yan et al., 2004). For the root system, however,
the time unit (T0) for root development was set prior according to
corresponding time unit of shoot model (Zhang et al.,
||The right panel was basic structural Unit of Root (UR). The
left panel was entire root system consisting of different URs and A was
for an apical meristem, B for lateral primordium, C for a UR, D for a new
||Illustration of microstate and macrostate in the root dual-scale
Based on the T0, the basic structural Unit of Root (UR) was defined
as the root segment with the lateral primordium and root tip produced at the
time interval of T0 in the root system. Figure 1
illustrated the relationships about URs, lateral primordia, apical meristem
and entire root system.
After definition of UR for root system, the dual-scale automaton was revised
to describe the topological structure (Zhao et al.,
2001; Zhang et al., 2006). The microstate
was for UR and the macrostate consisting of a certain number of microstates
served the root axis (Fig. 2). Based on the microstate and
macrostate, the root topological structure was simulated by the combination
of microstates and macrostates and transferring among different microstates
and macrostates (Zhang et al., 2006).
Biomass partitioning: The principle of biomass partitioning used in
this root model was from model of GreenLab (Yan et al.,
2004). Each UR obtained biomass available according to the relative value
of product of its sink and expanding rate. Considering the characteristics of
root system, we assumed that expanding process of each UR was divided into two
states. The first stage of expanding process of each UR was called axial expanding
stage which was finished in one growth cycle. The UR competed for biomass available
according to its axial sink strength. The second stage was called radial expanding
processes and started after the first stage was finished and was finished in
many cycles. The UR in each growth cycle of the second stage competed for biomass
available referring to the product of its radial sink strength and its sink
expanding rate which was the function of its growth age. Based on the above
assumption and principle of GreenLab model, we could calculate the total biomass
needed theoretically for all the URs in each growth cycle. If the biomass available
in each GC was known, the value of produce of sink and expanding rate revised
by the rate of biomass needed theoretically to biomass available was the actual
biomass of each UR by axial expanding or radial expanding (Zhang
et al., 2006).
Dynamic interaction between biomass partitioning and root structure: In the first GC, the topological structure was set, for example, there was one UR with RT 1 and GA 1 in the entire root system. The biomass that UR obtained was all biomass that root system provided. In the second GC, the length of UR which obtained biomass in the first GC was calculated by allometrical relationship between root length and biomass calculated by experimental data. The lateral primordium generated by UR was the product of length and branch density that was the lateral root number per unit length of UR. This method produced the topological structure of the second GC. Then using above methods describing the biomass partitioning, the biomass and accumulated biomass of each UR obtained in different GC were calculated dynamically.
Parameters for simulation growth and development of fibrous and tap root system: The main subject of parameterizing the model was to do some analysis on special scenarios, not did some exact prediction. The value of T0 was set to 20°C, corresponding to one or two days. The total accumulated temperatures for maize root system growth is taken 2000°Cd (base temperature is 6°C above zero) and for cotton root system growth is 2600°C (base temperature is zero°C). The accumulated biomass in the nth GC was calculated by experimental data of Eq. 1:
where, Qa (n) is the accumulated biomass of root system in nth GC.
For maize root system, the relevant parameters were listed in Table
1. The parameters of cotton root system were from the literature (Zhang
et al., 2006).
Visualization and application: Using our virtual crop root system model
with the parameters from Table 1 and relevant literatures,
development and growth of root system of maize and cotton depending for its
topological structure and biomass partitioning in the homogenous soil were simulated
|| Parameters of maize root system
Simulation of fibrous root system: When simulating the maize root system, initial seed root was firstly generated from seed. After several GCs, second seed roots were initiated from initial seed root. After more several GCs, the nodes root began to initiate from stems. And the initial seed root began to produce lateral roots with RT 5 after six GCs. Then, several growth cycles later, the roots with RT 5 begin to produce roots with RT 7.
According to such ways, the topological structure of maize root system maize
was produced (Fig. 3, 4a, c
||Visual simulation of fibre root system of maize in the different
||Simulation of change for the number of URs (a, c and e), biomass
partitioning (b, d and f) of URs for maize root system in different growth
cycle. P was for node root, L1 for the first lateral root and L2 for the
second lateral root
|| Visual simulation of taproot root system of cotton in different
||Simulation of change for the number of URs, root individual
number and biomass partitioning and accumulation of URs in cotton root system
in different growth cycle. T1-T5 were for different root type
In each growth cycle, biomass available partitioning is finished. Figure
4b, d and f described the results of
the processes of biomass partitioning in different URs in different Gcs.
Simulation of tap root system: When cotton root system began to grow,
the taproot with RT 1 firstly expanded, several growth cycles later, different
type roots with different RTs (URs with RT 2, or 3, or 4, or 5) were produced
in the taproot from it base to apical according to its branch probability (Zhang
et al., 2006). After several growth cycles, some lateral roots began
to produce new lateral roots.
Figure 5 and 6a and b
were the simulating results of the development and growth of cotton root system
in different GCs. The biomass partitioning for UR in taproot root system like
cotton included two steps. The first step was the axial expanding process, the
results were showed in Fig. 6b. The second step was the radial
expanding processes. Figure 6d showed the results by the radial
expanding of UR to obtain biomass. In another aspect, the model can simulate
the self-pruning of URs due to its ageing (Fig. 5).
The structure framework of functional-structural model of root system was developed.
The simulating results showed that the root model can describe the dynamic processes
of development and growth. The next work is to validate the model using the
special experiments systematically.
This research was supported by Shanxi Natural Science Foundation (2008021043) and National Key Technology R and D Program (2008BAD95B04).