Linking physiological and architectural models of cotton

Transcription

1 Agricultural Systems 75 (2003) Linking physiological and architectural models of cotton J.S. Hanan a, *, A.B. Hearn b a CSIRO Entomology & Centre for Plant Architecture Informatics, University of Queensland, Queensland 4068, Australia b Australian Cotton Research Institute, Narrabri, New South Wales 2390, Australia Received 21 July 2000; received in revised form 31 January 2001; accepted 23 August 2001 Abstract Despite the strong influence of plant architecture on crop yield, most crop models either ignore it or deal with it in a very rudimentary way. This paper demonstrates the feasibility of linking a model that simulates the morphogenesis and resultant architecture of individual cotton plants with a crop model that simulates the effects of environmental factors on critical physiological processes and resulting yield in cotton. First the varietal parameters of the models were made concordant. Then routines were developed to allocate the flower buds produced each day by the crop model amongst the potential positions generated by the architectural model. This allocation is done according to a set of heuristic rules. The final weight of individual bolls and the shedding of buds and fruit caused by water, N, and C stresses are processed in a similar manner. Observations of the positions of harvestable fruits, both within and between plants, made under a variety of agronomic conditions that had resulted in a broad range of plant architectures were compared to those predicted by the model with the same environmental inputs. As illustrated by comparisons of plant maps, the linked models performed reasonably well, though performance of the fruiting point allocation and shedding algorithms could probably be improved by further analysis of the spatial relationships of retained fruit. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Cotton; Crop model; Architectural model; L-systems 1. Introduction The yield of a crop depends on its ability to capture resources (Monteith, 1994). Above ground, this ability is strongly influenced by the plant s architecture, * Corresponding author. Fax: address: jim@cpai.uq.edu.au (J.S. Hanan) X/03/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S X(01)

2 48 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) particularly how it presents its leaves to intercept solar radiation. Recent developments in computer technology have made it possible to study plant morphogenesis and the resulting architecture at the level of leaves, stems, flowers and fruit in more detail than previously possible (Room et al., 1994). These developments, combined with new techniques for collection, analysis, and concise representation of topological and geometric data (Hanan and Room, 1997), have been applied to create a model of cotton morphogenesis and architecture based on L-systems (Room and Hanan, 1995). The model, referred to as L-Cotton, captures the dynamic development of the plant s three-dimensional architecture from emergence to maturity, which can be visualised as either schematic or realistic images. Potential for applications of this technology in research, decision support, education and extension (Room et al., 1996) include: 1. Agronomy Exploration of the properties of inter-plant competition relevant to skiprow configuration, intercropping and weed control. Improved action thresholds for pest management through simulation of insect plant interactions and varying pesticide application regimes. Better understanding of plant compensatory growth, for improved pest management and evaluation of hail damage. 2. Plant breeding/genetic engineering. Development of plant ideotypes that optimise architectural factors such as light interception and resistance to lodging. L-Cotton can be parameterised to represent the morphogenesis of any variety, in any growing conditions, given the appropriate data. Application of the model is limited, as it is only sensitive to temperature and not to other environmental variables and their associated metabolic stresses. One approach would be to simulate these processes at the level of detail of the individual organ within the architectural model. However, the processes are not well understood and completing such a model would require much experimentation. The beginnings of work using such an approach for cotton has been presented by de Reffye et al. (1999), who describe a hydraulic model of cotton, focussing on vegetative growth. Detailed models for maize are more advanced (Fournier and Andrieu, 1998, 1999) and incorporate specific models of light interception by leaves (Chelle and Andrieu, 1999). Functionalstructural models of trees have also received much attention (Sievanen et al., 1997). While such research is useful in its own right, this level of detail is probably not necessary for many of the possible applications. An alternative suggested by Room and Hanan (1995) is to interface the architectural model with a conventional croplevel simulation model that accounts for environmental factors such as water availability, nitrogen status, and temperature. One such crop model, OZCOT (Hearn, 1994), was developed for management applications. It has been applied to problems of water resource management (Dudley and Hearn, 1993), evaluation and risk analysis of on-farm irrigation strategies (Hearn, 1995) and rainfed cropping options (Bange and Carberry, 1998; Carberry

3 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) and Bange, 1998; Carberry et al., 2000). The visual representation of output provided by L-Cotton would enhance the value of OZCOT; for example, aside from the applications already noted, the schematic output would assist in interpretation of the plant maps that some managers employ to monitor crops. Similar values are ascribed to the COTONS model (Jallas et al., 1999) in which a visualisation component has been added to a mechanistic crop-level simulation of cotton. This paper describes the first steps in the linking of L-Cotton to OZCOT. First we discuss the growth and development of cotton, and how the individual models represent this. We will then describe how the models are linked in L-OZCOT, followed by our verification and validation of the linkage, before a concluding discussion. 2. Modelling growth and development of cotton 2.1. Morphological development The morphological development of the cotton (Gossypium hirsutum L.) plant follows an orderly and regular pattern. This process and the resulting structures can be described in terms of modular growth (Room et al., 1994). The plants are indeterminate, so that the main stem never terminates in an inflorescence, but its apical bud (or apex) produces a new metamer, or structural unit, composed of an internode, leaf and axillary bud, usually at regular intervals of about 3 days. The rate of production depends on environmental and metabolic conditions, particularly temperature, thus the interval (called a plastochron) can be conveniently expressed in day-degrees (Hearn and Constable, 1984). Axillary buds at lower main stem nodes may be either dormant or produce vegetative branches, while those at higher nodes produce fruiting branches. The number of vegetative branches on an intact plant is an inverse function of plant population density. The first fruiting branch usually occurs at between the 5th and 10th main stem node in modern varieties of cotton. Subsequent nodes usually bear fruiting branches. Vegetative branches do not appear until the first fruiting branch has appeared, and follow a pattern of development similar to the mainstem, producing metamers, whose axillary buds have the potential to develop branches. The axillary bud giving rise to a fruiting branch produces a metamer consisting of a compressed internode and prophyll, followed by an expanded internode and leaf, and terminated by a flower bud. The branch extends when the axillary bud between the leaf and the floral bud produces another metamer. Repetition of this process gives the fruiting branches their distinctive sympodial character and jointed appearance. Since two internodes are initiated between floral buds, the interval between them is equal to two main stem plastochrons, usually about 6 days. The rates of production of floral buds on a fruiting branch and nodes on the main stem are thus closely coupled, and there is potentially a constant ratio between them with a value of 2. A floral bud develops to anthesis, whereupon it forms a fruit that eventually matures, unless metabolic stress or pest damage causes it to abort and shed. Floral buds and fruit are popularly known as squares and bolls respectively, or collectively

4 50 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) as fruiting bodies. The positions on fruiting branches that can bear fruiting bodies are collectively referred to as fruiting points. The first fruiting point on a branch is referred to as position 1, followed by position 2, and so on. The rate of fruit development can be conveniently expressed as a function of temperature in the form of day-degrees (Hearn and Constable, 1984), but more accurately as a negative exponential function of temperature (Mutsaers, 1976) The L-Cotton model The pattern of development described produces the characteristic pyramidal shape of the cotton plant. L-Cotton, the architectural model, captures this morphological development and the emergent pyramidal shape, by expressing the process using the Lindenmayer system (L-system) formalism (Lindenmayer, 1968; Prusinkiewicz and Lindenmayer, 1990). At any stage of development, a plant s structure is expressed as a string of symbols, each representing a plant component such as a leaf, internode or apical bud (Fig. 1). The order of the symbols in the string corresponds to the order of the components in the plant from the ground up. Branches and their lateral positions are represented by enclosing the string of symbols for their components in distinctive brackets, placed between the appropriate symbols at the point of attachment on the subtending structure. Attributes of a component, such as its size or age, are included as a list of parameters associated with the symbol. Geometry is included in the model by incorporating symbols specifying the relative orientation of the neighbouring components (as described in Prusinkiewicz and Lindenmayer, 1990). Plant growth and development are captured by a set of rules applied to all symbols in the string in each time step. The units of architectural development in L-Cotton are complete metamers, so that, at regular intervals, an apical or axillary bud produces an appropriate metamer complete with all components, including the bud that will continue development. L-Cotton describes cotton morphogenesis on a daily time step using thermal time (Hanan, 1997). Each day, weather data are read from a file and the daily heat sum in day-degrees is calculated. When a component is initiated, the heat sum required for the occurrence of the next developmental event, such as the production of another Fig. 1. Three consecutive stages of development of an L-system model. The L-system has two rules A!I[L(1)]A and L(len)!L(len*1.2) Where the!is read as produces, I represents an internode, L(len) represents a leaf of length len and A represents an apical bud.

5 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) metamer, is recorded as a parameter. When the requisite number of day-degrees has accumulated, the appropriate developmental event occurs. Development of main-stem and vegetative-branch apices is expressed in rules that specify the initiation of metamers consisting of internode, leaf, axillary bud and continuing apex at appropriate thermal time intervals. Lateral axillary buds are dormant, until the first fruiting branch is produced. The vegetative branches are parameterised in the same way as the main stem. The sympodial development of a fruiting branch is expressed as a rule by which the axillary bud develops after an appropriate thermal interval into a fruiting branch metamer. Subsequently, the ongoing apex is transformed into a floral bud and the axillary bud produces another sympodial metamer. Development of the floral bud is expressed by rules that transform it, after the appropriate thermal time intervals, from square to flower to boll to open boll. Potential development is determined by the parameterisation of the model. In the prototype, L-Cotton arbitrarily produces the first fruiting branch at node 6, and a vegetative branch at node 5. Running the model for 1000 day-degrees produces the schematic diagram of the branching structure of an idealised cotton plant shown in Fig. 2. Fig. 2. Schematic visual output of the prototype L-Cotton model after 1,000 day-degrees of simulation.

6 52 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) Metabolic stresses In reality, plants in the field are not like Fig. 2. The lower fruiting branches are truncated, and many of the fruit are shed. Some plants will not have fruiting branches. Fig. 3 is a schematic diagram of the observed branching structures of two plants from recent crops in the Namoi Valley, NSW, Australia. The differences between Figs. 2and 3 are caused by physiological and environmental stresses for which the L-Cotton model does not account. These stresses may include over or under supply of water and shortage in supply of carbon, nitrogen or other nutrients. Processes modelled on supply and demand of carbohydrates within the plant can be used to explain these effects (Hearn and Constable, 1984). Once the first fruiting point appears, the number of fruiting bodies and their demand for assimilate increase exponentially. Although the number of leaves also increases exponentially, new leaves shade those already present, and assimilate supply does not rise at the same rate, eventually approaching an asymptote determined by incident solar radiation. The inevitable result is increasingly severe competition for assimilates. This competition has a dominant influence on development. In response to competition, lower fruiting branches stop producing fruiting points and the rate of morphological development of the main stem, vegetative branches and remaining fruiting branches slows down. Development eventually stops when the fruit load is large enough to monopolise the whole assimilate supply, a time known as cut out. By contrast, development of individual fruit does not slow down. Instead, an Fig. 3. Schematic diagrams of the two end-of-season cotton plants from the Namoi Valley.

7 increasing proportion of fruit abort development and are shed, usually as young squares or young bolls The OZCOT model J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) OZCOT is a top down cotton crop simulation model (Hearn, 1994). Its development was dictated by decision support needs so that it is no more complex than necessary to supply information for management decisions. It takes account of the major stresses encountered by cotton plants during normal growth and development. A simple model of the fruiting dynamics of cotton (Hearn and Da Roza, 1985) was linked to a widely used soil water balance model (Ritchie, 1972). A rudimentary soil and crop nitrogen model, a leaf area generator and a boll growth model were added. OZCOT is sensitive to climatic variables (temperature, rainfall and solar radiation), agronomic variables (irrigation, nitrogen, plant population, row spacing, and sowing date) and varietal parameters (leaf type, squaring rate, boll size and development rate and lint percentage). OZCOT keeps track of the total numbers of fruiting points, squares, bolls and open bolls by daily cohorts. A new cohort of squares is produced each day and subsequently develops through anthesis to maturity. A fraction of each cohort is shed in response to the metabolic stresses simulated. Although OZCOT does not explicitly simulate the branching structure of the plant, aspects of architecture and the plastochron concept are implicit in the function that generates the number of squares. 3. The linkage 3.1. Comparison of L-Cotton and OZCOT The linkage takes into account the similarities and differences between the models, which can be summarised as follows: 1. Both models advance on a daily time step. 2. Temperature drives development in both models, but they differ in the way temperature is handled, and therefore in how varietal and crop parameters are expressed. These differences are analysed and reconciled in the next section. 3. L-Cotton simulates the potential development, unconstrained by available resources. OZCOT simulates the development possible, taking into account the resources available. 4. The unit of structural development in L-Cotton is a metamer complete with apical and or axillary buds by which further development occurs. In OZCOT the structural unit is a fruiting point and apical or axillary buds are not explicitly simulated. 5. OZCOT simulates the development of a population of fruiting points on an area of land, while L-Cotton simulates the development of each plant in a

8 54 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) population individually. This allows L-Cotton to account for plant-to-plant variation. 6. L-Cotton deals with fruit in integer numbers, while OZCOT operates in continuous variables expressing fruit numbers per square meter. 7. L-Cotton locates each fruiting point at a specific position on a particular fruiting branch and plant in the population. OZCOT does not explicitly simulate the branching structure or, therefore, the location of fruiting points on the structure, but keeps track of numbers of squares and bolls by daily cohorts OZCOT expresses the effect of resource limitation in three ways: in the number of fruiting points produced, in the number of fruiting bodies subsequently shed, and in the size of the fruit retained. In linking the models, this information is passed from OZCOT to L-Cotton. The models are therefore run in tandem, with OZCOT running first. The linkage must determine which of the axillary buds in L-Cotton that are ready to develop into fruiting points do so, and which abort. Likewise the linkage must determine which fruiting bodies eligible to shed do so, and which are retained. The linkage is therefore designed to translate OZCOT s continuous variables into integer numbers of fruiting points and fruiting bodies to be shed. It must then allocate them to discrete positions on specific branches and plants in the population being simulated The plastochron concept and varietal parameters L-Cotton uses day-degrees with a base of 12 C (Hearn, 1969) for all developmental events controlled by temperature, such as the plastochron of the main stem and fruiting branches, and the duration of fruit maturation. The day-degree requirements for these events are varietal parameters. The rate of fruiting point production is not a specific varietal parameter, but is the outcome of the interaction of the L-system rules expressing the plant s architectural geometry with the plastochron day-degree requirements. By contrast, in OZCOT the rate of fruiting point production is a varietal parameter and a function of day-degrees. OZCOT uses daydegrees for most events but uses Mutsaer s (1976) negative exponential relationship with temperature for the boll period. Plastochron values for main stem and fruiting branch, and the plant s architectural geometry are implicit in OZCOT s rate of fruiting point production, and must be extracted for use in L-Cotton. Hearn and Da Roza (1985) derived the functional form of the differential equation used for fruiting point production in OZCOT as follows. If N is number of mainstem nodes bearing fruiting branches and R the ratio between the plastochron on a fruiting branch and on the mainstem, then S the potential number of fruiting points is S ¼ðN 2 =RÞ=2 ð1þ Differentiating, the rate of production of fruiting points is

9 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) ds=dn ¼ N=R ð2þ From Eq. (1), N can be expressed as a function of S thus N ¼ð2RSÞ 1=2 ð3þ Substituting in Eq. 2 ds=dn ¼ð2=RSÞ 1=2 ð4þ If the plastochron for mainstem nodes in day-degrees is DD n, then the rate of squaring per day-degree is ds ¼ð2=RSÞ 1=2 =DD n or re-arranging ds ¼ð2=RÞ 1=2 =DD n S 1=2 ð5þ In OZCOT, the rate of square production per plant per day-degree is calculated in the following FORTRAN statement: ds ¼ SQCON SQRTðSITESÞ ð1-bload=cutoutþ ð6þ where SQCON is the potential rate of square production per plant per day-degree, SITES is S, the total number of fruiting points per plant, BLOAD is the number of bolls per m 2 and CUTOUT is the number of bolls per m 2 that will cause the plant to cut out, or stop producing fruiting points. SQRT(SITES) is a positive feedback term that incorporates the geometry of the branching structure and expresses the increase in rate as the structure expands, while BLOAD/CUTOUT is a negative feedback term that expresses the competition for resources between fruit already produced and the production of additional fruiting points. From Eqs. (5) and (6) we can derive the plastochron values needed by L-Cotton as follows. If there are no fruit, there is no competition for resources between fruit and production of fruiting points, BLOAD is therefore zero, and the potential rate of square production per plant per day-degree can be derived from Eqs. (5) and (6) SQCON ¼ð2=RÞ 1=2 =DD n ð7þ The value of the mainstem plastochron (DD n ) can be calculated from Eq. (7) by solving for DD n and substituting values for R and SQCON. R, the ratio between the plastochron on a fruiting branch and on the mainstem, is 2; empirical values of SQCON are used in OZCOT. The fruiting point plastochron is derived from the

10 56 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) product of DD n and R. The results in Table 1 give plastochron values very similar to those measured directly and reported in the literature (cf. Constable, 1991) The linkage process in OZCOT OZCOT runs first. The linkage procedures written for OZCOT record the information required by L-Cotton in an output file. The information, listed in Table 2, is logged daily and consists of day-degrees for the day, numbers of fruiting points produced that day, numbers of fruit shed as squares or bolls, or open as mature bolls, and the weight of lint in open bolls. Shed and open fruit are identified by the day on which they were produced (i.e. by cohort), as well as by the day of shedding or opening The linkage process in L-Cotton L-Cotton is run after OZCOT. The linkage procedures written for L-Cotton (L-OZlink) read the file from OZCOT and use the information to regulate the standard L-Cotton development functions. As L-Cotton advances through its daily Table 1 Squaring rate and plastochron values for some varieties Variety SQCON squares/plant/day-degree Plastochron in day-degrees Mainstem Fruiting branch DP DP SIOKRA Table 2 Information passed from OZCOT to L-OZlink Record type OZCOT Subroutine Hearn (1994) Variable Units 1 PLTGRW Days from sowing Day-degrees for day Base 12 C Minimum temperature C Fruiting points produced No. plant 1 2FRUIT Squares shed on this day No. plant 1 Day on which squares produced Day on which squares shed 3 FRUIT Bolls shed on this day No. plant 1 Day on which bolls produced Day on which bolls shed 4 FRUIT Bolls opened on this day No. plant 1 Day on which bolls produced Day on which bolls opened

11 time step, L-OZlink reads the daily data provided by OZCOT and accumulates the day-degrees. As in OZCOT, day-degrees are adjusted for cold shock based on daily minimum temperature ( 5.2DD for each day with minimum temperature below 11 C). L-Cotton uses the accumulated day-degrees to control emergence and development Emergence L-Cotton initialises a population of plants, with each plant given a value for its day-degree requirement for emergence. The values are picked from a normal distribution with mean 60 and variance 1/60 in order to simulate a population of plants emerging over a period of time. Each plant s emergence is simulated when sufficient day-degrees have accumulated Development J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) L-OZlink converts OZCOT s continuous variables to integers by accumulating a running total of the numbers of fruiting points that are read daily from the OZCOT file. Whenever the running total exceeds 1, it is a signal that an axillary bud can become a fruiting point. Accordingly a fruiting point is allocated to an axillary bud on one of the plants in the L-Cotton population. For each one allocated, one is subtracted from the running total, with any remainder saved to continue the accumulation next day. In a similar way the L-OZlink routines accumulate running totals of shed fruit and open bolls from OZCOT. Whenever a running total exceeds 1, shed fruit or open bolls, as the case may be, are allocated until the total is less than 1, with the remainder saved for similar processing the next day. Concurrently each day, L-Cotton updates the number and location of axillary buds that are ready to become fruiting points, and the fruit that are ready to shed or open, using day-degrees from OZCOT and the plastochron values derived from the OZCOT parameters in Table Priorities for development L-Cotton simulates the potential development, while OZCOT simulates how much of that potential can be realised. Rules were formulated to determine which of L-Cotton s available axillary buds develop into fruiting points. Rules were similarly formulated to select which fruit would shed or open from amongst those available. The rules are based on the following common observations (e.g. Hearn, 1969): 1. Fruiting branches are rarely missing on the main stem, while positions 2and 3 are frequently not formed on lower fruiting branches. Since the production of higher fruiting branches occurs at the same time as production of the 2nd and 3rd positions on lower branches, this implies that with limited resources a plant will develop a new higher fruiting branch rather than extend an older lower one.

12 58 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) Position 1 on a fruiting branch has a competitive advantage over other positions for assimilate imported by the branch. 3. Fewer fruit are shed from position 1 than from 2and Fruiting branches are more frequently missing, or short, on vegetative branches than on the main stem, suggesting the mainstem has a competitive advantage over vegetative branches. 5. When population density is high, some plants do not develop fruiting branches and remain vegetative and infertile. We have interpreted these observations in the light of Ashley (1972), Brown (1973) and Constable and Rawson (1980) in order to derive priorities among fruiting points. We express these priorities in the rules that are described in detail in subsequent sections Main stem apex Initially, all plants in the simulated population are vegetative. L-Cotton uses the day-degrees from OZCOT to drive the production of main stem nodes for each plant, on the basis of the plastochron in Table 1. When the first fruiting point from OZCOT becomes available (the running total exceeds 1 for the first time), L-OZlink picks one plant at random from the population, without regard to age or state of development. The axillary bud at the second main stem node below the apex initiates a fruiting branch, and the fruiting point is allocated to it. The plant has now switched to the reproductive mode. Previously created main stem axillary buds at nodes below this branch may become vegetative, according to the process described later. Once a plant becomes reproductive, L-Cotton no longer controls development of the main stem apex by temperature alone (i.e. by meeting the day-degree requirement of the plastochron). The apex can only initiate another node when the fruiting branch 2nodes below the apex has been initiated and its day-degree requirement has been met. Since initiation of a fruiting branch depends on OZCOT s output of fruiting points, which is a reflection of resource supply and demand, this procedure provides for the lengthening of the plastochron as the boll load increases. The plastochron continues to lengthen until the crop finally cuts out when OZCOT ceases to produce fruiting points. In order for the plastochron to average the values in Table 1 before the boll load has increased, the minimum day-degree requirement for a new mainstem node is reduced to 40. There are now two categories of plant, vegetative and reproductive. Henceforth the following rule applies: reproductive plants with available potential fruiting sites take priority over vegetative plants for allocation of fruiting points. Consequently when the second fruiting point from OZCOT is available, if the next main stem node of the reproductive plant is ready (i.e. it is now the second node below the apex), its axillary bud initiates a fruiting branch which receives the fruiting

13 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) point. If the next main stem node is not ready, another vegetative plant is selected at random and is switched to the reproductive mode. This process is repeated for the remaining vegetative plants. If OZCOT supplies insufficient fruiting points, some plants remain vegetative, realistically reflecting what happens in the field. Another realistic outcome emerging from this process is that the position of the first fruiting branch on the mainstem varies by several nodes within the simulated population. Thus the interaction of the timing of fruiting point production in OZCOT, variable plant emergence and the timing of availability of fruiting sites in L-Cotton combine to produce the pattern of initial fruiting branches in the population. It should be noted that no plant age considerations are taken into account in the allocation process, but that when distribution of fruiting points on an oldest-plantfirst basis was tried, it resulted in an unrealistic pattern of initial fruiting branches at lower positions on the main stem. This may be due in part to the sharp rise in OZCOT s initial fruiting point production Fruiting branches As the units of development in L-Cotton are complete metamers, when an axillary bud on the mainstem becomes a fruiting branch and is allocated a fruiting point at the first position during the simulation, L-Cotton also initiates an axillary bud, which starts to accumulate day-degrees. Once the day-degrees accumulated for the bud reaches the fruiting branch plastochron, the second position is ready to become a fruiting point. If the position is selected to become a fruiting point, another metamer complete with axillary bud is initiated, with the potential to repeat the process. If the position is not selected for a fruiting point, it is aborted, and further development of the fruiting branch is terminated. When the number of positions in L-Cotton ready to receive fruiting points exceeds the supply available from OZCOT, the following rules are used to select which positions receive fruiting points: 1. any position 1 on a fruiting branch in the population takes priority over any position 2, which in turn takes priority over any position 3, and so on; 2. when more than one position 1 is available, the one at the lowest main stem node takes priority, and likewise among the position 2s, and so on; 3. if several positions have the same priority, the position to receive the fruiting point is determined at random, with equal probability to each Vegetative branches The number of vegetative branches that develop on a plant is strongly influenced by plant population density. In OZCOT, the contribution of vegetative branches to fruiting point production is accounted for by an empirical parameter that adjusts the number of fruiting points per plant for the effect of population density before fruiting points per plant are converted to fruiting points per square meter. The information is confounded with other effects of plant population and cannot be extracted. OZCOT therefore cannot provide information on the number

14 60 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) of vegetative branches nor on the proportion of total fruiting points produced by vegetative branches. As an alternative, L-OZlink uses a relationship that expresses the number of vegetative branches per plant as a function of population density. The relationship was parameterised from unpublished data collected by one of us (ABH) in population density experiments with three varieties in three seasons: NVB ¼ 1=ða þ bppmþ 1 where NVB is number of vegetative branches per plant, PPM is plants per square meter, and a and b are empirical constants with the following values: a ¼ 0:13; 0:118 and 0:177; b ¼ 0:033; 0:03 and 0:029; for Deltapine 61, Siokra 1-4 and Sicala 3-1 varieties, respectively. The L-OZlink routines use this function to calculate the mean number of vegetative branches per plant, and then the total number for the population being simulated. As soon as a plant becomes reproductive, every mainstem node below the first fruiting branch is the potential location of a vegetative branch. The linkage routines distribute the vegetative branches among these potential locations. One vegetative branch is allocated per reproductive plant per day until all are allocated. As a result, the earliest plants (first to produce a fruiting branch) typically have more fruiting branches than later plants, with the latest plants possibly having none. Vegetative branches are assigned to the highest available location. Thus the first vegetative branch will be at the first main stem node below the first fruiting branch, the second at the second node down, and so on. After three main stem plastochrons have elapsed, a vegetative branch produces its first node, which remains dormant (i.e. does not bear a fruiting branch). Subsequent development proceeds as for the main stem, so that the axillary buds at the second and higher nodes on a vegetative branch have the potential to become fruiting branches. Vegetative branches and their fruiting branches compete with the main stem for fruiting points according to the rationale set out earlier and expressed in the following rules: 1. a higher vegetative branch takes priority over a lower; 2. fruiting points at position 1 on vegetative branches have the same priority as fruiting points at position 2on the previous stem, position 2on the branches the same priority as position 3 on the previous stem, and so on. A realistic result emerging from the application of this rule is that the number of vegetative branches per plant varies, with the earliest plant having most, while some plants may have none Fruiting points The information from OZCOT on numbers of fruiting points is used in two ways in L-OZlink. It is used directly in combination with the already described rules to

15 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) determine which of the available axillary buds on fruiting branches become fruiting points. It is also used indirectly to control the development of the growing points at the apices of the mainstem and the vegetative branches, and to control the extension of the fruiting branches. The rules that were developed to express the priorities for allocation of fruiting points among the available locations are summarised in Table Development of fruit Once fruit have been initiated, the basic L-Cotton routines develop according to the day-degrees passed from OZCOT. Most fruit will either shed as squares or bolls, or open as mature bolls; however some fruit on the plants may be immature when the simulation terminates. The L-OZlink routines process the information from OZCOT on sheds and open bolls, as described previously, to allocate integer numbers to shed or open on the L-Cotton plants. The selection of squares and bolls to be shed from among those available is done in a similar way to the distribution of fruiting points, but with the priorities reversed, thus: 1. fruit at outer positions on the fruiting branches will be shed in preference to those at inner positions; i.e. 3rd position fruit are shed in preference to 2nd position fruit, 2nd in preference to 1st; 2. at any one position (1st, 2nd or 3rd, as the case may be) fruit on a fruiting branch at a higher main stem node is shed in preference to that at a lower; 3. fruit on vegetative branches have the same priority as those one position further out on the next higher branch, or on the main stem from the highest branch. Younger fruit of the appropriate type are chosen first, and then from the older category if any sheds remain unallocated. The result is that more fruit are shed from vegetative branches than from main stems, and from outer rather than inner positions on a fruiting branch. Table 3 Priority among axillary buds (potential fruiting points) in L-OZlink for allocation of available fruiting points from OZCOT Priority Mode of plant Stem Position on fruiting branch Comment 1 Reproductive MS 1 New fruiting branch on mainstem, triggers new mainstem node. 2Vegetative MS 1 First fruiting branch (FB1) 3 Reproductive MS 2 VB1 1 4 Reproductive MS 3 VB1 2 VB21 5 Reproductive MS 4 VB1 3 VB22 VB3 1

16 62 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) The open bolls from OZCOT allocated by the L-OZCOT routines are assigned at random among the mature bolls available on the L-OZCOT plants. If there are insufficient mature bolls, younger bolls are chosen. Within each plant, the bolls to be opened are determined in an inner to outer order, first on the main stem, then on higher to lower vegetative branches. The amount of lint in the open bolls is accumulated from the OZCOT data, and is also proportioned out as each boll is opened Verification of linkage While developing the linkage, in order to check that L-OZlink was using the information from OZCOT as intended and giving plausible results, a specific crop was simulated. The selected crop was a treatment reported by Constable and Hearn (1981) and part of the data set used to validate OZCOT (Hearn, 1994). The agronomic information pertaining to the crop together with observed and simulated yield is given in the Appendix. OZCOT was run with external stresses disabled (water shortage and waterlogging) to generate the information that L-OZlink required. L-Cotton was then run using this information. The resulting plastochrons were examined and found to be similar to the values in Table 1, until the internal stresses (competition for assimilates) slowed the rate of development. This result showed that in the absence of stress, the rate of fruiting point production in OZCOT could match the potential rate based on explicit simulation of morphogenesis and architecture in L-Cotton, and confirmed that the models were mutually consistent. A single exception was a large plastochron value for one mainstem node on one plant in the L-Cotton population. This aberrant value was a rare artifact caused by a long delay while the plant waited for a fruiting point associated with the conversion of OZCOT s continuous variables to integers by L-OZlink. Fig. 4 is a schematic representation of three plants selected from a population of 30 simulated by the linked models. The branching structure shown in Fig. 4 is similar to that of the real plants in Fig. 3, and contrasts markedly with that of the plant in Fig. 2, simulated by L-Cotton without resource limitation. Table 4 summarises several parameters describing the branching structure of the simulated plants. The lower fruiting branches were truncated and fruit have been shed realistically, with more retained at the first position (60%) than at the second (15%) and third (5%). Most fruiting points (72%) were produced on the mainstem. These results are reasonable, conforming to our knowledge of the crop, and verify that the linked models are doing what we intend. As no morphological data had been collected for the experimental crop, comparison of observed and simulated morphology was not possible. 4. Validation Crops were selected for validation on the basis of adequate weather and agronomic data to run OZCOT, and adequate morphological data to compare with the output generated by the linked programs. A further requirement was for some crops to

17 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) show a response to important agronomic variables. Data sets from five sources were used, comprising 15 crops, which are listed in the Appendix, together with agronomic data. The morphological data available consisted of plant maps or diagrams. The first three data sets are Australian and are typical of the high input temperate crops with, and for which, OZCOT and L-OZlink were developed. Constable (1991) supplied data for experiments done under contrasting weather conditions in three successive seasons. Gibb (1995) compares three irrigation treatments with different degrees of water stress. Gibb (personal communication) also provided data from an experiment comparing row spacings and configurations. Fig. 4. Schematic visualisation of three plants from the verification simulation showing number of vegetative branches (VBS) at 7 plants per meter (PPM). Table 4 Summary of verification simulation parameters Mean (n=30) Range Number of vegetative branches Per plant Main stem nodes Number per plant First fruiting branch At main stem node Highest boll At main stem node Longest fruiting branch Fruiting points Fruiting points Per plant Bolls Per plant

18 64 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) Table 5 Varietal parameters required by L-Cotton to simulate Munro and Farbrother (1969) and Rijks (1965) data sets. Variety Wilds Early Bar XL1 SQCON (squares/plant/day-degree) Day-degrees for: Sowing to 1st square Square to flower Square to open boll Mainstem plastochron Fruiting branch plastochron The remaining two data sets are for low input tropical crops and provide a marked contrast. Munro and Farbrother (1969) published a plant diagram from a crop in Uganda. Rijks (1965) presented plant diagrams from four crops grown with different amounts of water. The varietal parameters for simulating these crops were derived from Hearn (1969) and are shown in Table 5. We simulated these crops with OZCOT, and the simulated yields and yield components are compared with observed values in the Appendix. The linked model was then run for each crop using the relevant OZCOT output for these crops. L-OZlink produced output in a form suitable for comparison with the observed plant mapping parameters Constable s data set Constable s (1991) experiment compared three irrigation methods in three seasons ( , , and ) in the Namoi Valley, NSW, Australia. His raw data consist of the location of each fruiting point and harvested boll on the branching structure on 28 plants in each treatment for each season. The published results represent pooled data for treatments and seasons. The average mainstem node number of the first fruiting branch using L-Ozlink was 5.67, ranging from 5 to 8, compared to the observed average of 6.58 with 53% below node 7. Constable reported 82% of fruiting points on the mainstem, with the rest on the vegetative branches; the simulated value was 72%. Constable (1991, Fig. 2) gave profiles up the mainstem of fruiting point numbers, fruit survival, boll size and yield at each fruiting branch position at each mainstem node. These have been reproduced in Fig. 5 (a d) for comparison with profiles simulated using L-OZlink in Fig. 5 (e h). The longest fruiting branches, judged by the number of fruiting points at the third position, were produced at nodes 8 10 on the observed plants and at nodes 7 9 on the simulated plants (Fig. 5a,e). Fruit retention was greatest at nodes for both observed and simulated plants, with mature fruit retained at 68% of observed and 83% of

19 Fig. 5. Observed and simulated profiles of fruiting points, fruit retention, boll size and yield for data from Constable (1991). J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003)

20 66 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) simulated first position fruiting points (Fig. 5b,f). On both observed and simulated plants, boll size was greatest at the lower nodes ( < 15) and the first position, except for the first fruiting branch, which had notably smaller bolls on both observed and simulated plants (Fig. 5c,g). Mainstem nodes 7 13 produced the greatest proportion of yield, peaking between nodes 8 and 10, in both observed and simulated plants (Fig. 5d,h). There were several discrepancies between observed and simulated plants (Fig. 5). There were seven simulated first position fruiting points per m at each node from 8 to 20 (Fig. 5e), whereas there were only 6.7 observed first position fruiting points at node 8 and less at higher nodes (Fig. 5a). This means that there was a fruiting branch at every node between 8 and 20 on the simulated plants but not on the observed plants. Destruction of the apical bud of some plants by insects in the observed crop (known as tipping out ) accounted for the difference. The L-Cotton model can simulate tipping out, but no data were available from the observed crops to enable this to be done. Other considerable, and less easily explained, differences are the greater contribution of the first position (more fruiting points, more and larger bolls) relative to second and third positions on simulated plants compared with observed plants Gibb s data sets Gibb s (1995) experiment consisted of three irrigation treatments applied in the McIntyre Valley, northern NSW, Australia in The control was fully irrigated with six in-crop irrigations, while the last irrigation was omitted in one treatment (five irrigations) and the last two irrigations omitted (four irrigations) in another. The data available consist of percentage retention at the first and second position on the fruiting branches at each mainstem node. There was reasonable agreement between average simulated and observed retention (Table 6) at the first position for all fruiting branches (Fig. 6). The numbers of bolls above node 20 were negligible for observed and simulated plants in all treatments. Earlier termination of irrigation was reflected to the same degree in both observed and simulated plants, with retention starting to decline at progressively lower nodes: above node 17 with six irrigations, above 15 with five irrigations and above 13 with four irrigations. A shortcoming of the simulation was under-estimation of retention at the second position for treatments with five and six irrigations. Table 6 Percentage boll retention at the first fruiting position for Gibb s (1995) experiment Irrigations Observed 46.4% 44.6% 33.6% Simulated 42.9% 37.4% 34.4%

21 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) Fig. 6. Observed and simulated fruit retention for Gibb ( ). Gibb s (personal communication) experiment in the McIntyre Valley, consisted of four row-configuration treatments. Conventional planting at 1 m row spacing (solid) was compared with single skip (two rows planted, one skipped), double skip (two rows planted, two skipped) and 2m row spacing. The linked models successfully simulated the difference between 1 and 2m row spacing in first position retention, as shown in Fig. 7. Skip-row configurations were less well simulated by the underlying OZCOT model, therefore comparisons are not shown here Munro and Farbrother s data set These data are for a large single plant from a variety trial at Namulonge, Uganda in The plant is representative of a rain-fed crop with a low population density in the upland (i.e. cool) humid tropics. In order to account for less rigorous pest

22 68 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) Fig. 7. Observed and simulated fruit retention for Gibb ( ). control the parameter controlling background shedding of floral buds was increased from 20 to 50%. Fig. 8 compares Munro and Farbrother s Fig. 6 with a modal plant from the population simulated using L-OZlink. The diagrams are for plants at 125 days after sowing, just prior to opening of the first boll. The simulated plant was more advanced than the observed with 24 vs. 20 mainstem nodes and more positions per fruiting branch. The flowering line is similar in both the simulated and observed plant Rijks data set Plants were grown at a low population density in a desert environment. Treatments consisted of four amounts of irrigation water. Following local practice, all the water was applied before sowing so that the simulated crops grew on stored water. Plants developed until the stored water was exhausted, resulting in the progressively larger plants at maturity shown in Rijks (1965), Fig. 1, reproduced in our Fig. 9. The linked models were used to simulate a population for each treatment. A modal plant from each simulation is shown in Fig. 9 for comparison with the observed plants. The range in plant size was simulated well, along with the number of mainstem nodes, the position of the first fruiting branch and the number of positions per branch, apart from mainstem nodes on the 45-cm treatment. 5. Discussion The linked OZCOT and L-Cotton models simulated the branching structure of cotton reasonably well. Over a wide range of conditions the position of the first

23 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) Fig. 8. Single plant diagram and flowering line. Observed after Munro and Farbrother (1969, Fig. 6) and simulated from the linked programs. X indicates shed buds or bolls, b indicates flower buds, F indicates open flowers, and A, B and D indicate small, medium and full-diameter bolls, respectively.

24 70 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) Fig. 9. Diagrams of the plants grown with 15, 45, 60 and 90 cm of irrigation water. Observed redrawn from Rijks (1965), simulated from the linked programs. Mainstem sympodia to the right, vegetative branch sympodia to the left. The dashes indicate aborted fruit and the circles indicate retained fruit. The line represents the limit of flowering at the end of the season. fruiting branch, nodes per mainstem and the number of positions per fruiting branch were predicted well. There is a dearth of data for validation for vegetative branches, but the results are plausible. The distribution of harvestable bolls among the fruiting positions on fruiting branches is less satisfactory, with over-estimation of the number at position 1 and under-estimation at positions 2and 3. The effects

25 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) of water stress and row spacing on branching structure and fruit retention are realistic. The shortcoming in simulating the distribution of harvestable bolls among positions along fruiting branches reflects limited understanding of how priorities are ordered in the plant when carbon and nitrogen supplies are restricted. The bolls retained are those successful in competition for limited supplies; the unsuccessful ones are shed. The rules employed in the simulation clearly give too high a priority to fruit in position 1. One option, as suggested in the introduction, would be to build a more complex model to simulate supply and demand at each fruiting position. From the crop modelling side, steps in this direction have been taken, for example, in Mutsaers (1984) model. Rather than modelling the average plant as a whole, it is viewed as being composed of layers each with one main stem leaf and associated sympodial branch. A carbohydrate budget is used to allocate assimilates between growth and development for each stratum separately. On the architectural modelling side, the model presented by de Reffye et al. (1999) may provide a sound basis for the development of such a detailed process-based model of cotton architectural growth. Unlike L-OZCOT, it simulates a single plant undergoing strictly vegetative growth. The model uses details of simulated plant architecture and leaf area to estimate transpiration and therefore biomass production, which is then allocated based on sink strength of stem and leaves to model further morphogenesis. However, the effects of reproductive growth and fruit shedding on these processes are not well understood and would require a great deal of research to model at this level of detail. Such a development would also be a radical departure from the simple elegance of L-systems and OZCOT, with danger noted by Wang et al. (1977) that complex models can become more difficult to understand than the systems they represent. Models are often most useful when they provide simplifying abstractions of reality. Our results demonstrate the feasibility of linking the models, which was the main purpose of this work, and confirm the value of L-systems for describing morphogenesis. OZCOT and similar models are widely used in agricultural research, and to a lesser degree for crop management. Linking such models with L-Cotton has the potential to enhance their value for these applications. Among other applications, OZCOT can estimate damage likely to be done by infestations of fruit and leaf feeding pests of cotton. A potential application of linking OZCOT to L-Cotton is evaluation of the plant mapping data currently used in pest management. The retention rate of fruit is used to evaluate the impact of pest infestations and the need for pest control. A current recommendation is that if the retention rate on position 1 of lower fruiting branches early in the season falls below 50%, pest action thresholds are reduced (Shaw, 1999). However environmental and agronomic factors can also reduce retention rate and may result in reducing the threshold unnecessarily. The linked models could identify such situations, provided the allocation of fruit retained among positions along a fruiting branch can be solved.

26 72 J.S. Hanan, A.B. Hearn / Agricultural Systems 75 (2003) With the addition of details of cotton plant geometry such as branching angles, internode lengths and leaf growth rates, the linked system can capture the three-dimensional architecture of a cotton crop at any time in a season. A system for acquiring the necessary data has been developed and data collected for a normal and an okra-leafed variety (Room and Hanan, 1995). OZCOT provides a model of leaf area growth, and L-Cotton simulates individual leaf initiation and growth. These processes will need to be linked, incorporating varietal information on leaf morphogenesis, to build an accurate picture of the canopy. A prototype, based on greenhouse measurements, can be seen in Fig. 10, demonstrating that realistic images, readily recognisable as cotton plants, can be generated. In the APSRU Farmscape project (Carberry and Bange, 1998), simulation models, including OZCOT, are used in farmers participatory research groups to explore outcomes and risk of cropping strategies. Realistic three-dimensional visual Fig. 10. Realistic visualisation of L-Cotton model.