Published online 17 August 2005
Published in Agron J 97:1295-1303 (2005)
DOI: 10.2134/agronj2004.0251
© 2005 American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA
Modeling
Process-Based Modeling of Timothy Regrowth
Marcel van Oijena,*,
Mats Höglindb,
Hans Martin Hanslinb and
Nick Caldwella
a CEH-Edinburgh, Bush Estate, Penicuik, EH26 0QB, UK
b The Norwegian Crop Research Inst., Særheim Research Centre, Postvegen 213, N-4353 Klepp St., Norway
* Corresponding author (mvano{at}ceh.ac.uk)
Received for publication October 4, 2004.
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ABSTRACT
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Previously, the literature on the growth of timothy (Phleum pratense L.) in Scandinavia was reviewed and a simple process-based model was developed to explain and predict the response of this species to different environments and management regimes. The model could not be tested in detail, because only biomass data were available at the time. However, recent experimental work has generated a large (n = 633) and uniquely detailed dataset on the growth and underlying physiology of timothy and its response to cutting at different growth stages. The present study aimed to use this dataset to test the model, and to use the model to identify the key physiological and morphological mechanisms that determine the regrowth rate of timothy after cutting. Model testing consisted of comparing simulations and measurements for eight variables: biomass, leaf area index (LAI), tiller and leaf density, rates of leaf appearance and elongation, carbohydrate concentration, and specific leaf area. Although the new data referred to a different cultivar, a different site, and different years from those used in the original model parameterization, the model was still able to account for nearly half the variation in the dataset [r2 = 0.468, normalized root mean squared error (RMSE) = 0.631]. This suggested that the key assumptions of the model (i.e., dependence of growth and allocation on the source-sink balance of the plants and a close link between tillering and leaf area dynamics) were plausible. However, the original model was not able to account for the observation that cutting at early heading tended to be followed by a longer lag phase than cutting at anthesis. We identified six mechanisms, not previously incorporated in the model, that improved its behavior: (1, 2) dependence of tillering and leaf appearance rate on carbohydrate concentration, (3, 4) dependence of leaf appearance and leaf elongation rate on plant phenological stage, (5) sprouting of new tillers from decapitated generative tillers, and (6) proportionality of the number of elongating leaves with tiller size. Incorporation of these mechanisms, followed by reparameterization using a Metropolis-Hastings Monte Carlo method, improved performance statistics (r2 = 0.521, normalized RMSE = 0.415) and explained the long duration of slow growth after early cutting. These mechanisms may thus be keys to understanding timothy regrowth.
Abbreviations: CV, coefficient of variation • LAI, leaf area index • RMSE, root mean squared error
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INTRODUCTION
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TIMOTHY (Phleum pratense L.) is the most widely grown grass species used for silage and haymaking in Scandinavia and eastern Canada. Timothy is more winter-hardy than, for example, perennial ryegrass (Lolium perenne L.), which is grown in Norway. However, timothy suffers from poor regrowth after the grass is cut (Höglind et al., 2001). Because relatively little research has been performed on timothy (Hopkins, 2000), the causes for its intolerance to defoliation are not well understood. Regrowth of timothy is slowed down if cutting takes place during a period of rapid stem elongation (Jewiss and Powell, 1966, p. 67–72; Misley et al., 1977; Bonesmo and Skjelvåg, 1999), but this phenomenon applies to other grass species as well and does not explain the particular sensitivity of timothy. Mechanistic understanding of the processes determining regrowth may help to identify ways to address the problem, by means of management or breeding.
Various reports in the literature suggest that early cutting of a grass sward is likely to lead to fast regrowth if most of the tillers are still in the vegetative state (Jewiss and Powell, 1966, p. 67–72; Misley et al., 1977; Bonesmo and Skjelvåg, 1999). A sward that is not in an advanced generative state has: (i) few elongated stems, which are likely to be killed by cutting; (ii) many vegetative tillers whose apex is below cutting height so they can survive the cutting and initiate new tillers after the cut; and (iii) unused carbohydrate reserves, if the key demand on reserves is from elongating stems, allowing regrowth to benefit from a high source/sink ratio. However, when comparing two later growth stages, early heading and anthesis, our recent experiments suggest that regrowth in timothy is actually faster after a harvest at anthesis than at early heading (Höglind et al., 2005). Physiological mechanisms that may explain these observations are discussed in the present paper.
Correctly simulating the regrowth of a sward after cutting is an essential requirement of any grass growth model that aims to be applicable to problems of grassland management. However, the mechanisms involved have not been clarified sufficiently, and models tend to circumvent the problem of simulating regrowth in various ways. One example is the perennial ryegrass model LINGRA (Rodriguez et al., 1999), which forces post-cut growth to be delayed during a 2-wk period, and only thereafter resumes mechanistic simulation of growth. Other models do not simulate the dynamics of cutting at all but assume LAI to be maintained at a constant level by some external agent like grazing (Thornley, 1998), only simulate biomass growth, not leaf area dynamics (Gustavsson and Martinsson, 2001), or only simulate precutting dynamics of LAI (Bonesmo and Bélanger, 2002). Recently, we presented a mechanistic model of timothy growth (Höglind et al., 2001), and here we evaluate the model's capacity to explain timothy regrowth dynamics. In our model, we tried to simulate regrowth mechanistically based on the dynamics of the processes that contribute to source and sink strength (Höglind et al., 2001). Preliminary evaluation of the model identified the dynamics of tiller and leaf number as key uncertainties in understanding and simulating timothy growth. The large dataset on timothy growth we produced recently (Höglind et al., 2005) includes data on tiller and leaf number, which allowed us to test the model in detail here.
Compared with other grass models (Thornley, 1998; Rodriguez et al., 1999; Bonesmo and Bélanger, 2002), the model we use is characterized by two main features: (i) explicit simulation of leaf area dynamics and tillering for vegetative and generative tillers, and tight integration of these processes; and (ii) simulation of source-sink relations, with the source consisting of both current photosynthesis and mobilization of reserves, and sink size being determined by the dynamics of leaves and stems.
The present study has two goals. First, we aim to test our timothy model on independent data. The original model (Höglind et al., 2001) has been tested successfully on independent data but only for biomass accumulation. No data were available at the time to test the simulation of underlying processes, so the model may conceivably have simulated biomass correctly but for the wrong physiological reasons. Moreover, the data were at relatively low temporal resolution, so the key periods around cutting could not be inspected closely. However, new data are now available from more detailed experiments on timothy subjected to two different times of cutting (Höglind et al., 2005). The dataset collected in these experiments is large (633 data points) and includes growing season dry matter accumulation as well as details of changes in the number and size of tillers and leaves. We shall use this dataset here for a rigorous test of the timothy model.
The second goal of this paper is to use the model to identify the key growth and regrowth determining processes. Where the model is shown to deviate from the data, we develop hypotheses that may account for the observations, drawing on information from recent literature on grass growth. The likelihood of these hypotheses to apply to timothy is then determined by incorporating the hypothetical mechanisms into the model and testing for improvement.
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MATERIALS AND METHODS
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Data
All data used here are taken from experiments described in detail by Höglind et al. (2005). The experiments quantified the effect of early or late cutting—that is, taking a first cut around early heading or 22 to 28 d later, just before anthesis—on aboveground regrowth of timothy swards. The collected data are time series of biomass and other variables as they change through the growing season, which makes them particularly valuable for dynamic modeling.
The experiments were performed in the years 2000, 2001, and 2002, on sandy soil near Saerheim in southern Norway (58.46° N lat; 5.39° E long; 90 m above sea level). The cultivar ‘Grindstad’ was used in all 3 yr. Measurements began on 4 May 2000, 25 Apr. 2001, and 18 Apr. 2002 (day of year 124, 115, and 108), and finished 94, 132, and 130 d later, respectively. The early cuts took place on 30 May 2000, 13 June 2001, and 30 May 2002 (day of year 150, 164, and 150) and the late cuts on 22 June 2000, 5 July 2001, and 27 June 2002 (day of year 173, 186, and 178).
Global radiation levels were similar in the three measurement periods (on average 16.5, 17.0, and 16.6 MJ m–2 d–1), but temperature and rainfall were somewhat higher in 2002 than in the 2 previous years. Temperature averaged 11.9, 12.3, and 13.8°C in the 3 yr, and rainfall 3.1, 2.6, and 3.7 mm d–1. Each year, N fertilizer was applied in spring (20–30 April; 140 kg N ha–1) and immediately after each cut (80 kg N ha–1). Phosphorus and K were applied in spring at 30 and 150 kg ha–1, respectively. There were no symptoms of nutrient deficiency in any of the years, and lodging did not occur. More details of soil and weather are given by Höglind et al. (2005).
The dataset comprised measurements of eight variables: aboveground biomass, tiller density, LAI, water-soluble carbohydrate concentration in aboveground biomass, leaf appearance rate, number of elongating leaves per tiller, leaf elongation rate, and specific leaf area. Measurements were taken in each of the six combinations of year and treatment. The complete dataset consists of 633 points, most of which are the average of six replicates. For each variable, year, and treatment, approximately 13 samples were taken over the growing season spaced at approximately even intervals. The variability of the data was different for the eight variables. The main output variable of the model, aboveground biomass, was measured with an average coefficient of variation (CV = standard error divided by the mean of the replicates) of 0.090. The two key explanatory variables, tiller density and LAI, had an average CV of 0.115 and the five remaining variables were measured at an average CV of 0.346. In the comparison of data with model output, these three groups of variables were weighted differently (see section below on Model Testing).
Model
The timothy model was presented in detail by Höglind et al. (2001). The model simulates the growth of a timothy sward during a single growing season; overwintering is not simulated. Inputs are daily values of weather conditions (radiation, temperature, rain, humidity, wind). The soil is characterized by means of a soil water retention curve and initial water content. The model has nine state variables for the grass: biomass in leaves, stems, and roots (g m–2), density of vegetative and generative tillers (no. m–2), LAI (m2 m–2), water-soluble carbohydrate content in aboveground biomass (g CH2O m–2), rooting depth (m), and phenological stage. Aboveground growth is determined by the balance of source (photosynthesis plus mobilization of reserves) and sink (growing leaves and tillers). Sink strength is determined by the rate of leaf appearance, which provides sites for tillering; the newly added phenological stage, which determines the number of elongating leaves per tiller; and leaf elongation rate. Sink strength increases with temperature but decreases when soil water content is too low to support transpirational demand. If the source exceeds the sink, reserve levels are built up until a maximum concentration, above which overflow of carbohydrates feeds root growth.
Initial values of the plant state variables, except for phenological stage, are taken from site-specific measurements, but the 32 regular plant parameters of the model are assumed to have cultivar-specific values, taken from literature and our own observations (Höglind et al., 2001). In our initial model development, we had parameterized the model for the North-Norwegian timothy cultivar ‘Bodin’. In the present work, we apply the model to the South-Norwegian cultivar ‘Grindstad’, which heads 1 to 2 d earlier than Bodin in Southern Norway and has somewhat larger tillers (own observations). Because little cultivar-specific information for Grindstad was available, we kept all parameters initially at the default values for ‘Bodin’ (Höglind et al., 2001) except for a higher maximum average tiller weight (Table 1).
Model Testing
The model was tested by simulating timothy growth under the conditions used in the experiments, and quantifying the extent to which the results differed from observations of the eight measured variables. Two statistics were used to quantify the similarity between model and data. First, the extent to which model output accounted for variation in the data was quantified by means of the squared correlation coefficient (r2). Second, deviations between observations and model predictions were expressed as the normalized root mean square error, calculated as:
where the Oi represents n observations and Pi the corresponding predictions (Wallach and Goffinet, 1989). Because of the division by the mean of the observations 
, the RMSEnorm is a dimensionless positive number that can be compared for different variables. Perfect correspondence between data and model would give RMSEnorm = 0. When calculating the average RMSEnorm or r2 for all eight variables, we weighted the variables according to the importance we attached to their prediction, and the precision with which they had been measured (see section above on Data) as follows:
where wi = 0.3 for aboveground biomass, 0.15 for tiller density and LAI, and 0.08 for the five other variables. The six different year–treatment combinations carried equal weight. We will write RMSEnorm in the rest of this paper, dropping the overhead bar when the meaning is clear from the context.
Parameter Optimization
Model testing revealed differences between model outputs and observations. We proceeded by reparameterizing the model, to determine whether the differences could have been caused by incorrect parameterization for cultivar Grindstad. Parameterization was aimed at identifying the set of parameter values that would reduce RMSEnorm the most.
Parameterization was done by means of Monte Carlo simulation using a Metropolis-Hastings random walk (Metropolis et al., 1953; Robert and Casella, 1999). In a preliminary analysis, preceding the parameterization proper, we had found that the Metropolis algorithm performed better than steepest gradient optimization and random search, while being similarly efficient as genetic algorithms. The Metropolis algorithm required defining the uncertainty for each of the 32 parameters of the model. Ranges of possible values for 10 parameters had already been defined before (Höglind et al., 2001). For the remaining parameters we assumed ranges from 50 to 150% of their default values (Table 1). The Metropolis algorithm generated a random walk through the 32-dimensional parameter space delimited by the parameter ranges. At each step, a candidate set of parameter values was randomly chosen, the timothy model was run six times to simulate all year–treatment combinations with those parameter values, overall RMSEnorm was calculated, and the candidate parameter values were accepted with probability inversely proportional to the RMSEnorm. We used a random walk of length 50000 to ensure proper exploration of the parameter space.
Model Modification
After model reparameterization, some differences between model outputs and observations remained. We assumed that these differences were due to structural model error, and we identified six possibly misrepresented physiological mechanisms. Six structural changes to the model were thus examined (Table 2). Five of the changes concerned the addition to the model of a previously not considered process or effect, and one change implied that a process was no longer directly proportional to an influencing variable. In all cases the structural change was implemented by adding a "structural parameter" (S1, ..., S6) to the model, whose magnitude represented process rate or effect magnitude in such a way that the original model could be retrieved by setting the structural parameters to default values of 0 or 1 (Table 2).
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Table 2. Structural changes made to the timothy model. The changes are defined through six "structural parameters" S1–S6. The original model structure is represented by the indicated default values of the parameters. The optimum values of the structural parameters were determined while simultaneously optimizing the 32 regular parameters of the model (Table 1, rightmost column).
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Structural parameter S1 quantifies the degree to which tillering is proportional to the concentration of reserves expressed as a fraction of the maximum concentration. This represents the observation of Fulkerson and Donaghy (2001) that tiller initiation, in ryegrasses, depends strongly on water-soluble carbohydrate reserves. Parameter S2 allows for the possibility that leaf appearance, in contrast with the original model, may not depend on the reserves, which is consistent with the observation that leaf appearance is relatively insensitive to management activities like cutting that are likely to affect the level of reserves (Chapman and Lemaire, 1993). Parameter S3 quantifies the reduction in leaf appearance with advancing phenological stage. This accounts for the observations of Bélanger (1996)(1998), showing that leaf appearance rate decreased with thermal time during the vegetative phase, before stem elongation, whereas Höglind et al. (2005) reported a decrease in leaf appearance rate with time as more and more flag leaves developed in the sward during stem elongation. Parameter S4 represents the observation that leaf elongation rate, on generative tillers, decreases with advancing phenological stage (Höglind et al., 2005). Parameter S5 introduces the possibility that decapitation may induce some tillering at the base of generative tillers (Ito et al., 1997). Parameter S6 accounts for the obvious possibility that newly formed, small tillers carry fewer leaves.
The method of representing structural changes by means of structural parameters, whose magnitude determines the extent of the change, allowed optimization of the model by means of the same method that was applied before to optimize the regular parameters (previous section). When optimizing the six structural parameters we re-optimized the 32 regular parameters simultaneously, because changes in model structure imply different optimum values for all parameters.
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RESULTS
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Model Testing
Using the default values of all 32 parameters (Table 1), the model reproduced much of the observed behavior of the eight measured variables, in each of the three experimental years (Fig. 1–3)
. Agreement between simulated and observed values was seen not only at the systems level (biomass dynamics) but also at the level of the underlying processes. Overall RMSEnorm for all 633 data points was 0.631 and r2 was 0.468 (Table 3). However, some persistent differences between model and data were apparent in all six simulations.
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Fig. 1. Measurements (symbols) and simulations (lines) for the experiments in 2000. Two treatments were applied: early cutting (+,—) and late cutting (o, ___). Eight variables were measured and simulated: aboveground biomass (g dry matter m–2), leaf area index (LAI) (m2 leaf m–2 ground), water-soluble carbohydrate concentration (g CH2O g–1 aboveground dry matter), tiller density (no. m–2), leaf elongation rate (m d–1 tiller –1), number of elongating leaves (no. tiller–1), leaf appearance rate (no. tiller–1 d–1), and specific leaf area (m2 leaf g–1 leaf dry matter). Simulations made use of default, uncalibrated parameter values.
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Table 3. Summary statistics of the fit to data for three model variants. RMSEnorm is the normalized root mean square error.
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Aboveground biomass is the main output variable whose behavior the model was designed to explain and predict. The average growth rate of aboveground biomass was simulated reasonably well both before and after the cut (Fig. 1–3), and the simulations correctly showed a lag phase of slow growth immediately following the cuts. However, the length of the lag phase was not simulated correctly in each case. In particular, the model underestimated the lag phase after the early cut in the years 2000 (Fig. 1) and 2002 (Fig. 3). The overall pattern of LAI was simulated well but tiller density after cutting was underestimated. Water-soluble carbohydrate levels were consistently overestimated. The number of elongating leaves and specific leaf area were simulated adequately, in view of the large variability of these variables in the measurements, but end-of-season rates of leaf elongation and leaf appearance were overestimated.
Parameter Optimization
After optimization, aimed at minimizing RMSEnorm, all 32 parameters of the timothy model were changed (Table 1). The average difference with the default parameter values was 17.6%. Optimization changed the parameters related to sources-strength more than those related to sink-strength (27.0 and 10.4%, respectively). Parameters related to phenology and tillering, which affect both source and sink, were changed by 15.4%. We refer to the model with optimized parameter values as the "calibrated model."
The overall RMSEnorm of the calibrated model was 0.480, that is, 24% less than the default model, but r2 was not increased by much (Table 3). The improvement in RMSEnorm was mainly due to better simulation of the time courses of aboveground biomass, tiller dynamics and water-soluble carbohydrate concentration (Table 3). Figure 4
shows the simulations of the calibrated model for biomass and tiller density in all six combinations of year and treatment. The main improvement was in regrowth after cutting, where the model now was able to reproduce the relatively long lag phase after early cutting. The high tiller densities after cutting were also reproduced better. However, the calibrated model underestimated the large biomass increase before the late cut in 2000 and 2001.
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Fig. 4. Measurements and simulations of aboveground biomass and tiller density for each year and both treatments [i.e., early cutting (+, —) and late cutting (o, ___)]. Simulation results differ from those shown in Fig. 1–3 in that parameters were optimized for minimum RMSEnorm.
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Model Modification
After optimization of both parameters and model structure, all six structural parameters deviated strongly from their default values (Table 2), indicating that the hypothesized changes to the structure of the model were plausible. The simultaneously re-optimized values of the 32 regular parameters differed 17.3% from their default values (Table 1), and a similar amount from their values in the calibrated model (see previous paragraph). We refer to the model with optimized values for both the structural and the regular parameters as the "structurally optimized model."
The overall RMSEnorm of the structurally optimized model was 0.415, that is, 34% lower than the default model but only 13% lower than the calibrated model. The r2 was slightly higher in the structurally optimized model than in the other two variants (0.52 vs. 0.47). The small further improvement by structural change was mostly due to improvement in simulating the rates of leaf appearance and elongation rate (Table 3), rather than in any improvement for biomass or tiller density.
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DISCUSSION
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Testing the Default Model
Our first test consisted of running the model using default parameter values—except for maximum average stem weight, which was set at a high value of one gram per tiller to account for the use of the large South-Norwegian cultivar ‘Grindstad’ in the experiments (Höglind et al., 2005). The test of the default model showed that it could account for nearly half of the observed variation in the measurements (r2 = 0.47), with an average RMSEnorm of 0.631 (Table 2). These results were encouraging because they showed that a process-based grassland model, based on the concept of source-sink balance, and with only 32 plant parameters, could account for much of the variation in 633 measurements on eight different plant variables. Such a severe test of a grassland model is rare, as usually only biomass yield is known (Höglind et al., 2001). Moreover, the default model had not been reparameterized for the test conditions, and only the one parameter for maximum tiller weight had been modified to account for the fact that the test experiments used a larger cultivar than the one studied and simulated before.
The RMSEnorm and RMSE have been reported for other timothy models. Bonesmo and Bélanger (2002) reported a value of 0.19 for RMSEnorm of dry matter yield as well as LAI. Gustavsson et al. (1995) reported a value for RMSE of dry matter yield of 52 g m–2, which was similar to the value of 66 g m–2 found by Bonesmo and Bélanger (2002). These values are lower than the values of RMSEnorm we reported for our timothy model (Table 2), even after parameter optimization and structural modification (discussed below). However, the values for RMSEnorm of the different models are not comparable. We tested and calibrated our model against a much larger data set, in terms of both number of variables and data points, which made low values for RMSEnorm harder to achieve. Moreover, and in contrast to Bonesmo and Bélanger (2002), we simulated not only a continuous period of spring growth, but also interruptions by cutting at different times, followed by regrowth. The time courses of the different variables (Fig. 1–4) are therefore not smooth and thus harder to simulate. We suggest that RMSEnorm is better used as a tool in model calibration and model improvement, as it was used here, rather than as a means of comparing models that simulate different variables and conditions. Our model had been developed in particular to explain and predict how regrowth after cutting of timothy swards varies with environmental conditions and sward management. Given these aims, the default model did not perform fully adequately. The rate of regrowth after late cutting was simulated well, but the lag phase after cutting, and before regrowth starts, was underestimated after early cuts (Fig. 1–3). The default model also underestimated tiller density after cutting. Only in the experiments, tiller densities reached higher levels after cutting than before (Fig. 1–3).
Parameter Optimization
The test of the default model did not provide any information about the possible causes for model deficiencies. It remained unclear whether the default model had inappropriate parameter values for the specific cultivar used in the experiments, or whether model structure was incorrect. To determine whether the model structure was, at least in principle, capable of accounting for the observations, we calibrated the model on the test data. A simple Monte Carlo procedure, using the Metropolis algorithm to minimize RMSEnorm, proved to be an effective means for optimizing the parameter values. The parameter values, as optimized for cultivar Grindstad, differed on average by only 18% from the default parameterization for cv. Bodin, which suggests that the cultivars are similar and that the model is able to represent both with only small modification. One parameter that was changed by a relatively large fraction was the maximum concentration of reserves, which was decreased from a value of 0.30 for cultivar Bodin to 0.16 for Grindstad (Table 1). With the default high value of the parameter, water-soluble carbohydrate concentration was systematically overestimated by the model (Fig. 1–3), hence the large modification by the calibration. However, the original value was arrived at without information on reserve content of cultivar Bodin, so the actual difference between the two cultivars may be smaller than these results suggest. The light extinction parameter also changed considerably, from 0.63 to 0.48. This is within the range observed for timothy cultivars (Kornher, 1971) and is also comparable to variation in the light extinction coefficient observed within single growing seasons (Bélanger and Richards, 1997).
After calibrating the model on the data for cultivar Grindstad, the model was able to account for the longer lag phase that followed early cutting as opposed to cutting 22 to 28 d later (Fig. 4). The calibrated model was also able to simulate the increased tillering after cutting, albeit not to the extent observed after late cuts (Fig. 4). Overall the calibrated model performed better than the default model (RMSEnorm being reduced to 0.480), so the original model structure based on the concept of source-sink balance was sufficient to explain a large part of timothy sward behavior after cutting. However, unexplained phenomena remained, in particular the peak biomass levels before late cutting, and the reduction in rates of leaf appearance and elongation at the end of the growing season.
Structural Changes to the Model
We intended the timothy model to be relatively simple and parameter-sparse, to allow parameterization and testing to be based as much as possible on available data. However, the fact that even after calibration some differences between model results and observations remained, made us consider changes in model structure that involved adding processes and parameters. In selecting changes to be considered, we focused on the key areas of uncertainty in timothy modeling identified before (Höglind et al., 2001) (i.e., the dynamics of tillering and leaf growth). Tillering and foliar dynamics are processes that mediate between source and sink. A large source strength tends to stimulate tillering and leaf growth, thereby increasing both the number and size of future sinks in the sward as well as the photosynthesizing area that is the ultimate source of all plant C. Two of the changes we tested involved the effect of water-soluble carbohydrate concentration on the rates of tillering and leaf appearance. Two further changes introduced effects of phenological stage on the rates of leaf appearance and elongation. One change examined the possibility of new tillers sprouting near the soil surface from decapitated generative tillers, and the final change involved a smaller number of elongating leaves in small tillers.
The method for structural optimization, whereby each structural change was represented by a single structural parameter that determined both the presence and magnitude of the particular change, worked well. Optimization led to values for each of the six structural parameters that deviated strongly from their default values (Table 2), indicating that the data set provides evidence to support each of the changes. We therefore conclude that major structural improvements to the original model will involve the representation of tillering, leaf appearance, and leaf elongation. However, the overall performance of the structurally optimized model was not improved strongly compared with the calibrated model, RMSEnorm decreasing further from 0.480 to 0.415, and r2 increasing to 0.52. Structural optimization remedied the overestimated rates of leaf appearance and elongation at the end of the growing season, but could not explain the high growth rates observed before the late cut in 2000 and 2001.
We have no evidence for the assumption that key environmental factors were overlooked in our model. The model responds to variation in light, temperature, soil water content, wind speed, and atmospheric humidity, but nutrient availability is not considered. The timothy model of Bonesmo and Bélanger (2002) did include the effect of N availability on dry matter production and leaf expansion, and the authors showed that their model accounted well for observed differences in growth between different levels of N limiting conditions. Our model does not include N relations as it was developed for conditions of optimal nutrient availability. Such conditions were present in the experiments, which had high fertilization levels, and no symptoms of deficiency were observed.
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CONCLUSIONS AND OUTLOOK
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The objectives of this study were to test our timothy model against independent data, and to use the model to identify the key physiological and morphological mechanisms that determine the regrowth rate of timothy after cutting. Although the new data referred to a different cultivar, a different site and different years from those used in the original model parameterization, the model was still able to account for nearly half the variation in the dataset (r2 = 0.468, normalized RMSE = 0.631). The key assumptions of the model (i.e., dependence of growth and allocation on the source-sink balance of the plants) and a close link between tillering and leaf area dynamics, thus are plausible. However, six mechanisms, not previously incorporated in the model, were shown to improve model behavior: (1, 2) dependence of tillering and leaf appearance rate on carbohydrate concentration, (3, 4) dependence of leaf appearance and leaf elongation rate on plant phenological stage, (5) sprouting of new tillers from decapitated generative tillers, and (6) proportionality of the number of elongating leaves with tiller size. Because incorporation of these mechanisms improved performance statistics (r2 = 0.521, normalized RMSE = 0.415), and explained the observed long duration of slow growth after early cutting, they may be keys to understanding timothy regrowth.
Although perfect simulation (RMSEnorm = 0 and r2 = 1) is impossible in view of errors in the data, the scope for further model improvement needs to be assessed. Possibly, more significant conceptual changes to the model are required than the simple modifications of the rules governing the dynamics of tillers and leaves we examined here. A key aspect of our model is the tight integration of leaf area dynamics and tillering, with tillering rate being proportional to leaf appearance and the number of elongating leaves being proportional to tiller density. This close link may need to be loosened. One observation that points in this direction is the fact that, in timothy, newly produced sites for possible tillering are often not filled until much later, for example after a cut has opened up the sward. Such temporal uncoupling of site formation and site filling is not implemented in our model, or any other, and we intend to explore the importance of this idea in future model development.
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ABSTRACT
INTRODUCTION
