2 RESOURCE ALLOCATION PARAMETERS
Chapter 5: Validation of the Structural Behaviour of the Single Ramet Model
2.2 Seasonal growth distribution and goodness-of-fit
2.2.2 Model performance
The statistics above were applied to points selected from simulated data that match the empirical data set by date in the season. The compared series are shown graphically in Figures 5.15 to 5.19 and the summary statistics are presented in Table 5.2. The graphics indicate the number of points compared as derived from the empirical estimates.
The data in Table 5.2 indicates that the RMSPE is less than 1% for three of the considered parameters and less than 5% for the two other parameters, and as such we may deduce that the simulated data matches the empirical estimates very well. Stem length is greater than 4%, but the parameter shows large unequal covariance (U ) relative to the other error fractions. When one considers the shape of the two stem parameter graphs, it is possible that with greater sampling density the RMSPE values of both stem parameters might increase slightly. The larger RMSPE of stem length is of course due to the much
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100 200 300 400 Iteration (days)
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Figure 5.15 Comparison of summed leaf total length of simulated values and empirical estimates for the years 1961-62 at Ukulinga (— simulated; • empirical). (Environmental conditions: Plant activity restricted by daily temperature and soil water pressure data for the site, as defined in Sections 4.1 and 4.2 of Chapter 4. Soil nitrogen is not limiting to growth.)
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Figure 5.16 Comparison of summed leaf total mass of simulated values and empirical estimates for the years 1961-62 at Ukulinga (— simulated; • empirical). (Environmental conditions: Plant activity restricted by daily temperature and soil water pressure data for the site, as defined in Sections 4.1 and 4.2 of Chapter 4. Soil nitrogen is not limiting to growth.)
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Figure 5.17 Comparison of stem length of simulated values and empirical estimates for the years 1961-62 at Ukulinga (— simulated; • empirical). (Environmental conditions: Plant activity restricted by daily temperature and soil water pressure data for the site, as defined in Sections 4.1 and 4.2 of Chapter 4. Soil nitrogen is not limiting to growth.)
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100 200 300 400 500 600 Iteration (days)
Figure 5.18 Comparison of stem mass of simulated values and empirical estimates for the years 1961-62 at Ukulinga (— simulated; • empirical). (Environmental conditions: Plant activity restricted by daily temperature and soil water pressure data for the site, as defined in Sections 4.1 and 4.2 of Chapter 4. Soil nitrogen is not limiting to growth.)
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Figure 5.19 Comparison of tiller total mass of simulated values and empirical estimates for the years 1961-62 at Ukulinga (— simulated; • empirical). (Environmental conditions: Plant activity restricted by daily temperature and soil water pressure data for the site, as defined in Sections 4.1 and 4.2 of Chapter 4. Soil nitrogen is not limiting to growth.)
greater length simulated by the model for the reproductive phase and the increased length of time taken to achieve final length. This may in part be due to differences in the stem elevation data used to obtain the stem height, but such a large difference would suggest that water limitation may have restricted internode extension permanently. This permanent effect of water limitation on organ extension is not well-understood by the author, so I have avoided including functions to model it. It is clear that the process works at the cellular level between cellular division at the meristem and cellular expansion subsequent to this. What is important is that the model has captured the seasonal distribution of internode growth processes very well.
Table 5.2 Error analysis of the TILLERTREE model used to simulate the empirical data set of Tainton & Booysen (1965)
Variable
Summed leaf total length (mm) Summed leaf total mass (g) Stem length (mm)
Stem mass (g) Tiller total mass (g)
RMSPE (%)
0.385 0.4949
4.837 0.381 1.094
MSE (units2)
40527 0.0063 27541 0.0032 0.0087
Inequality statistics UM
0.011 0.083 0.321 0.083 0.001
Vs
0.294 0.395 0.619 0.633 0.000
Uc 0.695 0.522 0.060 0.284 0.999
Summed total leaf mass and length both have large Uc values relative to other error portions suggesting that the differences between empirical data and simulated data are due to random components not included in the model. The large hump in the empirical data during the first season (around day 230) occurred when moist conditions followed a dry period during summer. This effect could be caused by an accumulation of non-differentiated phytomers during the summer dry spell that expanded simultaneously when water conditions improved. This is a similar problem to that already mentioned for the stem length
differences during the reproductive phase. This effect is once again ignored because its effect is very small, as indicated by the small RMSPE value for the variable.
The increase in leaf mass during winter for the empirical data is strange, considering that moisture conditions were very dry, so growth was improbable. The most likely explanation is that this is a sampling anomaly arising from the small sample size employed by Tainton & Booysen (1965) (6 tillers measured at each sampling event). Therefore the fact that the model does not follow this increase during winter is considered irrelevant.
The RMSPE of tiller total mass is just over 1%, but the error is almost totally concentrated in unequal covariance (U ). This must be seen in context. The model appears to overestimate leaf mass and underestimate stem mass at the same times and vice versa.
This cancels some of the difference between the simulated and empirical values of tiller total mass. This partly explains why empirical and simulated estimates of this parameter are so similar at the end of flowering, because the empirical summed leaf total mass estimate is higher than the simulated value at this time, while the empirical stem mass estimate is lower than the simulated value. That said, the small size of the RMSPE for summed leaf total mass and stem mass gives us confidence that the simulated estimates for tiller total mass across time is sufficiently close to the empirical estimate not to require further adjustment.
CONCLUSION
It is apparent that the model is able to simulate the structural growth pattern of individual Themeda triandra tillers very well, both qualitatively in terms of the seasonal distribution of organ growth processes and quantitatively in terms of the actual values of organ mass and length predicted. It was anticipated that the model would produce reasonable results because of the low level at which values are measured, that being the organ level. The predicted success with one species suggests that the model will easily simulate growth in other tufted grasses, as long as there is sufficient data to parameterise the specific organ characteristics of the considered species.
SECTION 2
Growth of Single-Tiller Ramets
This section explores how changes in environmental resource availability interact with tiller structure and internal resource partitioning of single-tiller ramets clones. In order to do this, restrictions are introduced that both limit environmental resources and limit the ability of clones to retain unutilised resources. Secondary tiller recruitment is prevented in order to concentrate on the interactions between seasonal resource availability, tiller phenology, and resource partitioning. In doing this, behavioural complexity that may arise from the manner in which resources are allocated between connected tillers is avoided.
The first chapter in this section (Chapter 6) explores root-to-shoot partitioning. The chapter introduces a number of partitioning models, and then tests their behaviour in response to imposed dynamic resource environments.
The second chapter in this section (Chapter 7) concentrates on the problem of carbohydrate restriction during regrowth after the non-growing season, which is here termed the Spring Photosynthesis Bottleneck. This arises when tillers that have senesced their leaves over winter are forced to expand new leaves through the overlying dead canopy that substantially reduces photosynthetic potential. A number of morphological adaptations are introduced that may help bunchgrass tillers to overcome the bottleneck. These strategies are assessed, both separately and in combination with one another, in terms of the contribution they make in helping bunchgrass plants overcome the resource bottleneck.
For the remainder of the simulations in this thesis, the number of LAI layers is increased to 100 layers each of 10 mm depth. This is in order to smooth the dissipation of light and photosynthesis down the canopy.