The model presented here is parameterized on a major current commercial production clone. For the asymmetric spacing which allows dual row harvesting, the model predicts a daily crop photosynthetic gain of about 406 kg ha−1 day−1 of carbohydrate mass averaged across the growing season of 11 months (337 days) simulated here. Assuming that ca. 40% of this photosynthate is lost in respiration for cell maintenance and metabolism to other plant constituents [5, 6], this would equate to a total dry matter productivity of about 82 mg ha−1 year−1 (243 kg ha−1 day−1) (Fig. 3, Supporting Information 1 Sections 5). How does this compare to actual yields? The average yield of harvested stem in Brazil is about 80 mg ha−1 year−1 [23]. However, this is wet weight, of which only 30–40% is dry mass [24–26]; harvest index is about 50%, with the unharvested material being leaf litter, stem tops, and root [8, 27]), therefore total dry matter production would be about 48–64 mg ha−1 year−1. Since our row spacing simulations are based on the measurements from the first year ratoon crop, simulated dry matter productivity is higher than the average. The simulated dry matter yields of the first year plant for model validation are from 43.5 to 71.8 mg ha−1 year−1(Fig. 2c, e, Table S9), which are comparable to measured data and the dry matter calculated from the average yield in Brazil [23]. It should be noted that the row spacings chosen here were simply to demonstrate the utility of the model in dealing with agronomic and varietal questions; these were not intended to represent spacings used in any particular growing region. As noted later, although production is predicted here, the canopy model developed is intended as a more effective front-end to more detailed production models, in the context of questions such as row spacing and orientation at different locations and with different cultivars.
This study suggests that under the climatic conditions of cultivation in Planaltina, Goiás state, dual row versus regular row planting would have little effect on crop carbon gain, after canopy closure. The loss would be most severe in cultivars with upright leaves and could be largely mitigated by selecting cultivars with a more spreading habit, i.e., more horizontal leaf, and by planting in an N-S orientation area (Figs. 3–
6). E-W versus N-S orientation of rows has more significant effect on carbon gain with asymmetrical row spacing (Fig. 3). Compared to E-W rows, using a N-S row orientation with dual row planting would increase the projected harvested stem yield 8 mg ha−1 year−1, which could increase sugar production about 2 mg ha−1 year−1, assuming that sucrose is 50% of harvested stem dry mass [27, 28]. Given an ethanol yield of 86.3 L mg (cane)−1 [29], ethanol production would be increased by 690 L ha−1 year-1.
However, simulated losses due to dual row spacing may be underestimated. Over the whole cycle, the effect of asymmetric spacing is profound during the first months of growth, when the rows result in substantial areas of bare ground, and therefore light that is not intercepted by the crop (Fig. 3). This example simulation assumes that LAI is unaffected by poorer productivity in the asymmetric row spacing. If lower productivity results in lower leaf area production, losses will be compounded with time. Agronomically, this loss would be partially mitigated by planting rows in an N-S orientation or use of cultivars with more horizontal leaf angles (Fig. 3). Since the 155-cm gap between the edges of the dual planted rows is never fully closed, it will result in significantly lower solar radiation interception.
The model assumes that all the plants are in well-watered and sufficient nutrient conditions, so that the potential changes of root system in dual row planting are not taken into account in this study. The model also takes no account of the benefit that dual rows would bring in decreasing traffic and damage to rows, which might offset even the 7.5–11% loss in potential canopy photosynthetic biomass gain predicted here. The model also assumes that plant structure is unaltered by dual row planting. In reality, two factors could act to modify the outcome here. First, plants sense neighbors via phytochromes, which elicit responses in increasing height and seeking gaps in the canopy [8]. Increasing height may consume more energy in stem structure, while seeking more light could compensate to some extent for the increased shading interference produced by dual rows. Salter et al. [30] show row space, has little effect on sugarcane yield, which indicates the growth plasticity of sugarcane could even further reduce the loss of dual row. Our simulation shows that, on day 326, if the leaf angle of the dual row planting was increased from 15o to 45o, the potential loss of daily total carbon uptake was decreased from 5 to 1%, and the loss decreased from 16 to 8.5% on the 167th day in north-south rows (Fig. 5 and Fig. S5), which suggests that seeking more light and hence more horizontal leaves in dual row planting could halve the loss that would otherwise occur. As a proxy for plasticity, this shows that where a cultivar responds to the wider spacing by producing more horizontal leaves, the yield loss effects of asymmetry will be diminished.
The current simulations were developed to illustrate the potential of this new modeling tool (Supporting Information 1 Sections 2 and 3) for sugarcane agronomy and clone selection, since it can simulate realistic 3D crop canopies for in silico experimentation. One limitation here is that an early small effect of productivity may propagate to larger effects through compound interest during exponential growth and hence greatly affect final yields. Any such effect is not represented here. However, in the future this could be achieved by combining the canopy description and photosynthesis model developed here with crop growth and production models such as BioCro [11] or DSSAT/Canegro [8]. The framework to use such canopy representation for every day of the growth cycle of a crop is presented. However, the current model is limited to running MATLAB on CPU architecture, which makes execution of such a detailed representation of canopy microclimate relatively slow [9]. In the future, the computational simplicity of what is represented in each pixel of the 3D space would allow use of emerging parallel GPU architecture. This could speed computation by 1–3 orders of magnitude [10, 31].
This study provides the framework of a new computational approach, which could be used to evaluate the cost-benefit of different combinations of row spacing to fit both field equipment dimensions and cultivar forms in different locations. In effect it enables analysis of genotype x environment x management (GxExM). It brings potential for a closer link between field agronomy and modeling by allowing investigation of multiple permutations of population density, row spacing, row orientation, and cultivar selections, for example. As such, it allows prediction of the best combinations, in theory, for actual field testing. As shown here, the model can also be used to predict the form of cultivar that might be best suited to a given agronomy. The model could be combined with an evolutionary algorithm or other optimization routine to predict the ideotypes of sugarcane that would be best suited to dual row spacing or other variation in agronomy for a given climate zone. This would aid cultivar selection for a given situation and agronomy. Distances between stools, as another factor influencing sugarcane yield, could also be optimized by model prediction for higher productivity. While the model cannot replace agronomic field experiments, it provides a means to experiment with many more possibilities in silico to narrow down to the most promising strategy for field testing.