YIELD RESPONSE SURFACES FOR SPACING OF SUGARCANE PLANTS By J.K. LESLIE 1 and B.A. LESLIE 2

Transcription

1 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 YIELD RESPONSE SURFACES FOR SPACING OF SUGARCANE PLANTS By J.K. LESLIE 1 and B.A. LESLIE /36 Glen Rd., Toowong, Qld, Leslie Consulting Pty Ltd, 16 Medway St., Rocklea, Qld, 418 aresta@uq.net.au KEYWORDS: Plant Density, Row Spacing, Response Surface. Abstract YIELD response surfaces for plant cane that describe the effects of varying plant spacing are illustrated. Data from four experiments were used to generate cane yields from the yield components of plant density, final stalk number per plant and stalk weight by compounding equations that separately relate tillering, tiller mortality and stalk weight to the interrow and intrarow distances between established plants. The equations assume that cane stools sense distances equally in both the interrow and intrarow directions. Growth effects of irregular spacing within rows, additional to those that can be attributed to mean within row distances, could not be estimated. The surfaces presented show effects of soil fumigation as a soil fertility treatment, and of other unknown environmental factors inherent in differences between years and location on the magnitude of absolute and relative yield responses to changing plant spacing. They allow yield responses to be interpolated within experiments for combinations of interrow spacings from.25 to 1.5 m and intrarow spacings from.25 to.8 m. Tiller and whole plant mortality were high and yield response surfaces unstable below.25 m. The inference is that there is no practical value in spacing cane plants closer than.25 m. The surfaces do not predict cane yields or the absolute magnitude of yield responses to plant density for other environments. The significance of this to environmental differences across commercial cane blocks and the use of response surfaces for practical system design and guidance are discussed. Establishment of plants per sett decreased at high sett densities. Factors that cause variable establishment confound plant spacing effects with those of other agronomic treatments. They may result in differences up to four-fold above the plant spacings defined by eye spacing of setts, and these must be interpreted in plant responses. It is probable that 75% or more of the maximum response to narrow rows over 1.5 m single rows can be achieved in practice with options that create an average interrow spacing of.8.9 m and intrarow spacing of.25.3 m. Band-planting is expected to behave unpredictably, but similar to single rows of the same centre-to-centre row spacing. Given that responses to increased density appear to be reduced at high soil fertility under favourable environmental conditions for growth, it is recommended that research efforts focus on guiding farmers towards more positive control of suboptimal soil fertility in cane blocks. 144

2 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 Introduction The Australian sugar industry is endeavouring to combine yield benefits from increasing the plant density of cane crops (Bull and Bull, 2a,b; Norris et al., 2), enhancing soil fertility (Garside et al., 22; Bell et al., 23), and reducing soil compaction and plant damage by machinery to ratoon productivity (Chapman and Wilson, 1996; Braunack and Hurney, 2). Plant density is increased by reducing interrow (RS) and intrarow (IR) plant spacings with controlled-traffic pathways of varying widths and centre-tocentre distances. In some systems, cane is planted on raised beds and in others on the flat. The resultant spatial arrays of plants constitute complex geometries, and establishment irregularities introduce IR randomness into intended arrays. The design of practical systems would be facilitated if mathematical or mechanistic models were available to depict yield responses to varying RS and IR as continuous response surfaces. Accurate models would allow interpolation between results measured for specific spatial arrays in field experiments, thus reducing the need to repeat costly experimentation for minor changes to RS or IR. They could also assist the interpretation of interactions between plant density and soil fertility effects on yields that are a source of practical uncertainty. The mechanistic models presently available [APSIM Sugar (Keating et al., 1999); Bull and Bull, 2b)] simulate cane growth and biomass based on interception of solar radiation by leaves. They have been used to model yield for varying spatial arrays. This requires mathematical relationships to describe the interacting spatial effects of interplant competition for light, nutrients and water. While useful, the relationships introduce departures from the process-based treatments that are required to give mechanistic models a clear advantage over mathematical models. Mathematical modelling of yield response surfaces for RS and IR spacing of sugarcane plants has not been attempted. Willey and Heath (1969) reviewed quantitative relationships between plant population and yield for other crops and pastures. They addressed two common phenomena: (1) that increasing plant density may increase yield towards a yield maximum plateau; or (2) towards a maximum yield at an intermediate density with yield decreasing as density increases further. The former is common for vegetative yields, and the latter for reproductive yields, e.g. grain. However, the distinction is not consistent. For a given density and environment, yield tends to be maximal when RS = IR. Spatial analyses should provide for separate effects of RS, IR and RS:IR, and mean intrarow distances may be used as approximations for IR when plants are irregularly spaced within the row. Several relationships that appear potentially useful for response surface analyses of sugarcane experiments are documented in Willey and Heath (1969). They all give equal weight to the effects of RS and IR, implying that plants utilise space equally in the two directions. This may not be true if soil conditions vary due to interrow tillage, compaction or bedding-up, or if there are effects of row direction on radiation interception, i.e. relative to the path of the sun. They all require specification of plant arrays and derive estimates of yield per plant or plant part. 145

3 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 In sugarcane, plants commence tillering soon after emergence through the soil surface of the primary shoot arising from the sett bud. Each plant may produce several tillers some or all of which die before harvest. Cane yield is the aggregate of stem growth of primary shoots and tillers that survive as millable stalks at harvest. Sucrose accumulation measured as stalk sugar content (CCS) has rarely been found to be affected by RS or IR (see literature reviewed by Bull and Bull, 2a,b) and can, therefore, be disregarded as spatially nondynamic. The important dynamics are, therefore, plant density, tillering, tiller mortality and stalk growth. These dynamics underlie the common determination of cane yield as the product of the yield components plant density, stalks per plant and stalk weight (Equation 1). TCH = D x FSP x SW x (1) where Plant Density (D) (Plants/m 2 ) = 1/(RS x IR); Final Stalk Number per Plant (FSP) = 1 + (MTN x (1 TM))/1; MTN is Maximum Tiller Number per Plant; TM is Percent Tiller Mortality; Stalk Weight (SW) ( Kilograms per stalk); and TCH is Tonnes Cane per Hectare. One of us (JKL) was contracted initially by the Sugar Research and Development Corporation and then by BSES Ltd to analyse data from several plant-density experiments to develop and interpret mathematical yield response surface models based on yield component responses for variable RS and IR. This paper summarises the resultant models and discusses their utility for development of practical husbandry systems. Materials and methods Experimental designs Four experiments, referred to as Trials 1 to 4, are described briefly. They provided the base data for analyses that were undertaken with support from the originators. T.A. Bull conducted adjacent irrigated Trials 1 and 2 with plant cane at BSES Bundaberg on a site fallowed for 8 months from previous cane. Some results have been reported, but full interpretations have not been published. A.L. Garside and M.J. Bell examined interactions between row space, plant density and soil fumigation in Trials 3 and 4 described by Garside et al. (22) with further interpretations by Bell and Garside (24) and Bell et al. (24). Trial 1 Six RS levels.125,.25,.5,.75, 1. and 1.5 m were planted with 3 cm twoeye billets planted end-to-end in the row (nominal IR.17 m per eye) for all RS. There were three cultivars, Q124, Q151 and Q17 A. Cane was planted on 24 August 1999 and harvested on 2 September 2. Plot length was 3. m with 1. m bare strips between internal plot lengths or from buffer cane at the northern and southern ends of the trial. The number of rows per plot was 17 (.125 RS), 9 (.25 RS), 5 (.5 RS), 4 (.75 RS) and 3 (1. and 1.5 RS). Data were collected from all rows for.125,.25, 1. and 1.5 RS, the central three for.5 RS and the central two for.75 RS. Datum length was the full plot length. Row data were bulked for.125 and.25 RS, but recorded for each datum row for the other RS treatments on all occasions, except for the initial count, which was recorded for bulked datum rows. 146

4 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 Trial 2 This trial had three RS levels (.5, 1. and 1.5 m), three planting rates or nominal IR levels (.1,.2 and.4 m per eye in the row) and three cultivars (Q124, Q151 and Q17 A ). The trial was planted on the western side of trial 1 on 26 August 1999 and harvested on 9 October 2. Plot lengths were 2.8 m with.5 m bare strips between plot ends. Numbers of rows and datum rows and data recorded were as for trial 1. Trials 1 and 2 There were four replicates of each treatment, with RS main plots, planting rate subplots (Trial 2 only) and varietal sub- or subsub plots in split-plot randomised-block layouts. Planting for each RS main plot was achieved by changing furrow opener spacings on a tool bar that was tractor drawn north south on 3.5 m centres with longitudinal stops to change RS, planting rates and cultivars. Billets were placed manually in the furrows, covered by raking the soil level, and irrigated when each trial was planted. There were no lateral buffer rows between main plots additional to those excluded from datum sampling. Basal fertiliser was broadcast at planting onto each plot as CropKing 33 at 4 kg/ha. It was watered in by spray irrigation immediately after planting of each trial. Irrigation continued to apply cumulative pan evaporation deficits at regular intervals until four months prior to harvest after which (due to water restrictions) the trials were rainfed only. In both trials, shoot counts were made at frequent intervals from early shoot emergence up to about 22 d after planting (DAP) and then at final harvest 393 and 41 DAP for Trials 1 and 2. Estimation of plant establishment in each of the four trials involved interpretation of shoot number by sampling time records to identify primary shoot numbers (= plants) as temporary plateaux in shoot numbers prior to the onset of tillering. Actual IR was calculated as (metre row length)/(number of primary shoots per row). Actual RS of an individual datum row was the mean distance of that row from the two rows adjacent to it. As a result of the planting method, the actual RS for external datum rows often differed from the nominal RS which was achieved for internal datum rows. Actual RS for replicates was the mean actual RS for all individual datum rows constituting a replicate plot. Maximum shoot counts were identified from the progressive counts for each datum and were transformed to maximum tiller numbers per plant (MTN) by deducting the number of primary shoots and dividing by the latter number. Tiller mortality (TM) was the percentage loss of tillers from MTN to final stalk number, assuming that tiller losses occurred prior to primary shoot deaths. Stalk weight (SW) was measured by stripping leaf and cabbage from total green biomass for the datum row lengths, and dividing resultant clean stalk weight by the final stalk number for each row. These data provided the yield components of Eq. 1 for individual rows or replicates, but our analyses of individual rows are not reported in this paper. Trials 3 and 4 There were two plant-cane experiments Trial 3 at Mackay and trial 4 at Bundaberg each with two RS (.5, 1.5 m), two planting densities (27 and 81 two-eyed setts per hectare) and soil fumigation or not prior to planting. Trial 3 contained one cultivar (Q117) planted on 16 September 1999 and harvested 1 months later. Trial 4 contained two cultivars (Q124, Q155) planted on 13 March 2 and harvested 15 months later. There were three 147

5 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 replications of all treatments. Data were recorded from permanently pegged 15 m 2 areas within each plot surrounded by adequate guard areas of the same treatment. Datum was the central six rows by 5 m in 18-row plots for.5 RS and the central two rows by 5 m in 6-row plots for 1.5 RS. The two planting densities are equivalent to nominal IR levels of.41 and.123 m row per eye (1.5 RS) and.123 and.37 m row per eye (.5 RS). For planting, the entire experimental area was formed into furrows.5 m apart. Billets were laid manually in them according to the appropriate RS by plant density by cultivar combination and covered by backfilling. Trial 3 was irrigated twice for establishment and trial 4 was trickle irrigated throughout. The data allowed computation of the yield components for Eq. 1 at replicate level. Response surface analysis Plant establishment For trials 2, 3 and 4, early shoot counts captured the establishment plateaux adequately at one sampling time: trial 2, 49 DAP; trial 3, 57 DAP; trial 4, 43 DAP. In trial 1, shoot emergence was more rapid than in trial 2 and clearly the shoot counts made at 24 DAP and 51 DAP were respectively too early and too late to represent plant establishment numbers. For trial 1, shoot counts were linearly interpolated to a time, 34 DAP, which yielded an average 66% establishment of eyes planted across.5, 1. and 1.5 RS, approximating the average establishment level for the same RS treatments at 49 DAP in Trial 2. Trial 1 interpolation to 34 DAP for.125,.25 and.75 RS was then undertaken to give establishment estimates for those RS. Mathematical models Various equations were selected to describe patterns observed in data plots of MTN, TM and SW as dependent variables against RS and IR as independent variables, using the actual RS values for each row or replicate and the actual IR values calculated from establishment estimates. The equations were solved to minimise residual sums of squares by iteration using Microsoft Excel Solver and tested by linear regression of estimated on actual values. Solutions for MTN, TM and SW were derived separately for each variety and fumigation treatment and in some instances across these treatments. These solutions were utilised in Eq. 1 to estimate TCH for comparison with actual TCH values (Figure 1). The preferred equations and their statistical fits to the source data for Q124 (trials 1, 2 and 4) and Q117 (trial 3) are detailed in the Appendix. TCH response surfaces for Q17 A, trial 2 and for Q117, trial 3 are illustrated in Figures 2 and 3, respectively. Relationships reported in Willey and Heath (1969) were not applicable to models based on yield components. Results and discussion Plant establishment Average establishments (plant numbers as percent of eyes planted) across all treatments were 69.4% (trial 2), 59.2% (trial 3) and 69.8% (trial 4). In trial 2, establishment decreased with nominal IR from 85.4% at.4 IR to 54.7% at.1 IR; in trial 3 from 79.9% at 148

6 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: IR (.5 RS Low Density) to 44.7% at.4 IR (1.5 RS High Density), and the same treatments averaged 77.8 and 54.5% for Trial 4. These decreases are associated with the closeness of adjacent setts at planting and there were no cultivar differences. There was no effect of fumigation on establishment in trial 3. Trial 4 had significantly higher establishment in fumigated soil (79.%) compared with 6.6% in nonfumigated soil, but the proportionate effects of fumigation were similar across planting rates and row spacings. We do not attribute the effect of sett closeness on establishment to microbial influences and suggest it is due to diminished physical contact of setts with soil and possibly to direct contact effects between setts. Establishment in individual datum rows and replicates was also highly variable within the same nominal IR treatments. For example, in individual rows of trial 2 actual plant spacings in-the-row for.1,.2 and.4 nominal IR averaged.18 m (range.11.28),.29 m (.17.57) and.47 m ( ) actual IR, respectively. In trials 1, 2 and 3, IR differences were such that the nominal IR treatments were inadequate and inconsistent descriptors of intrarow spacing. This identifies a common difficulty fundamental to recognition of spatial effects, which is that plant density is rarely measured in field experiments. It is, therefore, possible that yield effects attributed to agronomic treatments may be incorrectly attributed to a treatment, whereas they may be partly or wholly due to an unrecognised effect of that treatment on plant establishment. 3 1a Q124, Q151 and Q17 A replicates, Trial 1 1b Q124, Q151 and Q17 A treatments, Trial 2 2 Estimated TCH Estimated TCH =.9693( ) X Actual TCH R 2 =.3899, n = 72 Q151 Q124 Q17 Predicted TCH Predicted TCH = 1.12( +.16) X Actual TCH R =.94; n = 27 Q124 Q151 Q Actual TCH Actual TCH Estimated TCH c Q117, fumigated and unfumigated replicates, Trial 3 Estimated TCH = +.161) 9935 ( R 2 =.973, Atn = ltch 24 Nonfumigated Fumigated Es ti 14 m at ed d Q124 and Q155 fumigated and nonfumigated treatments, Trial 4 Estimated TCH Q124, N f i t d = ) x Actual R 2 ( =.5798, TCH n 16 Q124, F i t d Q155, F i t d 2 11 Q155, N f i t d Actual TCH Actual TCH Fig. 1 Estimated TCH versus actual TCH for Trials

7 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 Cane yield Estimates of TCH based on actual RS and IR were derived by Eq. 1 from solutions for MTN, TM and SW analagous to those shown in the Appendix for replicates of all trials. Separately derived estimates for each cultivar and fumigation treatment are plotted against the actual TCH based on actual RS values, measured weights and stated row lengths in Figure 1. The beneficial effect of soil fumigation on TCH in trial 3 is obvious in Figure 1c. The estimates for trials 1 (with one widely aberrant point for Q17 A ), 2 and 3 are particularly good, and those for trial 4 while less precise, are highly significant (P<.1). The variability of MTN (Eqs. 2 and 3) and TM (Eq. 4) and, hence, of final stalks per plant (FSP not shown) is largely explained by RS and IR for each cultivar and soil condition. Estimated vs actual FSP regressions yielded R 2 values for replicates of.97,.896,.93 for trials 1 to 3 respectively, and of.977 for treatment means of trial 4. The majority of unexplained variability in TCH estimation for trials 1, 2 and 3 occurs in the SW equations (Eq. 5) rather than those determining FSP. For trial 1 and trial 3 nonfumigated, there was no significant effect of area per stalk (APS) on SW which is treated as constant. Hence, the spacing effects on FSP are sustained quantitatively into TCH estimates for these trials. In the other trials, significant linear effects of APS on SW ranged from weak (trial 3 fumigated) to strong (trial 4 nonfumigated). In these instances, spacing effects on FSP are reduced in TCH estimates to a degree dependent on the b coefficient for SW (Appendix). SW in trial 4 nonfumigated decreased markedly with decreasing APS to such an extent that FSP estimates were actually reversed in TCH estimates. Similar results were obtained for the other cultivars not included in the Appendix. The standard errors of stalk weight estimates (see Appendix) were similar across all trials ( kg). Overall, there were no instances where treatment mean SW was greater for closer than for more distant spacings, i.e. SW at higher densities was equal or less than at lower densities. This has been the general experience reported in literature reviewed by Bull and Bull (2a) and by Garside et al. (22). This could be used as a diagnostic in commercial comparisons between only two plant density treatments. If a higher plant density has higher SW, it is probable that the high density treatment has embodied a beneficial growth influence independent of plant density. If a higher density has similar SW, suboptimal environmental factors affecting both densities may have imposed overriding limitations on stalk growth rates which have precluded normal responses to greater space. One yield response surface, obtained for Q17 A in trial 2, is shown in Figure 2. This figure illustrates the continuity and magnitude of RS and IR effects on cane yield. It has been extrapolated well beyond the RS (.5 to 1.5) and IR (.1 to.4) limits of trial 2 data to expose: (1) Instability when RS or IR are both less than.3 m, which is due to very dynamic effects of plant density on MTN, TM and possibly SW that occur in this region; and, 15

8 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: IR (m) RS (m) Cane Yield (TCH/1) Fig. 2 TCH response surface, Q17 A, Trial 2 based on yield component analyses. (2) The asymptotic nature of yield estimates by the models for very wide spacings, which may be realistic for moderate extrapolations but must overestimate TCH for very wide spacings. In most experiments, there was significant mortality of primary shoots below.2 m spacings. In practical terms, the evidence is that it is counter productive to pursue such close spacings. For these reasons, plus the experience that establishment also diminishes and becomes more irregular at high in-row sett planting rates, it seems probable that heavy band-planting will not be an effective way of reducing either RS or IR. Figure 3 plots the response surfaces for fumigated and nonfumigated Q117. The nonfumigated surface (Figure 3a) is strongly responsive to plant density, but that for fumigated soil (Figure 3b) exhibits much lower yield responses at higher overall yields. Response surfaces can also be presented as RS x IR spreadsheets which enable comparisons across trials for identical RS and IR. A useful comparison of trial estimates which cannot be made using actual trial data is shown for Q117 and Q124 between.5 and 1.5 RS for a common, near optimal,.25 IR (Table 1). The table shows TCH increases for.5 RS relative to 1.5 RS that ranged from +43.3% (trial 2) to 7.% (trial 4 nonfumigated). The trial 3 response for.5 RS was reduced by fumigation from +33.% to +12.%. Trial 4 nonfumigated soil fertility was evidently high and the expected positive response to fumigation was believed to be countered by a negative effect on beneficial mychorrizae early in the growth of the crop (Garside et al., 22). The differences in TCH responses to.5 RS between the six data sets are probably reflecting soil fertility and other environmental differences impacting differentially on SW to convert similar responses in final stalk densities to widely different TCH responses. 151

9 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 3a - NonFumigated TCH Row Space (m) In Row Distance (m) 3b - Fumigated TCH Row Space (m) In Row Distance Fig. 3 TCH response surfaces, Q117, Trial 3. This does not mean that high density effects on TCH in other environments will be mediated only by SW rather than the tillering and mortality dynamics. It does, however, illustrate that high density TCH responses can vary from slightly negative to large positive across different environments. The fumigation effect in Trial 3 has already been documented by Garside et al. (22) and it remains the only concrete evidence that healthy, vigorous cane plants are able to utilise more fully the space in 1.5 m rows and therefore respond less proportionately to high density, than do less vigorous plants. 152

10 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 Bell et al. (24) provide further evidence that soil fertility interacts with stalk density on SW for numerous other soil fertility variants. Table 1 Comparisons of estimated stalk density, stalk weight and cane yields between.5 RS and 1.5 RS at.25 IR. RS (m) IR (m) Parameter Trial 1 Q124 Trial 2 Q124 Trial 3 Q117 + Fum Trial 3 Q117 Fum Trial 4 Q124 + Fum Trial 4 Q124 Fum.5.25 Stalks/m Stalk Wt (kg) TCH Stalks/m Stalk Wt (kg) TCH Stalks/m % Change.5 RS vs 1.5 RS SW TCH The high-density and yield-decline research literature has identified numerous environmental factors (soil fertility, weather, drainage, pests and diseases, husbandry operations) that affect plant vigour and are thought likely to modify responses to plant spacing. They may be grouped broadly into two categories: (1) factors that enhance the high-density response by restricting plant vigour and/or the duration of active stalk growth; and (2) factors that minimise or eliminate high-density responses by promoting plant vigour and/or extending phases of active growth. The dilemma created for industry by the lack of knowledge about the interaction of these factors with cane density is obvious. It is reduced only little by the high frequency of substantial high density responses recorded in the large number of trials and demonstrations conducted by the BSES high density program over a wide range of environments (locations, years and other treatments irrigation, fertiliser, cultivars). This could also be read as evidence that suboptimal conditions for growth are common in commercial and research station cane blocks. The technology for predicting these suboptimalities in advance and for correcting them is uncertain at best. Not surprisingly, high density planting is seen by some as a partial offset for these unspecified limitations. That may be a valid base for commercial action, but is a very unsatisfactory situation that warrants further research into the identification, prediction and correction of suboptimal factors for cane growth. The continued pursuit of high density yield gains vis-à-vis standard 1.5 m RS cane husbandry will depend on the magnitude and frequency distributions of environmental interactions with plant spacing in commercial cane crops. None of the TCH response surfaces generated from these experiments enable valid estimates of commercial high density response 153

11 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 distributions. The reasons are that they represent a very small sample of the diversity of commercial cane environments at block level. It is a feature of these experiments that variation in plant density measured after plant establishment has explained so much of the variability in stalk dynamics and cane yields within each experiment. This indicates that the RS and IR treatments did not impose associated but additional unrecognised factors influencing plant growth, apart from the partially confounding variations in plant establishment that have been accounted. It also stands as a lesson for researchers in cane agronomy and soil fertility to ensure that inadvertent imposition of other factors within density treatments, or of plant density variations within treatments examining other factors, is avoided or, if possible, accounted for properly. We, however, stress that response surface analyses cannot describe density effects if environmental influences are confounded with those of RS or IR. Examples are where narrow row cane has superior weed control or better surface drainage from bedding-up than wider row cane. Further, interrow traffic or tillage and mechanical harvesting can have negative effects due to soil compaction and to plant damage involving roots, plant crowns or stalks that are superimposed on density effects and the latter cannot then be interpreted as such. This will be more common for ratoon than for plant cane, and renders plant density analyses of ratoon crops difficult to interpret. Response surface analyses can assist the commercial evolution of higher density production systems in several ways: They indicate that near maximum TCH is achieved at.25.3 m IR and that closer plant spacing in the row should be avoided. That seems to be a sound objective for routine commercial plantings. Maximum TCH will probably occur for.25 m IR at approximately.25 m RS, or at greater spacings if crops experience stresses such as that from drought (Thompson and du Toit, 1965). The proportion of the maximum TCH response relative to 1.5 m RS attained at other RS appears to be less variable across environments than is the absolute magnitude of the maximum response. For example, all four experiments would have achieved at least 75% of their maximum responses at.25 IR with mean RS approximating.8.9 m RS, i.e. from.8.9 m RS single rows, m centre-tocentre dual rows, or m centre-to-centre triple rows. The distances between the multiple rows can be flexible, but probably should not be less than.3 m. Other target percentages are readily interpreted in this way from the response surfaces. This use should facilitate the development of low cost production systems to capture the bulk of the potential benefit from rows narrower than 1.5 RS. A similar use could be to guide minor RS or IR changes in developing production systems. The response surfaces can provide approximations of the relative changes in TCH that should result from altering an existing spatial array to a new layout. Our response surface analyses have utility for other areas of agronomic research where treatment effects may be exerted partly or wholly via 154

12 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 associated changes in plant spacing. Experimental designs do not have to embody the multilevel RS x IR factorials required for fitting equations to enable useful interpretations. Two treatments can be compared by measuring their plant spacings, MTN, TM, SW and TCH. Our response surfaces may then be used as references to assess whether the treatment differences are in accord with, or different from those that resulted from differences in plant spacing alone in the reference experiments. There are a number of ways of using response surfaces for such purposes, which do not require recalculation from the reference equations. Active spreadsheets embodying those equations or printouts from them can be provided, and linear interpolations of them for specific RS and IR values are reasonable approximations within the ranges of the source data. More generally still, anomalous treatment effects can be identified if tillering, tiller mortality or stalk weight differences are in directions contrary to their differences in RS and IR. Anomalous effects on tillering and stalk weight due possibly to differences in establishment, stalk age, waterlogging, frost damage and weed control have been identified in some site-replicated strip trials in this way. Acknowledgements We thank Jo Stringer for analyses of variance of trials 1 and 2, Julian Collins for resolution of some experimental details, Terry Bull, Alan Garside and Mike Bell for the free access to their data and for many helpful communications; and BSES, Eoin Wallis and SRDC for the sponsorship of these studies. REFERENCES Bell, M.J. and Garside, A.L. (24). Shoot and stalk dynamics, dry matter partitioning and the yield of sugarcane crops in tropical and subtropical Queensland, Australia. Field Crops Res., 66: In review. Bell, M.J., Halpin, N.V., Garside, A.L., Moody, P.W., Stirling, G.R. and Robotham, B.G. (23). Evaluating combinations of fallow management, controlled traffic and tillage options in prototype sugarcane farming systems at Bundaberg. Proc. Aust. Soc. Sugar Cane Technol. (CD-ROM), 25: 13 pp. Bell, M.J., Garside, A.L., Halpin, N.V. and Berthelsen, J.E. (24). Interactions between stalk number and stalk weight and the implications for cane yield. Proc. Aust. Soc. Sugar Cane Technol. (CD- ROM), 26: 1 pp. Braunack, M.V. and Hurney, A.P. (2). The position of harvesting traffic does affect yield. Proc. Aust. Soc. Sugar Cane Technol., 22: Bull, T.A. and Bull, J.K. (2a). High density planting as an economic production strategy: (a) Overview and potential benefits. Proc. Aust. Soc. Sugar Cane Technol., 22: Bull, T.A. and Bull, J.K. (2b). High density planting as an economic production strategy: (b) Theory and trial results. Proc. Aust. Soc. Sugar Cane Technol., 22:

13 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 Chapman, L.S. and Wilson, J.R. (1996). Economics of ratoon cycle length in sugar cane. In: Wilson, J.R., Hogarth, D.M., Campbell, J.A. and Garside, A.L. ed. Sugar Cane Research Towards Efficient and Sustainable Production, CSIRO Div. Tropical Crops and Pastures. Garside, A.L., Bell, M.J., Berthelsen, J.E. and Halpin, N.V. (22). Effect of fumigation, density and row spacing on the growth and yield of sugarcane in two diverse environments. Proc. Aust. Soc. Sugar Cane Technol., 24: Keating, B.A., Robertson, M.J., Wood, A.W. and Huth, N.I. (1999). Modelling sugarcane production systems. I. Development and performance of the sugarcane module. Field Crops Res., 61: Norris, C.P., Robotham, B.G. and Bull, T.A. (2). High density planting as an economic production strategy: (c) A farming system and system requirements. Proc. Aust. Soc. Sugar Cane Technol., 22: Thompson, G. D. and du Toit, J. L. (1965). The effects of row spacing on sugarcane crops in Natal. Proc. Int. Soc. Sugar Cane Technol., 12: Willey, R.W. and Heath, S.B. (1969). The quantitative relationships between plant population and crop yield. Adv. Agron. 21:

14 Leslie, J.K. and Leslie, B.A. Proc. Aust. Soc. Sugar Cane Technol., Vol. 27: 25 APPENDIX Solutions for equations derived from replicate data of Trials 1, 2 and 4 for Q124 and Trial 3 for Q117. Maximum tiller numbers per plant (MTN) MTN = PNT x (1 a ^ (k x (RS c))) x (1 a ^ (k x (IR c))).2. PNT Peak number of tillers per plant at infinite RS and IR. Solved for PNT, a, k and c. PNT a k c R 2 se n Trial Trial Trial 3 Fumigated Nonfumigated MTN = PNT x (1 a ^ (RS/c 1)) x (1 a ^ (IR/c 1))...3. Trial 4 Fum and Nonfum Tiller mortality (TM) TM= 1 MTS x (1 p ^ (q x (RS x IR r))) 4. MTS Maximum tiller survival (%) at infinite RS and IR. Solved for MTS, p, q and r. MTS p q r R 2 se n Trial Trial Trial 3 Fumigated Nonfumigated Trial 4 Fum and Nonfum Stalk weight (SW (kg)) SW = a + b x APS 5. APS Area per stalk (m 2 ). Solved for a and b. Coefficient Trial 1 Trial 2 Trial 3 Trial3 Trial Trial Fum Nonfum 4Fum 4Nonfum a b R se n