HORTSCIENCE 42(2):246–250. 2007.

Spatial Variability of Kiwifruit Qualityin Orchards and Its Implications forSampling and MappingJames A. Taylor1

Australian Center for Precision Agriculture, McMillan Building, A03,The University of Sydney, NSW, Australia, 2006

John-Paul Praat and A. Frank BollenSupply Chain Systems Research Group, Lincoln Ventures Ltd, Private Bag3062, East Street, Ruakura Research Centre, Hamilton, New Zealand

Additional index words. average variograms, sampling scheme, Actinidia deliciosa

Abstract. Published statistics on the spatial variation of fruit quality observed in orchardshas been rudimentary to date. Dry matter and fruit weight data were collected spatiallywithin 11 kiwifruit (Actinidia deliciosa var. deliciosa ‘Hayward’) orchards in the Bay ofPlenty, New Zealand, to characterize the variability in fruit quality in terms of nonspatialand spatial statistics. Fruit weight was statistically more variable and exhibited astronger spatial structure than the dry matter data. Individual variograms were derivedfor each orchard and then all the data were collated into average variograms for bothquality attributes. The average variogram parameters were used to determine theoptimum spacing for grid sampling to achieve a desired level of confidence wheninterpolating the data. A grid spacing of 28 m appears suitable for mapping fruit quality,provided sufficient area exists to collect enough points to perform block kriging. Plots ofindividual orchard and average variograms, and a table of nonspatial and variogramstatistics are presented as a reference for future work in this area.

Harvester-mounted yield sensors haveprompted many investigations into theamount of spatial variability present in grain,cotton, viticulture, and some mechanicallyharvested horticultural crops (usually vege-table crops). Investigations into the spatialvariability of hand-harvested crops, such askiwifruit (Actinidia deliciosa var. deliciosa‘Hayward’), are much less common becauseof the difficulty in gathering detailed site-specific harvest data (Schueller et al., 1999).In the kiwifruit literature, published informa-tion on within-orchard variability of kiwifruitquantity and quality has been limited to basicexamples, nonspatial statistics, and maps(Gillgren, 2001; Praat and Bollen, 2007;Praat et al., 2003). In general, mean orchard(or orchard block) statistics are all the datathat are presented to the grower (Praat et al.,2003). Information on the spatial variation ofquality should be of interest to growersbecause it forms the basis of price premiums.In 2001, a harvesting protocol for kiwifruitwas developed to semi-automate the collec-tion of bin-specific quality data (Gillgren,2001). The protocol uses barcodes to track

fruit from locales within the orchard throughthe supply chain and is summarized in‘‘Materials and Methods.’’ In 2003 and2004, the harvesting protocol was used tocollect and assign quality data spatially toseveral orchards. This produced a morecomplete set of data on spatial variation thatcan be visually represented as maps (Fig. 1).

In addition to providing a visual repre-sentation of the variation, these spatial datacan be modeled using average variograms(McBratney and Pringle, 1999) to providesome quantitative geostatistics. McBratneyand Pringle (1999) have shown that averagevariograms provide several benefits. First,they provide a benchmark of the values forvariogram parameters that are to be expectedfor a given property. Second, given no apriori information on variability in a pro-duction system, they provide a basis fordetermining sampling density, particularlyfor grid-based sampling.

An understanding of how crop productionvaries spatially within a production systemhas become increasingly significant with theadvent of precision agriculture technologiesand methodologies. Although these newtechnologies and methodologies have pre-dominantly been applied to broad-acre crop-ping systems, experiences in viticulture(Proffitt et al., 2006) indicate that they arerelevant to horticulture. Precision agricultureis a management philosophy that aims to makedecisions on input or operational procedures ata scale below the field scale. It advocates ashift from uniform management across indi-vidual fields according to the field average to

differential management of each site within afield according to the site requirements.

When considering whether site-specificmanagement decisions are feasible, then boththe magnitude of variation (i.e., the amountof variation) and the spatial structure ofvariation (i.e., how the variation is arrangedin space) are important. When the magnitudeof variation is small, then uniform manage-ment is likely to be preferable. If the variationis randomly distributed in space, then it isdifficult to adjust management given currenttechnology. However, if the variation has aspatial structure, then management can bedifferentially controlled at a subfield level.The spatial structure of variation also pro-vides information that can be used to deter-mine the density of sampling required toachieve a predetermined level of confidencein interpolation for map generation.

The objective of this report is to providesome indication of the magnitude of variabil-ity and the spatial structure associated withthe variability of two fruit quality parameters,dry matter (DM, measured as a percentage)and fruit weight (W, measured in grams) inkiwifruit orchards located around the Bay ofPlenty, New Zealand. These two parameters,DM and W, were selected because they areimportant quality determinants for marketsegregation and both have good calibrationswith the near-infrared (NIR) grading systemused to measure quality. The soluble solidsconcentration (or sugar concentration, mea-sured as a percentage) of the fruit is also animportant quality attribute. However, the cur-rent NIR calibration does not produce reliableresults, and the soluble solids concentrationdata were not considered in this study.

Materials and Methods

Eleven commercial orchards near TePuke, Bay of Plenty, New Zealand, wereused as study sites. Data were collectedduring the kiwifruit harvest from May toJune. The majority of data were collectedduring the 2003 harvest; however, oneorchard was monitored in 2002 and anotherwas monitored in both 2003 and 2004. Eachorchard is given an alpha indicator, with eachyear considered to be an independent obser-vation; thus, there were 12 orchard ‘‘years’’(orchards A–L). Some orchards consisted ofa single block whereas others had multipleblocks under the same management regimethat were aggregated to form a single orchardunit.

Each orchard block is divided into bays,which are the basic vine trellis units. Bays aretypically 5 · 5 m. The center of each bay wasgeographically referenced and the bayslabeled with a unique barcode. Harvest binswere also labeled with a unique barcode thatwas different to the bay barcodes. Duringharvest each bin was referenced to the baysfrom which fruit was picked into the binusing the barcodes. Typically, four to fivebays are picked into a single harvest bin.

At the pack house the bin barcodes werereferenced to the time that the fruit was put

Received for publication 31 Aug. 2006. Acceptedfor publication 9 Dec. 2006.Supported by Zespri Innovation Company Ltd.We thank the management and staff at ELEOSpack house, and the local growers around Te Puke,New Zealand, who kindly provided access to theirorchards and fruit. The assistance of Darryl Gillg-ren in data preparation is also acknowledged.1To whom reprint requests should be addressed;e-mail james.taylor@usyd.edu.au

246 HORTSCIENCE VOL. 42(2) APRIL 2007

through the kiwifruit quality grader. Theinline NIR Compac Kiwifruit Grader (Com-pac Sorting Equipment Ltd., Onehunga, NZ)measures the DM and W of each fruit.Individual kiwifruit data were aggregated toproduce mean bin DM and W. The mean binresults were referenced back to the bays in theorchard from where the kiwifruit was pickedusing the barcode information. The centroidof the assigned bays was used to reference thedata geographically. A full description of thisapproach is given in Gillgren (2001).

Nonspatial statistics. The orchard nameand orchard level nonspatial descriptive sta-tistics—mean (m), variance (s2), coefficientof variation (CV), skewness (k), and numberof bins (n)—for each quality attribute in eachorchard were calculated.

Spatial statistics. Individual variogramclouds for each orchard were plotted inVesper (Minasny et al., 2005). Preliminarygeostatistical analysis showed that the vario-gram cloud for the majority of data was bestfit by a spherical model (Eq. [1]) according tothe Akaike Information Criteria (Websterand McBratney, 1989).

The spherical model

gðhÞ= c0 + c13h2a

� �� 0:5 h

a

� �3on

for h # a;

c0 + c1 for h > a

(

[1]

where c0 is the nugget variance, c0 + c1 is thesill, and a is the range.

Standardizing the variogram model makescomparison between orchards easier. Thus, foreach orchard data the theoretical sphericalvariograms were calculated using the globalvariogram function in Vesper (Minasny et al.,2005) and the variogram parameters [nuggetvariance (c0), sill (c0 + c1), and the range (a)]recorded with the nonspatial statistics.

The c0 value estimates the amount ofvariance at a lag distance of 0 m and is afunction of stochastic effects and measure-ment error. The c1 value estimates theamount of autocorrelated variance in thesedata and contributes with c0 to define the sill(c0 + c1) or the total amount of variance inthese data. The range defines the distanceover which data are autocorrelated (i.e., thedistance at which the sill is reached).

The lags for each individual orchard vario-gram cloud were recorded, then were fourthroot transformed to normalize the response(McBratney and Pringle, 1999). For each lag,the mean was taken across the orchards foreach variable before the mean values wereraised to the fourth power to put them backon scale. Although a spherical function bestrepresented the raw lags from the individualorchards, an exponential variogram (Eq. [2])was the best fit to the ‘‘average’’ lags. The‘‘average’’ variogram parameters wererecorded and used to calculate the Cambar-della index (Cambardella et al., 1994) andmean correlation distance (MCD) (Han et al.,1994) according to Eq. [3] and Eq. [4].

The exponential model

gðhÞ= c0 + c1 1� exp�hrð Þ

n o[2]

In this model the range is denoted by r, and itsrelationship to a in the spherical model isdefined as a = 3r.

The Cambardella index

Cambardella Index =c0

c1 + c0� 100 [3]

where c0 is the nugget, c0 + c1 is the sill, andless than 25 indicates a strong spatial depen-dency, 25 to 75 indicates a moderate spatialdependency, and more than 75 indicates aweak spatial dependency.

The mean correlation distance

MCD ðmÞ= 3

8� c1

c0 + c1a [4]

where c0 is the nugget, c0 + c1 is the sill, a isthe range.

Both the Cambardella index and MCDprovide some indication of the spatial struc-ture in these data. The Cambardella index is aratio between the nugget (c0) and the sill (c0 +c1), and thus measures the amount of variancein these data that is autocorrelated andpotentially manageable. Although no accountis taken in the index of the range parameter,smaller values are indicative of a strongerspatial structure (Han et al., 1994). The MCDis an empirical index, calculated in meters,that was originally derived for soil properties.The MCD includes the range of the data, aswell as the ratio between the nugget and sill,to provide an estimate of the distance overwhich these data are autocorrelated. Thegreater the MCD, the greater the spatialstructure.

Optimizing the grid-sampling size. With apriori knowledge, randomized site-directedsampling schemes have been shown to bepreferable to grid sampling (Pocknee et al.,1996). However, when a priori knowledgedoes not exist, grid sampling can be effec-tive, especially when it is optimized usingblock-kriging and block-kriging parameters

Fig. 1. Example of a bay-based representation ofdry matter production (measured as a percent-age) across a kiwifruit orchard near Te Puke,New Zealand. Data were derived from analysisof the mean fruit quality within harvest bins andthen transferred back to the bays from whichthe bin was harvested. Courtesy of DarrylGillgren, Lincoln Ventures Ltd., New Zealand.

Table 1. Nonspatial statistics and variogram parameters for dry matter and fruit weight for each orchard inthe study.

OrchardNo. of

bins (n)Mean

(m)Variance

(s2) Skewness CVNugget

variance (c0)Sill variance

(c0 + c1)Range(a) (m)

Dry matter (%)A 534 15.20 0.19 0.11 2.92 0.264 4.655 163.7B 181 16.12 0.06 –0.02 1.56 0.045 0.083 183.5C 91 15.93 0.06 –0.07 1.52 0.006 0.017 66.0D 403 15.35 0.35 –0.47 3.86 0.242 1.915 237.4E 116 13.85 0.15 –0.91 2.83 0.275 0.452 67.7F 276 15.86 0.16 0.14 2.54 0.128 0.172 116.5G 80 16.07 0.10 –0.53 2.00 0.035 0.091 46.2H 247 16.09 0.11 –0.35 2.07 0.029 0.060 166.4I 169 16.11 0.05 –0.30 1.46 0.022 0.047 84.4J 639 16.45 0.10 0.22 1.87 0.013 0.064 192.1K 155 14.58 0.25 –0.14 3.40 0.511 4.745 127.5L 139 15.90 0.07 0.49 1.65 0.093 0.115 103.9

Fruit wt (g)A 116.42 35.28 –0.45 5.10 7.496 46.526 179.9B 113.68 25.50 0.33 4.44 13.720 30.360 207.1C 110.29 21.62 –0.12 4.21 3.935 26.905 81.9D 112.84 24.40 –0.07 4.38 10.260 30.470 146.7E 110.25 19.62 0.34 4.02 16.200 21.341 62.6F 105.23 9.30 0.10 2.90 5.349 12.028 250.0G 106.45 19.10 0.02 4.10 4.782 24.782 134.8H 111.01 25.81 –0.05 4.58 6.154 39.714 250.0I 112.94 50.69 –0.67 6.30 20.630 67.630 124.9J 110.66 25.20 0.29 4.54 8.508 30.128 199.7K 110.90 22.47 –0.92 4.27 12.710 25.750 18.0L 96.95 16.89 0.46 4.24 2.704 31.704 250.0

CV, coefficient of variation.

HORTSCIENCE VOL. 42(2) APRIL 2007 247

(Burrough, 1991). Given a certain krigingblock size and sampling grid size, McBratneyand Pringle (1999) have shown that estimatesof kriging variance (sk

2) and the �95%confidence interval (CI) of kriging predic-tion (where �95% CI = 2�Osk

2) can be madeusing the equations presented in Websterand Oliver (1990).

An average kriging variance has beenused in this calculation per the method ofMcBratney and Pringle (1999) (i.e., an aver-age kriging variance for the block in relationto the grid point was taken for 25 pointsaround the node). The output was plotted ascontour maps to display the interactionbetween varying block length and grid sizeon the average kriging variance. Only squareblocks have been used in this analysis; thus,block size has been specified by block length(in meters).

Results and Discussion

Nonspatial statistics. For the two qualityparameters, DM and W, the nonspatialdescriptive statistics for each orchard aregiven in Table 1. The number of bins (n)recorded in each orchard gives an indicationof the relative size of the area sampled. Onaverage a bin covers �112 m2 or 0.011 ha.The DM m and s2 are fairly constant acrossthe orchards. Harvest time is determined byDM, so it would be expected that there is littlevariation between orchards. The range inmean W across the orchards was large (19.5g); however, the s2 and CV were fairlyconstant across the orchards, indicating thatwithin each orchard a similar level of vari-ability exists. No measurement of skewnessfell outside the range –1 < k < 1, and themajority of measurements (21 of 26) were inthe range –0.5 < k < 0.5, indicating normaldistributions.

Average variograms. The variograms pre-sented here (Fig. 2) are done so to provide anindication of the spatial structure of kiwifruitquality parameters and as a reference for anyfuture spatial analyses.

The parameters for the average vario-grams, the average Cambardella index valuesand the average MCD are given in Table 2.Fruit weight exhibited the larger averagerange (238.4 m) and MCD (68.4 m), whereasDM had a smaller average range (166.5 m)and MCD (40.4 m). The Cambardella indexconfirms this, with W having a smaller scorethan DM. These results indicate that there is astronger opportunity to manage W spatiallywithin orchards. Again, there is a potentialmanagement bias in this result because of theuse of the DM values in determining harvestdate.

Determining an optimal grid-samplingscheme. Isoline plots of �95% CIs for krig-ing predictions of DM and W are presented inFig. 3. These were derived using the averagevariogram parameters presented in Table 2.The isoline plots allow practitioners to selecta suitable kriging block length and grid sizeto achieve a desired level of confidence in any

interpolation and mapping of the grid surveydata. Although encouraging users to selecttheir own threshold, McBratney and Pringle(1999) suggest that the �95% CI should be

�10% of the mean value of the desirableattribute. We have chosen to use one-third ofthe mean SD of each variable from these 12data sets because the kiwifruit industry relies

Fig. 2. (A, B) Individual orchard and average variograms for dry matter (A) and fruit weight (B; measuredin grams). Average variograms are in bold; individual orchards are labeled with their alpha indicator(Table 1).

Table 2. Average variogram parameters and spatial indices calculated from the average variogramparameters for dry matter and fruit weight.

Dry matter (%) Fruit wt (g)

c0 (nugget) (units2) 0.06 7.45c0 + c1 (sill) (units2) 0.17 32.08r (m) 55.49 79.47Effective rangez (m) 166.50 238.40Cambardella index 35.30 23.20Mean correlation Distance (m) 40.40 68.60zExponential models were fitted to the average variograms then the exponential range (r) was adjusted tothe same scale as the spherical models (a = 3r).

248 HORTSCIENCE VOL. 42(2) APRIL 2007

on measures of s to determine price premi-ums. For DM and W, this equates to 0.12%and 1.61 g respectively.

When designing a single samplingscheme for multiple variables, such as DMand W, the grid size needs to be optimizedacross the variables. This may be possible byusing a constant survey grid size, but varyingthe kriging block length between variables.From Fig. 3, an�95% CI of 0.12 for DM canbe achieved with a grid spacing of 28 m andblock length of 24 m. The �95% CI for Wgrid spacing can also be achieved at a 28-mgrid spacing using a block length of �32 m.Thus, by varying the block length, the sam-pling of different variables can be done atconcurrent locations on a 28-m grid whileachieving the desired level of confidence foreach variable.

A 28-m grid produces�12 samples/ha. Ingeneral, �100 samples are required to pro-duce effective variograms (Webster andOliver, 1992). Most of the orchard blocks usedin this study are less than the 8 ha required ona 28-m grid to achieve enough samples forvariogram estimation. Orchards, though, maybe more than one block, and sampling may bedone across several contiguous blocks withina maturity area. However, only blocks undera uniform management system and crop typeshould be joined together into larger sam-pling areas. In situations when samplingareas are less than 8 ha, the addition of nestedtransects (Pettitt and McBratney, 1993) ema-nating from randomly selected grid nodes inrandom directions can be used to increase thenumber of samples and to ensure good vario-gram estimation.

The nugget variance (c0) in these data iscalculated from a large number of fruitsamples (�1200–1500 fruit/bin), but proba-bly contain a significant contribution fromerror/noise in the NIR grader sensor. Forhand-sampled data sets, there will be varia-tion in the samples according to position inthe canopy and position in the cordon (Mileset al., 1996). The implication of this is thatalthough a sampling grid can be recommen-ded from the isoline plots, where the fruit arepicked and how many are picked will deter-mine how accurately quality is measured at agiven point. The calculation of the number offruit required at each sample point is beyondthe scope of this data set and requiresknowledge of the amount of variationobserved within a vine and between adjacentvines. If this variance is known, then thenumber of fruit required to measure qualityparameters within a certain CI or thresholdlevel, such as the average nugget variance,can be determined. Research into this area isbeing conducted but is yet to be published(Prof. Ray Littler, University of Waikato,New Zealand, pers. comm., May, 2006).

After samples have been taken, a vario-gram model can be derived from the data toestimate the nugget and sill variance. Giventhis information, the block kriging size can beadjusted in the interpolation process toachieve or approach an acceptable �95%CI. Fig. 4 is an example of how this may beapplied. It illustrates how the �95% CIchanges for both DM and W with varyingblock lengths and variogram sill values(given all other parameters are kept constantaccording to Table 2 and a survey gridspacing of 28 m).

The analysis presented here has focusedon the use of average variograms to deter-mine a regular (square) sampling grid size.However, it may be preferable to use thevariogram information to design an irregularsampling grid. Recent work (Marchant andLark, 2007) has demonstrated the use ofspatial simulated annealing to design irregu-lar sampling schemes. This process mini-mizes the total error incurred from bothvariogram estimation and the kriging processover a distribution of variograms for alterna-tive sampling schemes. The average andindividual variograms presented (Fig. 2) pro-vide information on the plausible distributionof variograms over which such simulationsshould occur.

Conclusion

Kiwifruit quality is variable withinorchards, with different quality variablesexhibiting different levels of nonspatial andspatial variation. Fruit weight appears toexhibit greater spatial variation than DMusing the MCD and Cambardella index. Thisindicates that there may be more advantage tomanage W spatially than DM. A collectionof nonspatial statistics, variogram parame-ters, and theoretical variograms plots for 11orchards were presented here as a referencefor future use.

Fig. 3. (A, B) Isoline plots of�95% confidence intervals of kriging predictions for dry matter (A) and fruitweight (B) with varying block lengths (measured in meters) and sampling grid spacing (measured inmeters). Average variogram parameters (c0, c0 + c1, and r) are held constant at the values given in Table 2.

HORTSCIENCE VOL. 42(2) APRIL 2007 249

Average variograms for each quality vari-able have been calculated from the individualvariograms. These have been used to opti-mize grid-sampling schemes for the purposesof mapping given no a priori information.Contour plots to assist researchers andgrowers select a grid size with an appropriate�95% CI have been presented for generaluse. Optimal grid size will depend on thelevel of confidence desired; however, a 28-mgrid appears to be a good compromise acrossthe two quality attributes presented. After thegrid survey, the collected data can be used to

derive variograms for each quality attributeand, given all other parameters remain con-stant, the block size can be refined furtheraccording to the derived sill values.

If the actual variogram parameters for aquality attribute are known, these parametersshould be used, in lieu of the average vario-gram parameters, to optimize the samplinggrid size.

Literature Cited

Burrough, P.A. 1991. Sampling designs for quan-tifying map unit composition, p. 89–126. In:

M.J. Mausbach and L. Wilding (eds.). Spatialvariabilities of soils and landforms. Specialpubl. 28. Soil Sci. Soc. of America, Madison,Wisc.

Cambardella, C.A., T.B. Moorman, J.M. Novak,T.B. Parkin, D.L. Karlen, R.F. Turco, and A.E.Konopka. 1994. Field-scale variability of soilproperties in central Iowa soils. Soil Sci. Soc.Amer. J. 58:1501–1511.

Gillgren, D. 2001. Finding the fruit: A spatialmodel to access variability within a kiwifruitblock. Proc. SIRC 2001, 13th Annu. Colloq. ofthe Spatial Information Research Centre, Uni-versity of Otago, Dunedin, New Zealand, 2–5Dec. 2001.

Han, S., J.W. Hummel, C.E. Goering, and M.D.Cahn. 1994. Cell size selection for site-specificcrop management. Trans. Amer. Soc. Agr. Eng.37:19–26.

Marchant, B. and M. Lark. 2007. Optimizedsample schemes for geostatistical surveys.Math. Geol. (In press).

McBratney, A.B. and M.J. Pringle. 1999.Estimating average and proportional vario-grams of soil properties and their potentialuse in precision agriculture. Precision Agr.1:125–152.

Miles, D.B., G.S. Smith, and S.A. Miller. 1996.Within plant sampling procedures: Fruit varia-tion in kiwifruit vines. Ann. Bot. (Lond.)78:289–294.

Minasny, B., A.B. McBratney, and B.M. Whelan.2005. VESPER version 1.62. Australian Centrefor Precision Agriculture, McMillan BuildingA05, The University of Sydney, NSW. 2006.<www.usyd.edu.au/su/agric/acpa>.

Pettitt, A.N. and A.B. McBratney. 1993. Samplingdesigns for estimating spatial variance compo-nents. Appl. Stat. 42:185–209.

Pocknee, S., B. Boydell, H.M. Green, D.J. Waters,and C.K. Kvien. 1996. Directed soil sampling,p. 159–168. In: P.C. Robert, R.H. Rust, andW.E. Larson (eds.). Proc. 3rd Intl. Conf.Precision Agr. ASA/CSSA/SSSA, Madison,Wisc.

Praat, J.-P. and A.F. Bollen. 2007. Characterisingspatial variation in quality. In: Proc. 6thIntl. Kiwifruit Symp., ACTA Horticulture.(In press).

Praat, J.-P., F. Bollen, D. Gillgren, J. Taylor, A.Mowat, and N. Amos. 2003. Using supplychain information: Mapping pipfruit and kiwi-fruit quality. Acta. Hort. (ISHS) 604:377–385.

Proffitt, T., R. Bramley, D. Lamb, and E. Winter.2006. Precision viticulture: A new era invineyard management and wine produc-tion. Winetitles Pty. Ltd., Ashford, SouthAustralia.

Schueller, J.K., J.D. Whitney, T.A. Wheaton,W.M. Miller, and A.E. Turner. 1999. Low-costautomatic yield mapping in hand-harvestedcitrus. Computers Electronics Agr. 23:145–154.

Webster, R. and A.B. McBratney. 1989. On theAkaike Information Criterion for choosingmodels for variograms of soil properties. J.Soil Sci. 40:493–496.

Webster, R. and M.A. Oliver. 1990. Statisticalmethods in soil and land resource survey.Oxford University Press, New York.

Webster, R. and M.A. Oliver. 1992. Sample ade-quately to estimate variograms of soil proper-ties. J. Soil Sci. 43:177–192.

Fig. 4. (A, B) Isoline plots of�95% confidence intervals for kriging predictions of dry matter (A) and fruitweight (B) with varying block lengths (measured in meters) and sill variances (measured in squareunits). The c0 and r values are held constant (Table 2), and the (square) sampling grid size isconstrained to 28 m.

250 HORTSCIENCE VOL. 42(2) APRIL 2007