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a Department of Plant Sciences, North Dakota State University, Fargo ND 58105
b Department of Agricultural Engineering, North Dakota State University, Fargo ND 58105
c Agronomy Department, Iowa State University, Ames IA 50011-1010
d Williston Research Extension Center, 14120 Highway 2, Williston, ND 58801
* Corresponding author (douglas.doehlert{at}ndsu.nodak.edu).
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ABSTRACT |
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 TOPNOTES ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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INTRODUCTION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Oat kernel size is, however, inherently nonuniform because of the multifloret habit of the oat spikelet. Oat spikelets may contain one, two, three, or more kernels. The outermost of these, called the primary kernel, is the largest, and mass decreases with higher orders of kernels. The study of Doehlert et al. (2002) indicated that primary kernels of triple kernel spikelets were the largest and were significantly larger than primary kernels of double kernel spikelets. Secondary kernels from triple kernel spikelets were not significantly different in size from primary kernels of single kernel spikelets, and these were larger than secondary kernels from double kernel spikelets. Tertiary kernels were the smallest kernel type studied. However the double kernel spikelet is by far the most abundant spikelet type in most oat genotypes (Takeda and Frey, 1980; Doehlert et al., 2002).
Early studies evaluating oat size uniformity emphasized size differences between primary and secondary kernels (Zade, 1915; Mader, 1927; Milatz, 1933). Later studies evaluated mass distributions of oat fractions separated by sequential sieving with slotted sieves (Sword, 1949; Hubner, 1951; Bruckner et al., 1956; Ganssmann, 1964; Doehlert et al., 2002). More recently, digital image analysis has been applied to size analysis of oat kernels (Symons and Fulcher, 1988; Pietrzak and Fulcher, 1995; Doehlert et al., 1999).
It is important to define dimensions of oat kernel size here because many different characteristics have been used to express size. The nomenclature used here is consistent with that introduced by de Villers (1935). He suggested kernel length to be the distance from the base to the tip of the lemma, the width being perpendicular to the crease and lemma venation when the kernel is lying with its crease down. The depth of the oat kernel was defined as being the distance from the dorsal to the ventral side of the oat kernel, taking the palea as the dorsal and the lemma as the ventral side. Different types of analyses measure different combinations of these dimensions. Kernel mass may be the best evaluation of kernel size, which is essentially a three-dimensional measurement (multiplied by kernel density). Digital image analysis, at best, measures only two dimensions. These are typically length and width, although kernel image area can also be derived from those data. Although it has not been characterized experimentally, it seems reasonable to presume that sequential sieving would separate kernels by their smallest dimension, being their depth. Thousand-kernel weight is a measure of the mean kernel mass of an oat sample, but distributions of individual kernel masses have not been measured in oats to the knowledge of the authors. Such measurements can be made in wheat with an automated single kernel analyzer (Martin et al., 1993). Such an instrument has been used to evaluate groat mass distributions (Doehlert, unpublished data), but oat hulls and trichomes tend to interfere with the pneumatic systems of this type of instrument, making the application impractical.
In this study we attempted to evaluate oat kernel size uniformity by both sequential sieving and digital image analysis, and to relate these with mean kernel mass whenever possible. Our objectives were to determine genotypic and environmental effects on oat kernel size distributions as measured by these two methods and to relate these characteristics with other quality characteristics in oat grain.
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MATERIALS AND METHODS |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Analyses
Grain yield was determined from the mass of grain harvested from the center two rows of the test plots, after cleaning. Test weight was determined by weighing a fixed volume of grain from a test weight filling hopper (Seedburo Equipment Company, Chicago, IL). Volumes of grain from size fractionation were not sufficient to fill the filling hopper required for test weight measurements, so bulk densities were determined on size fractions by dividing mass of a grain sample by its volume, as measured in a graduated cylinder. Crown rust (causal agent Puccinia coronata Cda. f. sp. avenae Eriks.) infection score was determined in the field at close to the peak infection time. Plots were scored from 0 to 5, where 0 indicated a plot free of crown rust and 5 indicated the heaviest possible infection. Groat percentage on field plot samples were determined with a compressed air dehuller (Codema, Eden Prairie, MN) correcting for hulled grain remaining after dehulling described as the final groat percentage in Doehlert and McMullen (2001). Groat percentages of size fractions were determined by hand dehulling, as described in Doehlert et al. (1999). Mean kernel mass was determined by counting the number of kernels in a 10-g sample. Kernels were counted with an automated seed counter (Seedburo Equipment Company, Chicago, IL).
Grain was fractionated into size fractions with slotted sieves and a sizer-shaker (Seedburo Company, Chicago, IL). Grain samples of 150 g were sieved sequentially on slotted 3.18-, 2.58-, 2.38-, and 1.98-mm sieves. All slots were, 19.05 mm long. Grains held back by these sieves were labeled as oversized, large, medium, and small, respectively. Kernels that passed through the 1.98-mm sieve were labeled as undersized. Sieve sizes used for separations were designed to mimic commercial systems as described by Deane and Commers (1986). The uniformity product (Doehlert et al., 2002) was calculated as the product of the percent large kernels, the percent medium kernels, and the percent small kernels.
Digital image analysis was used to measure the length, width, and image area of individual oat kernels in samples. Ten-gram samples of oat kernels were placed on a backlit glass platform within a predefined field of view. A scale (in mm) was also attached to the platform. An analog camera (using photographic film) was mounted at a fixed height of one meter from the platform. Oat kernels were manually positioned on the platform ensuring seeds were not touching each other and a photograph taken. The developed 10.2- by 15.2-cm photographic prints were digitized as 8-bit gray images with a resolution of 236 pixels per cm with scanner and were saved in a tiff format.
A separate image processing program was developed to determine the required measurements (lengths and widths) of each seed automatically from an image. The program was developed in macro environment of a commercial image processing software Aphelion (Amerinex Applied Imaging, Amherst, MA). The image was initially processed with a 3x3 low pass filter to reduce the noise. A separate program (not available in the Aphelion software) was incorporated within the Aphelion environment. This program is a histogram-based automatic background segmentation algorithm (Otsu, 1979). Using this program, a threshold is automatically selected to remove the background of this image. Thus, the segmented image only contained the objects (oat kernels). Subsequent image analysis programs–functions were used to extract each kernel as a region and determine its major and minor axes. The determined major axis represented the length and the minor axis represented the width of each kernel. It is to be noted that the determined parameters were in pixels. Thus, the program had the capability to obtain the scale conversion factor (from pixel to cm or mm). Extensive validation experiments were performed to assure that analyses generated accurate measurements of oat kernel length, width, and image area. Manual measurements of metal rectangles, pieces of toothpicks, and oat kernels made with slide calipers and with manual operation of the imaging software were compared the automated analysis from images. The average difference between the manual and the automated measurements was 1.6 and 7.6% of the manual measurement for length and width, respectively. Considering a scale conversion factor of 1 pixel = 0.12 mm, the average difference (between manual and automated measurements) for length and width measurements were 0.14 and 0.17 mm, respectively. Means and variances were calculated from collected individual data for each sample. Typically samples contained 250 to 400 kernels. Images also were collected of size fractions derived from the sequential sieving procedure, and analyzed as above.
Histograms showing size distributions of combined size fractions required a normalization of frequencies according to their occurrence in original samples. Proportions of size fraction, collected as mass proportions, were converted to proportion according to kernel number on the basis of mean kernel masses of the size fractions. Frequencies of kernel sizes in sequential sieving fractions, expressed as percentages of mass, were multiplied by the kernel number proportion of each fraction. The summation of these fraction proportions matched well with frequencies of sizes in the original sample (data not shown).
Test for Bimodality
Histograms of oat kernel size observations suggested that these data were not normally distributed, and we sought a statistical test for bimodality. The following test was performed on all original unfractionated samples and compares the likelihood that the data fit a single normal distribution with the likelihood that every data point belongs to either of two normally distributed subpopulations, each with its own mean and variance. The single normal distribution model (Model u) assumes the data have mean µ and variance 
2: Y 
N(µ, 2). The likelihood function for this model is
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2 that maximize Lu amounts to calculating the usual 
= 
yi and 
2 = 
2. The mixture of two normal distributions model (Model b) assumes that each data point belongs to one of two subpopulations P1 N
or P2 N
with probabilities of belonging to P1 and P2 of p and 1 – p, respectively. The likelihood for this model is
 | [2] |
, 1, 21, 2, and 22 that maximize Lb, as follows. Initial values are chosen for , 1, 21, 2, and 22. In practice, we took = 0.5, 1 = – , 21 = 2, 1 = + , and 22 = 2, though we verified that different initial values did not affect the final estimates obtained. The procedure then alternates the following two steps. In step one, the probability pi that each observation i belongs to P1 is calculated as
 | [3] |
, 1, 21, 2, and 22 are updated as follows:
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 | [5] |
 | [6] |
Updating 2, and 22 is done as for 1 and 21, except that and pi are replaced by 1 – and 1 – pi in Eq. [5] and [6]. Note that, to be maximum likelihood estimators in the strict sense, Equation [6] should not have –1 in its denominator, and likewise for the variance estimator in Model u above. The –1 factor corrects for the well-known downward bias in maximum likelihood estimators and otherwise has no impact on the validity of the test. To retain biological relevance, we constrained updates in step two such that 0.1 
0.9 and min
/2 
0.02. These steps were iterated until stable estimates are obtained. In practice, we iterated until Lb changed by less than 10–8 between iterations. A likelihood ratio can be calculated from Lu and Lb as follows:
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The distribution of (T) in (7) when observations are in fact normally distributed is currently the object of debate (McLachlan and Peel, 2000). For the specific problem at hand, we obtained the null distribution of T by repeatedly simulating normally distributed data sets and applying the test to them. Five thousand simulations were performed, producing a distribution of T that in its tail resembled a 
2 with four degrees of freedom, with a threshold for Type I error rate 
= 0.05 of 9.0.
Note that, strictly speaking, the test outlined above is not a test for bimodality per se but of the presence of a mixture of normal distributions. In the present context in which there are biological mechanisms causing kernel measures to be bimodal, de facto the test assesses bimodality. That said, support for Model b entails the following interpretation. The oat kernels harvested represent a mixture of two types, small and large. Each type has its own mean size and variance about that mean as given by the parameters 1, 21, 2, and 22. Among all kernels, represents the fraction that belongs to the small type. Thus, the biological mechanism that leads to the genesis of small type kernels may be considered more active in genotypes with high . The T statistic provides a measure of the extent to which small and large types are clearly differentiated in a given data set or genotype. Genotypes where 1 is close to 2 (as scaled by the overall standard deviation in kernel size) will have a low T and, conversely, when 1 and 2, are strongly divergent, a high T will arise. In what follows, we refer to as "Prob1." and to T as the bimodality coefficient.
Experimental Design and Statistical Analyses
Field plots were arranged in a random complete block design with three replicates. Analysis of variance was applied to data where genotypes were considered fixed and environments were considered random. Analyses of variance were calculated with the Statistix computer package (Analytical Software, Tallahassee, FL), where the environment x replicate mean square was used as an error term to test the environmental effect. The genotype x environment interaction mean square was used to test the genotypic effect, and the genotype x environment interaction was tested with the residual mean square. Mean separation was evaluated by the least significant difference, which was also calculated by the Statistix software program using the previously described error terms. For correlations across genotypes, correlations were first calculated for characteristics within each environment. A Chi square test was performed to verify that correlation coefficients were not significantly heterogeneous across environments (Steel et al., 1997). When heterogeneity was not observed, correlation coefficients were pooled over environments according to Steel et al. (1997). For correlations across environments, correlations were first calculated individually for each genotype, the pooled over genotypes by the procedure just described.
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RESULTS |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Much less variation was found in environmental means of size distributions (Table 4). Most differences in the uniformity product could be attributed to higher undersized proportions, and less variation was observed in the large size proportions.
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DISCUSSION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Samples with higher uniformity indexes may be more easily processed because those samples had kernels more evenly distributed across a range of expected kernel sizes. These samples also had higher variances of size parameters as determined by image analysis. The cultivars with higher uniformity products were also the ones with more large kernels (Table 3). Milling of cultivars with higher frequencies of smaller kernels could overwhelm the small or stub milling stream, leading to poorer operational efficiency.
Consistent with the hypothesis that digital image analysis and sequential sieving analyze different dimensions of the oat kernel is the differences in the shape of the distributions derived from these methods. Digital image analysis for area and length frequently appeared to be bimodal or multimodal (Fig. 1 and 2). Distributions from sequential sieving appeared to be unimodal (Tables 3 and 4). Although the resolution presented in this study allows for only five size classes, we have separated samples into as many eight fractions, and these have always appeared unimodal in shape (data not shown). Kernel width, as analyzed by digital image analysis, usually were unimodal in shape (Fig. 1 and 2), in spite of a high level of resolution allowed by digital image analysis. Distributions of oat kernel depth may be similar to width in this respect.
We presume the basis of the bimodal populations depicted by the digital image analyses to lie with the size differences among the different order of kernels within the individual oat spikelet. Because most oat spikelets contain two kernels, the larger mode in the bimodal population may represent primary kernels from these double kernel spikelets, whereas the second mode may represent secondary kernels from these spikelets. Such distributions would be expected to be complicated by the presence of single and triple kernel spikelets that could add additional modes and increase ranges of sizes. An earlier study from this laboratory (Doehlert et al., 2002) analyzed spikelets from many of the same plots used in this study from the year 2000. This study indicated a high frequency of double kernel spikelets at the Fargo location, and a higher frequency of triple kernel spikelets at the Williston location. Figures 1 and 2 in this study show that samples taken from Williston showed a greater range (and standard deviation) than the samples analyzed from the Fargo location, but there is no evidence for additional modes in the Williston samples.
Introduction of bimodal analysis has facilitated the interpretation of data from digital image analysis. Because area and length measurements frequently do not fit normal distributions, traditional statistical analyses have failed to provide meaningful descriptions of the data. The bimodal analysis (Table 6) provides statistics that give an estimation of the extent of bimodality (bimodality coefficient) and gives an estimation of the balance in the numerical size of the two subpopulations (Prob1). The mean sizes of each of the two subpopulations (Mean Group1, Mean Group2) could be used to evaluate differences in sizes between primary and secondary kernels, as proposed by Milatz (1933).
Although we have had no direct test to indicate what size distributions are better for milling, we would speculate that higher Prob1 values would be desirable because that would indicate a more even distribution of kernel sizes. High values of the bimodality coefficient would indicate a highly bimodal population, which could separate easily and consistently into two subpopulations. However, correlation analysis indicated that in this study the bimodality coefficient was negatively correlated with test weight (r = –0.45, P < 0.01) and groat percentage (r = –0.48, P < 0.01). Thus, unless quality problems associated with extreme bimodality are alleviated, the highly bimodal distribution would act as a signal of poorer quality grain. Although samples of the best milling quality observed in this study with higher test weights and groat percentages had higher Prob1 values and lower bimodality coefficients, it is not known if those distributions offer any milling advantage directly associated with the distribution pattern.
It is difficult at this stage of study to conclude what size distributions are best for milling, primarily because no study of oat kernel size distributions in relation to milling yield has appeared in the literature. Also, optimal distribution for one mill might be quite different than that for another facility, because different operations will size fractionate into different numbers of streams. It is likely that most oat mills have the ability to efficiently mill almost any distribution pattern that is delivered to them, but as with any large scale industrial process, small increases in efficiency can result in large increases in profitability. Thus, a better understanding of oat kernel size distributions has significant potential return in processing efficiency.
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NOTES |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Received for publication May 15, 2003.
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REFERENCES |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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