Taro (Colocasia esculenta) is the fifth most harvested root crop in the world with production estimated at 9.0 million t for 2011 (Food and Agriculture Organization of the United Nations, 2012). It is a tropical root crop that is grown primarily for its starchy, underground stem (i.e., corm), although leaf blades and petioles are eaten also (Plucknett et al., 1970). Corms are good sources of carbohydrates with easily digestible starch and have a favorable protein-to-energy ratio (Standal, 1983).
Taro is traditionally planted using vegetative propagules and is grown under flooded (i.e., wetland) conditions or non-flooded (i.e., upland) conditions (Plucknett et al., 1970). Typically, it is grown for six to 13 months.
Field trials are expensive to conduct both in terms of material inputs and time. There is a need to determine the minimum research plot size that will determine adequate yield characteristics as affected by various management options. In general, there are four methods for calculating optimum plot size (defined as number of measured plants in a plot): 1) determine maximum curvature of the relationship between variance of yield and plot size (Lessman and Atkins, 1963; Meier and Lessman, 1971; Smith, 1938); 2) minimize cost per unit of information (Smith, 1938; Swallow and Wehner, 1986; Zuhlke and Gritton, 1969); 3) use geostatistics to account for spatial autocorrelation in experimental design (Fagroud and Van Meirvenne, 2002); and 4) determine the plot size that maximizes the power to differentiate treatments.
Smith’s (1938) “law” was based on the empirical observation that a linear relationship was found between the logarithm of residual variance among plot means and the logarithm of plot size. When estimating mean yields from normally distributed data, the Fisher information is proportional to the inverse of the variance (Zucker, 2005), so modeling the variance is tantamount to modeling the Fisher information. Smith (1938) found that the variance (or equivalently the information) is often linear as described in Eq. .
The coefficient “b” can then be interpreted as an index of degree of correlation between neighboring plots because it measures how quickly the variance decreases with increasing plot size.
Often, optimum plot size has been estimated visually based on the maximum curvature in the plot of Vx vs. x (Boyhan et al., 2003; Vallejo and Mendoza, 1992); however, the apparent curvature in a figure plotting Vx vs. x is sensitive to the relative scaling in the y- and x-axes of the plot (Smith, 1938). Curvature is a well-defined mathematical concept and it is straightforward (see “Materials and Methods”) to determine the point of maximum curvature. Subjective, visual interpretation of the point of maximum curvature, as it appears that several previous publications have used, is often incorrect, sometimes significantly so.
Smith’s (1938) method estimated optimum plot size for unguarded plots (i.e., no border rows) based on an index of soil heterogeneity (“b”) and cost considerations (based on hours of labor). Larger plots could provide marginally more information about production attributes than smaller plots, but there is increased cost associated with increased plot size as described in Eq. .
The empirical method of Smith (1938) calculates a constant index of soil heterogeneity (“b”); however, if spatial autocorrelation between data points exist, then “b” may not be constant (Zhang et al., 1990). Spatial autocorrelation means that lower variances are found for observations separated by short distances compared with those separated by long distances (van Es and van Es, 1993). Fagroud and Van Meirvenne (2002) simulated 24 plot configurations, calculated variograms of each plot, and determined that the plot with the maximum nugget/sill ratio as the optimum plot size for a field experiment in Morocco.
A fourth method of determining the optimum plot size is based on the plot size and number of replications needed to detect a specific difference between treatments (Hatheway, 1961). Using uniformity data, the true difference between two treatments (expressed as a percent of the mean) is plotted against plot size and number of replications. The experimenter could decide on the desired difference between treatment means and then could estimate the plot size and number of replicates from the graph to detect this difference (Boyhan et al., 2003; Hatheway, 1961). This analysis was termed a power analysis, because it is related to the probability of finding a difference between treatments that does exist.
There is no previous literature discussing optimum plot size for field trials of taro. We hypothesized that: 1) flooded conditions would reduce moisture stress, resulting in more uniform growing conditions, reduced variability in yield, and reduced optimum plot size compared with upland conditions; 2) cultivars would differ in variability of yield, resulting in different requirements for optimum plot size; and 3) tissue-cultured planting materials would be more uniform in growth and exhibit less variance than traditional “huli” (i.e., stem cuttings).
Sweet potato (Ipomoea batatas Lam.) is a tropical root crop, and Vallejo and Mendoza (1992) plotted the relationship between the cv of yield and plot size using the maximum curvature method to visually estimate an optimum plot size of 30 to 60 plants covering 6 to 12 m2. Among several methods, Boyhan et al. (2003) visually estimated maximum curvature and calculated optimum plot size for short-day onions (Allium cepa L.) to be 280 to 320 plants covering 19 to 22 m2. Based on the power analysis of Hatheway (1961), Boyhan et al. (2003) estimated an optimum plot size of 240 plants or 11 m2 and six replicates or an optimum plot size of 480 plants or 22 m2 and three replicates. Using a segmented regression model to estimate the point of maximum curvature, Nokoe and Ortiz (1998) estimated optimum plot size for banana (Musa spp.) as 10 to 16 plants. Using a mathematical solution to the maximum curvature method, Meier and Lessman (1971) found an optimum plot size of 5.35 m2 for the oil seed [Crambe hispanica L. subsp. abyssinica (Hochst. ex R.E.Fr.) Prina]; in contrast, based on Eq. , they found a larger optimum plot size of 6.7 m2. Using the method of minimized cost per unit of information, Zuhlke and Gritton (1969) calculated optimum plot size for peas (Pisum sativum L.) of 3.3 m2 for unguarded plots and 3.1 m2 for guarded plots. Using Eq. , Swallow and Wehner (1986) found optimum plot size for conventionally harvested cucumbers (Cucumis sativus L.) ranged from 0.7 to 3.8 m2. Fagroud and Van Meirvenne (2002) found spatial autocorrelation in measurements of available water capacity in a field in Morocco, and they recommended a plot size of 4 × 8 m (32 m2) based on geostatistics.
The objective of this study was to determine the optimum plot size for field experiments of taro conducted either under flooded or non-flooded (upland) conditions and to compare the various methods of determination. We compared two methods of estimating optimum plot size and showed the importance of mathematically determining maximum curvature in the first method. In the second method, we developed a novel procedure of calculating the cost of border rows. In addition, we conducted geostatistical analysis, including variography and visual inspection of maps of the dry weight of corms grown under both flooded and upland conditions, and found no evidence of spatial autocorrelation. Finally, we examined the effect of plot size on the power of differentiating treatment means and found little effect of plot size on two statistical parameters used to estimate power.
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