Plot size variation to quantify yield of potato clones

Hortic. bras., v. 24, n. 4, out.-dez. 2006 Potato breeding programs generate many advanced new clones that need to be selected for yield potential and adaptation every year. This is a very important breeding step that requires high experimental precision to identify the best clones. Experimental precision involves experimental design, optimum plot size and adequate replication number adjusted to the availability of experimental area (Martin et al., 2004).

P otato breeding programs generate many advanced new clones that need to be selected for yield potential and adaptation every year. This is a very important breeding step that requires high experimental precision to identify the best clones. Experimental precision involves experimental design, optimum plot size and adequate replication number adjusted to the availability of experimental area (Martin et al., 2004).
The persistence of the soil heterogeneity index and the optimum plot size is about 50% in subsequent years of a particular crop (Lin et al., 1996). Since exact knowledge about the environmental variability of the experimental area is necessary to arrange more precise experiments, only unbiased estimations should be used to improve gain from selection in a particular step of the potato breeding program (Vermeer, 1990). Single-hill plots are not precise enough to detect differences among clones already selected in previous generations (Brown, 1987). Moreover, plots bigger than single hills are necessary to detect differences among clones in advanced selection steps (Bearzoti & Pinto, 1996).
The objective of this paper was to study plot size variation among potato clones to increase experimental precision of yield performance trials. Practical applications and strategies to increase experimental precision of yield performance trials of potato clones are discussed.

MATERIAL AND METHODS
Five potato clones ('SMIJ456-4Y', 'SMINIA95043-11', 'SMINIA-Iporã', 'Macaca' and 'SMINIA90244-1') differing in vine maturity, vigor and adaptation to local growing conditions were evaluated. High quality seed tubers of each clone were planted in two rows of 60 hills at the experimental area of the Horticulture Dept. of UFMS in Santa Maria, Rio Grande do Sul State, Brazil, on August 11 th , 2004. One seed tuber

ABSTRACT
The objective of this paper was to study plot size variation among potato clones to increase experimental precision of yield performance trials. The experiment was carried out at the experimental area of the Horticulture Dept., UFSM, Santa Maria, Rio Grande do Sul State, Brazil. Tubers of five potato clones were planted in two rows of 60 hills in August 2004. For all ten experimental rows, combined plots were formed adding a different number of adjacent hills of the same row. Soil heterogeneity index and optimum plot size were estimated for each row. Real differences between treatment means for each clone and all clones were estimated using the Hatheway technique. The experimental precision of potato yield trials varied with the evaluated clone because of different optimum plot sizes. Eight-hill plots are the optimum size to quantify yield of potato clones, but experimental precision depends upon adjustments of the number of treatments and replications to the availability of experimental area. Genetic diversity indeed decreases experimental precision and justifies the use of different plot sizes. Practical applicattions and strategies to increase experimental precision of yields performance trials of potato clones are discussed.
Palavras-chave: Solanum tuberosum; planejamento de experimento; tamanho de parcela; área experimental limitada. was considered a hill. Hills were separated by 0.80 m between rows and 0.30 m within rows. Soil and crop managements were uniform and followed technical recommendations adapted in the regions. Tubers were harvested on November 19 th , 2004 and total yield per hill quantified.
Each hill was considered one basic unit (BU) plot. Adding adjacent hills or BU of the same row produced combined plots. Combined plot size (X) was defined as the number of basic units or BU. Combined plots had X equal to 1, 2, 3, 4, 5, 6, 10, 12 and 15 BU, in each row. The total number of replications (N) of each combined plot was limited to 60 hills, meaning N= 60/X. Some statistics were estimated for each combined plot. Plot mean M(x) with X BU, where M(1) or M 1 was the average of one BU. Variance V(x), for each combined plot of X BU. The variance per BU, VU(x), for plot sizes of X BU, where VU(x)= V(x)/X 2 . Coefficient of variance CV(x) for plot sizes of X BU.
The parameters V 1 and b of the empirical relationship VU(x)= V 1 /X b (Smith, 1938) were estimated based upon logarithmic transformation and weighted according to degrees of freedom for each plot size (Steel et al., 1997). V 1 was the variance of one basic unit plots and b the soil heterogeneity index.
The same procedure was used to estimate the A and B parameters of the function CV(x)= A/X B . The optimum plot size (X 0 ) was estimated with the modified maximum curvature technique (Meier & Lessman, 1971) . The logarithmic transformation of the function CV(x)= A/X B that resulted in the model for both replications of k, varying from 1 to 5 clones, was used to test parallelism, same origin and coincidence among the five clones (Seber, 1976 was the sum of the sum square error of each clone; K was the number of compared clones (K= 5); and n was the number of total observations (plot sizes and replications).
The magnitude of treatment differences, expressed as mean percentage (D) of each and all clones, was estimated with , where r was the number of replications; X 0 was the optimum plot size (number of BU); A was estimated with the function CV(x)= A/X B and b estimated with the function VU(x)= V 1 /X b ; t 1 was the value of t in the test of significance (bilateral at 5%) and t 2 was the value of t in the table corresponding to 2(1-P), where P was the probability of obtaining a significant result (0,80) (Hatheway, 1961). The table value of the t distributions was obtained with degrees of freedom (DF) considering a complete random design, DF= I(r-1). The number of treatments (I) was designed as five and the replication number (r) obtained with the relationship between hill number of two rows (120) and optimum plot size (Xo). This relationship was done for each and all clones to fit the available experimental area. The statistical analysis was done considering a complete random design with total plot sampling. Mean comparisons were done with Duncan´s test. All analysis was done with the software NTIA (Embrapa, 1997) and FORTRAN language software (Abou- El-Fittouh et al., 1974) adapted to estimate mean and variance of different plot sizes.

RESULTS AND DISCUSSION
The five evaluated clones differed in yield per hill, even though the coefficient of variation was high (73.5%). The variation between the highest and the lowest yield per hill was 109.45 g hill -1 , which is equivalent to approximately 4,560 kg ha -1 ( Table 1). Considering that the experimental error was not significant, variation among hills was similar to replicate variation (total of 60 hills). Therefore, it is more important to increase the number of replications than plot size (number of basic units) to improve experimental precision.
In all experimental rows, increasing combined plot size by increasing the number of basic units reduced the coefficient of variation, the variation between maximum and minimum value as well as the ratio between maximum and minimum ( Table 2).
The parameter estimates of the functions VU(x)= V 1 /X b and CV(x)= A/ Table 1. Summary of variance analysis, clonal and trial averages and coeficient of variation for tuber yield (g hill -1 ) of five potato clones. Santa Maria-RS, UFSM, 2004. 1 Significant by the test F at 5% probability; ns not significant; 2 Clone averages not followed by the same letter differ by the Duncan´s test at 5% probability. X B and optimum plot size (Xo) varied between replications of the same clone (Table 3) and among clones (Table 4). Estimation variations among clones indicated that experimental precision was dependent upon genetic diversity. The clone 'SMINIA90244-1' had the smallest and 'SMIJ456-4Y' had the biggest optimum plot size estimations among the evaluated clones. 'SMIJ456-4Y' is the least adapted to the growing conditions and has the lowest vine vigor. The estimates of both A and B parameters of the function CV(x)= A/ X B alter optimum plot size (Oliveira, 2005) determined by the modified maximum curvature technique (Meier & Lessman, 1971). There was no differences among clones neither in origin (A) nor parallelism (B) of the function CV(x)= A/X B , but there were variation among clones in coincidence (Table 4). It happened because A and B parameters are simultaneously tested for coincidence among clones. As Xo depends on simultaneous variation of A and B parameters, the Xo estimation differed among clones.
The optimum plot size varied from four to ten hills among clones with an average of eight-hill plots ( Table 4). The optimum plot size in twelve trials with the clone 'Macaca' was seven-hill plots (Oliveira, 2005). We found the same optimum plot size as average of two replications of this clone, indicating high accuracy of the results. This experiment clearly showed that differences in plot size and/or number of replications were necessary to compare clones based upon similar experimental precision (D). However, varying plot size and/or number of replications have no practical application. Therefore, a researcher should separate clones in trials with similar plot size requirements. The adoption of optimum plot size increases experimental precision and the probability of detecting differences among clones.
In this experiment, adapted clones as 'Macaca' and 'SMINIA90244-1' had lower environmental error, resulting in higher yield precision. The evaluation of these clones together with others with high environmental error would increase the coefficient of variation and reduce experimental precision. Comparing to plot size estimations of 20 and 30 hills, respectively for potato plants growing during spring and autumn seasons (Oliveira & Estefanel, 1995), the average optimum size of eight-hill plots for five clones might be considered too small. However, the average was very close to seven-hill plots estimated for 'Macaca' in a uniform trial with 12 replications (Oliveira, 2005).
The highest experimental precision of a clone as 'SMINIA-Iporã' (D= 20.4%) can be achieved with eight-hill plots. As the experimental precision (D) depends upon the estimations of A and B parameters or the experimental arrangement (I, r, Xo, GLe), distinct Plot size variation to quantify yield of potato clones Table 2. Coefficient of variation of basic and combined plots of different size (X) of five potato clones cultivated in two rows of 60 hills. Santa Maria-RS, UFSM, 2004. Table 3. Tuber yield (g) per hill (M 1 ), parameter estimations of the functions VU(x)= V 1 /X b and CV(x)= A/X B , coeficient of determination (R 2 ) and optimum plot size estimated with the modified maximum curvature technique (Xo) of five potato clones cultivated in two rows of 60 hills. Santa Maria-RS, UFSM, 2004. Table 4. Potato tuber yield (g) per hill (M 1 ), parameter estimations of the functions VU(x)= V 1 /X b and CV(x)= A/X B , optimum plot size (Xo) and percentage of true differences among treatment means of each clone and all clones (D). Santa Maria-RS, UFSM, 2004. 1 Clones with same origin by F test at 5% probability; 2 Clones with parallelism by F test at 5% probability; 3 Clones without coincidence by F test at 5% probability.
combinations of experimental design can drastically change experimental precision. Therefore, the adoption of the same plot size (eight-hill plots) for all clones has practical applications and clone precision differences can be compensated by increasing number of replications. An area of 600 hills can be efficiently used (D= 27.4%) in an experimental arrangement of five treatments (I= 5) with 15 replications of eight-hill plots. A higher number of treatments would imply a reduction in the replication number (r) to adjust the function r= 600/(8*I). The estimation of the experimental precision (D) is necessary for each number of treatments.
The experimental precision of potato yield trial varies with the evaluated clone, because of different optimum plot sizes. Eight-hill plots are the optimum size to quantify yield of potato clones, but experimental precision depends upon adjustments of the number of treatments and replications to the availability of experimental area.