Cucurbit Genetics Cooperative Report 9:4446 (article 12) 1986
Optimum Allocation of Plots into Years, Seasons, Locations and Replications for OnceOver Harvest Trials of Cucumber
Todd C. Wehner
Department of Horticultural Science, North Carolina State University, Raleigh, NC 276957609
William H. Swallow
Department of Statistics, North Carolina State University, Raleigh, NC 276058203
This research was supported by a grant from the North Carolina Pickle Producers Association
Many cucumber breeders test large numbers of lines before discarding them or releasing them as cultivars. Lines that perform well over a wide range of environmental conditions are useful to growers and seed companies, because such lines have a high probability of being useful in future (untested) years, and in many production areas. Since, it is possible to test lines in trials over years, seasons, locations, and replications, the question arises as to the most efficient way to distribute resources in the planning of trials. The question of optimum sample size has been recently reviewed (5).
Optimum sample size and distribution has been examined for nested designs (2), and for crossed designs with tobacco (1), cotton (3) and maize (4). Generally, it was concluded that additional locations and years were more efficient in providing cultivar performance data than additional replications within locations or years.
Data analysis.
Cucumbers were grown in 2 years (1984, 1985), 3 seasons (spring, summer, fall), 4 north Carolina locations (Clayton, Clinton, Castle Hayne, and stress conditions of low fertilizer,irrigation and pest control) and 2 replications. Twentytwo genotypes in each of 2 crop types (pickle, slicer) were grown. The genotypes represented a diverse sample of available cultivars and lines (gynoecious vs. monoecious, dwarf vs. tall, indeterminate vs. determinate, disease resistant vs. susceptible, hybrid vs. inbred, adapted to southern vs. northern U.S.A., newly released vs. outdated).
Cucumbers were harvested onceover when the check plots ('Calypso' and 'Poinsett 76') had 10% oversized fruits. Data were collected on total fruit number, and average fruit quality (scored 1 to 9, where 1=poor, 5=average, 9=excellent).
The variance for a genotype mean can be expressed as an equation (A).
(A) Vx =

σ ^{2}GY
______
y 
+ 
σ ^{2}GS
______
s 
+ 
σ ^{2}GL
_______
1 
+ 
σ ^{2}GYS
______
ys 
+ 
σ ^{2}GYL
_______
ys 
+ 
σ ^{2}GSL
_______
sl 
+ 
σ ^{2}GYSL
______
ysl 
+ 
σ ^{2}e
______
rysl 
For data collected over y years, s seasons, l locations, r replications and g genotypes, with all factors viewed as random.
For each crop type, the variance components for total yield and average quality score were estimated (Table 1) using Type I estimates from the V ARCOMP procedure of the Statistical Analysis System (SAS Institute, Cary,North Carolina).
Table 1. Estimates of variance components for effects of genotype and environment.

Variance component ________________________________________________________________________________________________________ 

Crop and Variable 
σ ^{2}_{GY} 
σ ^{2}_{GS} 
σ ^{2}_{GL} 
σ ^{2}_{GYS} 
σ ^{2}_{GYL} 
σ ^{2}_{GSL} 
σ ^{2}_{GYSL} 
σ ^{2}_{e} 
Pickle 








Yield

17.13 
0.025 
2.60 
11.92 
3.07 
8.20 
15.58 
67.64 
Quality

0.020 
0.035 
0.0165 
0..013 
0.045 
0.061 
0.033 
0.821 
Slicer 








Yield

11.65 
7.79 
2.83 
6.67 
3.71 
6.89 
6.58 
64.20 
Quality

0.009 
0.099 
0.017 

0.011 
0.013 
0.141 
0.741 
Estimated variances of genotype means were calculated for each of 5 designs (combinations of y, s, l, and r), using equation (A) with the variance components replaced by their estimated values. The basic design took y=s=1=r=2. The other designs increased, in turn, the number of levels of one factor to 3, while holding the others at 2. We then compared the estimated variances of a genotype mean across designs in order to provide insight on the relative benefit (variance reduction) of increased allocation of resources in one direction or another.
Results.
Comparing estimated variances of genotype means across the designs (Table 2) showed that the response was similar for pickling and slicing cucumber lines. The following conclusions can be made. If total yield is of principal interest, allocating resources in favor of more years will be most beneficial in reducing the variance of a genotype mean. Increasing the number of replications will be least effective. If increasing the number of years is impractical, increasing the number of seasons is second best, followed by locations. If average quality is considered instead, increasing number of seasons of data collection will produce the greatest benefits.
Considering yield and quality together for either pickling or slicing cucumbers, the best allocation of resources is to use tests over years and/or seasons, rather than locations or replications. For initial testing in a breeding program, it would be easiest to use a spring and simmer (or fall) test to sample the effect of seasons. Tests over years would be better mainly for advanced lines, since additional years of testing in early stages will slow the progress in a breeding program.
Table 2. Estimated variances of genotype means for total yield and average quality score of pickles and slicers using 5 designs for performance trials^{Z}.
Model 
Total yield 
Average quality 
Increased 
r 
l 
s 
y 
Pickle 
Slicer 
Pickle 
Slicer 
Base 
2 
2 
2 
2 
19.4 
20.3 
0.076 
0.108 
Reps 
3 
2 
2 
2 
18.0 
19.0 
0.059 
0.093 
Locations 
2 
3 
2 
2 
16.8 
17.3 
0.059 
0.090 
Seasons 
2 
2 
3 
2 
15.6 
16.2 
0.048 
0.070 
Years 
2 
2 
2 
3 
13.2 
15.9 
0.059 

^{Z} Variances estimated for trials run with r replications, 1 locations, s seasons and y years (using 2 of each for the base model).
Literature Cited
 Jones, G.L. D.F. Matzinger and W.K. Collins. 1960. A comparison of fluecured tobacco varieties repeated over locations and years with implications on optimum plot allocation. Agron. J. 52: 195199.
 Marcuse, S. 1949. Optimum allocation and variance components in nested sampling with an application to chemical analysis. Biometrics 5: 198206.
 Miller, P.A., J.C. Williams and H.F. Robinson. 1959. Variety X environment interactions in cotton variety tests and their implications on testing methods. Agron J. 51: 132134.
 Sprague, G.F. and W.T. Federer. 1951. A comparison of variance components in corn yield trials: II. Error, year X variety, location X variety, and variety components. Agron. J. 43: 535541.
 Trout, J.R. and R.P. Marini. 1984. Estimating sample size to achieve efficient experiment designs. HortScience 19: 355358.