Skip to main content
Log in

On the design of early generation variety trials with correlated data

  • Published:
Journal of Agricultural, Biological, and Environmental Statistics Aims and scope Submit manuscript


This article considers the design of early generation variety trials with a prespecified spatial correlation structure and introduces a new class of partially replicated designs called p-rep designs in which the plots of standard varieties are replaced by additional plots of test lines. We show how efficient p-rep designs can be readily generated using the modified Reactive TABU search algorithm. The expected and realized genetic gain of p-rep and grid plot designs is compared in a simulation study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Atiqullah, M., and Cox, D. (1962), “The Use of Control Observations as an Alternative to Incomplete Block Designs,” Biometrika, 49, 464–471.

    MathSciNet  Google Scholar 

  • Butler, D. G., Cullis, B. R., Gilmour, A. R., and Gogel, B. J. (2003), “samm Reference Manual,” Training series, No QE02001, QLD Department of Primary Industries and Fisheries, Brisbane, QLD.

    Google Scholar 

  • Chan, B. (1999), “The Design of Field Experiments When the Data are Spatially Correlated,” PhD thesis, The University of Qld, Brisbane.

    Google Scholar 

  • Chauhan, N. (2000), “Efficient and Optimal Designs for Correlated Observations,” PhD thesis, University of Sheffield, U.K.

    Google Scholar 

  • Cochran, W. G., and Cox, G. M. (1957), Experimental Designs (2nd ed.), New York: Wiley.

    MATH  Google Scholar 

  • Coombes, N. (2002), “The Reactive Tabu Search for Efficient Correlated Experimental Designs.” PhD thesis, Liverpool John Moores University, Liverpool, U.K.

    Google Scholar 

  • Cullis, B., Lill, W., Fisher, J., and Read, B. (1989), “A New Procedure for the Analysis of Early Generation Variety Trials,” Applied Statistics, 38, 361–375.

    Article  MATH  Google Scholar 

  • Falconer, D. S. and Mackay, T. (1996), Introduction to Quantitative Genetics (4th ed.), Essex, UK: Longman Scientific and Technical.

    Google Scholar 

  • Gilmour, A. R., Cullis, B. R., and Verbyla, A. P. (1997), “Accounting for Natural And Extraneous Variation In The Analysis Of Field Experiments,” Journal of Agricultural, Biological, and Environmental Statistics, 2, 269–273.

    Article  MathSciNet  Google Scholar 

  • Glover, F. (1989), “Tabu Search—Part I,” ORSA Journal of Computing, 1, 190–206.

    MATH  MathSciNet  Google Scholar 

  • — (1990), “Tabu Search—Part II,” ORSA Journal of Computing, 2, 4–32.

    MATH  Google Scholar 

  • Kackar, R., and Harville, D. (1981), “Unbiasedness of Two-Stage Estimation and Predictions for Mixed Linear Models,” Communications in Statistics: Theory and Methods, A10, 1249–1261.

    Article  MathSciNet  Google Scholar 

  • Kempton, R. A. (1984), “The Design and Analysis of Unreplicated Field Trials,” Vortrage für Pflanzenzuchtung, 7, 219–242.

    Google Scholar 

  • Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983), “Optimization by Simulated Annealing,” Science, 220, 671–680.

    Article  MathSciNet  Google Scholar 

  • Martin, R. (1996), “Spatial Experimental Design,” in Handbook of Statistics 13: Design and Analysis of Experiments, eds. S. Ghosh and C. R. Rao, Amsterdam: Elsevier Science, pp. 477–514.

    Google Scholar 

  • Martin, R. J., and Eccleston, J. (1997), “Construction of Optimal and Near-Optimal Designs for Dependent Observations Using Simulated Annealing,” Research report 479/97, Dept. of Probability and Statistics, University of Sheffield.

  • Patterson, H. D., and Thompson, R. (1971), “Recovery of Interblock Information When Block Sizes are Unequal,” Biometrika, 31, 100–109.

    MathSciNet  Google Scholar 

  • Smith, A. B., Cullis, B. R., and Thompson, R. (2005), “The Analysis of Crop Cultivar Breeding and Evaluation Trials: An Overview of Current Mixed Model Approaches,” Journal of Agricultural Science, 143, 449–462.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to B. R. Cullis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cullis, B.R., Smith, A.B. & Coombes, N.E. On the design of early generation variety trials with correlated data. JABES 11, 381–393 (2006).

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI:

Key Words