Use of Alpha-Designs in Oil Palm Breeding Trials

Léon Rob Verdooren

doi:doi:10.11648/j.ajtas.20190804.12

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Use of Alpha-Designs in Oil Palm Breeding Trials

Léon Rob Verdooren

Published in American Journal of Theoretical and Applied Statistics (Volume 8, Issue 4)

Received: 26 June 2019 Accepted: 1 August 2019 Published: 14 August 2019

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Abstract

In Oil Palm Breeding trials the plots have palms at vertices of equilateral triangles with side length of 9 m. The plots consist of 6x6 = 36 palms, hence a plot is a rectangle of 46.8 x 54m. The number of tested varieties is 20 – 40, the experimental design needed is an incomplete block design, with usually 3 replications; the alpha-designs can give a connected incomplete block design. Current Oil Palm planting materials are DxP hybrid based on crossing selected dura palms (female parents) with pisifera palms (male parents) to produce tenera palms with thin shelled fruits. The crossing scheme of A dura and B pisifera is an incomplete diallel if he number of crossings C is smaller than A*B. To make a connected crossing scheme the alpha-design can be used. In the analysis of an oil palm breeding trial an additive model of the dura and pisifera effects is applied to estimate the general combining ability of the parents after removing the fixed replication effect and the random blocks within the replication effects. The analysis can be done with the package SAS or IBM SPSS Statistics with program Mixed; further with R and the R package lme4.

Published in	American Journal of Theoretical and Applied Statistics (Volume 8, Issue 4)
DOI	10.11648/j.ajtas.20190804.12
Page(s)	136-146
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Incomplete Block Designs, Alpha-designs, Incomplete Diallel Crossing Scheme, Use Alpha-designs for a Connected Crossing Scheme, Use SAS or IBM SPSS Statistics with Program Mixed for Analysis

References

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[2]	Caliński, T. (1971): On some desirable patterns in block designs, Biometrics, 27, 275–292.
[3]	Cochran, W. G. and Cox, G. M. (1957): Experimental Designs, second edition. John Wiley & Sons, New York, London, Sydney.
[4]	Corsten, L. C. A. (1958): Vectors, a tool in statistical regression theory. Thesis Landbouwhogeschool Wageningen, Veenman.
[5]	CycDesigN (2014): A package for the computer generation of Experimental Designs, http://www.vsni.co.uk/software/cycdesign/.
[6]	Gupta, S. S. (1965): On some multiple decision (selection and ranking) rules. Technometrics, 7, 225-245.
[7]	Kuiper, N. H. (1952): Variantie-analyse. Statistica, 6,149-194. An English translation of this Dutch article is published in 1983 as “Analysis of Variance”, Mededelingen van de Landbouwhogeschool te Wageningen, Nederland, 83 (10).
[8]	Laan, P. van der, Verdooren, L. R. (1989): Selection of Populations. An Overview and Some Recent Results. Biometrical Journal, 31, 383-420.
[9]	Patterson, H. D., Williams, E. R. (1976): A new class of resolvable incomplete block designs, Biometrika, 63, 83–92.
[10]	Patterson, H. D., Williams, E. R. and Hunter, E. A. (1978): Block designs for variety trials. Journal of Agricultural Science, Cambridge, 90, 395-400.
[11]	Patterson, H.. D, Silvey, V. (1980): Statutory and recommended list trials of crop varieties in the United Kingdom (with discussion). J R Stat Soc A, 143, 219–252.
[12]	Verdooren, Rob; Soh, Aik Chin and Roberts, Jeremy (2017): Field Experimentation, Chapter 12 in Soh, Aik Chin, Mayes, Sean and Roberts, Jeremy (editors): Oil Palm Breeding, Genetics and Genomics. Taylor & Francis Group, CRC Press, Boca Raton.
[13]	Williams, E. R. (1977): Iterative analysis of generalized lattice designs. Aust J Stat, 19, 39–42.
[14]	Stevens, W. L. (1948): Statistical analysis of a non-orthogonal tri-factorial experiment. Biometrika, 35, 346-367.

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Léon Rob Verdooren. (2019). Use of Alpha-Designs in Oil Palm Breeding Trials. American Journal of Theoretical and Applied Statistics, 8(4), 136-146. https://doi.org/10.11648/j.ajtas.20190804.12

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ACS Style

Léon Rob Verdooren. Use of Alpha-Designs in Oil Palm Breeding Trials. Am. J. Theor. Appl. Stat. 2019, 8(4), 136-146. doi: 10.11648/j.ajtas.20190804.12

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Léon Rob Verdooren. Use of Alpha-Designs in Oil Palm Breeding Trials. Am J Theor Appl Stat. 2019;8(4):136-146. doi: 10.11648/j.ajtas.20190804.12

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@article{10.11648/j.ajtas.20190804.12,
  author = {Léon Rob Verdooren},
  title = {Use of Alpha-Designs in Oil Palm Breeding Trials},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {8},
  number = {4},
  pages = {136-146},
  doi = {10.11648/j.ajtas.20190804.12},
  url = {https://doi.org/10.11648/j.ajtas.20190804.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190804.12},
  abstract = {In Oil Palm Breeding trials the plots have palms at vertices of equilateral triangles with side length of 9 m. The plots consist of 6x6 = 36 palms, hence a plot is a rectangle of 46.8 x 54m. The number of tested varieties is 20 – 40, the experimental design needed is an incomplete block design, with usually 3 replications; the alpha-designs can give a connected incomplete block design. Current Oil Palm planting materials are DxP hybrid based on crossing selected dura palms (female parents) with pisifera palms (male parents) to produce tenera palms with thin shelled fruits. The crossing scheme of A dura and B pisifera is an incomplete diallel if he number of crossings C is smaller than A*B. To make a connected crossing scheme the alpha-design can be used. In the analysis of an oil palm breeding trial an additive model of the dura and pisifera effects is applied to estimate the general combining ability of the parents after removing the fixed replication effect and the random blocks within the replication effects. The analysis can be done with the package SAS or IBM SPSS Statistics with program Mixed; further with R and the R package lme4.},
 year = {2019}
}

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TY  - JOUR
T1  - Use of Alpha-Designs in Oil Palm Breeding Trials
AU  - Léon Rob Verdooren
Y1  - 2019/08/14
PY  - 2019
N1  - https://doi.org/10.11648/j.ajtas.20190804.12
DO  - 10.11648/j.ajtas.20190804.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 136
EP  - 146
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20190804.12
AB  - In Oil Palm Breeding trials the plots have palms at vertices of equilateral triangles with side length of 9 m. The plots consist of 6x6 = 36 palms, hence a plot is a rectangle of 46.8 x 54m. The number of tested varieties is 20 – 40, the experimental design needed is an incomplete block design, with usually 3 replications; the alpha-designs can give a connected incomplete block design. Current Oil Palm planting materials are DxP hybrid based on crossing selected dura palms (female parents) with pisifera palms (male parents) to produce tenera palms with thin shelled fruits. The crossing scheme of A dura and B pisifera is an incomplete diallel if he number of crossings C is smaller than A*B. To make a connected crossing scheme the alpha-design can be used. In the analysis of an oil palm breeding trial an additive model of the dura and pisifera effects is applied to estimate the general combining ability of the parents after removing the fixed replication effect and the random blocks within the replication effects. The analysis can be done with the package SAS or IBM SPSS Statistics with program Mixed; further with R and the R package lme4.
VL  - 8
IS  - 4
ER  -

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Author Information

Léon Rob Verdooren

Danone Nutricia Research, Utrecht, The Netherlands

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Léon Rob Verdooren. (2019). Use of Alpha-Designs in Oil Palm Breeding Trials. American Journal of Theoretical and Applied Statistics, 8(4), 136-146. https://doi.org/10.11648/j.ajtas.20190804.12

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ACS Style

Léon Rob Verdooren. Use of Alpha-Designs in Oil Palm Breeding Trials. Am. J. Theor. Appl. Stat. 2019, 8(4), 136-146. doi: 10.11648/j.ajtas.20190804.12

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AMA Style

Léon Rob Verdooren. Use of Alpha-Designs in Oil Palm Breeding Trials. Am J Theor Appl Stat. 2019;8(4):136-146. doi: 10.11648/j.ajtas.20190804.12

Copy | Download

@article{10.11648/j.ajtas.20190804.12,
  author = {Léon Rob Verdooren},
  title = {Use of Alpha-Designs in Oil Palm Breeding Trials},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {8},
  number = {4},
  pages = {136-146},
  doi = {10.11648/j.ajtas.20190804.12},
  url = {https://doi.org/10.11648/j.ajtas.20190804.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190804.12},
  abstract = {In Oil Palm Breeding trials the plots have palms at vertices of equilateral triangles with side length of 9 m. The plots consist of 6x6 = 36 palms, hence a plot is a rectangle of 46.8 x 54m. The number of tested varieties is 20 – 40, the experimental design needed is an incomplete block design, with usually 3 replications; the alpha-designs can give a connected incomplete block design. Current Oil Palm planting materials are DxP hybrid based on crossing selected dura palms (female parents) with pisifera palms (male parents) to produce tenera palms with thin shelled fruits. The crossing scheme of A dura and B pisifera is an incomplete diallel if he number of crossings C is smaller than A*B. To make a connected crossing scheme the alpha-design can be used. In the analysis of an oil palm breeding trial an additive model of the dura and pisifera effects is applied to estimate the general combining ability of the parents after removing the fixed replication effect and the random blocks within the replication effects. The analysis can be done with the package SAS or IBM SPSS Statistics with program Mixed; further with R and the R package lme4.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Use of Alpha-Designs in Oil Palm Breeding Trials
AU  - Léon Rob Verdooren
Y1  - 2019/08/14
PY  - 2019
N1  - https://doi.org/10.11648/j.ajtas.20190804.12
DO  - 10.11648/j.ajtas.20190804.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 136
EP  - 146
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20190804.12
AB  - In Oil Palm Breeding trials the plots have palms at vertices of equilateral triangles with side length of 9 m. The plots consist of 6x6 = 36 palms, hence a plot is a rectangle of 46.8 x 54m. The number of tested varieties is 20 – 40, the experimental design needed is an incomplete block design, with usually 3 replications; the alpha-designs can give a connected incomplete block design. Current Oil Palm planting materials are DxP hybrid based on crossing selected dura palms (female parents) with pisifera palms (male parents) to produce tenera palms with thin shelled fruits. The crossing scheme of A dura and B pisifera is an incomplete diallel if he number of crossings C is smaller than A*B. To make a connected crossing scheme the alpha-design can be used. In the analysis of an oil palm breeding trial an additive model of the dura and pisifera effects is applied to estimate the general combining ability of the parents after removing the fixed replication effect and the random blocks within the replication effects. The analysis can be done with the package SAS or IBM SPSS Statistics with program Mixed; further with R and the R package lme4.
VL  - 8
IS  - 4
ER  -

Copy | Download