Interest of spatial methods for VCUS trials to the evaluation of … S... · 2018. 7. 2. · Saisissez votre texte Saisissez votre texte Interest of spatial methods for VCUS trials

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Interest of spatial methods for VCUS trials to

the evaluation of sugar beet varieties for their

registration in the French national catalog

06/27/2018

S.Daudé, S.Lassalvy, B.Richard, F.Masson



Acknowlegdements

F. Piraux – Arvalis Institut du Végétal

C. Pontet – Terres Inovia

J. Adrian – ITB (Institut Technique de la Betterave)



Plan

I) Introduction

1.1. Context

1.2. Aim of study

II) Materials & Methods

2.1. Designs of field trials

2.2. Mixed models

2.3. Data, selected models & software used.

III) Results & Discussion

3.1. Tables of statistics

3.2. Maps

3.3. Variograms

IV) Conclusion

4.1. In a nutshell

4.2. Prospects

1/19



Context

Optires Project :

- 2 years project

- Financed by the French Ministry of Agriculture

- Led by GEVES, partner institutes : INRA, Arvalis Institut du Végétal

Terres Inovia, Institut Technique de la Betterave

- Better control of soil heterogeneity with spatial methods

Current statistical methods may have difficulties to handle some types of soil heterogeneities

In this case, precision is inadequate and trials are not selected

Situations that may produce heterogeneity in sugar beet trials : Diseases like rhizomania and nematods

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Aim of study

Assess the interest of spatial analysis that could be used at CTPS for the

evaluation of variety trials

Make a choice of spatial methods

Assess the benefit compared to current methods used at GEVES

Offer R scripts of analysis

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Designs of field trials

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Mixed models

Block Model

𝑌 = 𝝁 + 𝑮𝒆𝒏 + 𝑅𝑜𝑤𝐵𝑙𝑘 + 𝜀

Latinized Alpha Design

𝑌 = 𝝁 + 𝑮𝒆𝒏 + 𝑅𝑜𝑤𝐵𝑙𝑘 + 𝐶𝑜𝑙𝐵𝑙𝑘 + 𝑅𝑜𝑤𝐵𝑙𝑘 ∗ 𝐶𝑜𝑙𝐵𝑙𝑘 + 𝜀

Spatial Model (from Gilmour et al., 1997)

𝑌 = 𝝁 + 𝑮𝒆𝒏 + 𝑅𝑜𝑤𝐵𝑙𝑘(+𝐶𝑜𝑙𝐵𝑙𝑘)(+𝜂) + 𝜉

5/19



Data, selected models & software used

Dataset of 9 VCUS sugar beet trials of 2016, including 44 varieties each

Response variable : root yield

Spatial correlation structures applied on residuals : AR1 x I, AR2 x I, AR1 x AR1, AR2 x AR1

Microsoft R Open software, with asreml, asremlPlus and agridat packages

6/19



Evaluation Criterion

AIC (Akaike’s Information Criterion)

𝐴𝐼𝐶 = 2𝑘 − 2 ln(𝐿)

Residual Standard Deviation computed with the mean of standard error of

difference

𝑅𝑆𝐷𝑆𝐸𝐷 =𝑆𝐸𝐷2 × 𝑁𝑏𝑙𝑜𝑐𝑘

2

7/19



Best models for each trial of the dataset

(in terms of AIC)

Trial 9011462 9011463 9011464 9011465 9011466 9011467 9011469 9011471 9011472

AR2+nugget (477,27) AR2 (494,25) AR1_RC (525,33)

BlockModelRC(601,55)

AR2xAR1 (454,40)

AR1xAR1+nugget (568,70)

AR2xAR1_RC

(496,24)AR1

(567,22) AR2 (693,19)

Top 3AR1+nugget

(477,71)AR2xAR1 (494,37)

AR1_RC+nugget (526,87) LAP (601,72)

AR2_RC (455,15)

AR1+nugget (570,76)

AR1xAR1_RC

(496,29)AR2

(568,14)AR2xAR1 (694,09)

AR2_RC+nugget (478,68)

AR2_RC (495,20) AR2_RC (526,95)

AR1_RC (602,29) AR2 (455,57) AR1_RC (571,11)

AR2xAR1 (497,05)

AR1+nugget (568,24)

AR2+nugget (694,55)

APL 482,36 519,54 549,01 601,72 457,9 573,05 519,25 591,23 703,81

Bloc simple 523,58 520,84 572,72 637,29 472,8 637,96 558,06 595,06 706,38

Model Number of selections

AR1 2

AR2 3

AR1 x AR1 1

AR2 x AR1 2

LAP/BlockModel_RC 1

8/19



Best models for each trial of the dataset

(in terms of AIC)

Trial 9011462 9011463 9011464 9011465 9011466 9011467 9011469 9011471 9011472

AR2+nugget (477,27) AR2 (494,25) AR1_RC (525,33)

BlockModelRC(601,55)

AR2xAR1 (454,40)

AR1xAR1+nugget (568,70)

AR2xAR1_RC

(496,24)AR1

(567,22) AR2 (693,19)

Top 3AR1+nugget

(477,71)AR2xAR1 (494,37)

AR1_RC+nugget (526,87) LAD (601,72)

AR2_RC (455,15)

AR1+nugget (570,76)

AR1xAR1_RC

(496,29)AR2

(568,14)AR2xAR1 (694,09)

AR2_RC+nugget (478,68)

AR2_RC (495,20) AR2_RC (526,95)

AR1_RC (602,29) AR2 (455,57) AR1_RC (571,11)

AR2xAR1 (497,05)

AR1+nugget (568,24)

AR2+nugget (694,55)

LAD 482,36 519,54 549,01 601,72 457,9 573,05 519,25 591,23 703,81

Bloc simple 523,58 520,84 572,72 637,29 472,8 637,96 558,06 595,06 706,38

Model Number of selections

AR1 2

AR2 3

AR1 x AR1 1

AR2 x AR1 2

LAD/BlockModel_RC 1

9/19



Statistics table of trial n°11465

Modèle logREML AIC ETR Gain/perte ETR rho.c pvalue.Variety rho.c1 rho.c2 rho.r

BlockModelRC -297,77 601,55 5,07 0,52% NA 0,00 NA NA NA

LAP -296,86 601,72 5,05 0,00% NA 0,00 NA NA NA

AR1_RC -297,33 602,67 5,01 -0,64% -0,12 0,00 NA NA NA

AR2_RC -297,08 604,16 5,02 -0,48% NA 0,00 -0,07 0,10 NA

AR1xAR1_RC -297,33 604,67 5,01 -0,65% -0,12 0,00 NA NA 0,00

AR2xAR1_RC -297,07 606,14 5,02 -0,46% NA 0,00 -0,06 0,10 0,02

AR2xAR1 -301,23 612,46 5,06 0,30% NA 0,00 0,18 0,36 0,24

AR2 -303,16 614,32 5,18 2,61% NA 0,00 0,19 0,38 NA

AR1xAR1 -307,37 622,73 5,37 6,37% 0,32 0,00 NA NA 0,29

AR1 -310,77 627,55 5,59 10,69% 0,37 0,00 NA NA NA

BlockModel -316,64 637,29 6,17 22,20% NA 0,00 NA NA NA

10/19



Statistics table of trial n°11471

Modèle logREML AIC ETR Gain/perte ETR rho.c pvalue.Variety rho.c1 rho.c2 rho.r

AR1 -280,61 567,22 3,41 -16,44% 0,55 0,00 NA NA NA

AR2 -280,07 568,14 3,47 -14,87% NA 0,00 0,47 0,11 NA

AR1+nugget -280,12 568,24 3,46 -15,10% 0,66 0,00 NA NA NA

AR1xAR1 -280,52 569,05 3,41 -16,46% 0,54 0,00 NA NA 0,05

AR1_RC -280,61 569,22 3,41 -16,44% 0,55 0,00 NA NA NA

AR2xAR1 -280,03 570,07 3,47 -14,95% NA 0,00 0,47 0,11 0,03

AR2+nugget -280,07 570,14 3,47 -14,87% NA 0,00 0,47 0,11 NA

AR2_RC -280,07 570,14 3,47 -14,87% NA 0,00 0,47 0,11 NA

AR1xAR1+nugget -280,07 570,15 3,46 -15,13% 0,65 0,00 NA NA 0,05

AR1_RC+nugget -280,12 570,24 3,46 -15,10% 0,66 0,00 NA NA NA

AR1xAR1_RC -280,52 571,05 3,41 -16,46% 0,54 0,00 NA NA 0,05

AR2xAR1+nugget -280,03 572,07 3,47 -14,95% NA 0,00 0,47 0,11 0,03

AR2xAR1_RC -280,03 572,07 3,47 -14,95% NA 0,00 0,47 0,11 0,03

AR2_RC+nugget -280,07 572,14 3,47 -14,87% NA 0,00 0,47 0,11 NA

AR1xAR1_RC+nugget -280,07 572,15 3,46 -15,13% 0,65 0,00 NA NA 0,05

AR2xAR1+nugget_RC -280,03 574,07 3,47 -14,95% NA 0,00 0,47 0,11 0,03

BlockModelRC -291,62 589,23 4,08 0,00% NA 0,00 NA NA NA

LAP -291,62 591,23 4,08 0,00% NA 0,00 NA NA NA

BlockModel -295,53 595,06 4,29 5,16% NA 0,00 NA NA NA

11/19



Maps of trial 11465

LAD residualsDeviation to the adjusted mean

AR1 residuals

12/19



Maps of trial 11471

Deviation to the adjusted mean

LAD residuals AR1 residuals

13/19



Experimental variograms of trial

11465

LAD AR1

14/19



Experimental variograms of trial 11471

LAD AR1

15/19



Adjusted variograms of

trials 11465 and 11471 for the

AR1 model

Trial 11465 Trial 11471

16/19



« Enveloped » variograms of

trials 11465 and 11471 for the

AR1 modelFrom Stefanova et al. 2009

Trial 11465 Trial 11471

17/19



In a nutshell

Spatial methods are more precise and handle better with heterogeneity than current methods

Choice of spatial methods : Specific conditions of soil heterogeneity

If gradients are well controlled by the repetitions : choice of LAD instead of spatial models

Uni or bi directional approach ? It depends on the trial’s shape

18/19



Prospects

Apply the methods to a larger number of datasets and different species

Test separability hypothesis comparing directional variograms

Test more spatial methods

Selection of models algorithm

18/18



Thank you for your

attention

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Interest of spatial methods for VCUS trials to the evaluation of … S... · 2018. 7. 2. · Saisissez votre texte Saisissez votre texte Interest of spatial methods for VCUS trials