Exploring specific combining abili�es

in incomplete factorial cross designs withLABKEY�� so�ware

Soula, Julie¹*; Vincourt, Patrick²; Bernard, Jean-Marc³; Bardet, Sébas�en¹; Royer, Frédéric³1 Doriane SAS, 31 avenue Jean Médecin, 06000 Nice, France ; 2 Open-Source-Biology, 12 avenue V. Segoffin, 31400 Toulouse, France ; 3 Biosearch Data Management, 39 boulevard Dubouchage, 06000 Nice, France

Results and discussionThe first two components of SCA are accoun�ng for the major part of the {female * male} interac�on (55% of the total variance): see Figure 1. Based on these first two components,

2there is a good adequacy (R = 0.68) between the observed and calculated SCA for observed combina�ons, as shown in Figure 2. We therefore propose to use the same predictor for unobserved combina�ons. In this way, we obtain a table of (posi�ve and nega�ve) predicted interac�ons: see Figure 3.

TMUsing the crosses matrix available in LABKEY , it is possible to display all the informa�on on the parents and on the hybrids (crosses done, predic�ons for the non-observed combina�ons) to help the breeder to choose his future crosses and to automa�cally

TMgenerate them in LABKEY : see Figure 4.As pointed out by Technow et al. (2014), hybrid breeders are o�en tes�ng the combining ability with a limited number and range of testers, thus limi�ng the possibility to explore a wider range of combina�on for the detec�on of par�cular hybrid combina�on. This example shows how, with the same investment in hybrid produc�on and experimenta�on, it becomes possible to explore a wider space of gene�c diversity and to propose inferences for unobserved combina�ons.

References 1. Soula J, Duminil T, Bardet S, Bernard JM, Royer F (2014) Considera�on Of Field Heterogenei�es In The Calcula�on Of Variety Means From Agronomic Trial Data:

Comparisons Between A Nearest Neighbor Adjustment Method And Experimental Designs Like La�ces And La�nized Alpha-Designs. Plant Animal genome Conf., San Diego 2. Technow F, Schrag TA, Schipprack W, Bauer E, Simianer H, Melchinger AE. (2014) Genome Proper�es and Prospects

of Genomic Predic�on of Hybrid Performance in a Breeding Program of Maize. GENETICS 197 (4): 1343-135 3. Yates F. (1933). The analysis of replicated experiments whenthe field results are incomplete. Emp. Jour. Exp. Agr. 1, 129-142

Introduc�onOne of the biggest challenges for plant breeders is to deal with interac�ons. Par�cularly, they aim at iden�fying which {female * male} combina�on is offering the most promising specific combining ability (SCA). A�er the pioneer works of Tukey (1949) and Mandel (1971), the AMMI (for “Addi�ve main effects and mul�plica�ve interac�on”) framework became very popular during the last decade. Based on a prac�cal example

TManalyzed using LABKEY , this study is intending to show how this so�ware is providing the users with tools helping them to predict and display specific combining abili�es (SCA) for non-observed hybrid combina�ons. These predic�ons are made using Principal Component Analysis (PCA) results obtained on the observed crosses, under the hypothesis that they represent a connected, unbiased subset of the complete set of possible combina�ons.

General FrameworkThe AMMI approach is modeling the result of the combina�on of two factors (Female and Male, herea�er named I and J) as the sum of addi�ve, main effects and of mul�plica�ve effects of both factors, those being actually calculated through a PCA on interac�on es�mates:

Where m is the grand mean, a and b are the main, addi�ve effects of the factors I and J, i j

and ab represents their interac�on: c and d are the coordinates of the component k of ij ik jkththe interac�on, and U is the k component eigenvalue.k

Material & Method25 female lines were crossed with 8 male lines to produce 90 hybrids, i.e. with a high propor�on of missing data. Each female line was crossed with a minimum of two male lines. Interac�ons between male and female parents (= SCA) were obtained in subtrac�ng the es�mates of addi�ve effects of the male parent and of the female parent from the

TMobserved yield. In the LABKEY so�ware, these es�mates are obtained through Yates' (Yates, 1933) method of es�ma�on of missing data, a method which implicitly assumes a null interac�on between the unobserved {female parent * male parent} combina�ons. These es�mates are also those produced by the LSMEANS statement of the GLM procedure under SAS© with a model including only addi�ve effects. PCA was performed on the FxM interac�on es�mates and we then used the SCA components on the first principal components to predict the SCA for unobserved combina�ons.

« With the same investment [..], explore a wider space of gene�c diversity and propose inferences for unobserved combina�ons. »

ConclusionLABKEY�� is currently developing tools to help breeders in their aim to deal with various types of interac�on. This study shows an example dealing with Female x Male interac�ons and mainly using two LABKEY�� tools, the PCA and the crosses matrix, configured to compute and display SCA predic�ons for a subset of non-observed hybrids.

Figure 1 (le�): Male and female parents on the first two principal components [graphs TMobtained with LABKEY so�ware].

Figure 2 (right): Modeling the specific combining abili�es (SCA): the first two components are

accoun�ng for 68% of the SCA varia�on on observed combina�ons [graph obtained with R so�ware].

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PCA Axis 1 : 30,74 %

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PCA Axis 2 : 24,39 %

FAN

FASHION

FAST

FATE

FEBRUARYFELIXFIDJI

FIRST FISH

FJORDFLAME

FLAMENCO

FLORAFLOWER

FLUOR

FOG

FORK

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FOX

FREE

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FUN

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C0100---MILK

C0100---MISTER

C0100---MEGA

C0100---MILES

C0100---MAD

C0100---MAGNET

C0100---MAGIC

C0100---MICRO

Figure 3: Predicted interac�on values using the first two principal components. Black: Predicted interac�on

values for tested hybrids. Red (nega�ve), green (posi�ve): predicted interac�on values for non tested hybrids. Grey: General Combining Abili�es (GCA). [Report generated from LABKEY�� so�ware].

MAD MAGIC MAGNET MEGA MICRO MILES MILK MISTER GCA - F FAN -1,36 0,37 -1,09 2,56 1,01 -1,83 1,73 -1,38 2,49

FASHION -0,04 0,03 -0,1 0,17 -0,01 -0,18 0,16 -0,03 -0,86 FAST -1,26 -0,07 0,45 0,19 1,9 1,15 -0,8 -1,55 -4,27 FATE 0,03 0,04 -0,15 0,2 -0,13 -0,29 0,24 0,06 1,88

FEBRUARY -0,89 0,01 0,09 0,47 1,18 0,36 -0,19 -1,05 6,16 FELIX 0,57 -0,07 0,17 -0,64 -0,62 0,2 -0,25 0,64 -2,53 FIDJI -0,08 -0,02 0,07 -0,06 0,15 0,16 -0,12 -0,1 0,54 FIRST 6,89 -0,75 1,61 -7,1 -7,66 1,66 -2,33 7,69 2,11 FISH -0,5 0,12 -0,34 0,85 0,4 -0,56 0,54 -0,51 -1,00

FJORD 0,77 0,18 -0,74 0,58 -1,47 -1,61 1,26 1,04 -2,74 FLAME -0,15 0,18 -0,63 1,04 -0,22 -1,19 1,03 -0,06 -2,69

FLAMENCO 0,41 0,17 -0,66 0,7 -0,96 -1,37 1,1 0,61 -3,51 FLORA 1,06 -0,13 0,29 -1,16 -1,15 0,34 -0,43 1,18 8,82

FLOWER -0,06 -0,02 0,08 -0,08 0,14 0,17 -0,14 -0,09 3,11 FLUOR 0,11 -0,39 1,37 -2,12 0,77 2,65 -2,25 -0,13 6,33

FOG -0,03 0,11 -0,37 0,57 -0,2 -0,71 0,61 0,03 -6,00 FORK 1,22 -0,49 1,56 -3,16 -0,5 2,78 -2,51 1,11 -0,36

FOSSIL -3,82 -0,75 3,22 -2,22 6,98 7,12 -5,49 -5,05 3,71 FOX 0,47 0,56 -2,06 2,76 -1,96 -4,12 3,42 0,94 -5,00

FREE 0,01 0 0 -0,01 -0,01 0 0 0,01 -7,10 FRESH 2,09 0,11 -0,7 -0,37 -3,12 -1,83 1,26 2,56 -2,41 FRIEND -3,04 0,65 -1,83 4,81 2,63 -2,93 2,88 -3,17 -0,85

FUCHSIA -0,02 -0,46 1,62 -2,41 1,1 3,16 -2,67 -0,33 4,54 FUN -2,23 0,61 -1,82 4,24 1,61 -3,08 2,9 -2,24 -3,21

FURY -0,16 0,02 -0,05 0,18 0,17 -0,06 0,07 -0,17 2,83

GCA - M -2,30 1,67 4,25 1,24 2,04 -2,63 -3,40 -0,87

TM Figure 4: Genera�on of new crosses in LABKEY (picture on the bo�om right) from the crosses

matrix (background picture). The GCA of the parents is always displayed whereas the predicted SCA for non tested hybrids (tested hybrids are in grey) are displayed on the tool�p. Hybrids for which the SCA predic�on is larger than 0.5 or smaller than -0.5 are highlighted by colored squares: red colors for nega�ve predic�ons and green colors for posi�ve predic�ons.

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Observed interaction values