The Implementation of AMMI (Additive Main Effect and Multiplicative Interaction) Method for Determination of Potato Varieties Specific Location
Atiek Iriany
1). Statistics Department, University of Brawijaya
Aniek Iriany
2). Agrotechnology Department, Faculty of Agriculture, Muhammadiyah University of Malang, Indonesia
Email of the Corresponding Author:
atiekiriany@yahoo.com: aniek55@yahoo.co.id
Abstract
Additive Main Effect and Multiplicative Interaction (AMMI) is a mixed method of analysis of variance (ANOVA) for the main effect and principal component analysis (PCA) for the interaction effect. AMMI model formed on potato production data is AMMI1 model. The variance of interactions that can be explained by AMMI1 model is 94.01%. The result of analysis indicates that Granola Germany variety (V3) is the most stable genotype. Granola Korea variety (V5) is specific to Ngadiwono (L4), Granola Flower variety (V1) and Granola Holland (V2) are specific to Tulungrejo (L1) and Sumberbrantas (L3), Granola Germany variety (V3) is specific to Jurang Kuali (L2), Granola Local variety (V4) and Granola Australia (V6) are specific to Sumber (L5).
Keywords: AMMI1, Genotype
1. INTRODUCTION
In general, trial of yield is conducted with multi location trials, namely testing a number of varieties of potatoes in several locations. The results of multi location trials are expected to determine varieties of potatoes with specific yield to a particular location and stable in all locations.
The statistical analysis applied to the multi location trials is analysis of variance (ANOVA). Analysis of variance is a method to test the main effect and interaction effect, but it can not explain the interaction effect. To be able to explain the interaction effect, principal component analysis is used. However, principal component analysis is only able to describe interaction effect but is unable to examine the main effect. Since both analyses still have weaknesses, AMMI (Additive Main Effects and Multiplicative Interaction) method, a method that is able to test the main effect and interaction as well as explain the simultaneous interaction effect is used. AMMI is a multivariate method often used in plant breeding research to describe the interaction of genotype and location (Hadi and Halimatus, 2004).
2. LITERATURE REVIEW
In conducting the analysis of variance, the assumptions in the analysis of variance should be fulfilled. Assumptions in analysis of variance are additive effect, homogeneity of error variance, error normality, and independence of error. Furthermore, a mixed analysis of variance can be done if the assumptions are met. The effect of genotype interactions with real locations can be continued with AMMI analysis. AMMI analysis model is as follows (Mattjik and Sumertajaya, 2006):
= α_{i} _{j}_{ }+
The step in AMMI in modeling is arranging interaction effects in the form of a matrix in which the genotype (row) x location (column), and the order of the matrix is g x l.
(αβ) =
Biliner decomposition on the matrix of interaction effect.
(αβ)_{ij} =
= + . . . + +
According to Mattjik (1998), if the analysis of variance is performed on the mean data of each genotype and location, the sum of squares for nth component interaction effect is the nth root trait (). If analysis of variance is performed on the data origin, the sum of squares of n–th component interaction effect is .
3. RESEARCH METHODS
3.1 Source of the Data
The data used is primary data from the research results () about the result of multilocation trials in potato crop yield. There are 6 potato varieties used in the experiment is namely Granola Flower (V1), Granola Holland (V2), Granola Germany (V3), Granola Local (V4), Granola Korea (V5) and Granola Australia (V6). There are 5 locations used by 5 in this research, they are Tulungrejo (L1), Jurang Kuali (L2), Sumberbrantas (L3), Ngadiwono (L4) and Sumber (L5).
3.2 Analysis Method
Steps in AMMI analysis are as follows: (1) Conducting mixed analysis of variance, and when the effect of interaction is real, it is continued with AMMI analysis. (2) Singular value Decomposition (SVD) on matrix of interaction effect. (3) Calculating the sum of squares of each KUI. (4) Analysis of variance of AMMI model to determine the real KUI. (5) Making a biplot and calculating ASV for the interpretation of AMMI model.
4. RESULTS AND DISCUSSION
4.2 AMMI Analysis
The number of real PCI (Principle Component of Interaction) axes based on postdictive success method is 1, namely PCI_{1}. AMMI model being formed is AMMI1 model. The contribution of variance of interaction that can be explained by AMMI1 model is 94.01%. The Analysis of variance of AMMI1 model is presented in Table 4.
Table 4. The Analysis of variance of AMMI1
Source of Variance

Degrees of Freedom

Sum of Squares

Central Squares

F_{calculate}

Pvalues

Varieties

5

776.84

155.3 7

45.36

0.000

Location

4

1820.55

455.1 4

132.89

0.000

Repetition (Location)

15

94.88

63.3

1.85

0.043

Interaction

20

339.45

16.97

4.96

0.000

PCI_{1}

8

319.11

39.89

11.63

0.000

Residue

12

20.34

1.69



Error

75

256.88

3.4 3



Total

119

119

3288.59



Thus the AMMI1 model for estimation of potato production is:
Some peanut genotypes adapted stably in all locations and specific in particular locations can be viewed using the AMMI biplot2. AMMI2 Biplot is shown in Figure 1.
AMMI2 Biplot is able to describe the variance of interactions as much as 97.92%. In AMMI2 biplot, Ngadiwono (L4) location is a location with the greatest variance because from the 5 locations, Ngadiwono Location (L4) has the longest vector. The location that has a relatively small variance is Jurang Kuali (L2), so this site is relatively stable for the growth of all varieties. Granola Germany variety (V3) has the smallest variance because the location of Granola Germany variety (V3) is approaching the center of coordinate point (0.0). Thus, Granola Germany variety (V3) adapts well in all of the experiment locations.
Potato varieties that adapt specific to particular location among others are Granola Korea variety (V5) which adapts specific to Ngadiwono location (L4). Granola Flower variety (V1) and Granola Holland (V2) adapt specific to Tulungrejo (L1) and Sumberbrantas locations (L3). Granola Germany Variety (V3) adapts specific to Jurang Kuali location (L2). Granola Local variety (V4) and Granola Australia (V6) adapt specific to Sumber location (L5).
5. CONCLUSION
AMMI model that can explain the data of potato production is AMMI1 model with the percentage of variance of interactions that can be explained by AMMI1 model as much as 94.01%. Based on the biplot analysis, the variety that adapts well in all of the trial locations is Granola Germany (V3). Meanwhile, four other varieties are varieties that adapt specific to certain locations, they are Granola Korea (V5) specific to Ngadiwono (L4), Granola Flower (V1) and Granola Holland (V2) specific to Tulungrejo (L1) and Sumberbrantas (L3), Granola Germany (V3) specific to Jurang Kuali (L2), Granola Local (V4) and Granola Australia (V6) specific to Sumber (L5). 