Stability Models: Eberhart and Russell Model and Perkins and Jinks

In the context of genotype-environment interaction (GxE), where the performance of genotypes (varieties) varies across different environments, stability analysis helps in identifying genotypes that are consistently performing well. Stability analysis allows plant breeders to develop genotypes that can perform well not only in optimal conditions but also under varying and unpredictable environments.

Two widely used stability models for this purpose are the Eberhart and Russell model and the Perkins and Jinks model. These models are crucial for ensuring that newly developed genotypes are resilient and can be successfully cultivated in diverse environments. Both models are fundamental tools in plant breeding programs aiming to enhance crop productivity and adaptability across different geographical regions and climate conditions.

Eberhart and Russell Model (1966)

The Eberhart and Russell model, introduced by S.A. Eberhart and W.A. Russell in 1966, is one of the most popular methods for stability analysis. This model focuses on two key parameters for each genotype:

Regression Coefficient (bi): It measures the responsiveness of the genotype to environmental changes.
- bi = 1: The genotype is considered stable, responding linearly to environmental changes.
- bi > 1: The genotype is more sensitive to favorable environments, meaning it responds better under good conditions but may perform poorly under unfavorable ones.
- bi < 1: The genotype is less responsive to environmental changes, indicating stability under poor conditions but lesser improvement in favorable ones.
Deviation from Regression (S²di): This is the variance around the regression line. It indicates the consistency or predictability of the genotype.
- S²di = 0: The genotype shows consistent performance across environments.
- S²di > 0: Higher deviations indicate more erratic or unpredictable performance.

When to Use the Eberhart and Russell Model:

The model is used when you want to assess the stability of genotypes across multiple environments.
It is especially useful when linear regression between genotype performance and environmental index can explain most of the variation in the data.
It helps in identifying responsive genotypes (those that do well in favorable environments) and stable genotypes (those that perform consistently).

Significance of the Eberhart and Russell Model:

It provides a way to balance high yield potential with stability by allowing breeders to consider not only how well a genotype performs but how reliably it performs across various environments. The model emphasizes the importance of both average performance (mean yield) and stability, which are critical for selecting genotypes suited to variable environmental conditions.

Perkins and Jinks Model (1968)

The Perkins and Jinks model, introduced by J.M. Perkins and J.L. Jinks in 1968, offers another method for analyzing GxE interactions. This model focuses on partitioning the genotype-environment interaction into components that help to identify the nature of the interaction. It distinguishes between:

Linear Components of Interaction: These components are predictable, meaning they can be explained by the linear relationship between genotypes and environments.
Non-linear Components of Interaction: These are unpredictable and result from complex, random interactions between genotypes and environments.

Key Parameters of Perkins and Jinks Model:

Linear and Non-linear Terms: The model separates the GxE interaction into linear and non-linear parts to assess how much of the interaction can be predicted and how much is due to erratic or random environmental factors.
Mean Performance: The mean performance of the genotype is also considered, with the idea that more predictable responses (linear components) are preferable for breeding stable varieties.

When to Use the Perkins and Jinks Model:

This model is particularly useful when both linear and non-linear components of the genotype-environment interaction are important to assess.
It is applicable in cases where non-linear interactions (unpredictable responses) are significant and need to be factored into stability analysis.

Significance of the Perkins and Jinks Model:

The model provides a more detailed breakdown of GxE interaction, allowing breeders to focus on predictability and randomness in genotype performance. By distinguishing between predictable and unpredictable interactions, it offers a more comprehensive view of stability.

Comparison and Use in Plant Breeding

Eberhart and Russell model: It is simpler and focuses on the regression of genotypes on the environmental index, making it ideal for situations where the response to the environment is mostly linear.

Perkins and Jinks model: It is more complex, taking into account both linear and non-linear components of GxE interaction. It is suitable for situations where random variations significantly affect genotype performance.

Practical Use in Plant Breeding:

Eberhart and Russell: This model is widely used by plant breeders for preliminary screening of genotypes across multiple environments to select those with consistent performance and desired responsiveness to environmental changes.

Perkins and Jinks: This model is employed when breeders want to understand complex GxE interactions, especially when non-linear and unpredictable responses are observed. It helps in refining selection when random environmental effects are significant.

Stability Analysis Using OPSTAT

The OPSTAT online tool allows you to perform stability analysis using the Eberhart and Russell model and the Perkins and Jinks model. Follow these steps to input your data and perform the analysis.

1. Input Character/Response Data:

Data Format: You are required to enter only the numeric data of the character/trait for each environment-genotype-replication combination. The data should be arranged in a specific order for the analysis.

Data Arrangement:

The data should be entered row-wise by genotypes and replications for each environment.
Each row corresponds to the data for a particular environment, and the values represent the character/trait responses of different genotypes across replications.

Entering Data: Paste the numeric data into the text area provided in the interface, ensuring that the data is structured as described above.

2. Enter the Required Parameters:

After pasting the data, you need to provide details about the structure of the experiment:

Number of Environments: Enter the total number of environments in the experiment.
Number of Genotypes: Enter the total number of genotypes tested.
Number of Replications: Enter the number of replications for each environment-genotype combination.
Number of Characters/Traits: Enter the total number of character/trait responses being analyzed.

3. Select the Stability Analysis Model:

Choose the stability model for analysis:

Eberhart and Russell Model: This model identifies genotypes that are stable and responsive across different environments. It calculates the regression coefficient (bi) and deviation from regression (S²di).
Perkins and Jinks Model: This model breaks down the genotype-environment interaction into linear and non-linear components, focusing on predictable and unpredictable variations in genotype performance.

4. Perform the Analysis:

Once all the data is entered and the appropriate model is selected, click the "Perform Analysis" button to run the stability analysis. The results will display detailed information on genotype stability, including regression coefficients, variance from regression, and mean performance across environments.

Sample Data Example:

Here's a sample of how your data should be structured:

ENV	GEN	REP	PH	EH	EP
1	1	1	2.612	1.706	0.657976661
1	1	2	2.872	1.76	0.627531892
1	1	3	2.684	1.584	0.59123283
1	2	1	2.55	1.222	0.480714767
1	2	2	2.904	1.406	0.483989161
1	2	3	2.922	1.392	0.477352764
1	3	1	3.044	1.43	0.470260768
1	3	2	2.944	1.66	0.563929324
1	3	3	2.818	1.67	0.592956349
1	4	1	3.022	1.818	0.601206001
1	4	2	2.842	1.686	0.592974869
1	4	3	2.742	1.524	0.556260458
1	5	1	2.904	1.58	0.543619116
1	5	2	2.816	1.61	0.57198341
1	5	3	2.784	1.588	0.572574834
1	6	1	2.898	1.588	0.547949756
1	6	2	2.738	1.69	0.631020532
1	6	3	2.67	1.446	0.541138664
1	7	1	2.866	1.556	0.541879872
1	7	2	2.776	1.6704	0.617030971
1	7	3	2.6796	1.556	0.587668367
1	8	1	2.588	1.302	0.502693596
1	8	2	2.756	1.55	0.562575176
1	8	3	2.732	1.542	0.563706598
1	9	1	3.002	1.714	0.573822821
1	9	2	2.96	1.606	0.542500396
1	9	3	2.814	1.69	0.600559749
1	10	1	2.832	1.644	0.58135197
1	10	2	2.794	1.706	0.615970354
1	10	3	2.724	1.512	0.553869773
1	11	1	2.752	1.512	0.54944029
1	11	2	2.72	1.558	0.572828381
1	11	3	2.774	1.666	0.6004274
1	12	1	2.73	1.538	0.563271462
1	12	2	2.558	1.556	0.616483463
1	12	3	2.79	1.528	0.546137861
1	13	1	2.742	1.602	0.586170455
1	13	2	2.642	1.366	0.517245027
1	13	3	2.932	1.768	0.601898874
2	1	1	3.002	1.878	0.625629446
2	1	2	2.974	1.834	0.61740553
2	1	3	2.814	1.674	0.593638878
2	2	1	2.984	1.756	0.588347095
2	2	2	3.034	1.868	0.615344932
2	2	3	2.822	1.61	0.571693095
2	3	1	2.8	1.796	0.639583211
2	3	2	3.04	1.796	0.59059908
2	3	3	2.982	1.656	0.554828783
2	4	1	2.942	1.708	0.579465021
2	4	2	2.746	1.62	0.591239569
2	4	3	2.85	1.552	0.544526416
2	5	1	2.79	1.42	0.508915403
2	5	2	2.554	1.362	0.533422647
2	5	3	2.77	1.478	0.533516758
2	6	1	2.922	1.6	0.547905621
2	6	2	2.608	1.466	0.562404832
2	6	3	2.944	1.582	0.534990748
2	7	1	2.184	1.186	0.544340117
2	7	2	2.158	1.11	0.514626349
2	7	3	2.068	1.03	0.497579403
2	8	1	2.024	0.93	0.455506413
2	8	2	1.814	0.752	0.438959163
2	8	3	2.04	0.856	0.417686534
2	9	1	2.098	1.064	0.507246641
2	9	2	2.292	1.428	0.629531171
2	9	3	2.208	1.172	0.527886935
2	10	1	2.104	0.91	0.433747741
2	10	2	2.12	1.034	0.487046407
2	10	3	1.924	1.018	0.560032107
2	11	1	2.132	1.052	0.493139936
2	11	2	2.126	1.012	0.476325829
2	11	3	2.182	0.992	0.455228534
2	12	1	2.148	0.982	0.45692983
2	12	2	2.186	0.874	0.409656559
2	12	3	1.946	0.828	0.42110573
2	13	1	2.218	1.088	0.489045837
2	13	2	2.274	1.172	0.513139651
2	13	3	2.19	1.064	0.486277897
3	1	1	2.106	1.046	0.49723326
3	1	2	2.198	1.086	0.492139439
3	1	3	2.288	1.154	0.502225667
3	2	1	2.048	0.998	0.485799252
3	2	2	2.102	0.984	0.467094697
3	2	3	2.312	1.158	0.500649769
3	3	1	2.094	1.022	0.484993213
3	3	2	1.96	0.926	0.472923613
3	3	3	2.076	0.9106	0.438322457
3	4	1	1.99	0.918	0.461841029
3	4	2	2.142	1.034	0.48167266
3	4	3	2.016	0.876	0.433744257
3	5	1	2.01	0.948	0.47114535
3	5	2	2.046	0.932	0.45396751
3	5	3	2.228	0.998	0.460915478
3	6	1	2.11	1.152	0.546323075
3	6	2	2.09	1.062	0.507672383
3	6	3	2.26	1.24	0.548991032
3	7	1	2.192	1.182	0.538524218
3	7	2	2.136	1.046	0.489022924
3	7	3	2.204	1.212	0.54975737
3	8	1	2.102	1.052	0.500567331
3	8	2	2.152	1.106	0.514286572
3	8	3	2.046	1.116	0.544830057
3	9	1	2.09	1.056	0.504812457
3	9	2	2.01	0.826	0.41105292
3	9	3	1.984	0.84	0.421707001
3	10	1	1.788	0.888	0.513537987
3	10	2	2.054	1.032	0.503906397
3	10	3	2.272	1.114	0.491106168
3	11	1	1.71	0.808	0.488513382
3	11	2	2.094	1.06	0.508723403
3	11	3	2.5	1.44	0.57734657
3	12	1	2.522	1.516	0.601180251
3	12	2	2.766	1.582	0.571957431
3	12	3	2.002	0.782	0.385648496
3	13	1	2.52	1.094	0.434353875
3	13	2	2.584	1.324	0.51148111
3	13	3	2.692	1.52	0.56596859
4	1	1	2.376	1.28	0.53701979
4	1	2	2.724	1.52	0.557685834
4	1	3	2.806	1.532	0.545994641
4	2	1	2.618	1.544	0.587577094
4	2	2	2.34	1.186	0.504486385
4	2	3	2.614	1.41	0.539698737
4	3	1	2.47	1.458	0.589265495
4	3	2	2.3604	1.186	0.501272062
4	3	3	2.55	1.416	0.555637406
4	4	1	2.606	1.608	0.617084473
4	4	2	2.596	1.44	0.554976198
4	4	3	2.466	1.318	0.534337068
4	5	1	2.688	1.506	0.557388018
4	5	2	2.79	1.764	0.632468627
4	5	3	2.436	1.27	0.523851242
4	6	1	2.426	1.274	0.523167282
4	6	2	2.582	1.424	0.550822881
4	6	3	2.448	1.452	0.590867985
4	7	1	2.222	1.206	0.539124786
4	7	2	2.68	1.606	0.59887406
4	7	3	2.686	1.476	0.549268793
4	8	1	2.692	1.568	0.584743275
4	8	2	2.4608	1.2338	0.506112182
4	8	3	2.512	1.454	0.579522425
4	9	1	2.416	1.446	0.598458249
4	9	2	2.106	1.108	0.524790075
4	9	3	2.392	1.304	0.547421592
4	10	1	2.268	1.48	0.660499691
4	10	2	2.45	1.42	0.573658793
4	10	3	2.448	1.38	0.564754595
4	11	1	2.674	1.562	0.584415983
4	11	2	2.68	1.312	0.493083467
4	11	3	2.336	1.218	0.519456072
4	12	1	2.524	1.41	0.559963807
4	12	2	2.702	1.506	0.557089089
4	12	3	2.376	1.286	0.540642258
4	13	1	2.396	1.43	0.615270714
4	13	2	2.808	1.64	0.584336965
4	13	3	2.466	1.172	0.475916872

You have to Enter only numeric after arranging it above mentioned manner. The data for 4 Environment, 13 Genotyples, 3 replications and 3 characters should be like this:

2.612	1.706	0.657976661
2.872	1.76	0.627531892
2.684	1.584	0.59123283
2.55	1.222	0.480714767
2.904	1.406	0.483989161
2.922	1.392	0.477352764
3.044	1.43	0.470260768
2.944	1.66	0.563929324
2.818	1.67	0.592956349
3.022	1.818	0.601206001
2.842	1.686	0.592974869
2.742	1.524	0.556260458
2.904	1.58	0.543619116
2.816	1.61	0.57198341
2.784	1.588	0.572574834
2.898	1.588	0.547949756
2.738	1.69	0.631020532
2.67	1.446	0.541138664
2.866	1.556	0.541879872
2.776	1.6704	0.617030971
2.6796	1.556	0.587668367
2.588	1.302	0.502693596
2.756	1.55	0.562575176
2.732	1.542	0.563706598
3.002	1.714	0.573822821
2.96	1.606	0.542500396
2.814	1.69	0.600559749
2.832	1.644	0.58135197
2.794	1.706	0.615970354
2.724	1.512	0.553869773
2.752	1.512	0.54944029
2.72	1.558	0.572828381
2.774	1.666	0.6004274
2.73	1.538	0.563271462
2.558	1.556	0.616483463
2.79	1.528	0.546137861
2.742	1.602	0.586170455
2.642	1.366	0.517245027
2.932	1.768	0.601898874
3.002	1.878	0.625629446
2.974	1.834	0.61740553
2.814	1.674	0.593638878
2.984	1.756	0.588347095
3.034	1.868	0.615344932
2.822	1.61	0.571693095
2.8	1.796	0.639583211
3.04	1.796	0.59059908
2.982	1.656	0.554828783
2.942	1.708	0.579465021
2.746	1.62	0.591239569
2.85	1.552	0.544526416
2.79	1.42	0.508915403
2.554	1.362	0.533422647
2.77	1.478	0.533516758
2.922	1.6	0.547905621
2.608	1.466	0.562404832
2.944	1.582	0.534990748
2.184	1.186	0.544340117
2.158	1.11	0.514626349
2.068	1.03	0.497579403
2.024	0.93	0.455506413
1.814	0.752	0.438959163
2.04	0.856	0.417686534
2.098	1.064	0.507246641
2.292	1.428	0.629531171
2.208	1.172	0.527886935
2.104	0.91	0.433747741
2.12	1.034	0.487046407
1.924	1.018	0.560032107
2.132	1.052	0.493139936
2.126	1.012	0.476325829
2.182	0.992	0.455228534
2.148	0.982	0.45692983
2.186	0.874	0.409656559
1.946	0.828	0.42110573
2.218	1.088	0.489045837
2.274	1.172	0.513139651
2.19	1.064	0.486277897
2.106	1.046	0.49723326
2.198	1.086	0.492139439
2.288	1.154	0.502225667
2.048	0.998	0.485799252
2.102	0.984	0.467094697
2.312	1.158	0.500649769
2.094	1.022	0.484993213
1.96	0.926	0.472923613
2.076	0.9106	0.438322457
1.99	0.918	0.461841029
2.142	1.034	0.48167266
2.016	0.876	0.433744257
2.01	0.948	0.47114535
2.046	0.932	0.45396751
2.228	0.998	0.460915478
2.11	1.152	0.546323075
2.09	1.062	0.507672383
2.26	1.24	0.548991032
2.192	1.182	0.538524218
2.136	1.046	0.489022924
2.204	1.212	0.54975737
2.102	1.052	0.500567331
2.152	1.106	0.514286572
2.046	1.116	0.544830057
2.09	1.056	0.504812457
2.01	0.826	0.41105292
1.984	0.84	0.421707001
1.788	0.888	0.513537987
2.054	1.032	0.503906397
2.272	1.114	0.491106168
1.71	0.808	0.488513382
2.094	1.06	0.508723403
2.5	1.44	0.57734657
2.522	1.516	0.601180251
2.766	1.582	0.571957431
2.002	0.782	0.385648496
2.52	1.094	0.434353875
2.584	1.324	0.51148111
2.692	1.52	0.56596859
2.376	1.28	0.53701979
2.724	1.52	0.557685834
2.806	1.532	0.545994641
2.618	1.544	0.587577094
2.34	1.186	0.504486385
2.614	1.41	0.539698737
2.47	1.458	0.589265495
2.3604	1.186	0.501272062
2.55	1.416	0.555637406
2.606	1.608	0.617084473
2.596	1.44	0.554976198
2.466	1.318	0.534337068
2.688	1.506	0.557388018
2.79	1.764	0.632468627
2.436	1.27	0.523851242
2.426	1.274	0.523167282
2.582	1.424	0.550822881
2.448	1.452	0.590867985
2.222	1.206	0.539124786
2.68	1.606	0.59887406
2.686	1.476	0.549268793
2.692	1.568	0.584743275
2.4608	1.2338	0.506112182
2.512	1.454	0.579522425
2.416	1.446	0.598458249
2.106	1.108	0.524790075
2.392	1.304	0.547421592
2.268	1.48	0.660499691
2.45	1.42	0.573658793
2.448	1.38	0.564754595
2.674	1.562	0.584415983
2.68	1.312	0.493083467
2.336	1.218	0.519456072
2.524	1.41	0.559963807
2.702	1.506	0.557089089
2.376	1.286	0.540642258
2.396	1.43	0.615270714
2.808	1.64	0.584336965
2.466	1.172	0.475916872

5. Interpret Results:

After running the analysis, the OPSTAT tool will provide the following outputs:

For the Eberhart and Russell Model: Regression coefficients (bi) and deviations from regression (S²di) for each genotype.
For the Perkins and Jinks Model: Components of GxE interaction (linear and non-linear) and overall genotype performance.