Trait selection using procrustes analysis for the study of genetic diversity in Conilon coffee

Trait selection is occasionally necessary to save money and time, as well as accelerate breeding program processes. This study aimed to propose two criteria to select traits based on a Procrustes analysis that are poorly explored in genetic breeding: Criterion 1 (backward algorithm) and Criterion 2 (exhaustive algorithm). Then, these two criteria were further compared with Jolliffe’s criterion, which has often been used to select traits in genetic diversity studies. Sixteen agronomic traits were considered, and 40 Conilon coffee (Coffea canephora) accessions were evaluated. This study showed that the flexibility in selecting traits by researcher preference, graphical visualization, and Procrustes M² tatistic through criteria 1 and 2 is a fast and reliable alternative for decision-making. These decisions are based on the removal and addition of traits for phenotyping in studies of Conilon coffee diversity that can be applied to other crops. Other relevant aspects of selection traits criteria were also discussed.

Keywords:
principal components; graphical comparison; selection criteria; discard of variables; plant breeding

Authorship

Daiana Salles Pontes ^**Author for correspondence. E-mail: salles.yana@gmail.com

Departamento de Estatística Aplicada e Biometria, Universidade Federal de Viçosa, Av. Peter Henry Rolfs, s/n, Campus Universitário, Viçosa, Minas Gerais, Brazil. Universidade Federal de ViçosaBrazilViçosa, Minas Gerais, BrazilDepartamento de Estatística Aplicada e Biometria, Universidade Federal de Viçosa, Av. Peter Henry Rolfs, s/n, Campus Universitário, Viçosa, Minas Gerais, Brazil.

https://orcid.org/0000-0002-5324-0820

Renato Domiciano Silva Rosado

Cosme Damião Cruz

Moysés Nascimento

Ana Maria Cruz Oliveira

Departamento de Biologia Geral, Universidade Federal de Viçosa, Viçosa, Minas Gerais, Brazil. Universidade Federal de ViçosaBrazilViçosa, Minas Gerais, BrazilDepartamento de Biologia Geral, Universidade Federal de Viçosa, Viçosa, Minas Gerais, Brazil.

Scott Michael Pensky

Louisiana State University, Baton Rouge, Louisiana, USA. Louisiana State UniversityUSABaton Rouge, Louisiana, USALouisiana State University, Baton Rouge, Louisiana, USA.

*Author for correspondence. E-mail: salles.yana@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Louisiana State University, Baton Rouge, Louisiana, USA. Louisiana State UniversityUSABaton Rouge, Louisiana, USALouisiana State University, Baton Rouge, Louisiana, USA.

Figures | Tables

Figures (5)
Tables (5)

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Figure 1
Representation of steps involved in a Procrustes analysis: (a) original configurations where the triangle ABC was used as reference configuration; (b) configurations after standardization (i.e., similar size and common center); (c) configurations after mirror reflection, if necessary; (d) configuration after rotation so that the sum of the squared differences between homologous observations (A/a, B/b, C/c) is a minimum (Peres-Neto & Jackson, 2001Peres-Neto, P. R., & Jackson, D. A. (2001). How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test. Oecologia, 129(2), 169-178. DOI: 10.1007/s004420100720
https://doi.org/10.1007/s004420100720... ).

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Figure 2
Diagram illustrating Procrustes analysis data by Krzanowski (1987Krzanowski, W. J. (1987). Selection of variables to preserve multivariate data structure, using principal components. Journal of the Royal Statistical Society: Series C (Applied Statistics), 36(1), 22-33. DOI: 10.2307/2347842
https://doi.org/10.2307/2347842... ).

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Figure 3
Dispersion ranking of Conilon coffee accessions using two principal components (CP1 and CP2), according to: A - evaluation of 16 agronomic traits, B - Criteria 1 without Procrustes transformation, C - Criteria 1 with Procrustes transformation, and D - A and C superimposed (M² = 0.089445).

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Figure 4
Dispersion ranking of Conilon coffee accessions using two principal components (CP1 and CP2), according to A - evaluation of 16 agronomic traits, B - Criteria 2 without Procrustes transformation, C - Criteria 2 with Procrustes transformation, and D - A and C superimposed (M² = 0.1)

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Figure 5
Dispersion ranking of Conilon coffee accessions using two principal components (CP1 and CP2), according to A - evaluation of 16 agronomic traits, B - Jolliffe criteria without Procrustes transformation, C - Jolliffe criteria with Procrustes transformation, and D - A and C superimposed (M² = 0.33585).

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Table 1
Optimal selection using Procrustes and Jolliffe criteria.

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Table 2
Variables excluded by the backward algorithm for the Conilon coffee.

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Table 3
Total subsets determined by the exhaustive algorithm with M² _critical < 0.1.

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Table 4
Eigenvalue estimates from the correlation matrix, containing 16 traits and associated eigenvectors (components).

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Table 5
Total number of analyzes performed by exhaustive algorithm on the Conilon coffee.

Figure 1 Representation of steps involved in a Procrustes analysis: (a) original configurations where the triangle ABC was used as reference configuration; (b) configurations after standardization (i.e., similar size and common center); (c) configurations after mirror reflection, if necessary; (d) configuration after rotation so that the sum of the squared differences between homologous observations (A/a, B/b, C/c) is a minimum (Peres-Neto & Jackson, 2001Peres-Neto, P. R., & Jackson, D. A. (2001). How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test. Oecologia, 129(2), 169-178. DOI: 10.1007/s004420100720
https://doi.org/10.1007/s004420100720... ).

Figure 2 Diagram illustrating Procrustes analysis data by Krzanowski (1987Krzanowski, W. J. (1987). Selection of variables to preserve multivariate data structure, using principal components. Journal of the Royal Statistical Society: Series C (Applied Statistics), 36(1), 22-33. DOI: 10.2307/2347842
https://doi.org/10.2307/2347842... ).

Figure 3 Dispersion ranking of Conilon coffee accessions using two principal components (CP1 and CP2), according to: A - evaluation of 16 agronomic traits, B - Criteria 1 without Procrustes transformation, C - Criteria 1 with Procrustes transformation, and D - A and C superimposed (M² = 0.089445).

Figure 4 Dispersion ranking of Conilon coffee accessions using two principal components (CP1 and CP2), according to A - evaluation of 16 agronomic traits, B - Criteria 2 without Procrustes transformation, C - Criteria 2 with Procrustes transformation, and D - A and C superimposed (M² = 0.1)

Figure 5 Dispersion ranking of Conilon coffee accessions using two principal components (CP1 and CP2), according to A - evaluation of 16 agronomic traits, B - Jolliffe criteria without Procrustes transformation, C - Jolliffe criteria with Procrustes transformation, and D - A and C superimposed (M² = 0.33585).

Table 1 Optimal selection using Procrustes and Jolliffe criteria.

Criteria	Optimal selection	M² estimated	VTa%†	Discarded traits	Solution
Procrustes (backward)	GY, ChCo, MG%, S17, S15, and MS	0.0895	62.57	CoBe, S11, D, PH, S13, FG%, ChBe, DCA, GM%, and CG%	Only
Procrustes (exhaustive)	DCA, ChBe, CoBe, MG%, GM%, S15, S11, and MS	0.1	56.82	D, GY, PH, ChCo, CG%, FG%, S17, and S13	1 in 9,841
Jolliffe	D, DCA, ChCo, CoBe, CG%, FG%, and S17	0.3359	51.50	S13, MS, MG%, ChBe, S11, GY, PH, S15, and GM%	Only

†VTa%: Cumulative percent of the total variation explained by the two primary components.

Table 2 Variables excluded by the backward algorithm for the Conilon coffee.

Discarded											Selected
Excluded variables	CoBe	S11	D	PH	S13	FG%	ChBe	DCA	GM%	CG%	MS	GY	ChC	S15	MG%	S17
M²	0.0074	0.0111	0.0239	0.0236	0.0331	0.0399	0.0528	0.0569	0.0678	0.0894	0.1535	0.1903	0.2538	0.4325	-	-

CoBe: Coconut and green coffee relationship, S11: Percentage of grains retained on the sieve mesh size #11, D: Number of days, plant height (PH, in cm), S13: Percentage of grains retained on the sieve mesh size #13, FG%:“Flat” grain percentage, ChBe: Cherry and green coffee relationship, DCA: Diameter crown average (cm), GM%: Grain moisture percentage, CG%: Coarse grain percentage, MS: Medium strainer (medium grain size), GY: Grain yield (kg ha^-1), ChCo: Cherry and coconut dry coffee relationship, S15: Percentage of grains retained on the sieve mesh size #15, MG%: “Mocha” grain percentage and S17: Percentage of grains retained on the sieve mesh size #17.

Table 3 Total subsets determined by the exhaustive algorithm with M² _critical < 0.1.

Traits	Subsets
5	2
6	64
7	322
8	735
9	1,538
10	2,490
11	2,504
12	1,502
13	548
14	120
15	16
Total	9,841

Table 4 Eigenvalue estimates from the correlation matrix, containing 16 traits and associated eigenvectors (components).

†λ	VT%	VTa%	Traits
†λ	VT%	VTa%	D(Days)	GY(kg/ha)	PH(cm)	DCA(cm)	ChCo	ChBe	CoBe	CG%	FG%	MG%	GM%	S17(%)	S15(%)	S13(%)	S11(%)	MS
4.7455	29.6592	29.6592	0.1232	0.2484	0.0986	0.0411	-0.0074	-0.2062	-0.2427	-0.2021	-0.0141	0.004	0.1996	0.342	0.3336	-0.4028	-0.4001	0.4227
3.1508	19.6928	49.352	-0.2224	-0.2399	-0.2168	-0.3252	-0.3129	-0.2551	0.0065	0.1987	0.4322	-0.4125	-0.298	0.1998	-0.0455	-0.1696	0.0173	0.1449
1.8687	11.6794	61.0314	-0.4702	0.3076	0.4762	0.4349	-0.2447	-0.1216	0.1346	0.2525	0.0954	-0.0763	-0.1413	-0.166	0.1811	0.0727	-0.1023	-0.0282
1.4027	8.7669	69.7983	-0.1501	-0.02	-0.2756	-0.0342	-0.3937	-0.3792	-0.1923	0.1677	-0.4756	0.5244	-0.1734	0.0329	-0.0332	-0.024	0.0379	-0.0253
1.2503	7.8145	77.6128	-0.0331	-0.1849	-0.1226	-0.1889	-0.2062	0.3865	0.6281	0.018	-0.1457	0.1555	-0.0683	-0.0699	0.3876	-0.0783	-0.3189	0.1195
1.0303	6.4394	84.0522	-0.288	0.1108	-0.011	0.0506	0.4514	0.2802	0.1072	0.3921	-0.1596	0.1161	-0.1815	0.4425	-0.2793	-0.2514	0.0874	0.195
0.7983	4.9891	89.0414	0.1637	-0.159	0.2618	-0.23	-0.0063	-0.2259	0.1373	0.592	-0.0278	0.0232	0.6126	-0.0197	0.056	-0.1	0.1183	-0.0434
0.526	3.2875	92.3288	0.4582	0.4745	-0.4142	0.3515	-0.265	0.0038	0.2984	0.2031	0.1034	-0.1152	0.0385	0.086	-0.1336	-0.045	0.1274	0.0155
0.404	2.5249	94.8538	-0.0673	0.4471	-0.2347	-0.3525	0.1958	0.1661	-0.298	0.2442	0.044	-0.04	-0.113	-0.3364	0.4588	-0.1351	0.1391	-0.1559
0.3091	1.9316	96.7853	0.4837	0.1882	0.5185	-0.3681	-0.1591	0.0768	-0.0435	0.1166	-0.0752	0.0513	-0.4681	0.0842	-0.1564	0.1078	-0.0927	0.0172
0.2653	1.658	98.4434	-0.3596	0.476	0.0239	-0.4555	-0.223	0.0711	0.157	-0.2914	0.0094	0.0394	0.3586	0.0962	-0.3195	0.1564	0.0545	0.0509
0.1043	0.652	99.0954	0.0063	-0.109	0.2333	0.0856	-0.3495	0.3045	-0.071	-0.2121	-0.0187	0.0504	0.0186	0.0451	0.107	-0.4886	0.6371	0.0065
0.0971	0.6071	99.7025	-0.0315	-0.1175	-0.0767	0.1131	-0.3579	0.568	-0.499	0.2734	0.1014	0.0066	0.2121	0.0733	-0.1139	0.1845	-0.288	0.0371
0.0306	0.1915	99.8939	0.0435	-0.0098	0.0044	0.009	0.0832	-0.0273	0.019	0.0275	0.6156	0.6287	-0.0318	-0.1773	-0.0176	0.0978	0.1208	0.3976
0.0166	0.1037	99.9976	0.0087	-0.033	-0.0218	0.0062	-0.0013	0.0124	-0.0486	0.0578	-0.3497	-0.3066	-0.0044	-0.3427	-0.0304	0.228	0.2194	0.7467
0.0004	0.0024	100	0.0037	-0.0035	-0.0031	0.003	0.0051	-0.0025	-0.0023	0.0041	0.0068	0.0053	0.0021	0.5659	0.4906	0.5772	0.3249	0.0126

†λ: Eigenvalue. VT%: Percentage of total variation explained by the i-th principal component. VTa%: Cumulative percentage by components.

Table 5 Total number of analyzes performed by exhaustive algorithm on the Conilon coffee.

# of variables	Analyses
10	1,012
16	65,518
20	1,048,554
30	1,073,741,792

50	1,125,899,906,842,570

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Trait selection using procrustes analysis for the study of genetic diversity in Conilon coffee

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[1] *Author for correspondence. E-mail: salles.yana@gmail.com