# Artificial Neural Networks in the Prediction of Genetic Merit to Flowering Traits in Bean Cultivars

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{−1}(in the 1970s) [1] for more than 1331 kg ha

^{−1}(in the 2018/2019 season) in the mean of three planting seasons (first crop or water (1504.50 kg ha

^{−1}), second crop or drought (1492 kg ha

^{−1}) and third crop or irrigated (996.5 kg ha

^{−1}), seeing current Black, Carioca and other grain color patterns of common beans cultivars [2]. The progress in grain yield, productivity components, grain technological quality and nutritional quality, is mostly attributed to genetic improvement [3,4]. Besides these, flowering time traits, for example, days to flowing (DTF) and days to first flower (DFF) presents importance in a breeding program of common bean. The identification of cultivars with an early cycle allows the planning of harvests for periods of less rain, the reduction of water consumption by irrigated crops, and reduction of the time exposed to the risk of plague and disease [5,6,7].

## 2. Materials and Methods

#### 2.1. Experiment and Experimental Material

#### 2.2. Phenotypic Data Analysis

^{2}and Lilliefors [23]. The means were grouped by the Scott and Knott test [24].

#### 2.3. Prediction Models for Genomic Estimated Breeding Values

#### 2.4. Artificial Neural Networks

#### 2.4.1. Multilayer Perceptron (ANN—MLP)

#### 2.4.2. Artificial Neural Networks—Radial Basis Function Network (ANN-RBF)

#### 2.5. Comparison of ANN-RBF, ANN-MLP and RR-BLUP to Estimate GEBV in 5-Fold CV

^{2}) and the predictive ability, which is given by the Pearson’s correlation between the predicted values and the phenotypes were calculated using a five-fold cross-validation (CV) random process (Figure 3).

## 3. Results

^{2}higher than the values found by GS (RR-BLUP (DFF: $\mathbf{0.772}\pm \mathbf{0.02}$ e DFT: $\mathbf{0.841}\pm \mathbf{0.01}\text{}$)) during the training phase. It is worth mentioning that, for the validation phase, the results obtained by ANN were 90% and 40% times higher than those observed using RR-BLUP for DFF and DFT, respectively (Figure 4—$R$

^{2}). Several authors have used this parameter in order to verify the efficacy of methodologies that involve problems of prediction or classification of simulated populations [29,30,31] and has also observed efficacy in the use of ANNs. In this case, it is worth noting that ANN-MLP was the methodology that provided predictive abilities above 90%, which quantifies its efficacy (Figure 4).

## 4. Discussion

^{2}) of 0.77 for corn and 0.81 for soybean—compared to Multiple Linear Regression—R

^{2}of 0.42 for maize and 0.46 for soybeans [47].

^{2}and RMSE, than those obtained by RR-BLUP methodology (Figure 4). Methodologies based on neural networks that do not depend on stochastic information tended to be more efficient because these phenotypic traits are obtained by DFF and DFT and depend on traditional methodologies based on normality. The variables DFF and DFT had ANN based methodologies that were significantly better when compared to the RR-BLUP methodology.

^{2}, RMSE, and PC to GEBV of individuals for phenological traits of flowering compared to RBF methodology (Figure 4), estimation of their marker effects with those of RR-BLUP was deemed more appropriate.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of Artificial Neural NetworksMultilayer Perceptron. Two intermediate layers (n

_{i1}and n

_{i2}) constituted of $i$ neurons ($i\text{}$= 1, …, 4). The Artificial Neural Network (ANN) returns the vector of genomic estimated breeding values ($GEBV$).

**Figure 2.**Schematic of a Radial Base Function Network. Inputs X

_{1}through X

_{384}in the input layer refer to the markers considered in the analyses. A hidden layer considering rays of size r (r ranging from 1 to 80) and consisting of $k$ neurons ($k$ = 1, …, 100). The RBF returns the vector of genomic estimated breeding values (GEBV).

**Figure 4.**Correlation coefficient (R

^{2}), root-mean-squared error (RMSE) of training (T) and validation (V) and predictive ability (PC) of the phenological traits for days to first flower (DFF) and days to flowering (DTF) obtained through the GS methodologies: RR-BLUP and ANNs: RBF and MLP for the bean cultivars of carioca and black beans recommended in Brazil between 1960 and 2013.

**Figure 5.**Behavior of Carioca (brown beans) and Preto (Black beans) bean cultivars on estimated genomic breeding values (GEBV) and the phenotypic average of phenological traits for days to flowering (DTF). Groups of bean cultivars allocated to the same block (

**a**) IPR Andorinha, BR-2 Grande Rio, Carioca 1070, IPR Colibri, IAC Imperador, Capixaba Precoce; (

**b**) Moruna, BRS Notável, BRSMG Madrepérola, BRS Majestoso, Diamante Negro, BR 6-Barriga verde, Ouro Negro, BRSMG Talismã; (

**c**) Milionário 1732, Onix, BRS Requinte, Varre-Sai, IPR Tuiuiú, BRS Estilo, IAPAR 16, BRSMG Pioneiro, IAC—Carioca Pyatã, VC15, IRAÍ, FT 120, VP 22, IAC Formoso, IAC Tunã, IAC Alvorada, Carioca 1030, Aporé, IPR Eldourado, Xamego, IAC—Carioca Akytá, BRS Esplendor, IAPAR 44, RP1, Rio doce, BR-IPAGRO 1- Macanudo, BRS Expedito, BRS Grafite, BR-3 Ipanema, IAC-Ybaté, BRS Pontal, Carioca 80, IAC-Una, BR 1- Xodó, IAPAR 57, BRS Campeiro, BRS Supremo; and (

**d**) BR-Ipagro 2 Pampa, IAC Votuporanga, IPR Gralha, IPR 139, Rico 23, IAPAR 81, IAC-Apuã, Rio Tibagi, IPR Tangará, IPR Saracura, IAPAR 31, BR- IPA 11-Brígida, IPR Uirapurú, SCS Guará, IAPAR 65, IPR Tiziu, IAPAR 20, Iapar 8-Rio Negro, BR- IPA 10, Rudá, Pérola, BRS Cometa, BRS Valente, Rico 1735, IPR Graúna, Preto Uberabinha, IAC Carioca, FT bonito, Campos Gerais for DFT, do not statistically differ by Scott Knott’s means clustering test at 5% probability.

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**MDPI and ACS Style**

Rosado, R.D.S.; Cruz, C.D.; Barili, L.D.; de Souza Carneiro, J.E.; Carneiro, P.C.S.; Carneiro, V.Q.; da Silva, J.T.; Nascimento, M.
Artificial Neural Networks in the Prediction of Genetic Merit to Flowering Traits in Bean Cultivars. *Agriculture* **2020**, *10*, 638.
https://doi.org/10.3390/agriculture10120638

**AMA Style**

Rosado RDS, Cruz CD, Barili LD, de Souza Carneiro JE, Carneiro PCS, Carneiro VQ, da Silva JT, Nascimento M.
Artificial Neural Networks in the Prediction of Genetic Merit to Flowering Traits in Bean Cultivars. *Agriculture*. 2020; 10(12):638.
https://doi.org/10.3390/agriculture10120638

**Chicago/Turabian Style**

Rosado, Renato Domiciano Silva, Cosme Damião Cruz, Leiri Daiane Barili, José Eustáquio de Souza Carneiro, Pedro Crescêncio Souza Carneiro, Vinicius Quintão Carneiro, Jackson Tavela da Silva, and Moyses Nascimento.
2020. "Artificial Neural Networks in the Prediction of Genetic Merit to Flowering Traits in Bean Cultivars" *Agriculture* 10, no. 12: 638.
https://doi.org/10.3390/agriculture10120638