Variance analysis

The combined analysis of variance showed the significant influence of the environment on the 10 genotypes in all response variables. Significant differences between the genotypes were observed in six of the seven variables, excluding NPP (Tab. 2). The interaction of the 10 genotypes with the eight environments was significant in all variables; therefore, the genotypes were influenced by the environmental conditions of each locality. This sensitivity to environmental effects generates changes in the classification or range of genotypes among environments, hides the expression of characteristics of interest, decreases the correlation between phenotypic and genotypic values, reduces the progress of selection and makes selection and subsequent recommendations of genotypes for one or several locations difficult (^{Kumar et al., 2013}; ^{Abate et al., 2015}; ^{Ferrari et al., 2018)}. According to ^{Mendonça et al. (2007)}, the presence of a genotype x environment interaction, justifies environmental stratification in order to take advantage of environmental stimuli that favor genotype expressions.

The experiment precision of the study according to the registered coefficients of variation was acceptable. The records ranged from low to medium according to ^{Oliveira et al. (2009)}, providing reliable and valid conclusions.

Correlations

The phenotypic and genotypic correlation coefficients estimated for the seven variables are shown in Table 3. Only four phenotypic correlations and 10 genotypic correlations were significant out of a total of 21 for each one. In general, the coefficients of genotypic correlations were of greater magnitude than the phenotypic ones, and, because of their greater genetic contribution (^{Silva and Neves, 2011}; ^{Ullah et al., 2011}; ^{Agrawal et al., 2018}) they allowed better selection. In addition, not all characteristics were significantly correlated, which is consistent with the report by ^{Bezerra et al. (2001)} and ^{Meena et al. (2015)}. The positive genetic correlations between two variables make the improvement of both characteristics much easier because, by exerting selection pressure on one, the other is indirectly affected in the same way because of the joint action of genes that govern them or the pleiotropic action between these characteristics (^{Gupta et al., 2017}).

The phenotypic correlations between DF and the other response variables were not significant, while the genotypic ones showed a positive and significant correlation with the height of the first pod (HFP) rG = 0.66* and number of pods per plant (NPP) rG = 0.70*. In addition, there was a negative and significant correlation with the number of seeds per pod (NSP) rG = - 0.66* (Tab. 3) that will allow breeders to select plants that flower later in time with a higher HFP and NPP, providing more progress than direct selection. Contact between the pods and soil is avoided, pod rot is reduced, and both manual and mechanical harvesting is facilitated (^{Salinas et al., 2008}; ^{Silva et al., 2014}). Simultaneously, a lower NSP is achieved through the competition of photoassimilates for grain filling. These results are consistent with previous reports by ^{Mohammed et al. (2010)}; ^{Hemavathy et al. (2015)}; and ^{Singh et al. (2018)} but divergent from the report by ^{Meena et al. (2015)}.

Negative and highly significant correlations were recorded between HFP and 100SW (rP = -0.91** and rG = -0.95**), GW (rP = -0.92** and rG = -0.95**) and GY (rG = -0.67) (Tab. 3), which indicated similar genetic control. In addition, it can be inferred that, in semi-prostrate habit cultivars, improving yield could be done by increasing HFP, making the characteristics 100SW, WG and GY decrease, with a physiological limit in the selection of plants whose architecture favors mechanical harvest and supports a high number of pods per plant, as suggested by ^{Velho et al. (2017)}.

The NSP did not correlate significantly at the phenotypic level with 100SW, while at the genotypic level the correlation was significant and negative (rG = -0.62*) (Tab. 3) because long pods with many ovules are produced as the result of the competition for photoassimilates, as reported by ^{Bezerra et al. (2001)}, ^{Andrade et al. (2010)}, ^{Silva et al. (2014)} and ^{Meena et al. (2015)}. It is possible to select shorter pods with heavier seeds. Similar trends were reported by ^{Andrade et al. (2010)}, ^{Silva et al. (2014)} and ^{Singh et al. (2018)}.

The absence of significant correlations between NPP and NSP and grain yield is explained by morphological and physiological modifications that were influenced by the environment, which can increase or decrease the magnitude of correlations, as well as the relation of the themselves, as argued by ^{Ferrari et al. (2018)}.

The phenotypic and genotypic correlations between 100SW and GW behaved similarly, with a high magnitude and significant at P<0.01 (rP = 0.97** and rG = 0.99**), as shown in Table 3. An increase in GW facilitates a greater accumulation of biomass and, simultaneously, GY could also increase because the genetic correlation between the GY and GW was positive and significant (rG = 0.78*), along with 100SW (rG = 0.64*), which suggested a linkage or pleiotropic genetic effect. In an improvement program, the GW must be considered because of its effect on 100SW and GY and because of its impact on the commercial value of the grain, which, in the international market, confers economic benefits between 1 and 4% for the best quality grain (^{Mishili et al., 2009}), especially with a cream color. These significant associations have been shown in previous studies by ^{Moura et al. (2012)}, ^{Meena et al. (2015}), ^{Hemavathy et al. (2015)} and ^{Lekshmanan and Vahab (2018)}. Selection with 100SW, AG and NPP should be considered as the selection criteria for genotypes with the highest production per unit area.

The differences in the correlation coefficients between quantitative characteristics reported by different authors in legumes may be due to differences in genetic variability and environmental conditions (^{Pantoja et al., 2014}).

Path analysis

The direct and indirect effects of agronomic characteristics on grain yield were estimated by path analysis, as shown in table 4.

Based on the phenotypic correlations, the greatest direct effect on grain yield (GY) was estimated with the GW and a path coefficient of 2.07, followed by 100SW with -0.92, interpreted as absolute values. The lowest direct effect was estimated with the NSP and 0.15, followed by DF, HFP and NPP. The results partially agree with those reported by ^{Bezerra et al. (2001)}; ^{Meena et al. (2015)} and ^{Agrawal et al. (2018)} in regards to the low contribution of these characteristics to grain yield at the phenotypic level.

The characteristics NPP, HFP and NSP exerted direct, positive effects on grain yield; however, their indirect effects were negative by way of the GW. Selection with NPP and HFP can decrease the grain yield per plant when the purpose is the simultaneous modification of the plant architecture and grain yield because plants with a high number of pods and inserted higher cannot sustain their productive branches if they do not have a larger stem diameter, as indicated by ^{Rocha et al. (2009)}. However, the contribution of GW and 100SW in the selection of semi-prostrate growth habit plants should be considered because of their simultaneous, negative and positive influence, respectively, on grain yield.

Based on the genotypic correlations, the greatest direct effect was exerted by 100SW with a path coefficient of -13.64, followed by the GW with 11.42, while the lowest direct effect was obtained with NPP, 0.28. The characteristics GW, with 11.42, and NPP, with 0.28, exerted positive, direct effects on the grain yield, while HFP, NSP and 100SW exerted direct, negative effects. The NPP had a direct, positive effect on the grain yield, and its indirect effect on yield was negative by way of the GW.

The direct, negative effect at the genotypic level of 100SW may be the cause of the poor correlation with performance, as indicated by ^{Santos et al. (2014)} and ^{Velho et al. (2017)}. The importance of 100SW in breeding programs is seen when selecting for an increase in grain yield since it can be affected by GW, NSP and HFP through the competition for assimilates between pods of the same plant (^{Godim et al., 2008}).

The direct effects found at the phenotypic and genotypic levels with respect to grain yield presented a contrasting association in their magnitudes. Similar results were reported by ^{Ferrari et al. (2018)} for soybean when stratifying environments into favorable and unfavorable and reporting positive effects in the combined analysis of variance in favorable environments and negative effects in unfavorable environments. These authirs concluded that direct effects are altered by the edaphoclimatic conditions and genetic constitution of the cultivars (^{Santos et al., 2014}) and that environment stratification is a good strategy for minimizing the effects of the genotype x environment interaction and avoiding variation of the direct effects.

The path analysis at the phenotypic level recorded an R² = 0.984 and a residual effect of h = 0.016. At the genotypic level, the R² = 1.00 and residual effects (h = 0), which showed that all the variables that contribute to grain yield were included in the present study (^{Santos et al., 2014}).