Correlations between the stability and adaptability statistics of popcorn cultivars

Abstract

In plant breeding, correlations between the statistics of stability and adaptability of popcorn cultivars are not yet well understood. Therefore, the objectives of the present experiment was to investigate the correlations between $\sigma_{\rm di}^{2}$ and $\beta_{\rm i}$ from Eberhart and Russell, ω_i from Wricke, ${\text{S}}_{\text{i}}^{(1)}$, ${\text{S}}_{\text{i}}^{(2)}$ and ${\text{S}}_{\text{i}}^{(3)}$ from Huehn, P_i from Lin and Binns and the rank-sum from Kang, and indicate the most reliable method for selecting popcorn cultivars. These statistics were estimated by data of crop yield from 19 Brazilian genotypes under 21 environments and popping expansion under 16 environments. The ω_i, ${\text{S}}_{\text{i}}^{(1)}$, ${\text{S}}_{\text{i}}^{(2)}$, ${\text{S}}_{\text{i}}^{(3)}$ and $\sigma_{\rm di}^{2}$ were positively and significantly correlated indicating that just one in these five statistics is sufficient for selecting stable genotypes although they were not correlated with the means of crop yield and popping expansion. The $\beta_{\rm i}$ was negatively and significantly correlated with P_i for crop yield indicating that the most adaptable genotypes tend to have the lowest estimates of P_i. Although P_i was not correlated with ω_i, ${\text{S}}_{\text{i}}^{(1)}$, ${\text{S}}_{\text{i}}^{(2)}$, ${\text{S}}_{\text{i}}^{(3)}$, or $\sigma_{\rm di}^{2}$ statistics, it displayed positive correlation with the Index 1 (crop yield and popping expansion + ${\text{S}}_{\text{i}}^{(1)}$ rank) and Index 2 (crop yield and popping expansion + W_i) indicating that superior popcorn genotypes are also stable. Finally, both P_i and the rank-sum are useful statistics in breeding programmes where crop yield, popping expansion and stability are essential traits for selecting genotypes.