Improving melon root systems by traditional breeding is one component of the program to develop multiple-stress-resistant melons at the Texas Agricultural Experiment Station, Weslaco. Ten diverse melon lines representing four horticultural groups were intercrossed utilizing a Design II mating scheme. The male parents were: `PI 403994,' `Perlita,' `Doublon,' `Caravelle', and `PI 525106.' The female parents were: `Créme de Menthe,' `Magnum 45,' `BSK,' `PI 124111 × TDI', and `Deltex.' F1 progeny were grown in pasteurized sand in the greenhouse using a randomized complete-block design with four reps. After 4 weeks, root systems from all plants were carefully washed to remove the sand. Each root system was then placed onto a glass, plated, and scanned into the computer software Rhizo Pro 3.8 (Regent Instruments, Quebec). This software calculated root lengths of various diameter classes, root area, and root tip number. All data was input into Agrobase software for calculation of genetic variances based on Design II analysis. Significant differences of contributions by male parents to progeny variation were few. Only length of roots with 1.0- to 1.5-mm-diameter and vine length were significantly different. Differences in contributions by female parents to all traits except root tip number were highly significant. No significant interaction effects were observed for any trait. Narrow-sense heritability estimates were moderate to high for all traits. The range was from 0.56 for root tip number by males to 0.81 for both length of 0.5- to 1.0-mm-diameter roots and vine length for females. Estimates for total root length (0.76) and root surface area (0.77) were high. The lack of male by female interaction suggests very low dominance genetic variation and contributed to high heritability estimates, which represent predominantly additive gene action. Additive genetic variation allows more-efficient progress by selection, making the potential for root system improvement favorable.
estimates. Broad-sense heritability (H) was calculated as the ratio of the genotypic variance over the phenotypic variance of the F 2 generation ( Allard, 1960 ): Narrow-sense heritability (h 2 ) was estimated using F 2 and backcross generation
), and the sum of growth phase interactions (V G×E ) was also estimated, where G is genotype and E is environment. Narrow- (h 2 ) and broad-sense (H 2 ) heritability was estimated by the genetic variance from the REML model, where V P = (V A + V D + V
4-year-old offspring including 16 full-sib and 28 half-sib families ( Table 1 ) grown in Kamal Abad Research Station, Seed and Plant Improvement Institute, located at Karaj, Iran (lat. 35°48′ N, long. 51°2′ E). Table 1. Narrow-sense heritability in
population ( Falconer and Mackay, 1996 ; Nyquist, 1991 ): where H is broad-sense heritability, VG is genetic variance, VP is phenotypic variance, VA is additive variance, VD is dominance variance, and VE is error variance. Narrow-sense heritability ( h 2
( Robinson et al., 1955 ). Heritability, effective factors, and genetic gain. The method used to estimate narrow-sense heritability was adapted from Fehr (1991) : Broad-sense heritability estimates were calculated using the method described by Wright (1968
Galleta and Maas, 1990 ; Hancock et al., 2008 ). Information on genetic parameters for annual production systems have mainly been generated using the University of California–Davis breeding population. Narrow-sense heritabilities for plant growth traits
was regarded as genotypic variance ( V g ), and the interaction of genotype (FP, PP, or Progeny) and the season/pruning severity was treated as the genetic-environmental variance ( V g × e ). The narrow-sense heritability was calculated as h 2 = V
coefficients of the genetic effects in the equation ( Carson and Hooker, 1981 ; Mather and Jinks, 1971 ). The significance of the joint scaling test, as tested by χ 2 , provided evidence of non-allelic interactions. Narrow-sense heritability was calculated as
within-family effect, an error associated with an observation on an n-th tree in the j-th family planted in the i-th block, (0, σ 2 ω ). Individual-tree, within-family, narrow sense heritability was calculated according to Cotterill (1987) . Narrow sense