| Summary: | Abstract Morphobiological indicators and selection index are helpful tools to obtain promising genotypes and selecting multiple traits for genetic improvement of the predator, Cryptolaemus montrouzieri (Mulsant) (Coleoptera: Coccinellidae). The present study was carried out at the Biological Control Department, Lattakia, Syria, during 2016. Three quantitative traits (QTs), fecundity, preying potential of the 3rd larval instar and larval developmental period, were studied through inbreeding program of 12 successive generations. The numerical changes of the (QTs) were studied across the generations and according to the three tested lines in comparison with control in order to determine the effect of each genetic line. Genetic parameters variances (phenotypic, genetic, environmental, phenotypic coefficient, genotypic coefficient, environmental coefficient, and broad-sense heritability) were estimated for each trait, separately and according to their approved lines, as well as the relative economic value of each trait involved in the design of the selection index equation. Obtained results showed that there were significant reductions in all the studied quantitative traits in the control, when (Po) was compared with (F12). Fecundity and reproduction showed the highest depression and response to the inbreeding program (42.28 and 46.93%), respectively. Statistical analyses of the fecundity line showed significant increases in length of the female, fecundity, and reproduction attained (+ 9.53, + 40.96, + 37.78%), respectively, while significant decreases in all other quantitative traits, survival rate, preying potential of female, preying potential of the 3rd larval instar, and larval developmental period, were recorded (− 2.09, − 27.81, − 15.84, and − 11.10%), respectively. Results of the second line (preying potential of the 3rd larval instar) showed significant reductions in all the studied quantitative traits except, preying potential of the 3rd larval instar and preying potential of female recording (+ 22.81 and + 0.83%), respectively. The third genetic improvement line (larval developmental period) significantly increased only in the same trait (+ 23.83%), while there were significant decreases in all others. Obtained results revealed that broader sense heritability of the three quantitative traits attained 47.43, 31.66, and 17.66%, respectively in the control, increased to 63.70, 40.80, and 33.50% in the three genetic lines of each trait, respectively. A selection index (index weights of the quantitative traits) was calculated. The application of this selection index is necessary to apply it in the genetic improvement programs in order to increase the efficacy of the predator breeding.
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