Grandparent roosters are crucial in poultry breeding programs and significantly influence future bird generations' genetic makeup and performance. However, these roosters face considerable challenges from heat stress, which can adversely affect their reproductive performance, semen quality, and overall health and welfare. Our study aimed to investigate the effects of heat stress on the genetics of semen characteristics, identify the appropriate temperature and humidity indices (THI), and determine the threshold point of heat stress to prevent thermal stress. We analyzed data from 3,895 records of 242 Thai native grandparent roosters in conjunction with the THI using 7 THI functions and the regression method. The threshold point of heat stress, genetic parameters, rate of decline of semen characteristics per level of THI, estimated breeding values and selection index values were analyzed using the multivariate test-day model in the AIREML and BLUPF90 programs. Based on the regression coefficient and statistical criteria of the lowest -2logL and AIC values, the results showed that a THI of 78 was considered the threshold point of heat stress. The estimated heritability values ranged from 0.023 to 0.032, 0.066 to 0.069, 0.047 to 0.057, and 0.022 to 0.024 for mass movement, semen volume, sperm concentration, and the semen index, respectively. The reduction rates of mass movement, semen volume, sperm concentration, and semen index at a THI of 78 were -0.009, -0.003, -0.170, and -0.083 per THI, respectively. The genetic correlations among the semen traits were moderately to strongly positive and ranged from 0.562 to 0.797. The genetic correlations between semen traits and heat stress were negative and ranged from -0.437 to -0.749. The permanent environmental correlations among the semen traits (0.648-0.929) were positive and greater than the genetic correlations. Permanent environmental correlations between semen traits and heat stress were negative and ranged from -0.539 to -0.773. The results of the selection indices showed that the higher the selection intensity was, the greater the degree to which the selection index corresponded to genetic progress. The recommendation for animal genetic selection is that the top 10% is appropriate because it seems most preferred. Therefore, using a multivariate test-day model and selection index for the high genetic potential of semen traits and heat tolerance in Thai native grandparent roosters makes it possible to achieve genetic assessment in a large population.
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