Estimating quantitative genetic parameters in haplodiploid organisms

Haplodiploid organisms (diploid females and haploid males) are genetically distinct in that they have asymmetrical genetic segregation, gene dosage compensation in the haploid male, maternal effects, and a general propensity to inbreed. Taking these characteristics into account, we demonstrate how conventional experimental designs and statistics derived to measure quantitative genetic parameters for diploid organisms can be applied to haplodiploid ones. First, the C matrix of the joint-scaling test is modified to test the additive-dominance model and then the calculations for fractions in the C matrices (for males and females) are shown for an infinite number of generations with both random and brother-sister mating. Second, analytical adjustments are outlined for the derivation of covariance between relatives using populations at either Hardy-Weinberg equilibrium or those that prefer to inbreed. Finally, four of the conventional designs (sib-analysis, offspring-parental regression, North Carolina III (NC III), and diallel cross) are modified and then compared according to their ability to deal with the experimental conditions encountered in haplodiploid systems. Although all designs can be used with caution, our analysis suggests that the NC III design is the most broadly applicable because it consistently meets the theoretical assumptions. The parameters we derive here for inbred populations are recommended for analysing the typically skewed genotypic distributions found in many natural populations of haplodiploid organisms. The theoretical and applied aspects of our work as well as the difference between our work and that for X-linked genes are discussed.