Heterosis, inbreeding depression and genetic divergence in maize

Heterosis and inbreeding depression are known to be opposite phenomena that depend on allele frequencies and directional dominance. Heterosis refers to the superiority of the hybrid over its parents by an increase in the mean of crossbred individuals, while inbreeding depression refers to the reduction in the phenotypic mean of a population. Heterosis has been described as a function of the squared of the genetic divergence in allele frequency of the parents (Δ), and dominance (d), while inbreeding depression depends on d and allele frequencies. We derived a model of heterosis based on genetic divergence in allele frequencies between the parents (Δ), dominance, and inbreeding depression. Similarly, to better understand Δ and inbreeding depression we estimate shared identical by descent (IBD) segments between inbred lines of maize. The main objective was to understand the underlying basis of heterosis and to estimate genetic diversity and progenitor’s genetic contribution based on the amount of shared IBD segments. To describe heterosis, six synthetic maize populations and eight inbred lines were used. Three crosses between synthetic populations, three between synthetic populations and the B129 inbred line, and six between inbred lines were evaluated in nine environments under a modified split-plot design with three replications. For easy deductions, heterosis model was defined under a single-locus two-alleles case and tested using a “goodness-of-fit” test. To estimate IBD segments, a set of 44 ex-PVP lines along with eight key ancestors of maize in the U.S. Corn Belt were selected. Shared IBD segments were identified by using a probabilistic approach based on a Hidden Markov Model (HMM) framework. Genetic diversity between individuals was estimated as 1 minus the kinship coefficient. Genome-wide kinship coefficients were calculated from the posterior probability of the IBD status at each locus. Our results showed that a single-locus two allele model of heterosis was adequate to describe the variation in