In classical quantitative genetics, the correlation between the phenotypes of individuals with unknown genotypes and a known pedigree relationship is expressed in terms of probabilities of IBD states. In existing models of the inverse problem where genotypes are observed but pedigree relationships are not, probabilities and correlations have either a Bayesian or a hybrid interpretation. We introduce a generative evolutionary model of the inverse problem based on the classic infinite allele mutation process, IBF (Identity by Function). Describing genetic resemblance in terms of functional (IBF) states defines a genetic architecture for a trait without reference to specific alleles or a population, treating a gene-scale functional region, rather than a SNP, as a QTL, and emphasizing locus weights and patterns of dominance over multiple alleles. This allows the reconciliation of bottom-up (genome sequence based) and (pedigree/population) calculations of heritability, as well as phenotype and gene effect prediction. We perform these calculations with simulated, pig, and human traits and identify new sources of uncertainty in heritability estimation that help explain differences in heritability estimates obtained by different methods, i.e. the 'missing heritability' problem.