Fig. 1. Theoretical and empirical behavior of existing and corrected estimators.

HE regression (${\widehat{h}}_{\mathrm{HE}}^2$) and REML (${\widehat{h}}_{\mathrm{REML}}^2$) estimates for varying phenotypic mate correlations ($r$) in simulated datasets ($n$ = 64,000) assuming that $h_0^2=.5$, that all causal variants are measured, and that AM has reached equilibrium. Values of ${\widehat{h}}_{\mathrm{HE}}^2$ are consistent with our closed-form approximation ($\mathbb{E}\left[{\widehat{h}}_{\mathrm{HE}}^2\right]$) under the assumption of exchangeable loci. Our corrected estimators, ${\widehat{h}}_{\mathrm{\infty }}^2$and ${\widehat{h}}_0^2$, which are based on ${\widehat{h}}_{\mathrm{HE}}^2$ and $r$ and assume equilibrium, recover the true equilibrium ($h_{\infty }^2$) and panmictic ($h_0^2$) heritabilities. Further, for a given observation of ${\widehat{h}}_{\mathrm{HE}}^2$ for a trait under disequilibrium AM, the current generation heritability ($h_t^2$) and $h_0^2$ are probabilistically bounded in expectation (teal and red regions respectively; see main text).