Table A1. List of parameters used in the conStruct model, along with their descriptions and priors.

Parameter	Description	Prior
$\mathit{\gamma }$	Global covariance due to shared ancestral frequency	$\gamma \sim \mathcal{N}\left(\mu =\mathrm{Var}(\overline{f}),\sigma =0.5\right)$
${\mathit{\alpha }}_0^{\left(\mathit{k}\right)}$	Controls the sill of the covariance matrix in layer k	${\alpha }_0^{\left(k\right)}\sim \mathcal{N}\left(\mu =0,\sigma =1\right)$
${\mathit{\alpha }}_{\mathit{D}}^{\left(\mathit{k}\right)}$	Controls the rate of the decay of covariance with distance in layer k	${\alpha }_D^{\left(k\right)}\sim \mathcal{N}\left(\mu =0,\sigma =1\right)$
${\mathit{\alpha }}_2^{\left(\mathit{k}\right)}$	Controls the shape of the decay of covariance with distance in layer k	${\alpha }_2^{\left(k\right)}\sim U\left(0,2\right)$
${\mathit{\eta }}_{\mathit{i}}$	The nugget in population i (population specific drift parameter)	${\eta }_i\sim \mathcal{N}\left(\mu =0,\sigma =1\right)$
${\mathit{\phi }}^{\left(\mathit{k}\right)}$	Layer-specific shared drift in layer k	${\phi }^{\left(k\right)}\sim \mathcal{N}\left(\mu =0,\sigma =1\right)$
${\mathit{w}}_{\mathit{i}}$	Admixture proportions sample i draws across K layers	$w_i\sim \text{Dir}\left({\alpha }_1\dots {\alpha }_K=0.1\right)$

The mean of the Normal prior on γ, $\text{Var}\left(\overline{f}\right),$ is the variance of the sample mean allele frequencies across loci.