Table 1.

Parametrizing a historically informed model.

Generation g	Birth year	Epoch	$c_{g-1}$
1	1635–1640	1	1
2	1660–1665	1	0.9835
3	1685–1690	1	0.8602
4	1710–1715	1	0.8551
5	1735–1740	1	0.7826
6	1760–1765	1	0.5380
7	1785–1790	1	0.1418
8	1810–1815	2	—
9	1835–1840	2	—
10	1860–1865	2	—
11	1885–1890	3	—
12	1910–1915	3	—
13	1935–1940	3	—
14	1960–1965	3	—

For the non-European contributions in generations 1–7, the model enforces specified ratios of the African to the African-American contributions. For all generations g in epoch 1 (g from 1 to 7), the quantity $c_{g-1}=s_{1,g-1}/(1-s_{2,g-1})$ denotes, for individuals born in the African-American population in generation g, the fraction of their non-European parents who are African arrivals to North America rather than African-American residents. In our model, we inserted numerical values for this quantity estimated based on demographic data.