Table 5.

Comparison of exact solution (E) for the correlations of population gene frequencies in a 10-stone stepping-stone model for n = 10, m_∞ = 0.001, m = 0.1, N = 250, and p̄ = 0.2 with the approximation of this paper. The 10 × 10 lower triangle contains three numbers, the uppermost one being the exact correlation and the lower two our approximations F1 and F2. Approximation F1 is calculated with one value of σ² for all populations; approximation F2 is calculated using variances from approximations of σ² local to the two populations involved, and an average of these values is used to compute the covariance between the two populations.

	1	2	3	4	5	6	7	8	9	10
1	1.0
2	0.9332	1.0
	0.9286
	0.9287
3	0.8657	0.9226	1.0			Exact
	0.8600	0.9223				F1
	0.8600	0.9223				F2
4	0.7985	0.8501	0.9151	1.0
	0.7924	0.8499	0.9174
	0.7925	0.8499	0.9174
5	0.7350	0.7816	0.8398	0.9106	1.0
	0.7279	0.7807	0.8428	0.9144
	0.7279	0.7807	0.8428	0.9144
6	0.6770	0.7193	0.7715	0.8346	0.9092	1.0
	0.6679	0.7164	0.7734	0.8392	0.9134
	0.6680	0.7164	0.7734	0.8392	0.9134
7	0.6259	0.6645	0.7115	0.7681	0.8346	0.9106	1.0
	0.6136	0.6581	0.7104	0.7709	0.8392	0.9144
	0.6136	0.6581	0.7105	0.7709	0.8392	0.9144
8	0.5820	0.6174	0.6603	0.7115	0.7715	0.8398	0.9151	1.0
	0.5655	0.6065	0.6548	0.7104	0.7734	0.8428	0.9174
	0.5655	0.6065	0.6548	0.7105	0.7734	0.8428	0.9174
9	0.5449	0.5778	0.6174	0.6645	0.7193	0.7816	0.8501	0.9226	1.0
	0.5238	0.5618	0.6065	0.6581	0.7164	0.7807	0.8499	0.9223
	0.5238	0.5618	0.6065	0.6581	0.7164	0.7807	0.8499	0.9223
10	0.5140	0.5449	0.5820	0.6259	0.6770	0.7350	0.7985	0.8657	0.9332	1.0
	0.4883	0.5238	0.5655	0.6136	0.6679	0.7279	0.7924	0.8600	0.9286
	0.4883	0.5238	0.5655	0.6136	0.6680	0.7279	0.7925	0.8600	0.9287