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. Author manuscript; available in PMC: 2013 Apr 21.
Published in final edited form as: J Theor Biol. 2011 Apr 5;299:97–105. doi: 10.1016/j.jtbi.2011.03.034

Table 1.

Neighbor IBD probabilities on graphs

Graph family Neighbor IBD probability q Low-mutation approximation
Infinite 1D lattice 1u(2u)1u 12u+O(u)
Finite 1D lattice qN21+q1N2qN2+qN2 * 1(N1)u+O(N3u2)
(Infinite) k-Cayley tree kk24(1u)2(k1)2(1u)(k1) 1k1(1kk2u)+O(u2k2)
Infinite 2D lattice 1agm(u,2u)1u ** 1πln(8u)+O(u)
Other finite graphs see text 1(N1)u+O(u2) ***
*

Due to Grafen (2007). The notation q=1u(2u)1u represents the q value for the infinite 1D lattice.

**

Obtained using equations (1), (6), and (3) in the case i = •.

***

Due to Taylor et al. (2007). The magnitude of the error term with respect to N depends on the graph structure.