Table 1.

Possible alternative models of spatial versus phylogenetic effects. These could be used to replace equation (2.2) in the text.

equation	description
$v_{ij}=(1-\varphi )p_{ij}+\varphi d_{ij}$	variance is a linear function of spatial and phylogenetic distances; ϕ measures the relative contribution of each.
$v_{ij}=(1-\varphi )p_{ij}+\varphi \text{exp}(\alpha d_{ij})$	variance is a linear function of phylogenetic distance and an exponential function of spatial distance. ϕ measures the relative contribution of each; α models the change in autocorrelation in space.
$v_{ij}=(1-\varphi )p_{ij}+\varphi d_{ij}^{\alpha }$	variance is a linear function of phylogenetic distance and a power function of spatial distance. ϕ measures the relative contribution of each; α models the change in autocorrelation in space.
$v_{ij}=\alpha [(1-\varphi )p_{ij}+\varphi d_{ij}]+(1-\alpha )v_m$	variance is a linear function of spatial and phylogenetic distances, plus a term measuring the contribution of other effects (vm); ϕ measures the relative contribution of spatial and phylogenetic effects; a measures the relative contribution of the spatial+phylogenetic versus other effects.