quite close to those in SDM, which are replicated in DW and DWa. It is, therefore, interesting to compare our findings on jointness with those in DW, based on their criterion _Jij_<sup>_DW_</sup> in (3) and those in DWa, based on _Jij_<sup>_DW a_</sup> in (4). We do not find much evidence of jointness (see Fig. 5), with only pairs (1 _,_ 2) and (2 _,_ 4) displaying posterior odds in favor of jointness greater than 3. Weak jointness (with posterior odds over 2.5) exists for pairs (1 _,_ 3), (1 _,_ 4), (2 _,_ 3), (3 _,_ 5) and (5 _,_ 6). No jointness is found for triplets, with 2.2 being the highest posterior odds in favor of trivariate jointness, corresponding to the triplet (1,2,4). In contrast, evidence for disjointness abounds, with 99.1% of possible pairs indicating some disjointness and 70% displaying decisive disjointness. Such disjointness is found almost exclusively between relatively unimportant regressors. There is only one occasion of decisive disjointness between two variables each having over 10% marginal inclusion probability: the Latin American and Spanish colony dummies. Clearly, these dummies are likely to be substitutes, given the large amount of former Spanish colonies in Latin America. If we consider triplets of variables, we even find decisive disjointness in 98.2% of all combinations. Again, this tends to affect mostly combinations with relatively unimportant variables. Exceptions are the triplets (Fraction in tropical area, Malaria prevalence, Life expectancy) and (Fraction in tropical area, Malaria prevalence, Sub-Saharan dummy), where it is clear not all three variables involved are required to provide the information. We do, however, need two of them, since the variables are not found to be decisively pairwise disjoint.

<!-- Start of picture text --> j = 2 G Positive<br>3 G 4<br>4 G G GG GGG GGG GG G G<br>G G G<br>G G G<br>i = 1 GGGGGGGGG G GG G G G GGGGGGGGG G GG GGGG G G G G GGG GGGGG G GG GG GG GGGGG GG G GGGG GGGGGGG GGGG G G G GG G GGGG 2 G GG G GG G G G G GGGGG G G G G GG GGG G GGGG GG G GGGGGGGGGGGGG G GGGGGGGGGGG 3 GG G GG GGG GGG G G GG G GGGGGG G GGGGGG G G G GGGGGG G GG G G GG GG 4 GG GG G GGGGG GG G GG G GGGG GG GGGGGGGGGGGGGGGGGGGGGGGGG G GGGGGGG 5 GG G GGGGGGGG G G GG G G GG GGGGGGG G GGGGGGGGGGGGGGGGGGGGGGGGGGGGGG G G G G G GGGGG G G GG GGG G G G GGG GGGGGGG G GGGG ... GGG G GGGGGGGGGGG G GGGG G GGGGGGGGGGGGGGGG G G G G GG G GGGGG GG GGGGGGGGGGGG GG GG G GGGGGGGGGGGG G G GGGG G GGGG GG GG G GGG G GGG G GGGGGGGGGGGGGGGGGGG G GGGGGGGGGGG GG GGGGGGGGGGGG GG GGG GGGGGGGGGG G GGGGGGGGGG G GGGGGGG G GGGGGGGGGGGGGGGGGGGG GG GGG GG GGGGG G GGGGGGGGGGGGGGGGGGGGGG G GGGGGGGGGGGGG GGGG GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG G G G G G GGGGG G GG G GGGGGGGG G GGGG GG GGGGGGGGGGGG G GGGGG G GGG G GGGGG G GGGGGGG G GGG G GGGG GGG G G GGGGGGGGGGGGGGG G GGGG G GG G GG G GGGGGGGG GG GGGGG G GGG G G G G GG GGGGGGGGGGGGGGGGGGGGGGGGGGGG G G G G GG G GGGGG G GGG G G G GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG G GGGGGGGGGGGGG G GGGGGGG G GGGGGGG G GGGGGGGGGGGGGGGGGGGGGG G G G GGGGGGGGGG G GGGGGGGGGGGGG G GGGGGGG G GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG G GGG G GGGGGGGGG G GGGGGGGGGGGGGGG G GG G GGGGGGGGG GG GGGGGG G G G GGGGGGGGGGGGG G G GG GGGGGGGGGGGGG G G GGGG G GGGGGGGGGGGG G GGGGG G GG G GGGG G GGGG G G G GG G G G GGGGG G GGGGGGG GG G GGG GGGG G GGGGGGGG G GGG G GGG G G G GGGGG G GGGGGGGGGG G G G GGGG G G G GGGGGG G GGG G GGGGGGG G GGGGGGGG G GGG G GGGGGGGGGGGGGGGG G GGG G GGGGGGGGGGGGGGGGGGGG GG GGG G GG GG G GG GGG G GG G GGGGGG G G G GGGGGGGGGG G GGGG G GGGG G G GGGGGGG GG GGGGGGGGGGGGGGGGGGGGGGGG GG G GGGGGGGGGGGGGGGG G GGGGGGGGGGG G G G G GGGGGGGGGGGGGGGGGGGGGGGGGGG G GGGGGG G GGGGGGGGG GG GGGG G GGGGGGGGGGGGGGGGGGGGGGGG GG GGG G GGGGGGG GGG GGGG G G G GGG G GGGGGGGGGGGGGGGGG G GG G GGGG G GGGGGGG G GGGGGGGGGGGGGGGGG G GGGG G GGG G G G GGGGGGGGGGGGGGGGGGGGGGG G GGGGGGGGGGGGGGGGGGG G GGGGGGG GGG GGGGGG G GGGGGGGGGGGGGGGGGG G GGGGGG G GGG G GGGGGG G GGGGGGGGGGGGGGGGGGG GG GGGGG G G G GGGGGGGG G GGG G GGGGGGGG G GG G GGGGGGGGGGGG G GGGGGGGGGGGG G GG G GGGGGGGGGGGGGGG G G G GGGGG G G G GGGGGGGG G GGGGGGGGGGGGG G GGGGGGGGGG G GGGGGGG G GGGGGG G G GGGGGGGGGGGGGGGGGGGG G GGGGGG G GG G GGGGGGGGG Very Strong GGG GGGGGGGGGGGGGG GG G GG Decisive GGG GG G Positive GGGG G G GGG Strong GGG G GGG G G G G GGGGGGGGGGGGG G GGGG G GGGGGGGGGGGG G GGGGGGG G GG G GG G GGGGGGGGGGGGGGGGGGGGGGGGGGG G GGGGGGGGGGGGG G G GGG GGGGGGGGGGGGGGGGGGGG G GG G GGGGGGG G GG G G G G GG GGGGGGGGGGG G G G GGGGG GG GGGGGGGG G GGGGG G G GG GGGGGGGG G GG G GGGG G GGGGGGGGGGGGGGGGGGGGG GG GGGGGG G GG<br>G G GGG<br>G G<br>G<br>0 500 1000 1500 2000<br>Ordered by P(i), then by P(j)<br>2<br>0<br>−2<br>−4<br>−6<br>−8<br>log of Posterior Odds: P(i and j) vs P(i or j but not both)<br>−10<br><!-- End of picture text --> Fig 5. DW Data: Log posterior odds in favor of jointness, log( _Jij_ ).

In sharp contrast, DW and DWa find disjointness only between variables with more than 10% inclusion probabilities. However, they both identify the disjointness between the Latin American 13