The modified gap excess ratio (GER*) and the stratigraphic congruence of dinosaur phylogenies

Palaeontologists routinely map their cladograms onto what is known of the fossil record. Where sister taxa first appear as fossils at different times, a ghost range is inferred to bridge the gap between these dates. Some measure of the total extent of ghost ranges across the tree underlies several indices of cladistic/stratigraphic congruence. We investigate this congruence for 19 independent, published cladograms of major dinosaur groups and report exceptional agreement between the phylogenetic and stratigraphic patterns, evidenced by sums of ghost ranges near the theoretical minima. This implies that both phylogenetic and stratigraphic data reflect faithfully the evolutionary history of dinosaurs, at least for the taxa included in this study. We formally propose modifications to an existing index of congruence (the gap excess ratio; GER), designed to remove a bias in the range of values possible with trees of different shapes. We also propose a more informative index of congruence--GER*--that takes account of the underlying distribution of sums of ghost ranges possible when permuting stratigraphic range data across the tree. Finally, we incorporate data on the range of possible first occurrence dates into our estimates of congruence, extending a procedure originally implemented with the modified Manhattan stratigraphic measure and GER to our new indices. Most dinosaur data sets maintain extremely high congruence despite such modifications.