THE SHORTEST DISTANCE BETWEEN TWO POINTS ISN'T ALWAYS A GREAT CIRCLE: GETTING AROUND LAND MASSES IN THE CALIBRATION OF MARINE GEODISPARITY

In the assessment of Phanerozoic marine global biodiversity, there has been longstanding interest in quantifying compositional dissimilarities among sampling points as a function of their distances from one another (geodisparity). Previous research has demonstrated that dissimilarity tends to increase significantly with great-circle distance (GCD), but begins to stabilize at transoceanic distances. The accuracy of these assessments, and absolute comparisons among different temporal intervals, may suffer, however, because of intervening land masses that are not accounted for when distance is calibrated simply as GCD. Here, we present a new method for determining the shortest over-water distance (WD) between two marine locations, and we use the method to recalibrate for several Phanerozoic intervals previous measures of global geodisparity in the taxonomic compositions of marine biotas.

WD was determined using a cost-distance approach in ArcGIS, modified to work on a spherical, as opposed to a planar, surface. For a given time interval, a paleogeographic map with water and landmasses delineated was first digitized and converted to a raster with a cell size of 0.5 by 0.5 degrees. All cells covering water were assigned a value of 1, whereas land cells were assigned “No Value” so they would be excluded in calculations. The cost-distance algorithm was then used to determine the shortest over-water cell path and distance between any two sample points, taking into account latitudinal variations in the distances traversed across individual cells.

Results demonstrate two major effects of using WD. First, compositional dissimilarity between locations tends to increase more slowly with WD than with GCD. Second, pairs of locations with WDs that are at least 50% greater than their GCDs tend to have greater compositional dissimilarity to one another than those with more closely matching WDs and GCDs. These differences are expected as WD better represents the “true” distance between locations; they diminish at GCDs of 6000 km or more, when clear transoceanic paths between locations become more common. Despite these effects, using WD does not alter fundamental patterns of global geodisparity observed in previous research, but it does add interesting details to the picture.