Beta diversity quantifies the spatial structuring of ecological communities and is a fundamental partition of biodiversity, central to understanding many macroecological phenomena in modern biology and paleobiology. Despite its common application in ecology, studies of beta diversity in the fossil record are limited, particularly at regional spatial scales that are important for understanding macroevolutionary processes. The spatial scaling of beta diversity in the fossil record is poorly understood, but has significant implications due to temporal variation in the spatial distribution of fossil collections and the large spatio-temporal scales typically employed. Here we test the spatial scaling of several common measures of beta diversity using the Cenozoic shallow marine molluscan fossil record of New Zealand, and derive a spatially standardized time series of beta diversity. To measure spatial scaling we use and compare grid cell occupancy based on an equal-area grid and summed minimum spanning tree length, both based on reconstructed paleocoordinates of fossil collections. We find that beta diversity is spatially dependent at local to regional scales, regardless of the metric or spatial scaling utilised, and that spatial standardization significantly changes apparent temporal trends of beta diversity and, therefore, inferences about processes driving diversity change.

Supplementary Figure 1 - Cenozoic fossil collection locality paleocoordinates for each time bin

Supplementary Figure 2 - Cenozoic additive (β_Add) beta diversity plotted against summed MST length for each time bin

Supplementary Figure 3 - Cenozoic multiplicative (β_Whit) beta diversity plotted against summed MST length for each time bin

Supplementary Figure 4 - Cenozoic pairwise (β_Sor, β_Sim and β_Nest) beta diversity plotted against summed MST length for each time bin

Supplementary Figure 5 - Cenozoic multi-site (β_MSor, β_MSim and β_MNest) beta diversity plotted against summed MST length with fitted logarithmic trendlines

Supplementary Figure 6 - Cenozoic multi-site (β_MSor, β_MSim and β_MNest) beta diversity plotted against grid cell occupancy with fitted logarithmic trendlines

Supplementary Figure 7 - Cenozoic time series of spatially standardized (summed MST length and grid cell occupancy) multi-site beta diversity (β_MSor, β_{MSim and} β_MNest)

Supplementary Figure 8 - Plio-Pleistocene time series of spatially standardized (summed MST length and grid cell occupancy) multi-site beta diversity (β_MSor, β_{MSim and} β_MNest)

Supplementary Figure 9 - Cenozoic time series of multiplicative and additive beta diversity (β_Whit and β_Add)

Supplementary Table 1 - Time bins used for measuring the spatial scaling of beta diversity

Supplementary Table 2 - Equations and notations for measures of beta diversity adopted