DOI: 10.5061/dryad.rxwdbrv6g
title: Supplementary information for: The effects of geographic range size and abundance on extinction during a time of ‘sluggish’ evolution

description: Geographic range size and abundance are important determinants of
 extinction risk in fossil and extant taxa. However, the relationship
 between these variables and extinction risk has not been tested
 extensively during evolutionarily ‘quiescent’ times of low extinction and
 speciation in the fossil record. Here we examine the influence of
 geographic range size and abundance on extinction risk during the late
 Paleozoic (Mississippian–Permian), a time of ‘sluggish’ evolution when
 global rates of origination and extinction were roughly half those of
 other Paleozoic intervals. Analyses used spatio-temporal occurrences for
 164 brachiopod species from the North American midcontinent. We found
 abundance to be a better predictor of extinction risk than measures of
 geographic range size. Moreover, species exhibited reductions in abundance
 prior to their extinction, but did not display contractions in geographic
 range size. The weak relationship between geographic range size and
 extinction in this time and place may reflect the relative preponderance
 of larger-ranged taxa, combined with the physiographic conditions of the
 region that allowed for easy habitat tracking that dampened both
 extinction and speciation. These conditions led to a prolonged period (19
 – 25 Myr) during which standard macroevolutionary rules did not apply.
description: <strong>Spatiotemporal occurrence
 data</strong>: Individual, global specimen occurrences for
 brachiopod species present in the Carboniferous–Permian of the
 midcontinent of the United States were obtained from multiple,
 spatially-explicit databases, including the Division of Invertebrate
 Paleontology, Biodiversity Institute (KUMIP), the Yale University Peabody
 Museum of Natural History (YPM), and the Paleobiology Database (PBDB). A
 total of 32,766 specimen occurrence records were obtained from existing
 databases and digitization efforts, comprising 4,998 records from the PBDB
 and 27,768 records from the KUMIP and YPM. Only midcontinent species were
 targeted. However, the entire geographic range of these midcontinent
 species was reconstructed globally to capture true extinctions rather than
 local extirpations. Specimen records from KUMIP and YPM were chosen
 because these institutions have large numbers of brachiopod specimens from
 the midcontinent, with a high degree of stratigraphic and geographic
 control. We retained only occurrences with geographic uncertainty radii
 under 50 km. Records that lacked species-level identifications (those
 including sp., cf., aff., or ? in the species designation) or those that
 did not have stratigraphic information to the level of formation were
 removed. Taxonomy was standardized and updated using Muir-Wood and Copper
 (1960), Hoare (1961), Moore (1964), Williams et al. (1965), and Carter and
 Carter (1970), which represent key references on brachiopods from this
 region and time interval. To ensure that distributional
 data were derived from geologic units of similar ages, a stratigraphic
 database for the midcontinent was generated from extensive survey of the
 primary literature (see Suppl. Material). Informal North American stages
 (e.g., Kinderhookian – Guadalupian, Heckel and Clayton 2006; Menning et
 al. 2006) were followed to allow for the highest temporal resolution
 whilst maintaining the greatest sample size. Occurrences that could not be
 classified confidently to a North American stage were removed from
 analysis. Origination and extinction rates in each LPIA North American
 stage (Chesterian – Leonardian) were calculated using the modified
 gap-filler method of Alroy (2015) in R v.3.4.1 (R Core Team 2017) using
 the ‘divDyn’ v0.8.0 package (Kocsis et al. 2019). The modified gap-filler
 method of Alroy (2015) was used to minimize potential bias (e.g., those
 associated with the Signor-Lipps effect) whilst maintaining precision and
 accuracy. Rates from stages with &lt; 100 occurrences were not
 recorded but used in calculations. To facilitate comparison with published
 species-level Paleozoic rates (e.g., Stigall 2010; Kolis 2019), we
 additionally calculated extinction and speciation rates as
 per-million-year rates using the equations of Foote (2000).
 We assigned each species a chronostratigraphic duration based on
 the longest combination of (1) the chronostratigraphic duration reported
 in the PBDB; (2) the lithostratigraphic units the species occurred in
 according to Carter and Carter (1970); and (3) the lithostratigraphic
 units containing the species within museum databases. The
 chronostratigraphic ages of the lithostratigraphic units listed in the
 above sources were determined using the compiled stratigraphic literature
 (see Suppl. Material) and the National Geologic Map Database (or Geolex
 https://ngmdb.usgs.gov/Geolex/search). These chronostratigraphic durations were consulted when calculating per-million-year extinction and speciation rates, such that species with gaps in their records were never spuriously counted as extinctions. We tested the correlation between extinction and speciation rates using a generalized linear model (GLM) with a Gaussian distribution in R v.3.4.1. To test for the effect of differential preservation on macroevolutionary rates, speciation and extinction rates were correlated with sampling intensity (estimated as the total number of brachiopod occurrences per stage, Powell 2005) using a GLM with a Gaussian distribution in R v.3.4.1. A positive correlation between evolutionary rates and sampling intensity could indicate that macroevolutionary rates were driven by differences in sampling intensity rather than biological patterns (Powell 2005). We ensured that paleogeographic analyses were conducted on spatially unique occurrences by culling each species to a single occurrence within an occupied grid cell of 0.025° x 0.025° resolution for each stage (equivalent to ~3 km at the equator). This procedure removed artificial inflation of spatially unique occurrences caused by differences in georeferencing protocols among institutions and individuals; for example, two museum workflows yielding different decimal degree latitude and longitude estimates for the same collection locality. We removed singletons from analyses (i.e., any species by time bin with n = 1 spatially unique occurrence) to limit the effect of poorly sampled taxa. After removal of singletons, there remained 29,720 individual occurrences (4,915 of which were spatially unique) belonging to 164 species in 83 genera. The resulting species by time bin datasets were imported into ArcGIS v.10.5.1, and the present-day latitude/longitude coordinates were rotated to their paleo-position using the University of Texas Institute for Geophysics (UTIG) plate model in PaleoWeb v.1.0 (Rothwell Group Inc). Paleo-coordinate reconstructions were performed based on the start of the appropriate stage in millions of years before present (Fig. 1). Due to the equatorial position of Laurasia in the late Paleozoic, we applied the South American Albers Equal Area Conic map projection to reconstructed paleolatitude and paleolongitude occurrences before range-size metrics were calculated. The South American projection was chosen given the preponderance of coordinates located in the region occupied by present-day Brazil once they were rotated to their paleolatitude and paleolongitude. <strong>Geographic range-size metrics: </strong>We quantified geographic range size and abundance for each unique species by stage. Geographic range was quantified using two different metrics: minimum convex hull and latitudinal range (for an example, see Fig. 1). A convex hull is a two-dimensional metric that estimates the amount of area occupied by a taxon and was calculated as the median of a series of convex hulls produced by exhaustive jackknifing of individual occurrence points (e.g., Stigall and Lieberman 2006; Hendricks et al. 2008; Myers and Lieberman 2011; Darroch and Wagner 2015; Saupe et al. 2015; Darroch et al. 2020). This method has been shown to be especially efficacious for quantifying ranges of fossil taxa (Darroch and Saupe 2018; Darroch et al. 2020). If a species was characterized by only two spatially unique occurrences, a 10 km buffer was applied to each occurrence, and the area of the resulting line substituted for the convex hull (Hendricks et al. 2008; Myers and Lieberman 2011). Each convex hull geographic range estimate was log transformed for normality. Latitudinal range (maximum observed paleolatitude minus minimum observed paleolatitude) is also used commonly to characterize geographic range sizes (Powell 2005; Powell 2007; Foote and Miller 2013; Finnegan et al. 2016; Balseiro and Halpern 2019; Darroch et al. 2020). Unlike a convex hull, latitudinal range is a linear metric and may reflect breadth of thermal tolerance (Jackson 1974; Stanley and Powell 2003; Powell 2007; Sunday et al. 2012), with larger latitudinal ranges potentially indicating greater thermal tolerances. Latitudinal range estimates were square root transformed for normality. Abundance was quantified as the number of occurrences for a species within a stage. Calculating population size is not easy, even for modern organisms (He and Gaston 2000). However, occurrence data have been shown to provide adequate estimates of average abundance for both fossil and modern organisms (Buzas et al. 1982; Kunin 1998; Alroy 2000; He and Gaston 2003). Abundance estimates were square root transformed for normality. All three variables (convex hull, latitudinal range, and abundance) were calculated in R v.3.4.1 (R Core Team 2017) using the packages sp v.1.3-2 (Pebesma and Bivand 2005; Bivand et al. 2013) and PBSmapping v.2.72.1 (Schnute et al. 2013).