Paleobiology, 41(3), 2015, pp. 369–376 DOI: 10.1017/pab.2015.10 Paleobiology Letters RAPID COMMUNICATION Phanerozoic diversity and neutral theory Steven M. Holland and Judith A. Sclafani Abstract.—Although Phanerozoic increases in the global richness, local richness, and evenness of marine invertebrates are well documented, a common explanation for these patterns has been difficult to identify. Evidence is presented here from marine invertebrate communities that there is a Phanerozoic increase in the fundamental biodiversity number (θ), which describes diversity and relative abundance distributions in neutral ecological theory. If marine ecosystems behave according to the rules of Hubbell’s Neutral Theory of Biodiversity and Biogeography, the Phanerozoic increase in θ suggests three possible mechanisms for the parallel increases in global richness, local richness, and evenness: (1) an increase in the per-individual probability of speciation, (2) an increase in the area occupied by marine metacommunities, and (3) an increase in the density (per-area abundance) of marine organisms. Because speciation rates have declined over time and because there is no clear evidence for an increase in meta- community area through the Phanerozoic, the most likely of these is an increase in the spatial density of marine invertebrates over the Phanerozoic, an interpretation supported by previous studies of fossil abundance. This, coupled with a Phanerozoic rise in body size, suggests that an increase in primary productivity through time is the primary cause of Phanerozoic increases in θ, global richness, local richness, local evenness, abundance, and body size. Steven M. Holland and Judith A. Sclafani. Department of Geology, University of Georgia, Athens, Georgia 30602-2501, U.S.A. E-mail: [email protected] Submitted: 18 December 2014 Accepted: 31 January 2015 Published online: 23 March 2015 Supplemental materials deposited at Dryad: doi:10.5061/dryad.n1d61. Introduction unique answer to how diversity has changed The species richness and evenness of local through the Phanerozoic. marine invertebrate communities have The Unified Neutral Theory of Biodiversity increased through the Phanerozoic (Bambach and Biogeography (Hubbell 2001) addresses 1977; Powell and Kowalewski 2002; Bush and diversity at scales from a local community to a Bambach 2004; Kowalewski et al. 2006; Alroy province or metacommunity, and therefore has et al. 2008). These trends mirror those of global the potential to offer a unified explanation for marine biodiversity, a pattern that is robust to changes in diversity at local, regional, and taxonomic level, methods of diversity tabula- global scales. Neutral theory simulates diver- tion, and sample standardization (Sepkoski sity and relative abundance structure through et al. 1981; Alroy et al. 2008). The connection models of birth, death, dispersal, and specia- between these parallel trends has been unclear, tion within a single trophic level. In neutral in part because local richness is typically much theory, diversity and relative abundance are less than 1% of global richness (Holland 2010). described over a wide range of spatial scales by Furthermore, the increase in evenness through θ, a recurring parameter in the models that is the Phanerozoic has been viewed primarily as defined as two times the metacommunity size a problem for sample standardization of (measured in numbers of individuals) multi- diversity, because the relative order of stan- plied by the per-individual probability of dardized diversity values can depend on the speciation (Hubbell 2001). Metacommunity sample-size quota (Alroy et al. 2001; Powell size is the product of metacommunity area and Kowalewski 2002). If estimated diversity and the density (per-area abundance) of organ- depends on sample-size quota, then changes in isms in the metacommunity. Metacommunities evenness are a concern because they prevent a and communities with larger values of θ have © 2015 The Paleontological Society. All rights reserved. 0094-8373/15 Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.126, on 26 Sep 2021 at 04:05:38, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2015.10 370 STEVEN M. HOLLAND AND JUDITH A. SCLAFANI TABLE 1. Classes and orders consisting primarily of suspension and deposit feeders that were included in this analysis. Classes Bivalvia, Hyolitha, Hyolithomorpha, Orthothecimorpha, Rostroconchia, Lingulata, Paterinata, Chileata, Kutorginata, Obolellata, Rychonellata, Strophomenata, Archaeocyatha, Irregulares, Regulares, Calcarea, Demospongea, Heteractinida, Hexactinellida, Stromatoporoidea, Gymnolaemata, Stenolaemata, Crinoidea, Blastoidea Orders Coenothecalia, Gorgonacea, Helioporacea, Cystiphyllida, Heterocorallia, Stauriida, Auloporida, Favositida, Halysitida, Heliolitida, Lichenariida, Sarcinulida, Tetradiida, Actiniaria flatter relative abundance distributions, greater metacommunity. Most data sets have five or evenness, and greater richness than those with fewer collections, but some have as many as 213. smaller values of θ. Overall, 1140 data sets with a total of 7916 Neutral theory has two critical assumptions. collections were analyzed. Analyzed collections First, a metacommunity is assumed to have a are included in Supplementary Appendix 1. fixed number of sites that can be occupied by Because neutral theory is based on diversity organisms, and those sites are always occu- dynamics at a single trophic level (Hubbell pied; this is known as the zero-sum rule. 2001), this study focuses on first-order con- Second, neutral theory assumes that all indivi- sumers, specifically suspension feeders and duals of all species are competitively equal, deposit feeders. For each data set, only species such that long-term changes in the abundance belonging to classes or orders that consist of any given species are controlled by ecological primarily of suspension and deposit feeders drift, not by niche characteristics. These were included (Table 1). In most collections, assumptions have attracted much criticism this culling results in the removal of a few (Chase 2005; Ricklefs 2006; Purves and Turnbull producers (algae) and predators (nautiloids 2010) and are unlikely to be strictly true. Even and vertebrates, for example). Trophic infor- so, neutral theory successfully predicts many mation was determined from the Paleobiology aspects of biodiversity and biogeography even Database. with modest departures from these assumptions An abundance matrix, with collections in (Rosindell et al. 2011), including a Phanerozoic rows and taxa in columns, was prepared for decline in speciation rates (Wang et al. 2013). each data set, and θ was calculated from the Therefore, neutral theory serves as a useful species abundance distributions of each data baseline for understanding biodiversity and set. For each data set, the best-fit θ was biogeography (Rosindell et al. 2012). estimated using the Etienne (2007) likelihood method, which produces a single estimate of θ when using all collections from a data set. This Materials and Methods method also produces a single estimate of the Relative abundance data from shallow marine migration parameter m, which was not used fossil communities were obtained from the in this analysis. Tests using the Etienne (2009) Paleobiology Database (paleobiodb.org, down- likelihood method, which allows for a different load June 2014). Supplemental data on deposi- value of m for each collection, but a single tional environment, lithology, lithification, and overall value of θ, showed that the values geologic age were also downloaded from the of θ did not differ between the 2007 and 2009 Paleobiology Database. Collections containing method, and that the 2007 method was only a single species, fewer than five individuals, substantially faster. Etienne’s methods, which or no numerical abundance values were removed. are available as an online supplement to his Collections were grouped into data sets, with articles, run in the PARI/GP algebra system, each data set representing a single reference available as a free download and run within a source and containing one or more collections UNIX terminal. from the same geographic region, geologic age, Estimates of θ for all data sets are included and depositional environment. Each data set in Supplementary Appendix 2, as are data on therefore contains replicate collections from the sample size, depositional environments, rock same setting and is regarded as a sample of a type, and lithification. Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.126, on 26 Sep 2021 at 04:05:38, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2015.10 PHANEROZOIC DIVERSITY AND NEUTRAL THEORY 371 Results The value of θ in marine invertebrate suspension-feeding and deposit-feeding meta- communities increases through the Phanerozoic, in both its median value and its variance (Fig. 1). Although data coverage is sparse during some periods, the intervals of relatively dense sam- pling indicate a first-order trend of an increase in θ through the Phanerozoic. Through the Silurian, median θ is generally less than 5, and slowly increases to values generally above 5 by the Recent, with a slope of 0.008 (95% boot- strapped confidence is 0.004 – 0.012). Variance likewise increases erratically through the Phanerozoic (Fig. 2). The time series is marked by several abrupt