Olson's Gap or Olson's Extinction? A Bayesian tip-dating approach to resolving stratigraphic uncertainty

Abstract

Adaptive radiations and mass extinctions are of critical importance in structuring terrestrial ecosystems. However, the causes and progress of these transitions often remain controversial, in part because of debates surrounding the completeness of the fossil record and biostratigraphy of the relevant fossil-bearing formations. The early–middle Permian, when a substantial faunal turnover in tetrapods coincided with a restructuring of the trophic structure of ecosystems, is such a time. Some have suggested the transition is obscured by a gap in the tetrapod fossil record (Olson's Gap), while others suggest a correlation between North American and Russian tetrapod-bearing formations allows the interval to be documented in detail. The latter biostratigraphic scheme has been used to support a mass extinction at this time (Olson's Extinction). Bayesian tip-dating methods used frequently in phylogenetics are employed to resolve this debate. Bayes factors are used to compare the results of analyses incorporating tip age priors based on different stratigraphic hypotheses, to show which stratigraphic scheme best fits the morphological data and phylogeny. Olson's Gap is rejected, and the veracity of Olson's Extinction is given further support. Tip-dating approaches have great potential to resolve debates surrounding the stratigraphic ages of critical formations where appropriate morphological data is available.

1. Introduction

Adaptive radiations and mass extinctions have occupied a central position in macro-evolutionary theory as explanations for major shifts in prevailing faunas/floras at particular points in time [1,2]. Examples of rapid radiations of novel lineages to fill ecospace left vacant by large-scale extinction events are common in the palaeontological literature [1,3–6]. However, such rapid turnovers are frequently surrounded by debates regarding the completeness of the fossil record; do these rapid turnovers represent genuine evolutionary events, or do they reflect gaps in the fossil record? Incomplete sampling of the replacement lineages prior to the turnover may lead to it appearing more abrupt than in reality, as may preservation gaps in the fossil record. Such debates as to whether such rapid turnovers and radiations represent genuine evolutionary events or gaps/incomplete sampling in the fossil record surround the radiation of placental mammals [7–9], crown birds [7,10], terrestrial animals (Romer's Gap) [11,12], angiosperm plants (Darwin's ‘abominable mystery’) [13] and the origin of Metazoa (the Cambrian Explosion) [14].

A variety of methods have been employed to separate the true biological signal of speciation and extinction from the vagaries of sampling and preservation to better understand such events. Gap analysis can place confidence intervals on the first and last appearances of taxa based on the length of gaps in the fossil record between occurrences [15,16]. These have been used to assess, for example, the radiation of neornithine birds [17]. Approaches like PyRate are also able to assess uncertainty in first and last appearances [18]. Alternatively, survivorship analyses based around proportions of taxa crossing boundaries between time intervals seek to simultaneously infer accurate origination and extinction rates as well as sampling/preservation probabilities [19–21]. However, these approaches require relatively dense fossil records, and in the case of the latter class of analyses, relatively finely dated fossil occurrences [19]. However, there are cases where such criteria are not met, such as in the debate surrounding the faunal transition between the early and middle Permian, a crucial period in the establishment of terrestrial ecosystems [22,23].

Terrestrial ecosystems in the early Permian were dominated by pelycosaurs (a paraphyletic grade of synapsids) [23,24] and amphibians (non-amniote tetrapods) [25,26]. During the middle and late Permian, this fauna was replaced by one dominated by therapsids (the larger synapsid clade containing mammals) and parareptiles (a stem reptile lineage) [27–29]. This faunal transition coincided with a substantial changes in the trophic structure of terrestrial ecosystems, when assemblages more characteristic of modern faunas start appearing in the fossil record [1]: herbivorous tetrapods dominating both in diversity and abundance [22,29].

Unfortunately, the progress and causes of both the faunal and ecological transition are obscured by uncertainties in stratigraphy and the completeness of the record. The early Permian tetrapod-bearing formations are found almost entirely in the USA and western Europe, then occupying equatorial latitudes, while those of the middle and late Permian are mostly known from palaeotemperate latitudes in Russia and South Africa [23,24]. This geographical separation of the localities makes it difficult to separate biogeographical and temporal trends [24,26]; do the differences between fossil assemblages represent latitudinal differences in environments or a global faunal shift at a point in time?

This difficulty is exacerbated by the uncertain stratigraphic correlations of latest Cisuralian formations of the USA and earliest Guadalupian formations of Russia. Lucas & Heckert [30] suggested a complete gap in the terrestrial vertebrate record during the Roadian, dubbed ‘Olson's Gap’. The pelycosaur-dominated formations from the USA (the youngest being the Chickasha Formation of Oklahoma and the San Angelo Formation of Texas) were deemed to provide a record only until the end of the Kungurian [31], while the earliest therapsid-dominated assemblages from Russia (the Kazanian fauna) were assigned a Wordian age [31] (figure 1a). Excepting the negligibly sampled Inta assemblage from Russia [31,33], Olson's Gap was considered devoid of tetrapod fossils, and so the progress of the transition was unknowable.

Figure 1.

Hypotheses of the stratigraphic correlations between the tetrapod-bearing assemblages of North America and Russia, and the timing of Olson's Gap. Intervals in grey do not bear tetrapod fossils. (a) The Gap A hypothesis, based on [14,32]. (b) The Extinction hypothesis, based on [18]. (c) The Gap B hypothesis, based on [22].

The discovery of the Russian parareptile Macroleter in the Chickasha formation was used as evidence for a correlation between the Chickasha and the San Angelo Formations in the USA and the Kazanian fauna in Russia during the Roadian [34] (figure 1b). Under this stratigraphic scheme, the period of the ecological and faunal transition, far from being unknowable, would be documented in greater detail than other stages in the Cisuralian and Guadalupian; the Roadian would be one of the few intervals in the Permian where tetrapods were sampled from both equatorial and temperate latitudes [35]. This stratigraphic scheme has formed the basis for many examinations of macro-evolutionary patterns in tetrapods [6,23,24,32,35], which have suggested the ecological and faunal turnover at this time was accompanied by a mass extinction: ‘Olson's Extinction’ [23].

Lucas [31,36] criticized this interpretation, suggesting the ammonite fauna of the Blaine Formation (a marine formation immediately overlying the San Angelo Formation) supported a Kungurian age. However, the ammonite fauna of the Blaine formation has also been used to support its equivalence with the Russian Kazanian fauna [33,37].

More recently, the stratigraphy of the Russian formations has been thoroughly revised, confirming the Roadian age of the Kazanian fauna [38]. Following this, Lucas & Golubev [39] argued that this does not close Olson's Gap, but rather shifts it earlier in time. The uppermost records from the USA were re-dated to earliest Kungurian, and Olson's Gap formed the latter half of the Kungurian (figure 1c).

Settling the stratigraphy of these formations is critical for understanding early–middle Permian faunal turnover. While traditional biostratigraphy has failed to provide a consensus, it is proposed here that a novel approach towards testing biostratigraphic hypotheses using Bayesian tip-dating methods might provide some resolution.

2. Materials and methods

(a). Use of Bayesian tip-dating in stratigraphy

Tip-dating approaches, such as the fossilized-birth-death (FBD) model [40], are methods of phylogenetic analysis where both phylogenetic relationships and branch lengths scaled to time are inferred simultaneously using both the character data and the ages of the fossil taxa. Uncertainty in the ages of fossils may be incorporated into such analyses with age priors, allowing the ages of tips to fall within a certain range rather than being fixed [41,42].

However, there are also means to explicitly test different stratigraphic hypotheses rather than simply allowing for uncertainty. Bayes factors are often used to compare the results of analyses produced using different priors, to see which best fit the observed data [43]. They have been used to test the impact of using different substation models [43,44] or models of rate variation [44–46]. Here, it is proposed that Bayes factors be used to test the impact of varying the age priors assigned to each taxon, to infer which ages best fit the data.

(b). Datasets

Three datasets were chosen for analysis. The first is the most recent analysis of early amniote phylogeny spanning a broad range of clades [47]. Two other datasets were used, representing more comprehensive analyses of subclades within amniotes: Caseidae [48] and Captorhinidae [49]. These two clades were selected because (A) they are among the most diverse and abundant taxa within the disputed formations, in particular the Clear Fork, Hennessey, San Angelo and Chickasha formations, and (B) they also contain a number of species from more reliably dated formations before and after this interval.

The specimen MBCN 15730 (a captorhinid from Mallorca) and the genus Kahneria (from the San Angelo formation) were added to the captorhinid dataset. Character scores for the former were taken from Liebrecht et al. [50], while the latter was scored from direct study of the specimens. The morphometric characters of the caseid dataset were removed due to concerns raised about the formulation and treatment of these characters [51] and a lack of a robustly tested method of treating such characters in the FBD model.

(c). FBD analysis

All three character matrices were subjected to an FBD skyline analyses in BEAST [52], using the sampled-ancestors package [53]. A relaxed clock model was employed, with rates drawn from a lognormal distribution. Rate heterogeneity between characters was modelled as a γ-distribution. The analyses were carried out with two runs containing four chains for 10 000 000 generations, sampling every 1000. 25% of trees were discarded as burn-in.

Each matrix was analysed three times, with the age priors each time representing the three stratigraphic hypotheses. Under the first (hereafter referred to as the Gap A hypothesis), Olson's Gap is judged to lie within the Roadian (figure 1a) [54]. Under the second (hereafter referred to as the Gap B hypothesis), the ages represent the most recent assessment of Olson's Gap, where it lies within the late Kungurian (figure 1b) [39]. Under the third (hereafter referred to as the Extinction hypothesis) Olson's Gap is closed [32].

In all analyses, the formation containing first appearance of each taxon is used to determine its age. The age priors were represented by a uniform distribution between the lowermost and uppermost age of each formation (as constrained by the tree hypotheses described above). Taxa from the Fort Sill locality, which has been radiometrically dated [55], were assigned fixed age priors at 289 Ma. While radiometric ages do have error margins, these are small, and including at least one fixed age prior in each analysis provides an ‘anchor taxon’ (Beast does not output where each taxon is inferred to sit on an absolute time scale if all taxa are assigned a range as their age prior). Ascendonanus from the Chemnitz formation was also assigned a fixed age prior of 290.6 Ma [56].

Stepping-stone analyses (a series of MCMC simulations that iteratively sample from probability distributions forming discrete steps between the posterior and prior distributions, placing increasing emphasis on priors, to see if hypotheses more consistent with the prior assumptions are producing trees with high likelihood) [57] in BEAST were used to infer the marginal likelihood of each hypothesis. The Bayes factor is double the difference in log likelihoods between two hypotheses.

3. Results and discussion

All three datasets support similar conclusions: the hypothesis best supported by Bayes factors is overwhelmingly the Extinction hypothesis (table 1). Relative support for the Gap A and Gap B hypotheses is variable; in the amniote dataset the Gap A hypothesis receives stronger support, but the Gap B hypothesis is found to better fit the captorhinid and caseid datasets (table 1). In all datasets, the Bayes factor separating the Extinction hypothesis for the two Gap hypotheses is ‘very strong’ (as defined by Kass & Raftery [58]).

Table 1.

Likelihoods and Bayes factor comparisons of the tip-dating analyses with age priors based on the three hypotheses. lnL = log likelihood; BF = Bayes factor.

dataset	hypothesis	lnL	BF compared with Gap A hypothesis	BF compared with Gap B hypothesis
amniotes [29]	Extinction	−5504.75	244.42	579.88
amniotes [29]	Gap A	−5626.96	—	335.46
amniotes [29]	Gap B	−5794.69	—	—
caseids [30]	Extinction	−1287.47	106.26	58.26
caseids [30]	Gap A	−1340.6	—	47.00
caseids [30]	Gap B	−1317.1	—	—
captorhinids [31]	Extinction	−638.93	45.04	26.4
captorhinids [31]	Gap A	−661.45	—	18.64
captorhinids [31]	Gap B	−652.13	—	—

The maximum clade credibility tree produced by the analyses receiving the highest support all show numerous taxa falling into the period supposedly covered by Olson's Gap and devoid of tetrapods (figure 2). In particular, the bulk of casied diversification occurs at this time, with the majority of divergences falling within the latest Kungurian (figure 2c).

Figure 2.

The maximum clade credibility tree from the analyses of each dataset with the highest likelihood (in each case the analysis where tip age priors are based on the Extinction hypothesis), with branch lengths representing time to first appearance of the tips, showing the inferred ages of taxa relative to the hypothesized position of Olson's Gap. (a) Amniotes [29]; (b) captorhinids [31]; and (c) caseids [30].

With three datasets strongly supporting the closure of Olson's Gap and the correlation of the Kungurian and Roadian tetrapod-bearing formations in Russia and the USA, we may provide much greater insight into the faunal and ecological transition, and in particular place greater constraint on the timing of the transition. The late Kungurian formations at both equatorial and temperate latitudes represent pelycosaur-dominated faunas, with the most abundant tetrapods being caseids, sphenacodontids and amphibians [59]. Across the Kungurian/Roadian boundary a divergence between the equatorial and temperate faunas is visible, with the equatorial faunas continuing to be dominated by pelycosaurian-grade synapsids, albeit with reduced diversity of amphibians [35]. The contemporary temperate faunas, on the other hand, were already characteristic of the middle–late Permian faunas dominated by therapsids and parareptiles [35]. This faunal transition doesn't occur until later in equatorial latitudes [35].

Analyses of species richness that have assumed a stratigraphic correlation between the Kungurian and Roadian formations of North America have shown a mass extinction at this time: Olson's Extinction. The initial study which showed the extinction [23] has been criticized not only for the ages assigned to the formations [60], but also for generating the diversity curve at the family rather than species or genus level [24,26], not accounting for incomplete sampling [24,26], and using stage-level time bins, thus conflating extinctions occurring throughout the Kungurian into a single event [60]. Recent studies, however, have found the extinction to still be shown when addressing these issues [6,15,26,28,61]. With the results obtained here it is hoped that the final uncertainty regarding the ages of the relevant formations may be better resolved, and Olson's Extinction may be considered robustly supported.

4. Conclusion

The uncertainty surrounding the ages of the early–middle Permian tetrapod-bearing formations has persisted for nearly two decades. This might be surprising given the geology of the early Permian formations in the USA; the terrestrial formations are intercalated by marine formations, which one would hope could provide more reliable age constraints. However, in this case, the debates regarding the age of the index fossils within the Blaine Formation have not been resolved. Similar debates regarding the precise timing of turnovers and mass extinctions have surround, for example, the late Devonian and end Triassic mass extinctions; such debates have great implications for studying the causes and progress of these events [62–65].

The method proposed here provides data sources from which the ages of formations may be inferred rather than relying on correlations between specific taxa with desirable properties (which are often not applicable to terrestrial tetrapods). The tip ages are assessed using a combination of morphological data, evolutionary modelling and priors regarding stratigraphic uncertainty, and the method may be applied to any group of organisms for which a phylogenetic character matrix exists. Skyline models also permit variation sampling and extinction priors, providing a further means of testing gap and extinction hypotheses [66]. Whereas previous attempts to quantify sampling and extinction rely on assumptions of particular conditions being met, Bayesian tip-dating approaches are able to sum likelihoods over a range of specific hypothesis more consistent with a general one. Bayesian tip-dating approaches are a flexible and potentially powerful tool for examining a variety of macro-evolutionary questions.

Data accessibility

This article has no additional data.

Competing interests

I declare I have no competing interests.

Funding

N.B.'s research was funded by Deutsche Forschungsgemeinschaft grant no. BR 5724/1-1, Palaeontological Association Research grant no. PA-RG201901 and a Collections Study Grant from the American Museum of Natural History.