Mannion and Upchurch (2010) introduced two metrics as a means of quantifying the completeness of the fossil record of a clade, applying it to sauropodomorph dinosaurs as their case study. These metrics are as follows: •

the Skeletal Completeness Metric (SCM) represents a value that approximates the completeness of a given specimen (SCM1) or taxon (SCM2) based on the number of elements preserved and their physical bulk, achieved by assigning percentages to different divisions of the skeleton, whereas;

Brocklehurst et al. (2012) applied this approach to Mesozoic birds but only used the CCM, arguing that it is a more appropriate metric than the SCM to evaluate the relationship between the quality of the fossil record and taxic diversity. In the present study we follow this approach for the same reasons. Following Brocklehurst et al. (2012), we also exclusively consider the CCM2 variant of the CCM, for which the combined information from all individuals is considered for taxon completeness rather than only the single most complete individual (Mannion and Upchurch, 2010). This provides the most complete measure of anatomical information about a given taxon.

For the purpose of this study, the CCM2 for the different anomodont species was determined based on the recently published phylogenetic dataset of Kammerer et al. (2011), which represents the most comprehensive (87 taxa, 71% of all anomodont species), balanced and up-to-date phylogenetic analysis of Permian and Triassic anomodonts. This dataset is a compilation of phylogenetic characters selected from 26 different references and the majority of character codings are based on personal examination of holotypes and additional specimens as well as information from original descriptions. A total of 163 characters were divided into four anatomical parts of the skeleton (skull, pectoral girdle, pelvic girdle, and limb). The only vertebral character in the dataset was included with characters of the pelvic girdle, as it is often identified based on the articular facets of the sacral ribs on the medial side of the ilium. The majority of anomodont characters relate to the anatomy of the skull (81.60%), followed by the limbs (9.20%), pectoral girdle (4.91%), and pelvic girdle (4.29%) (Fig. 1). In addition, we further subdivided these anatomical groupings of the characters based on the individual or multiple skeletal elements to which they refer (see Supplementary data). Using this approach, a completeness score was determined for each taxon included in the phylogenetic data matrix. In addition, an average CCM2 for each time bin was calculated in order to detect fluctuations through time.

The fossil record is generally considered to be strongly influenced by a number of different biases (Alroy et al., 2001, Peters and Foote, 2001 and Smith, 2001). An example for this particular study is that a lower completeness (CCM2 score) could be the result of a smaller number of preserved specimens in a given time bin. Hence, sampling effort may cause biases that could be reflected in a lower or higher mean CCM2, merely because a lack of sampling effort may mean not as many “good” or complete specimens are found, and vice versa. For this reason, we tested our CCM2 for correlation with three different proxies: •

number of localities;

For this part of the study, we restricted our analyses to the well-studied Karoo Basin, South Africa. Smith et al. (2012) published an up-to-date compilation of the number of individuals per taxon for each Assemblage Zone (AZ). In addition, we extracted the number of localities (farms) from the Karoo Database and ordered them by time bin. Outcrop area values for the individual assemblage zones were taken from King (1991). We also tested for correlation between completeness (CCM2 score) with taxic, phylogenetic and residual diversity estimates (see below), for example to test for potential Lagerstätten effects.

We calculated the correlations using: •

the non-parametric tests: Spearman's rank correlation and Kandell's tau, and;

With the Shapiro–Wilk normality test, we examined our data for normal distribution. We executed generalized differencing of time series (http://www.graemetlloyd.com/pubdata/functions_2.r). Statistics were performed using computer language “R” (R Development Core Team, 2012).

To determine the diversity pattern of anomodonts through time we compared taxic and phylogenetic diversity estimates to gain a comprehensive picture. Our taxic diversity estimate is based on the recent studies by Fröbisch (2008, 2009, 2013a, b). For the phylogenetic diversity estimate we used the phylogeny of Kammerer et al. (2011) as framework and plotted it on three different time scales following Fröbisch, 2008 and Fröbisch, 2009. The stratigraphic correlations of the South African assemblage zones with the international marine stages are based on Rubidge (2005; see also Fröbisch, 2009). Therein, the assemblage zone boundary dates match perfectly with the recently published radiometric dates in Rubidge et al. (Rubidge et al., 2013). A phylogenetic approach to determine diversity estimates by incorporating ghost lineages has long been suggested as means to avoid obvious biases resulting from a literal reading of the fossil record (Norell, 1992 and Norell and Novacek, 1992). We followed the criteria of Cavin and Forey (2007) for the marking ghost lineages. Finally, we calculated residual diversity estimates following the methods introduced by Smith and McGowan (Smith and McGowan, 2007) and refined by Lloyd (Lloyd, 2012) implemented in “R” (R Development Core Team, 2012)

For the global scale, Fig. 2B shows the mean completeness (CCM2) score plotted against substages of the Standard Global Chronostratigraphic Scale SGSC, which indicates an average completeness of 66.80% for the known anomodont fossil record. Anomodont completeness starts off relatively low with a CCM2 score of only 60.12% in the Middle Permian (Roadian) and thereafter more or less continuously increases throughout the Permian. The highest mean completeness level is recorded in the Earliest Triassic (Induan) with 86.63% followed by a drop down to the lowest CCM2 score of 0% in the anomodont-devoid Olenekian. Excluding the Olenekian, the mean CCM2 increases to 73.47%. The mean values for the Anisian, Ladinian and Carnian form a plateau increasing only slightly from 71.68% to 80.25% of completeness.

At the regional scale of the South African Karoo Basin, the mean completeness (CCM2) score for the anomodont fossil record is 77.37%, which is higher than for the global scale, with the highest completeness values in the early Late Permian Pristerognathus (91.33%) and Tropidostoma (90.75%) assemblage zones (Fig. 2D). The lowest completeness scores are recorded in the late Middle Permian Tapinocephalus AZ with 62.71%. After the early Late Permian high, anomodont completeness drops down to 69.17% in the Latest Permian Dicynodon AZ. However, most interestingly, the quality of the fossil record of anomodonts increases from the Late Permian to the Early Triassic despite the impact of the end-Permian extinction event, confirming the same signal at the global scale.

Figs. 2A and 2C show the taxic diversity estimate (TDE) and phylogenetic diversity estimate (PDE) over time at the global scale and the regional scale of the South African Karoo Basin. Anomodont TDE at the global scale (Fig. 2A) shows a consistent increase from one genus (Roadian) up to the maximum of thirty-nine genera in the Changhsingian. In the Induan, TDE collapses down to five genera and the Olenekian is completely devoid of anomodonts, which certainly represents an artificial gap and hence a bias of their fossil record. After the Permian–Triassic Boundary (PTB), the generic richness reaches a second peak of eighteen genera in the Anisian, followed by a subsequent decrease until the end of the Triassic. The pattern of anomodont PDE is very similar. It increases continuously throughout the Permian from one genus in the Roadian up to nineteen genera, but this overall peak is already reached in the Wuchiapingian rather than in the Latest Permian Changhsingian as in the TDE. The lowest level of PDE is recorded in the Olenekian, where just two genera are predicted. Thereafter, anomodont PDE rises to seven genera in the Anisian, followed by a final decline until the end of the Triassic.

The diversity pattern at the regional AZ-scale of the South African Karoo Basin demonstrates a similar pattern to that at the global scale but with some minor differences (Fig. 2C). For example, the first peak of TDE is already in the late Middle Permian Tapinocephalus AZ (Capitanian), followed by a distinct decline in the Pristerognathus AZ, where anomodont richness decreases from thirteen to eight genera. After this first decline, the observed occurrence increases continuously to a second and overall peak of 26 genera in the Cistecephalus AZ (boundary Wuchiapingian and Changhsingian). Hence, like in the PDE but in contrast to the TDE at the global scale, the TDE in South Africa does not collapse right after the overall peak. In the Latest Permian Dicynodon AZ (Changhsingian) the number of genera (24) is still high. However, a rapid decline occurs in the Earliest Triassic Lystrosaurus AZ with only five known genera. Following this, anomodont diversity increases one last time to 18 genera in the Cynognathus AZ followed by their final extinction at the end of Triassic. The phylogenetic diversity estimate counted for the AZ-scale shows two peaks over time: after a trough in the Tapinocephalus AZ, the PDE reaches a peak of thirteen genera in the Tropidostoma and Cistecephalus assemblage zones. Then the PDE shows a similar decline to the PDE at the SGCS-scale. The overall minimum is represented by just three genera in the Lystrosaurus AZ. A second and final peak is recorded for the Cynognathus AZ with ten genera. The residual diversity estimates at the AZ-scale are based on the outcrop and the number of farms per assemblage zone as proxies for rock volume (Fig. 3). The former is in good correspondence with recently published estimates (Fröbisch, 2013b), which used the same proxy but slightly older taxonomic treatments, for example regarding Dicynodon (Kammerer et al., 2011). Interestingly, there is a minor divergent signal between the RDEs using the different proxies, sometimes displaying peaks or troughs, respectively, in the same time zones. However, none of these divergent signals are significant as they are within the confidence intervals. More importantly, the general pattern of all curves is identical: •

there is no significant trough at the end of the Middle Permian;

The Shapiro–Wilk test confirms that all data series used in this study have a normal distribution (see Supplementary data). Subsequent correlation tests between biodiversity data, completeness scores and sampling proxies suggest a strong independence of these variables. Only at the global scale, the taxic and phylogenetic diversity show a borderline significant correlation with the completeness (CCM2) scores (Table 1; see also Supplementary data). However, this result changes into a weak and statistically nonsignificant correlation, when the anomodont-devoid Olenekian time bin is excluded from the analysis (see Discussion and Conclusion). This is further supported by our regional investigations of anomodont completeness, demonstrating a lack of statistically significant correlation between either taxic or phylogenetic diversity and completeness (CCM2) in South Africa (Table 1).

As a result of the well-studied assemblage zones in the South African Karoo Basin, we have been able to investigate different controls such as outcrop area in square kilometres, number of specimens and number of localities, to examine to what extent anomodont diversity and completeness are potentially biased by sampling effects. To test for potential biases caused by human sampling effort it is necessary to look at: •

the potential influence of the number of specimens (abundance) on the number of species (richness);

None of our tests display a significant correlation, rejecting these aspects of human sampling effort.

In general, the magnitude of each assemblage zone could have an impact on the fossil record, which is the reason why we have tested the outcrop area (km²) versus number of species as well. There is no evidence for a bias caused by geological factors, when considering the complete data. However, previous studies have demonstrated that Early Triassic time intervals represent distinct outliers with unusually low taxon counts despite increased sampling as a result of the end-Permian mass extinction (Benton et al., 2004, Fröbisch, 2008, Fröbisch, 2013a, Fröbisch, 2013b and Irmis and Whiteside, 2012). Hence, the Early Triassic Lystrosaurus AZ was here subsequently excluded from the respective datasets in an additional set of analyses to test the impact of the end-Permian extinction event on the relationship between anomodont diversity, completeness, and sampling proxies. After exclusion of the Lystrosaurus AZ from all data series, anomodont TDE shows a statistically significant and strong positive correlation with outcrop area as well as the number of farms (Table 1; see also Supplementary data).

As the completeness metric (CCM2) comprises information from multiple specimens for each anomodont species based on their phylogenetic character codings, a high completeness score could simply reflect a high abundance of the species. Hence, we tested whether there is a correlation between the CCM2 scores and the number of specimens. However, there is no statistically significant correlation between these variables, rejecting the hypothesis that abundance drives completeness in the anomodont fossil record (Table 1).

Finally, we calculated residual diversity estimates (RDE) for anomodonts based on the proxies for outcrop area and number of farms (localities) and subsequently tested for potential correlation between RDE and CCM2 as well as the phylogenetic diversity estimate (PDE). It is notable that in contrast to some previous studies (Mesozoic birds), there is no significant correlation between RDE and completeness. Moreover, residual diversity estimates for anomodonts are also not correlated with phylogenetic diversity estimates.