Badgley and Finarelli, Supplementary Information (text and Figures S1, S2)
Methods supplement: Quorum-based subsampling
We performed a random subsampling procedure modified from Alroy’s (2010a, b)
Shareholder Quorum Subsampling (SQS) method. Here, we use sampled sites as our proxy for sampling intensity. Within each region, we assigned each taxon a proportion,
p, equal to the number of fossil localities at which it was observed (i.e., species occurrences), divided by the total number of species occurrences. Therefore, if Species A were observed at 10 localities, and we were to observe a total of 1000 species occurrences over all the localities, then for Species A, p = 0.001.
We then randomly subsampled the taxa within each region. For each species taken in order, we tallied its p the first time it was sampled (but not subsequent times).
It is from this restriction that Alroy (2010b) derived the name for SQS; each shareholder of a company has a vote weighted to the proportion of the company s/he owns, but only exercises that vote once. We summed the cumulative proportions up to a predefined “quorum” level: q (Alroy 2010a, b). Because it is impossible to sample all rare taxa in the fossil record, we applied a correction to the quorum level by estimating completeness, calculating the percentage of occurrences for species occurring at multiple localities, and excluding those known from only a single locality (Good 1953,
Alroy 2010b). Dividing q by this value inflates q as a function of sampling completeness, such that if all taxa are sampled at multiple localities, q is unaffected, with the correction increasing as the proportion of taxa from single sites increases. For our data set, the records are actually quite complete: 96.3%, 86.5% and 92.3% of the occurrences in

Regions 1, 2 and 3, respectively, come from taxa that are found at multiple localities, and the impact of this correction for this particular study was minimal.
The aim of this random subsampling procedure was to assess diversity across regions, while attempting to control for differential sampling. For each iteration, the common taxa tend to be sampled to which a random sample of the rarer taxa is added.
This is true whether the common taxa are found in many localities, spread across many time intervals, or in many localities broadly distributed geographically, but restricted to a narrow temporal span. In either case, these are exactly the taxa we wish to recover in a subsampling iteration: it is the impact on the diversity curve of the extremely rare taxa
(those found only in a few localities) that we wish to ascertain. If oversampling of a specific time interval (for example the immediate post-MCO of Region 2) were responsible for a large number of occurrences of rare taxa in the NeoMap database that are restricted to that time interval, then this subsampling procedure would dampen such artificially inflated diversity peaks.
We randomly subsampled each region 1000 times, using values of q = 0.25, 0.33,
0.50, 0.67, 0.75, and 0.80. To avoid edge effects, we used all of the species occurrences in our data set, ranging from the late Oligocene (~30 Ma) to the Recent. The resulting subsampled diversity curves (mean species richness per interval over the 1000 iterations) in comparison to the raw presence-absence species richness curves for each region are shown in Fig. S1.
Literature cited in supplementary text

Alroy, J. 2010a. Geographical, environmental and intrinsic biotic controls on
Phanerozoic marine diversification. Palaeontology 53:1211-1235.
Alroy, J. 2010b. The shifting balance of diversity among major marine animal groups.
Science 329:1191-1194.
Good, I. J. 1953. The population frequencies of species and the estimation of population parameters. Biometrika 40:237-264.
Figure S1. Subsampled diversity curves for each region. Mean subsampled species richness per million-year time interval is given for 1000 iterations and compared to the raw presence-absence (PA) species richness curves (black line/symbols). The overall shape of the diversity curves is preserved through all of the quorum levels, although a notable flattening of the curves occurs at severely reduced sampling levels (e.g., q=0.25).
Large peaks in diversity are present during the MCO for both of the tectonically active regions (1 and 2), whereas the tectonically passive Region 3 shows a peak in diversity in the immediate post-MCO interval.

Figure S2. Subsampled diversity curves for each region scaled to a similar target sampling effort. Regions 1 and 3 are sampled to a quorum level of 0.33, yielding target sampling efforts of 341 and 335 species occurrences, respectively. Region 2 is subsampled to a quorum level of 0.75, yielding a target sampling effort of 315 occurrences. Error bars represent 2 standard deviations of 1000 iterations. The MCO diversity peak in Region 2 does not appear to be an artifact of sampling effort, nor are periods of greater passive-region diversity (Region 3) in the early Miocene and the immediate post-MCO intervals.