Badgley, Smiley, Finarelli, supporting information , p. 1
Supporting Information
Supporting Information S1.—Calculation of diversity metrics
We followed methods of tallying diversity and calculating measures of diversification outlined in Finarelli and Badgley (2010) and Badgley and Finarelli (2013). To avoid sampling biases in estimates of origination and extinction rates, we excluded “singleton” taxa (those observed in a single time interval) (Foote 2000a). We estimated per-lineage rates of origination (p) and extinction (q) for each time bin i by: 𝑝(𝑖) = 𝐿𝑛[
𝑁 𝑏𝑡
(𝑖)+𝑁
𝐹𝑡
𝑁 𝑏𝑡
(𝑖)
(𝑖)
] , and 𝑞(𝑖) = 𝐿𝑛[
𝑁 𝑏𝑡
(𝑖)+𝑁 𝑏𝐿
𝑁 𝑏𝑡
(𝑖)
(𝑖)
]
(Foote 2000a, 2000b). In these expressions, N bt is the number of taxa surviving from time interval i–1 to i+1 (“bottom-top” boundary crossers), N
Ft is the number of taxa first appearing in bin i and surviving to bin i+1 (“First-top” crossers), and N
bL is the number of taxa surviving from time interval i–1 and appearing last in bin i (“bottom-Last” crossers).
We applied a continuity correction to N
Ft and N bL
, adding 0.5 to either count if it was zero in a given interval (Finarelli 2007). Diversification rate was calculated as: d ( i )

N
Ft
( i )

N bL
( i )
,
N bt
( i ) that is, the difference between originations and extinctions in each time interval i, scaled to the diversity passing through i. Turnover rate, which compares the set of species that did not pass through an interval to those that did pass through the interval, was expressed as: t ( i )

N
Ft
( i )

N bL
( i )
.
N bt
( i )
In order to assess the statistical significance in p(i), q(i), and d(i), we bootstrapped the temporal durations of fossil taxa with replacement for the well-sampled interval from 17 to
3 Ma, randomly assigning first appearances within the observed temporal range for 1000

Badgley, Smiley, Finarelli, supporting information , p. 2 replicates, and calculated estimates of origination, extinction, and diversification rates from the bootstrapped values. Confidence intervals around observed values were taken as 2 standard deviations of the bootstrap distribution (Table S2).
Assessing significance for t(i) differs from the procedures for the other metrics since we are interested in whether t(i) exceeds the amount of change necessitated by d(i). (Intervals of high diversification (positive or negative) must possess high numbers of taxa that do not pass through one interval boundary. In contrast, nearly balanced, but absolutely large p(i) and q(i) should produce high turnover even when d(i) ≈ 0.) For the case in which extinction rate is 0 with net positive diversification, d(i) is driven solely by originations. Manipulating extinction rates, as q(i) increases, the contribution of the extinction rate to t(i) increases. (A similar argument can be made for the absolute value of d(i) in the case of negative diversification with origination rate = 0.) A test statistic that determines whether the difference between d(i) and t(i) is significantly different from 0 is given by:

( i )
 d ( i )
 t ( i ) .
Relating δ (i) to p(i) and q(i) gives: if 𝑑(𝑖) ≥ 0, then 𝛿(𝑖) = −2𝑒 𝑞(𝑖)
+ 2
, and if 𝑑(𝑖) < 0, then 𝛿(𝑖) = −2𝑒 𝑝(𝑖) + 2 .
For further details about this test statistic, see Badgley and Finarelli (2013). Significance for δ (i) was assessed using 1000 bootstrap replicates (Table S2).

Badgley, Smiley, Finarelli, supporting information , p. 3
Supporting Information S2. Diversity metrics for fossil mammals of the Great Basin, based on data downloaded from the NeoMap database in September, 2012. Calculation of diversity metrics is explained in the supplementary text above. p(i) = per-capita origination rate, q(i) = per-capita extinction rate, d(i) = diversification rate, t(i) = turnover rate.
3
2
5
4
8
7
6
12
11
10
9
16
15
14
13
Time interval start
(Ma)
30
29
28
27
26
25
20
19
18
17
24
23
22
21
55
28
53
43
58
47
55
49
53
61
59
76
84
49
59
Presence/ absence diversity
26
29
31
17
17
14
1
28
0
0
14
0
0
0
2
1
4
3
7
6
5
11
10
9
8
15
14
13
12
19
18
17
16
23
22
21
20
Time interval end
(Ma)
29
28
27
26
25
24
41
26
43
36
41
46
54
49
53
55
56
67
84
49
59
Diversity excluding singletons
26
29
31
17
17
14
1
7
0
0
14
0
0
0
Number of
Originations
26
3
0
0
2
0
0
0
0
0
0
0
1
6
Number of
Extinctions (pi) (qi) (di) (ti)
0 0.000 0.000
0 0.109 0.000 0.115 0.115
14 0.125 0.659 -0.800 1.067
0 0.000 0.000 0.000 0.000
3 0.000 0.194 -0.214 0.214
0 0.000 0.000 0.000 0.000
14 0.000 0.000
0 1.946 0.000 6.000 6.000
1 2.398 0.154 9.833 10.167
35 0.458 0.756 -0.548 1.710
28
4
15
7
60
18
0
10
10
15
17
6
5
20
0
0
38
0
13
6
25
20
3
0.000
0.647
0.847
0.105
0.365
0.256
0.336
0.245
0.000
1.494
0.000
0.308
0.163
0.714
0.847
0.154
-0.933
0.111
1.733
0.444
7 0.811 0.363 0.813 1.688
36 0.000 0.000
0.000
-2.545
1.333
-0.250
0.265
-0.750
0.000
4.364
1.333
0.472
0.618
1.333
10 0.389 0.389 0.000 0.952
9 0.520 0.343 0.273 1.091
19 0.665 0.721 -0.111 2.000

Badgley, Smiley, Finarelli, supporting information , p. 4
Supporting Information S3.—Bootstrap confidence intervals for diversity metrics over the period from 17 to 3 Ma. p(i) q(i) d(i)
 (i)
All Great Basin mammals Great Basin rodents
Mean St Dev 2 St Dev Mean St Dev 2 St Dev
0.1585
0.1545
0.3126
0.4861
0.3171
0.3090
0.6252
0.9723
0.4347
0.4208
1.2053
1.3864
0.8693
0.8416
2.4107
2.7728
Supporting Information S4.—Subsampling methods
To evaluate the effect of variable sampling intensity on the record of mammal diversity, we implemented a subsampling procedure based on the shareholder-quorum subsampling
(SQS) of Alroy (2010). Our modification of the SQS method involves random subsampling of species, weighting each species by its proportion of the total number of species occurrences in the dataset, i.e., the number of fossil localities at which the species is documented, divided by the total number of species occurrences over all fossil localities.
For each species that is drawn, its proportional occurrence in the total sampling pool contributes once to the “quorum level” of sampling, and subsampling of species is carried out, summing their proportional occurrences, until the specified quorum level (percentage of the total species occurrences) is reached. We analyzed quorum levels of 0.80, 0.75, 0.67,
0.50, 0.33, and 0.25 for three datasets: (1) all mammals of the Great Basin (Fig. S1), (2) rodents of the Great Basin (Fig. S2), and (3) rodents of the Great Plains (Fig. S2). We applied a correction factor to the quorum level based on the proportion of species occurring only once from the entire set of species occurrences. This correction factor compensates for incomplete sampling of rare taxa. For additional details, see Badgley and Finarelli (2013, supplementary text) and Alroy (2010).

Badgley, Smiley, Finarelli, supporting information , p. 5
Supporting Information S5.—Results of subsampling for the Great Basin mammal record.
Compare subsampled curves with main text Figure 5A. “PA diversity” is presence-absence diversity, assuming range-through. Data were analyzed over the well-sampled time interval from 18 to 3 Ma at six different quorum levels.. The general pattern in the PA data is maintained through degraded sampling levels, with some damping at extremely low rates of sampling.

Badgley, Smiley, Finarelli, supporting information , p. 6
Suporting Information S6. Results of subsampling of rodent diversity from the Great
Plains and the Great Basin. Compare with main text Figure 8A. As with Figure S1, “PA diversity” is presence-absence diversity, assuming range-through. Great Plains data are from Finarelli and Badgley (2010). Data were analyzed over the well-sampled period from
17 to 6 Ma common to both datasets, at six different quorum levels. Note that for both records, the overall trends in diversity are captured at reduced sampling intensities.