SPECIAL FEATURE
Test of Martin’s overkill hypothesis using radiocarbon
dates on extinct megafauna
Todd A. Surovella,1, Spencer R. Peltona, Richard Anderson-Sprecherb, and Adam D. Myersc
a
Department of Anthropology, University of Wyoming, Laramie, WY 82071; bDepartment of Statistics, University of Wyoming, Laramie, WY 82071; and
Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071
c
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Pleistocene extinctions overkill radiocarbon
temporal frequency distributions
J
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ust over 42 y ago, Paul Martin (1) proposed that humans
entered the contiguous United States via the Ice Free Corridor at ∼13,500 BP and there encountered almost three dozen
genera of now-extinct megafaunal mammals. Hunting of these
naïve prey fueled rapid human population growth, he argued,
resulting in both the colonization of the landmass stretching from
the southern terminus of the North American ice sheets to the far
tip of South America in 1,000 y, and the extinction of the mammoths, mastodons, camels, horses, ground sloths, and other large
mammal taxa that had inhabited the Western Hemisphere for
hundreds of thousands to millions of years before human arrival.
Martin (p. 973) closed his paper with the statement, “Should the
model survive future findings, it will mean that the extinction
chronology of the Pleistocene megafauna can be used to map the
spread of Homo sapiens through the New World.”
Central to this hypothesis is the idea that small numbers of
humans can have large ecological impacts and that those impacts
should be directly observable in the paleontological record. If we
accept that premise as true, then as Martin argues, it is possible to
assess the timing of human arrival independently of direct archaeological evidence by examining when megafaunal decline occurred across time and space. In this paper, we use databases of
radiocarbon dates on extinct megafauna from Eastern Beringia
(EB), the contiguous United States (CUSA), and South America
(SA) to estimate the timing of initial population declines that ultimately resulted in extinction. We intend this exercise to be both a
direct test of the timing of extinction as proposed by Martin (1) and
as an independent means of estimating the timing of human arrival
to each region. Similar approaches using paleoecological proxy
records as possible indicators of human arrival have been applied
elsewhere, particularly on islands (2–7).
www.pnas.org/cgi/doi/10.1073/pnas.1504020112
From this premise, we make two complementary arguments
pertaining to New World colonization. First, we expect initial
megafaunal declines for each region to correspond temporally
with the first evidence of human presence. Second, we expect that
the timing of megafaunal declines should be geographically patterned according to Martin’s (1) model in which the founding
population moved through EB and then south into the CUSA and
SA. When Martin published his classic work, radiocarbon calibration was not possible, so by necessity, he worked within the
radiocarbon time scale. For the CUSA, Martin estimated a mean
colonization age of ca. 11,200 14C y BP, or ca. 13,100 BP, and for
SA, ca. 10,700 14C y BP, or ca. 12,700 BP. Martin did not specify a
human arrival date for EB, except to suggest his model required
that “the time of human entry into Alaska need be no older than
11,700 [radiocarbon] years ago,” or roughly 13,600 BP.
Importantly, the expectation of a north to south spatiotemporal extinction trend across the Western Hemisphere should be
largely unique to the overkill hypothesis. There is no single climatic (8, 9) or catastrophic (10) extinction hypothesis that shares
this prediction. Therefore, this kind of analysis is not only capable of testing the overkill hypothesis, but of posing legitimate
challenges to other extinction hypotheses, with the possible exception of multifactor models that also invoke “first contact”
effects, such as the keystone herbivore (11), habitat modification
(12), and hyperdisease hypotheses (13).
We use two analytical techniques to identify dates of initial
megafaunal decline: for technical precision, an approach based on
spacings (time lags between consecutive ordered dates), and, for
simple understanding, an approach based on histograms of observed dates. The key property of spacings is that mean spacings
Significance
Coincident with the human colonization of the Western Hemisphere, dozens of genera of Pleistocene megafauna were lost to
extinction. Following Martin, we argue that declines in the record
of radiocarbon dates of extinct genera may be used as an independent means of detecting the first presence of humans in
the New World. Our results, based on analyses of radiocarbon
dates from Eastern Beringia, the contiguous United States, and
South America, suggest north to south, time, and space transgressive declines in megafaunal populations as predicted by the
overkill hypothesis. This finding is difficult to reconcile with other
extinction hypotheses. However, it remains to be determined
whether these findings will hold with larger samples of radiocarbon dates from all regions.
Author contributions: T.A.S. and S.R.P. designed research; T.A.S. and S.R.P. performed
research; T.A.S., S.R.P., R.A.-S., and A.D.M. analyzed data; R.A.-S. and A.D.M. contributed
new reagents/analytic tools; and T.A.S., S.R.P., R.A.-S., and A.D.M. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. Y.M. is a guest editor invited by the Editorial
Board.
1
To whom correspondence should be addressed. Email: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1504020112/-/DCSupplemental.
PNAS Early Edition | 1 of 6
ANTHROPOLOGY
Following Martin [Martin PS (1973) Science 179:969–974], we propose the hypothesis that the timing of human arrival to the New
World can be assessed by examining the ecological impacts of a small
population of people on extinct Pleistocene megafauna. To that end,
we compiled lists of direct radiocarbon dates on paleontological
specimens of extinct genera from North and South America with
the expectation that the initial decline of extinct megafauna should
correspond in time with the initial evidence for human colonization
and that those declines should occur first in eastern Beringia, next in
the contiguous United States, and last in South America. Analyses of
spacings and frequency distributions of radiocarbon dates for each
region support the idea that the extinction event first commenced in
Beringia, roughly 13,300–15,000 BP. For the United States and South
America, extinctions commenced considerably later but were closely
spaced in time. For the contiguous United States, extinction began at
ca. 12,900–13,200 BP, and at ca. 12,600–13,900 BP in South America.
For areas south of Beringia, these estimates correspond well with the
first significant evidence for human presence and are consistent with
the predictions of the overkill hypothesis.
POPULATION
BIOLOGY
Edited by Yadvinder Malhi, Oxford University, Oxford, United Kingdom, and accepted by the Editorial Board August 5, 2015 (received for review February
26, 2015)
are inversely proportional to population levels. For spacings, individual spacing values are regressed onto the midtime (ti+1 + ti)/2
of the spacing interval using a generalized linear model with estimated breakpoints (representing times of onset of extinction).
Decline dates are identified as the time before extinction for which
waiting times between dates begin to increase, implying population
declines. This method produces both a likely date for extinction
onset and an associated approximate 95% CI (confidence interval).
For histogram creation, we first apply a jackknife method to identify
optimal binning parameters for histogram creation (14) to create
frequency distributions of calibrated radiocarbon dates, which are
then corrected for taphonomic bias following Surovell et al. (15).
Taphonomic correction adjusts frequency distributions of radiocarbon dates to account for the loss of sedimentary contexts through
time due to erosion and weathering. Decline dates are estimated as
occurring within the last mode before extinction. Spacings are also
taphonomically corrected (SI Materials and Methods).
Both spacings and frequency analyses rest on three assumptions: (i) our radiocarbon datasets are representative of the relative frequencies of megafauna in the paleontological records of
each region; (ii) after taphonomic correction, temporal frequency
distributions positively correlate with population densities of
megafaunal taxa through time; and (iii) the same taphonomic correction model characterizes each region.*
Results
Spacings analyses (Fig. 1 and Table 1) are consistent with a north
to south trend in initial megafaunal decline dates. For EB, our
best estimate for the date of initial megafaunal decline is 14,661
BP; because EB spacing between dates are fairly consistent from
ca. 20,000 to 13,400 BP, there is a very wide 95% CI associated
with that estimate, ranging from 13,613 to 19,958 BP. For CUSA,
the most likely decline date is 13,001 BP, with a 95% CI of 12,861–
13,232 BP, and the estimated decline date for SA is 12,967 BP,
with a 95% CI of 12,595–13,921 BP.
Best-fit histograms for all radiocarbon dates yield estimates of
extinction onset that are very similar to those derived using
spacings, but with smaller observed uncertainty for EB and more
uncertainty for CUSA and SA (Fig. 2 and Table 1). The analysis
produces distinct bin widths and ranges among regions (Table
S1). The precision with which we are able to estimate the initial
date of decline by date binning correlates somewhat with sample
size and with the extent to which date distributions are uniformly
distributed or skewed. For binning results, there is considerable
ambiguity with respect to the relative timing of events in CUSA
and SA, and their median dates for final modes before extinction
are virtually identical (Table 1).
Both analyses are consistent with the hypothesis that declines
first began in EB followed in order by the CUSA and SA. The
commencement of extinction in EB appears to have preceded
those in the CUSA by about 1,600 y, and the extinction event in
EB may have been completed before it even began in CUSA. By
comparison, initial megafaunal declines in the CUSA and SA
appear to have been very closely spaced in time, probably separated by at most a few centuries. These conclusions are essentially the same for both spacing and binning analyses and are also
robust to alternate approaches to data analysis (Fig. S1 and
Table S2).
*Although there are reasons to believe that different taphonomic corrections might
apply to each region (e.g., bone preservation conditions are likely better in arctic environments), to date no regional models of taphonomic correction have yet been developed, in part because individualized corrections specific to fossil or artifact data would
be confounded by patterns such as population cycles. Furthermore, no taphonomic
correction models have been developed specifically to account for the loss of bone
through time. For these reasons, we chose to apply the global taphonomic correction
model developed by Surovell et al. (15) to each dataset.
2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1504020112
One pattern that emerges from comparative analyses of these
three regions is that the shape of the EB frequency distribution is
distinct from those of the CUSA and SA (Fig. 2). Given the
progressive loss of materials through time, radiocarbon ages are
expected to decrease nonlinearly with age from recent modes,
producing a heavily right-skewed distribution (15, 16). Even after
correction for taphonomic bias, the CUSA and SA datasets form
curves typical of this phenomenon. Potentially, loss should be
even greater for these datasets than for others due to these dates
having been derived from bone and organic materials (e.g., dung),
which may progressively be lost to weathering and/or dissolution
even if site sediments are not lost to erosion. Quite distinctly, there
appears to be considerably less loss of bone through time in the
EB dataset. We expect that this is due to a combination of excellent bone preservation in periodically frozen “muck” deposits
(17) and the sampling of extensive exposures of Pleistocene deposits due to gold mining activities (18). This pattern suggests that
unique taphonomic corrections are preferable for each region, but
natural cycles in populations and sampling concerns are confounding factors that make such unique corrections impracticable.
However, it is important to note that the taphonomic corrections
we applied have little effect on estimating dates of megafaunal
decline (Fig. S2).
The curve for EB suggests that megafaunal population levels
remained relatively constant from ∼45,000 to 15,000 BP with a
few minor periods of increase, most notably around the Last
Glacial Maximum (LGM; Figs. 1A and 2A). This peak may imply
that glacial climatic conditions are particularly favorable for extinct megafauna in arctic regions, when the so-called “Mammoth
Steppe” flourished (19, 20). This pattern conforms well to Guthrie’s
(21) hypothesis that size diminution among Alaskan Pleistocene
horses was linked to post-LGM climatic and ecological change.
Unlike the curves for the CUSA and SA, there is no major mode in
date frequencies that precedes extinction. However, all five best fit
histograms estimate that the final mode before extinction, or the
onset of population decline in EB, occurred between ∼14,440
and 14,990 BP. The spacings-based 95% CI is much wider, but an
early date of onset with constant exponential rate of decline is
inconsistent with the observed rapid arrival of extinction at the
end of record. An alternative reading of data should be mentioned, although it requires speculation beyond the information
in the data as observed. As stated above, early estimates of onset
in the 95% CI for EB imply a precipitous population decline at
the end of record, and even the best estimate of 14,661 BP leads
to a more rapid than expected break in data time-adjacent to the
most recently observed fossils. Thus, there may have been a
catastrophic extinction event around 13,300–13,400 BP, probably
but not certainly preceded by a more gradual onset of extinction
ca 14,660 BP.
In contrast to the Beringian curve, the dataset from the CUSA
suggests two major periods of megafaunal population increase,
both associated with climatic warming (Figs. 1B and 2B). High
frequencies of radiocarbon dates occur at ∼32,000 BP toward the
end of the Marine Isotope Stage 3 interstadial and correlating well
with Heinrich Event 3 (22, 23), although this peak could be a
sampling artifact. The second period of increase occurs in the
terminal Pleistocene, just before extinction. Onset of extinction is
estimated with a 95% CI between 12,861 and 13,232 BP, and,
notably, the younger range of this estimate is very close to the
terminal date of many extinct taxa, which most researchers place at
∼12,800 BP (24–26), implying a very rapid extinction event likely
occurring within 1,000 y, consistent with Alroy’s simulation results
(27). Finally, we note that in histogram solutions with finer binning
(Fig. 2B), a temporary decline in date frequencies occurs at ca.
14,000 BP, a phenomenon that has been observed by others (28,
29), but date frequencies increase over the next 500 y or so, suggesting that whatever forcing factor caused this decline was not
long lasting.
Surovell et al.
SPECIAL FEATURE
Relative Intensity
A
10
0.1
10000
15000
20000
25000
30000
35000
40000
Eastern
Beringia
Contiguous
USA
Age (cal yr BP)
Relative Intensity
B
10
0.1
10000
15000
20000
25000
30000
35000
40000
30000
35000
40000
POPULATION
BIOLOGY
Age (cal yr BP)
10
0.1
10000
15000
20000
25000
South
America
Age (cal yr BP)
Fig. 1. Comparison of estimated dates of initial megafaunal decline using generalized linear model analyses of taphonomically corrected spacing lengths for
(A) EB, (B) the CUSA, and (C) SA. Inverse spacings (°) and inverse estimated mean lengths (—) are on a scale proportional to frequency of occurrence and are
labeled as relative intensity. Times of descent (EB = 14,661; CUSA = 13,001; SA = 12,967 BP) correspond to estimated onset of decline for each region.
Taphonomically corrected data for SA suggest relatively low
population levels of megafauna persisting throughout the Late
Pleistocene with population expansion occurring in post-LGM
times, but, as stated above, this curve is also typical of temporal
frequency distributions that have been affected by taphonomic bias,
suggesting that a unique taphonomic correction would also be
desirable for the South American record. A sharp shift in spacings
and a major mode in date frequencies are nonetheless evident
(Figs. 1C and 2C), with a 95% CI between 12,595 and 13,921 BP,
entirely overlapping our age estimates for CUSA.
In Fig. 3, we summarize our estimates for the timing of megafaunal decline for all three regions in comparison with archaeological evidence of human colonization. In EB, the evidence for
overlap between human and megafaunal populations lasts for ∼600 y.
The youngest megafaunal dates occur around 13,400 BP and the
oldest archaeological sites, in the Tanana River Valley of central
Alaska, date to around 14,000 BP (30–32). The earliest evidence
for human occupation of EB overlaps with the wide 95% CI from
our spacings analysis, but it does not overlap with our estimate
from binning. Relevant to this possible temporal incongruity is that
most, if not all of the evidence for interaction between humans
and extinct megafauna in EB can be attributed to the scavenging
of old ivory or bones for tool production and fuel (31, 33).
Therefore, it is possible that initial megafaunal declines in Beringia
are not explained by human occupation or that with a larger archaeological sample, the date of initial colonization of this region
by humans will be pushed back several centuries. Notably, the estimated timing of megafaunal decline in EB correlates well with
Surovell et al.
the Bolling Interstadial and a major human population expansion
event into northeast Asia (31, 34, 35).
In the CUSA, the evidence for overlap between human and
megafaunal populations lasts for almost 6,000 y, but much of that
time is accounted for by a few Holocene megafaunal dates
and temporally isolated pre-Clovis sites. Our estimated dates of
megafaunal decline from the spacings and binning analyses overlap
with the age range for Clovis (36). Various sites have been argued
to date considerably earlier than the oldest dates for the Clovis
complex, perhaps as early as 15,500 BP (37–40). If there was a
significant human presence in North America before the onset of
Clovis, pre-Clovis foragers had no measurable impact on megafaunal populations, despite the fact that they were apparently
hunting these species (37, 39, 40). However, we would suggest that
these few early sites need not dictate our view of the colonization
event. We must not assume that these few spatio-temporally
Table 1. Estimated dates of decline for EB, the CUSA, and SA
using gap and binning analysis methods
Gap analysis
Region
EB
CUSA
SA
Binning analysis
Best fit age
(yr BP)
95% CI
(yr BP)
Median age
(yr BP)
Bin range
(yr BP)
14,661
13,001
12,967
13,613–19,958
12,861–13,232
12,595–13,921
14,714
13,473
13,480
14,440–14,988
12,819–14,127
12,021–14,939
PNAS Early Edition | 3 of 6
ANTHROPOLOGY
Relative Intensity
C
with Martin’s estimate of 13,100 BP. For SA, our 95% bounds
are 12,595 and 13,921 BP in comparison with Martin’s estimate
of 13,100 BP.
Relative Frequency
A
5000
Eastern
Beringia
10000
15000
20000
25000
30000
Age (cal yr BP)
35000
40000
45000
50000
Relative Frequency
B
5000
Contiguous
USA
10000
15000
20000
35000
40000
45000
Relative Frequency
C
25000
30000
Age (cal yr BP)
5000
50000
South
America
10000
15000
20000
25000
30000
Age (cal yr BP)
35000
40000
45000
50000
Fig. 2. Taphonomically corrected calibrated radiocarbon frequency polygons for (A) EB, (B) the CUSA, and (C) SA. For each region, the optimal
binning solution is presented for five histograms varying bin number with
the highest likelihood values using the Hogg method. Colored rectangles
represent the mean location of the final mode preceding extinction.
isolated sites are indicative of an extensive, as yet undiscovered and
hemisphere-wide pre-Clovis record. In other words, it is possible
that they resulted from occasional dispersal events that did not
result in true colonization. It is interesting to note that much of the
strongest evidence for a pre-Clovis population occurs in close
proximity to the southern margin of the continental ice sheets (37–
39, 40, 41). What is clear is that abundant, continuous, and widespread archaeological evidence in CUSA does not occur until after
ca. 13,200 BP, about 200 y before estimated onset of extinction, and
if people were present at earlier times, their numbers were not large.
In SA, the evidence for overlap between human and megafaunal
populations also lasts for close to 6,000 y, but, again, much of that
time is accounted for by 10–12 Holocene megafaunal dates (42)
and a single, possible archaeological component at Monte Verde in
Chile (43). Permanent human occupation of SA began around
13,000 BP (44–46), within the range of our estimated date of initial
megafaunal decline as estimated by both spacing and binning
analysis methods. The abundance of Holocene dates on megafauna
from South America may suggest that even though the extinction
process may have been initiated around the time of human arrival,
it was considerably more prolonged than in North America (42).
In comparison with Martin’s (1) estimates for the timing of
human colonization and megafaunal decline, the evidence cited
above from EB is considerably earlier than Martin anticipated.
Human occupation begins by at least 14,000 BP, compared with
Martin’s estimate of 13,600 BP, and megafaunal decline likely
commenced earlier, around 14,600 BP. We note, however, that
extinction itself ca. 13,300–13,400 BP occurred very rapidly,
which is concurrent with human occupation. For the CUSA and
SA, our analyses of radiocarbon date frequency distributions and
spacings are unambiguously similar to Martin’s predictions. For
CUSA, our 95% bounds are 12,861 and 13,232 BP in comparison
4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1504020112
Conclusion
Paul Martin’s classic model of New World colonization and
Pleistocene extinctions stands as an iconic work in Quaternary
studies. For more than 40 y, it has stood as a caricature of not
only the Clovis-first paradigm, but also the idea that human
hunting was the primary driver of Pleistocene extinctions in the
Western Hemisphere. In that regard, it has regularly served as a
target of researchers who have proclaimed that both of these
ideas have long since gone the way of the Columbian mammoth
and Shasta ground sloth (47, 48). It is indeed a rare phenomenon
in science for such large-scale ideas to have lifespans of more
than four decades. Nonetheless, using only temporal patterns of
radiocarbon dates for extinct Pleistocene fauna, our estimates
for the initial dates of megafaunal declines leading to extinction
are consistent with Martin’s predictions. If Martin’s model was
seriously flawed, no doubt by today, it would be little more than a
curious artifact of the state of Quaternary science in the late
1970s. That it continues to be a matter of discussion and debate
in and of itself may speak to its lasting value.
Initial megafaunal declines do appear to correlate with the
first evidence for permanent human occupation in much of the
Americas and are time-space transgressive in the manner predicted by Martin’s model, except that megafaunal declines in
Beringia began much earlier than Martin expected, unless the real
decline was the abrupt drop at the end of our fossil record. With
the exception of the wide error range for SA and the consequent
overlap between CUSA and SA, the north to south time-transgressive pattern is striking, and, barring significant new data, it
would be difficult to reconcile this pattern with extinction hypotheses that invoke a single climatic, ecological, or catastrophic extinction mechanism across the entirety of the Americas. We do not
mean to suggest that the issue is fully resolved. First, there remains
a possible temporal incongruity between initial megafaunal declines
Human Occupation
Eastern Beringia
Human Occupation
Clovis
MM
PC S&H
Contiguous USA
MVII
Human Occupation
South America
10000
12000
14000
16000
Age (cal yr BP)
18000
20000
Fig. 3. Comparison of estimated dates of initial megafaunal decline (colored rectangles) with earliest archaeological evidence for each region (gray
bars). Lighter colored bars indicate estimated decline dates based on binning, and horizontal error bars indicate the minimum and maximum values
for the final mode preceding extinction for the five optimal histogram solutions for each region. Darker colored bars indicate the 95% CI for the gap
analysis and vertical white lines indicate the best fit decline date. MM, Manis
Mastodon; PC, Paisley Cave; S&H, Schaefer and Hebior; MVII, Monte Verde,
Component 2.
Surovell et al.
Materials and Methods
For each study region, we compiled radiocarbon dates on extinct megafauna
from published sources (Datasets S1–S3). For EB and SA, we draw heavily
from Guthrie (49) and Barnosky and Lindsey (44), respectively. We vetted
these dates following the criteria of Barnosky and Lindsey (44) to isolate only
the highest quality radiocarbon associations. We averaged statisticallyindistinguishable dates on individual specimens to eliminate the problem of
overrepresentation following Long and Rippeteau (50). We excluded specimens from archaeological contexts to isolate demographic trends of fauna
independent of archaeological research. We expected that the inclusion of
dates from archaeological contexts (e.g., dozens of Clovis sites) would introduce a degree of sample bias into the dataset because these contexts are
often more thoroughly dated, and have played a central role in determining
terminal dates for extinct taxa (11, 12). Our interest is not in estimating
extinction dates, but rather in determining the timing of initial declines that
lead to extinction. We calibrated all dates using OxCal v. 4.2 using the
Intcal14 calibration curve to produce 2σ contiguous age ranges. We used the
median age of the contiguous 2σ age range for the age of each specimen.
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Surovell et al.
logðμt Þ =
β1 ðt − T0 Þ + C β2 ðt − T0 Þ + C
t ≤ T0
.
t > T0
For each T0 this model was fit as a gamma-family generalized linear
model (GLM) with log link (51). The model as given is nonlinear in T0, and we
evaluated GLMs at yearly fixed values of T0 to select the estimate of T0 based
on the maximum profile likelihood. Patterns in the distant past effectively
introduce excess noise into likelihood calculations unless models are simple,
and for spacings analysis we restricted data to dates post-LGM for estimating
change points in GLMs. Details of spacing-based estimation and confidence
interval specification, including taphonomic correction, are described in SI
Materials and Methods, and R code is provided in Dataset S5.
ACKNOWLEDGMENTS. We thank Chris Doughty, Yadvinder Malhi, and the
other organizers and participants of the Megafauna and Ecosystem Function
conference at Oxford University in 2014 for the opportunity to participate in
that event and this volume. Two anonymous reviewers provided very valuable
and critical feedback that dramatically improved our analysis, text, and interpretations, one of whom provided significant methodological advice. We thank
Danny Walker for insights regarding Wyoming megafaunal dates.
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PNAS Early Edition | 5 of 6
SPECIAL FEATURE
POPULATION
BIOLOGY
For spacings analyses, in the presence of duplicate medians ages were adjusted to median ± 1=2 ·(expected range) (SI Materials and Methods).
To examine demographic trends in extinct taxa over the Late Pleistocene,
we created temporal frequency distributions of radiocarbon dates. During
initial analyses, it became clear that arbitrary decisions made in histogram
creation (i.e., choices of histogram bin boundaries and widths) had dramatic
effects on results. Accordingly, we turned to a jackknife algorithm developed by
David Hogg (14) for histogram creation that results in objectively chosen bin
widths and boundaries that best fit the underlying distribution. In Hogg’s
method, each histogram is characterized by a likelihood value that describes
the degree of fit between the histogram and underlying distribution (SI Materials and Methods, Dataset S4). For each set of histograms of n = 2–101 bins,
we identified the solution with the greatest likelihood of fit resulting in 100
histograms of variable bin width. Of those 100, we chose the five bin width
solutions with the greatest likelihood values and corrected each for taphonomic
bias following Surovell et al. (15). We determined the bin in which initial
megafaunal population declines occurred as the last major mode before extinction. Finally, for each region, we identified the most likely date of decline as
the average of the minimum and maximum boundaries for the five modal bins.
We also analyzed temporal patterns using spacings, i.e., times between
consecutive ordered dates. The expected size of a spacing is inversely proportional to the concurrent population intensity, so spacings can indirectly
lead to estimates of when populations change. Use of spacings avoids the
need to select bin boundaries and uses a finer time scale than is used with
binning, but it does pose other challenges. T0, the initial time of movement
toward extinction, is the parameter of interest in Martin’s hypothesis, and
we modeled μt, the mean for the taphonomically corrected spacing for (t2 t1) at t = (t2 + t1)/2 as
ANTHROPOLOGY
and human colonization of EB. Given the small population of
people that initially colonized EB and the small number of archaeologists looking for them, maybe we are seeing the impact of
their presence before the appearance of their archaeological remains. Only more extensive investigations of terminal Pleistocene
deposits in EB will resolve this issue. Second, we need to understand what exactly pre-Clovis sites represent. In our view, these
sites may represent pulses of population expansion that failed to
result in permanent colonization, paleontological sites mistaken for
archaeological sites, poorly dated archaeological sites, or a combination of these. Regardless, based on our results, we must question
whether they represent the presence of a permanent and widespread pre-Clovis population in the New World.
Finally, we would like to reassert the value of using paleoecological data to study the human past. The heavy ecological
footprint of human societies throughout prehistory is becoming
increasingly apparent through a variety of environmental proxies
independent of the archaeological record. Past human societies
have disrupted ecological communities in dramatic ways for
many tens, if not hundreds of thousands, of years. In some ways,
the record of ecological disruption marked by the arrival of a
small founding human population may be more evident in the
paleoecological record on a large scale than in the archaeological
record itself. If archaeologists come to accept paleoecological
proxies as also a record of human ecological disruption, rather
than as solely a proxy for human boundary conditions, we believe
that many new areas of research will emerge.
24. Faith JT, Surovell TA (2009) Synchronous extinction of North America’s Pleistocene
mammals. Proc Natl Acad Sci USA 106(49):20641–20645.
25. Fiedel S (2009) The chronology of terminal Pleistocene megafaunal extinction.
American Megafaunal Extinctions at the End of the Pleistocene, ed Haynes G
(Springer, Heidelberg, Germany), pp 21–37.
26. Haynes CV, Jr (2008) Younger Dryas “black mats” and the Rancholabrean termination
in North America. Proc Natl Acad Sci USA 105(18):6520–6525.
27. Alroy J (2001) A multispecies overkill simulation of the end-Pleistocene megafaunal
mass extinction. Science 292(5523):1893–1896.
28. Boulanger MT, Lyman RL (2014) Northeastern North American Pleistocene megafauna chronologically overlapped minimally with Paleoindians. Quat Sci Rev 85:
35–46.
29. Gill JL, Williams JW, Jackson ST, Lininger KB, Robinson GS (2009) Pleistocene megafaunal
collapse, novel plant communities, and enhanced fire regimes in North America. Science
326(5956):1100–1103.
30. Goebel T, Waters MR, O’Rourke DH (2008) The late Pleistocene dispersal of modern
humans in the Americas. Science 319(5869):1497–1502.
31. Hoffecker JF, Elias SA (2007) Human Ecology of Beringia (Columbia Univ Press, New York).
32. Holmes CED (2001) Tanana River Valley archaeology circa 14,000 to 9,000 B.P. Arctic
Anthropol 38(2):154–170.
33. Kedrowski BL, et al. (2009) GC-MS analysis of fatty acids from ancient hearth residues
at the Swan Point Archaeological Site. Archaeometry 51(1):110–122.
34. Surovell T, Waguespack N, Brantingham PJ (2005) Global archaeological evidence for
proboscidean overkill. Proc Natl Acad Sci USA 102(17):6231–6236.
35. Hamilton MJ, Buchanan B (2010) Archaeological support for the three-stage expansion of modern humans across northeastern Eurasia and into the Americas. PLoS One
5(8):e12472.
36. Waters MR, Stafford TW, Jr (2007) Redefining the age of Clovis: Implications for the
peopling of the Americas. Science 315(5815):1122–1126.
37. Joyce DJ (2006) Chronology and new research on the Schaefer Mammoth (?Mammuthus primigenius) site, Kenosha County, Wisconsin, USA. Quat Int 142-143:44–57.
38. Jenkins DL, et al. (2012) Clovis age Western Stemmed projectile points and human
coprolites at the Paisley Caves. Science 337(6091):223–228.
39. Waters MR, et al. (2011) The Buttermilk Creek complex and the origins of Clovis at the
Debra L. Friedkin site, Texas. Science 331(6024):1599–1603.
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40. Overstreet DF, Kolb MF (2003) Geoarchaeological contexts for Late Pleistocene archaeological sites with human modified woolly mammoth remains in southeastern
Wisconsin, U.S.A. Geoarchaeol 18(1):91–114.
41. Waters MR, Stafford TW, Jr, Kooyman B, Hills LV (2015) Late Pleistocene horse and
camel hunting at the southern margin of the ice-free corridor: Reassessing the age of
Wally’s Beach, Canada. Proc Natl Acad Sci USA 112(14):4263–4267.
42. Hubbe A, Hubbe M, Neves W (2007) Early Holocene survival of megafauna in South
America. J Biogeogr 34(9):1642–1646.
43. Dillehay T (1997) Monte Verde: A Late Pleistocene Settlement in Chile. Volume 2: The
Archaeological Context and Interpretation (Smithsonian, Washington, DC).
44. Barnosky AD, Lindsey EL (2010) Timing of Quaternary megafaunal extinction in South
America in relation to human arrival and climate change. Quat Int 217:10–29.
45. Méndez Melgar C (2013) A Late Pleistocene/early Holocene archaeological 14C database for Central and South America: Palaeoenvironmental contexts and demographic
interpretations. Quat Int 301:60–73.
46. Prates L, Politis G, Steele J (2013) A Late Pleistocene/early Holocene archaeological 14C
database for Central and South America: Palaeoenvironmental contexts and demographic interpretations. Quat Int 301:104–122.
47. Meltzer DJ (1997) Monte Verde and the Pleistocene Peopling of the Americas. Science
276:754–755.
48. Grayson DK, Meltzer DJ (2003) A requiem for North American overkill. J Archaeol Sci
30(5):585–593.
49. Guthrie RD (2006) New carbon dates link climatic change with human colonization
and Pleistocene extinctions. Nature 441(7090):207–209.
50. Long A, Rippeteau B (1974) Testing contemporaneity and averaging radiocarbon
dates. Am Antiq 39(2):205–214.
51. McCullagh P, Nelder JA (1989) Generalized Linear Models (Chapman and Hall, London).
52. Dobson A, Barnett A (2008) An Introduction to Generalized Linear Models (Chapman
& Hall/CRC, Boca Raton, FL), 3rd Ed.
53. R Core Team (2013) . R: A Language and Environment for Statistical Computing (R
Foundation for Statistical Computing, Vienna).
54. Wang X-F (2010) fANCOVA: Nonparametric Analysis of Covariance. R package version 0.5-1. Available at https://cran.r-project.org/web/packages/fANCOVA/index.html.
Accessed July 14, 2015.
Surovell et al.
Supporting Information
Surovell et al. 10.1073/pnas.1504020112
SI Materials and Methods
Radiocarbon Datasets. The large majority of the SA and EB
datasets are derived from Barnosky and Lindsey (44) and Guthrie
(49), respectively. However, we made several edits to these data.
Some dates in Guthrie’s supplementary table were either duplicates or individual laboratory numbers had distinct radiocarbon
ages. In these cases, we either deleted one date, or threw them
both out, respectively. The supplementary table for Barnosky and
Lindsey (44) differs from the table in print by several dates, the
latter possessing more. To maximize the number of dates from this
region, we used the printed dataset. We also added 10 dates to SA
and 11 to EB.
We compiled the dataset for the CUSA from a large number of
sources, but the dataset is overwhelmingly dominated by remains
from two areas, Ranch la Brea and Colorado Plateau cave sites,
from which dates were derived from megafaunal dung. We used
another large sample of dates from Boulanger and Lyman (28) for
the northeast United States.
We vetted radiocarbon dates according to the method presented in Barnosky and Lindsey (44) and included only those
dates that ranked an 11 or 12. For the North American dataset, we
added several categories of material, which are listed in Dataset
S2. Around 40 of the dates provided in Guthrie’s (49) dataset are
from previously published studies by that author. We did not
rank these dates, but assumed that they would all score 11 or
higher on this scale because they were included in Guthrie’s (49)
study. All of the dates listed as new in Guthrie’s study rank a 12.
Binning Analysis. One critical measurement we make in this work
concerns the peak of a histogram of binned data. The final major
peak of the histogram before extinction is our best estimate for
the initial date of decline of megafaunal populations. Measuring
the peak of a histogram is a procedure fraught with choices that
could potentially bias our result. Most obviously, the choice of
binning for a histogram is subjective. If one chooses a binning that
is too wide, the measured decline date may approach the mean of
the range of measured data. If one chooses a binning that is too
narrow, the histogram becomes noisy. With either (bad) choice,
the overall shape of the distribution becomes poorly constrained.
Rather than arbitrarily selecting a histogram binning, a more
defensible choice is to allow the data to inform us of the optimal
binning for the histogram. This method is the approach we take in
this paper. We adopt the formalism of Hogg (14), which uses a
jackknife, or “leave-one-out” approach to infer the correct histogram binning. Broadly, the procedure is to create a series of all
possible histogram bin sizes, each of which will have a different
number of bins over the range of the data. Variation in boundaries
can also be explored. Within a given one of this series of bin sizes
and edges, each of the individual datum are looped through and
discarded in turn. With this datum missing, the fraction (compared with the total across all bins) of the remaining objects
contributing in their bin is calculated for each remaining datum.
These fractions are summed in logarithmic space to create a
likelihood for that choice of bin size and boundaries in the series.
Typically a small positive value is added to the numerator of each
bin fraction, to smooth the data by preventing zero values from
corrupting the likelihood sum.
In this manner, a single likelihood can be constructed for each
possible choice in the series of bin sizes and boundaries, and the
maximum value among these likelihoods represents the optimal
binning choice. This procedure allows the data to inform us of how
we should bin it, in the sense that every time a datum is discarded,
Surovell et al. www.pnas.org/cgi/content/short/1504020112
the remaining data have been used to test the question “what was
the likelihood of a new datum populating a particular bin”? The
resulting histogram is then defensible in that it is the choice that
best predicts where any new set of data would fall if we were to
continue to probe the paleontological record reflected by the histogram, and if we did so repeatedly using a consistent experiment.
The Hogg method was applied using a macro written in Visual
Basic for Microsoft Excel. Bin number was varied from 2 to 101.
Starting bin boundaries were varied in 10-y increments. The
smoothing variable, α, was varied from 0.9 to 3.0 in increments of
0.1. In the case of α ≤ 1 for histograms with empty bins, negative
fractions result, meaning that likelihood cannot be calculated
because it would require taking the logarithm of a negative value.
When such histograms were encountered, they were discarded.
The Microsoft Excel Visual Basic code used to find optimal
histogram solutions is provided in Dataset S4. To use this code, a
spreadsheet should be set up with the following specifications.
Column A should contain mean radiocarbon ages beginning in
row 2, with row 1 reserved for a header label. The list of dates
should have no gaps or empty rows. Cell D1 should contain the
maximum radiocarbon age [e.g., the formula =MAX(A:A)]. Cell
D2 should contain the minimum radiocarbon age [e.g., the formula =MIN(A:A)]. Cell D3 should contain the number of radiocarbon dates [e.g., the formula =COUNT(A:A)]. Summary
histogram statistics are outputted in columns F through K,
starting on row 2. The following headers should be placed in cells
F1 to K1: Bin Min, n Bins, Alpha, Likelihood, Bin Width, and
Good Solution. All histograms for which a value of NO occurs in
column K should be discarded.
Analysis of Spacings between Observations. Although Hogg’s procedure provides automatic selection of bin numbers and boundaries,
any histogram analysis ultimately depends on the bins selected. An
analysis at the finest possible scale of time is possible by looking at
time lags between dates—long lags correspond to infrequent events
and short lags correspond to frequent events.
Time lags can be conceptualized either as spacings between the
order statistics for a sample of dates or as waiting times in a
temporal point process (such as a Poisson process), with occurrences in the process being observations at some specified date. In
an idealized setting over a period of demographic stability, the
frequency of randomly obtained dates in a unit interval is Poisson
distributed with intensity λ, and spacings are exponentially distributed with mean μ = 1=λ. The present setting is not quite ideal,
and accommodations made are described below.
A few independent samples gave duplicate dates (one pair in
the CUSA and six pairs in EB), even though the theoretical
chance of exact duplication is zero. Zero spacings cause problems
for formal analysis, but it would be inappropriate to simply discard
duplicates. The fact that all calibrated dates are reported as
medians within a 2σ interval suggests a way to replace duplicate
pairs by alternate nonduplicate estimates. For two independent
observations (t1, t2) from normal distributions with the same
mean
and respective
variances σ 21 and σ 22 the expected range is r =
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
ðσ 21 + σ 22 Þ 2=π , suggesting using date substitutions median ± 1=2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
range = median ± ðσ 21 + σ 22 Þ=2π .
Once a set of unique dates t1, t2, . . .,tm is found for each region,
dates are sorted, and ordered values t(i) are used to create
baseline spacings t(i+1) − t(i) for i = 1, 2,. . ., m − 1.
Because of taphonomic bias, observed spacings are longer than
would be expected without loss of sedimentary contexts through
1 of 5
time. The average spacing over a block of time is the inverse
frequency over that block, so the desired taphonomic correction is
based on the inverse taphonomic correction formula for frequencies.
Rt
Over the observed time interval [t1, t2], the correction is t12 nðtÞdt,
where n(t) ∝ ðt + 2,176.4Þ−1.3925309 is the taphonomic bias in Surovell et al. (15). The integral is easily solved to be proportional
to ðt1 + 2,176.4Þ−0.3925309 − ðt2 + 2,176.4Þ−0.3925309. For purposes
of detecting onset of decline, the proportionality constant does
not matter.
We note that using uncorrected spacings instead of corrected
spacings in our data could change relative values between early
and late spacings by a factor greater than six, so taphonomic
adjustment is recommended. Nonetheless, we compared results
using uncorrected values and found similar estimates for onset of
extinction but generally wider confidence intervals. This comparison helps alleviate possible concerns about the quality of the
standard taphonomic correction for data in this study.
Because interest is in population changes over time, and adjusted
time lags are indirect measures of population levels, we associate
spacing lengths with particular times. For simplicity, each taphonomically deflated spacing is linked to the midpoint of the original
spacing interval, t = ðt1 + t2 Þ=2 . Spacing data thus consist of m – 1
pairs ðt, yt), where yt is the value of the integral above. The taphonomically corrected value yt is the actual response used in
generalized linear model analyses, not the raw spacing t2 − t1.
According to Martin’s hypothesis, population levels before T0
(time of onset of extinction) are easiest to envision as varying
about a smooth curve of unspecified shape over time or else as a
stationary correlated time series with some fixed mean. Spacings
correspond to measures of inverse population levels, so these
same modeling structures apply for spacings. We found that a
simple parametric model for spacings over times post-LGM gave
the most coherent information about T0 and the best goodness of
fit. For CUSA and SA, we observed population increases postLGM and before extinction, so we chose a model that admitted
different nonzero rates of change before and after extinction
onset. For EB, frequencies and spacings were very stable before
onset, and we set the preonset slope to zero. We also considered
that rates of population decline leading to extinction should be
Surovell et al. www.pnas.org/cgi/content/short/1504020112
close to exponential. These facts motivate the choice of model
for spacings post-LGM (defined as younger than 22,000 BP)
β1 ðt − T0 Þ + C t ≤ T0
logðμt Þ =
.
β2 ðt − T0 Þ + C t > T0
Here μt is the expected value of spacing yt. In a Poisson process
spacings are exponentially distributed, and exponential distributions are generalized by the family of gamma distributions, so a
gamma distribution model for spacings is sensible. For a known
value of T0 , the above model can be fit using a generalized linear
model (glm) with a gamma family and a log link function (51, 52),
but the parameter T0 is nonlinear with respect to other parameters.
It is possible to fit generalized nonlinear models, but the delicacy of
the EB data, in particular, relative to Martin’s hypothesis, motivated us to estimate T0 not from purely asymptotic behavior at the
optimum but based on profile likelihoods obtained for a broad grid
of values of T0. Further information about generalized linear models may be found in McCullagh and Nelder (51) and in Dobson
and Barnett (52). 95% CIs are given as likelihood ratio confidence
intervals: any onset time producing −2 log likelihood values
within χ 20.95;1 = 3.8415 of the optimum value is considered to be
within the confidence region. Autocorrelations of model residuals
were assessed approximately by treating spacings as though they
occurred at regular time lags. Using the above models, observed
approximate autocorrelations at lags greater than zero were small
and statistically insignificant. All programming and analyses for
spacings were done using R (53).
Alternative approaches to modeling with spacings were also
considered. Approximate autoregressive time series models for log
(yt) can be fit if we treat observed spacings as though they were
regularly spaced. Following this approach, EB and SA data fit firstorder AR (autoregressive) models and CUSA data fit a fifth-order
AR model. We also considered a nonparametric smoother (loess fit
optimized via generalized cross-validation) (54). These models were
fit over the entire time series of taphonomically corrected spacings.
In both cases, estimates for onset of extinction were similar relative
to conclusions about Martin’s hypothesis, but confidence intervals
and diagnostics for goodness of fit for these methods were either
inferior or not easily obtained. (Table S2, Fig. S2, and Dataset S5).
2 of 5
10
East Beringia
0.1
relativ e intens ity
A
10000
15000
20000
25000
30000
35000
40000
30000
35000
40000
30000
35000
40000
time (BP)
10
Contiguous USA
0.1
relativ e intens ity
B
10000
15000
20000
25000
time (BP)
10
South America
0.1
relativ e intens ity
C
10000
15000
20000
25000
time (BP)
Fig. S1. Comparison of estimated dates of initial megafaunal decline using generalized linear model analyses, approximate AR analyses, and optimized loess
fits of taphonomically corrected spacing lengths for (A) EB, (B) the CUSA, and (C) SA. Inverse spacings (°) and inverse estimated mean lengths are on a scale
proportional to frequency of occurrence and are labeled as relative intensity. Fits are distinguished as GLMs (—), approximate AR (- - -), and loess (......).
Surovell et al. www.pnas.org/cgi/content/short/1504020112
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Surovell et al. www.pnas.org/cgi/content/short/1504020112
47357 to 51818
42896 to 47357
0.4
47042 to 49339
44745 to 47042
42448 to 44745
40151 to 42448
0.4
37854 to 40151
35557 to 37854
33260 to 35557
30963 to 33260
28666 to 30963
26369 to 28666
0.6
38435 to 42896
33974 to 38435
29513 to 33974
1
24072 to 26369
21775 to 24072
19478 to 21775
17181 to 19478
45498 to 46117
44260 to 44879
43022 to 43641
41784 to 42403
40546 to 41165
39308 to 39927
38070 to 38689
36832 to 37451
35594 to 36213
34356 to 34975
33118 to 33737
31880 to 32499
30642 to 31261
29404 to 30023
28166 to 28785
26928 to 27547
25690 to 26309
24452 to 25071
23214 to 23833
21976 to 22595
20738 to 21357
19500 to 20119
18262 to 18881
17024 to 17643
15786 to 16405
14548 to 15167
13310 to 13929
Relative Frequency
0.8
25052 to 29513
20591 to 25052
16130 to 20591
14884 to 17181
12587 to 14884
10290 to 12587
7993 to 10290
Relative Frequency
0
11669 to 16130
7208 to 11669
Relative Frequency
1
0.6
Eastern Beringia
0.4
0.2
Age (cal yr BP)
0.8
1
Contiguous USA
0.2
0
Age (cal yr BP)
0.8
0.6
South America
0.2
0
Age (cal yr BP)
Fig. S2. Optimal histogram binning for EB (54 bins), the CUSA (18 bins), and SA (10 bins) comparing raw date frequencies (gray bars) and taphonomically
corrected frequencies (red lines). Over long time scales, the taphonomic correction process can have major effects on the shapes of curves, but over short time
scales (<4,000 y), the effects are minimal. Therefore, unless adjacent bin frequencies are very similar, taphonomic correction does not affect the position of the
last major mode before extinction.
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Table S1. Optimal histogram binning for the three study
regions using the Hogg (14) method
Bin
number
Bin width
(yr)
EB
54
57
58
78
63
CUSA
18
69
71
38
20
SA
16
17
23
15
10
Bin 1 start date
(yr BP)
α
Likelihood
rank
619
587
577
428
531
13,310
13,237
13,343
13,249
13,146
1.7
1.9
1.9
1.7
1.9
1
2
3
4
5
2,297
574
558
1,055
2,055
7,993
8,574
8,692
8,373
8,484
1.4
1.2
1.1
1.4
1.4
1
2
3
4
5
2,723
2,553
1,857
2,917
4,538
7,323
7,128
7,096
5,955
7,115
1.1
1.1
1.1
1.1
1.1
1
2
3
4
5
Table S2. Spacings-based estimated dates of decline and 95% CIs for EB, the CUSA, and SA
using the generalized linear model and the approximate AR model and estimates for the
optimized nonparametric loess fit
Region
EB
CUSA
SA
GLM
14,661
13,001
12,967
13,613–19,958
12,861–13,232
12,595–13,921
AR
14,652
12,727
12,712
13,308–40,000
11,749–13,636
10,816–13,635
Loess (estimate only)
14,702
13,027
12,937
Other Supporting Information Files
Dataset
Dataset
Dataset
Dataset
Dataset
S1
S2
S3
S4
S5
(XLSX)
(XLSX)
(XLSX)
(DOCX)
(DOCX)
Surovell et al. www.pnas.org/cgi/content/short/1504020112
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