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Appendix S1: Detailed description of analyses and models
Database of body masses
We compiled an exhaustive dataset of estimated body masses for a diverse range of 198
extinct and 433 surviving terrestrial Late Quaternary eutherian and marsupial mammal
species >5 kg, from Australia, Eurasia, North and South America and Madagascar. Over
95% of the known extinct mammal taxa from this period were larger than 5 kg (Lambert &
Holling, 1998), the minimum ungulate body mass (Owen-Smith, 1988). Our sources for
extinct species were Martin & Klein (1984), Damuth & MacFadden (1990), Farina et al.
(1998), MacPhee (1999), Alroy (2001), Burness et al. (2001), Johnson (2002), and
Johnson & Prideaux (2003). For surviving species our sources were Tanner (1975),
Caughley & Krebs (1983), Hennemann (1983), Owen-Smith (1988) and Silva & Downing
(1995), the last reference encompassing over 65% of modern mammal species.
Statistical analyses
We used binomial logistic regression to evaluate statistically the phenomenological
relationship between body mass, continent, and extinction probability in Late Pleistocene
mammals (illustrated in figure 2a), using the iterative re-weighted maximum likelihood
method in MINITAB v12 (Ryan et al., 1994). A similar approach has been used to test for
the influence of body mass on the Plio-Pleistocene extinctions which followed the Great
American Biotic Interchange (Lessa & Farina, 1996, Lessa et al., 1997).
There are a number of potential sources of bias in these data, with perhaps the most
important being the inability to partition the affect of landmass area from the phylogeny and
biogeographic history of the mammal assemblage of a given area (Ambrose, 1998,
Marquet & Taper, 1998). In order to develop a global extinction-body mass model which
considers the affect of continent, we used the empirical relationship developed by Burness
et al. (2001) to correct for the strong relationship between body mass and continental area,
by dividing each species’ body mass by the maximal predicted value for their respective
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land-mass.
Our sample does not include the entire Late Quaternary mammal assemblage,
because body mass estimates are unavailable for some species. To evaluate the
importance of this incomplete coverage, we used bootstrap re-sampling (see Brook &
Bowman, 2002) to generate confidence intervals around our statistical parameter
estimates. This shows the extinction risk-body mass relationship is robust to sampling bias
(95% confidence intervals for concordance = 82.9%, 87.9%, based on the percentiles of
1000 replicate logistic regression fits). Another potential bias is taphonomic – smaller
fossils are more fragile and less likely to be preserved than larger fossils. However, Alroy
(2001) found the body mass-preservability relationship for North American mammals
explained only 4.7% of the observed variance, surmising that the slower decay and
weathering of large species is likely counter-balanced by greater numbers of individuals of
smaller species.
Mechanistic simulation modelling
For mechanistic explanations, we developed a relatively simple model of human and
megafauna population dynamics, implemented in @RISK v4.5 (Palisade Corporation,
Newfield, New York) for Microsoft Excel. The model was based on five key parameters
(see Brook & Bowman, 2002): maximal replacement rate (rm) and equilibrium density (D) of
megafaunal prey populations, density of human populations (H), maximal rate of off-take by
human hunters (O), and relative naivety of prey (z). Prey population dynamics were
modelled using the logistic growth equation, with rm and D constrained by the means and
variances estimated from body mass allometry meta-analyses of extant species. In a given
simulation iteration, a body mass was first generated randomly from within the set bodymass bounds of a given scenario, and then the derived parameters (rm and D) were
sampled randomly from a normal distribution using the following allometric equations
provided by Henneman (1983) and Damuth (1981): log10(rm) [mean, SD] = N[0.72 – 0.27
log10 body mass (g), 0.295] and log10(D) = N[4.23 – 0.75 log10 body mass (g), 0.456].
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The population dynamics of prehistoric humans was also modelled using a logistic
growth function, with growth and density parameters sampled randomly from a uniform
distribution between the minimum and maximum levels cited in the literature, based on
anthropological studies on contemporary hunter gatherers, where gm [min, max] = U[0.01,
0.025], and H = U[0.02, 0.21] (Alroy, 2001, Brook & Bowman, 2002, Choquenot & Bowman,
1998, Grayson, 2001, Holdaway & Jacomb, 2000, based on Martin, 1973, Winterhalder &
Lu, 1997).
The overall human-megafauna predator-prey system was mediated by a non-linear
relationship relating hunting success (HS) to prey density, where HS = ODz/[G + Dz], with D
being the density of prey populations, O the maximal predation rate (hunting off-take), G a
saturation constant equal to the prey density at which predation is half-maximal, and z a
measure of the departure from maximal predation efficiency (see Real, 1977). Variations in
the values of F, G and z are thought to reflect the integrated effect of ensembles of
behavioural, genetic and habitat-related factors (Brook & Bowman, 2002, Choquenot &
Bowman, 1998).
We used this model to simulate 150 alterative single- or multi-causal scenarios of
human impact on megafaunal prey populations, with model parameters assigned any of the
following possible values in random combination: (i) hunting off-take (number of prey
items/person/year; O) = [subsistence, 5, 10, 15, 30], (ii) prey naivety (z) = [1.1, 1.2, 1.3, 1.5,
1.7], and (iii) prey replacement (rm) and (iv) density (D) = [100, 90, 80, 70, 50] percent of
maximum (reflecting anthropogenic habitat alteration and/or climate change). For each
scenario, we iterated the model 1,000 times for each of seven size classes of areacorrected log10 body mass (g) shown in figure 1, and matched the simulation results to the
empirical extinction-body mass relationship using the mean squared deviation from the
mid-points of the size class data.
The parameter values for O and z represent the upper bound of a uniform sampling
distribution, with a lower limit of O = 0 (i.e., no off-take) and z = 1 (complete naivety). O was
assumed to be independent of prey body mass, except for “subsistence” scenarios, when
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O was defined as the number of prey items of a given body mass required to meet the
annual subsistence needs of a single person, assuming 290 g of meat per person per day
with 25% wastage (Alroy, 2001, Choquenot & Bowman, 1998). The upper and lower limits
to hunting off-take for a given species can never be reliably quantified (Brook & Bowman,
2002), as this will depend on a complex mix of the proportion of time prehistoric humans
directed towards big game hunting, and whether the motivation for hunting was solely for
meat procurement or involved other anthropological factors such as social prestige or
sexual selection (Bowman & Robinson, 2002, Hawkes et al., 1997).
Rate of extinctions
The rapidity of the extinction process is an important consideration, as it has direct bearing
on the plausibility of the overkill hypothesis via a “blitzkrieg” (Brook & Bowman, 2002,
Martin, 1984). To examine the rate of extinction we introduced an initial founder human
population of 50–150 individuals (based on Alroy, 2001, Holdaway & Jacomb, 2000, Martin,
1973), with prey populations initially set at maximum densities and absolute population size
determined by land-mass area (given in Burness et al., 2001). Although our model ignores
the potential complexities of spatial heterogeneity, Alroy’s (2001) model generated very
similar results under either spatially-implicit or spatially-explicit assumptions.
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