The Reality of Neandertal Symbolic Behavior at the Grotte du Renne, Arcy-sur-Cure, France

Background The question of whether symbolically mediated behavior is exclusive to modern humans or shared with anatomically archaic populations such as the Neandertals is hotly debated. At the Grotte du Renne, Arcy-sur-Cure, France, the Châtelperronian levels contain Neandertal remains and large numbers of personal ornaments, decorated bone tools and colorants, but it has been suggested that this association reflects intrusion of the symbolic artifacts from the overlying Protoaurignacian and/or of the Neandertal remains from the underlying Mousterian. Methodology/Principal Findings We tested these hypotheses against the horizontal and vertical distributions of the various categories of diagnostic finds and statistically assessed the probability that the Châtelperronian levels are of mixed composition. Our results reject that the associations result from large or small scale, localized or generalized post-depositional displacement, and they imply that incomplete sample decontamination is the parsimonious explanation for the stratigraphic anomalies seen in the radiocarbon dating of the sequence. Conclusions/Significance The symbolic artifacts in the Châtelperronian of the Grotte du Renne are indeed Neandertal material culture.


The statistical model
Let K k , 1, = K be the index for the different types of elements (ornaments, red pigments, etc.) (3). Let k i X be the initial number of elements of type k at level Let i T be the time difference between level i and now. Consider an element starting at level i and ending in level j . We assume that at some random times 1 t , 2 t , etc.
between 0 and i T the element can move to an upper/lower level with equiprobability.
We assume that the random times are distributed according to a Poisson process of unknown rate 0. > ! Figure S1 shows a realization from this process, starting from level XI and ending in level XII.
For any element, the number of events (up or down) over a period i T thus follows a discrete Poisson distribution of parameter i T ! . Let + N be the number of events where the element went to an upper level and ! N the number of events where the element went to a lower level, then we have where '~' means 'statistically distributed from' and Poisson ( ! ) is the usual discrete Poisson distribution of parameter ! . For any given item, the difference between the ending level and the starting level is and where + N is the number of times an item moved up and is the number of times an item moved down. N is distributed from a Skellam distribution whose probability mass function is given, where ) (z I k is the modified Bessel function of the first kind. As we need to have , we need to consider the truncated Skellam probability distribution. It follows that the probability ij ! to go from a level } , over the time i T for a single element is given by Let k ij Z denote the number of items of type k that were in level i at the initial time and end up in level j at the final time (after i T ). As every item moves independently, denote the standard multinomial distribution of parameters ! and X . The items observed at the final time are the sums of items coming from different levels, hence, for n j , 1, Here is the pseudo-code to sample from the model: where ! F is the distribution defined above, to emphasize the dependency with respect to ! .

Hypothesis testing
We want to perform a goodness of fit test to see whether the above model gives a good or a bad fit to the observed data. We assume that To do so, we can consider the classical Pearson chi square statistic, defined by

Parameter estimation
We need to estimate the rate parameter 0 > ! . To do so, we can choose the value that minimize the test statistic S . Optimization can be done over a one-dimensional grid.

Summary
The whole strategy is described below

Results
The final (observed) conditions are given in Table 1. The initial conditions for the different hypotheses are given in Table S1, and the values of ) (! S , computed over a grid of values for ! , are reported in Figure S2. . It means that an element will move to an upper/lower level every 200000 = 1 ! years on average (the distribution between time events indeed follows an exponential distribution with this parameter). The quantities ! and E associated to this best fitted value are given in Tables Tables S2-S3,

Probability models
Let ! be the probability that an element found in Châtelperronian levels VIII-X is intrusive from Protoaurignacian level VII. This probability is unknown and we assume that it is distributed a priori from a uniform distribution over the interval [0,1]. Given that 0 out of 287 Dufour bladelets intruded and 0 out of 2800 unretouched bladelets intruded, if we apply the Bayes theorem (1), the posterior probability of ! now follows a Beta distribution of parameters a=1, b=3088. Consequently, over a new set of 47 items (the total number of ornaments found in levels VII and VIII-X), the number of items that are intrusive from VII into VIII-X follows a Beta-binomial distribution of parameters n=47, a=1 and b=3088, whose probability mass function evaluated at k is given by where Γ is the Gamma function. The probability mass function is represented in Figure  S3a for the given parameters. It puts most of its mass at zero and the probability that more than 1 item is intrusive is <0.01.
For a set of 26 items (the total number of dated samples from levels VII and VIII-X), the number of items that are intrusive follows a Beta-binomial distribution with the same parameters as in the ornaments case except for n=26. The probability mass function is represented in Figure S3c. It puts most of the mass at 0, and the probability that more than 1 item is intrusive is <0.01.
Using a different approach, we can also assess the implications for the personal ornaments and the Neandertal teeth derived from accepting that the 38% anomalously young results obtained for Châtelperronian levels VIII-X reflect stratigraphic intrusion instead of incomplete sample decontamination. For the 39 personal ornaments, the probability that any one is intrusive is 0.38 with a 95% confidence interval of [0.18, 0.62]. Taking the higher limit of the interval (the most favorable for the disturbance hypothesis), the probability that all 39 are intrusive is 0.62 39 , or 6e-9 (and, for a threshold of 1%, the maximum number of ornaments that could have been displaced under these probabilities is 31). By the same token, the probability that the 29 Neandertal teeth found in the Châtelperronian levels are all displaced can be calculated as 0.62 29 , i.e., 8e-7 (and, for a threshold of 1%, the maximum number that could have been displaced under these probabilities is 24). As discussed above, however, such a level of disturbance should also be reflected in the distribution of the diagnostic stone tools, but it is not.