Life tables and Leslie matrices for mammalian cohorts in different paleobiological contexts during the Pleistocene

International audienceFor decades studying the Pleistocene human subsistence strategies has been a key area of research in archeology to address the ability or inability of human populations to exploit optimally their prey, and by extension, their environment. To answer this question the theoretical concept of attritional and catastrophic mortality have together emerged in paleontology and zooarchaeological literature, with methodological approaches to establish mortality curves. Some of them were directly rooted in ecological approaches, such as the introduction of life tables by Kurtén [1-5]. Since these pioneering works, new methods based on age-specific sequences of tooth eruption, tooth wear, and crown height now correspond to the main criteria used to assess mammalian mortality curves. As a matter of fact, fossil dental material is better preserved than bones and frequently identifiable to species. Consequently, teeth are very useful for estimating the minimum number of individuals and for constructing mortality curves in order to interpret the fossil demographic structures [6-13]. In zooarchaeology, the most common techniques to assign individual age are based on current tooth eruption and wear sequences, from which each stage is codified starting from known age individuals of domestic species [sheep/goat : 14, 15] or collected in the wild as for example in deer [16-18], Roe deer [19- 21], Ibex or Chamois [22-23] to mention just a few. Unfortunately tooth eruption sequences do not allow distinguishing between adults and older individuals ; the distinction being only possible between juveniles and adults. Furthermore, the visual comparison may be difficult between current species wear sequences and fossil teeth with intermediate dental wear. The problem is more complicated when species are extinct : how to relate them to current representatives ? Last but not least, the degree of hypsodonty is measured from the height of the crown, usually from the root to the occlusal surface of the tooth and regressed against age using animals of known age. Starting from the work of Kurtén this method was developed by Spinage [24-25] who focused on African taxa (bovids and equids). Similarly, the innovative quadratic method of Klein et al. [26], also called QHCM (Crown Heights Quadratic Method), provides a set of quadratic formulae for each tooth, according to his rank, that can be used to predict age-at-death from tooth crown height. QHCM has been applied to many Pleistocene deposits to interpret the exploitation of certain large ungulates by African Hominids [27-31]. However, the main bias of the QHCM is related to the non-linear wear of teeth from different ages [28, 32-35], and, more importantly, to the absence of average prediction error of the estimated age for eachtype of tooth [36]. This latter study by Fernandez & Legendre offers a model based on a regression analysis of curvilinear type, starting from both age and dental height intervals of known age individuals from the referential of Levine [37]. To each tooth position (i.e. P/2, M3/. . . ) corresponds a polynomial equation whose parameters are estimated by bootstrap [38]. The randomisation makes possible to estimate the individual age of teeth and its standard deviation with median values of regression coefficients (slope, intercept, coefficient of determination) [36, tabl. 5, 39, fig. 1). This model was applied to different Pleistocene and Holocene equid populations [40-45]. We present here (Figure 1, A to D), a step-by-step procedure to estimate the age distribution from a hypothetical P4/ of fossil horse. This example clearly shows that the model resolution is based on a reliable prediction error of median age to derive appropriate age class intervals in order to properly distribute age frequencies. Indeed, it appears that no ageing method based on dental material allows obtaining exact absolute ages because individuals vary in the age of achievement of a given stage [46]. By ruling out the distribution information around the mean or median age, we gain a false sense of statistical power about statements based on absolute age. Consequently, it is crucial to reach a correct distribution of individual ages rather than focusing on an exact age [47]. Finally, it appears in all these approaches that the lifetime, the eruption and the tooth wear sequences can only be derived from current domesticated species or from wild representatives of fossil species. This analogy may lead to “mimicry age”, where the estimated age structure partly resembles that of the reference population [48]. Moreover, it is always difficult to assess the degree of abrasion induced by the diet that determines tooth wear [49]. Nevertheless, dental meso-wear [50-51] or micro-wear analyses are highly relevant to determinate the proportion of grass, twigs, or fruit in the diet of extinct species [52-53]. Regardless of the ageing method, this approach is still underused although it recently provided information about changes in seasonal equid diet and the presence of one or several horse cohorts through time in Schöningen 13 II-4 [54], both using isotopic analyses