A mathematical model for Neanderthal extinction

Inbreeding, Allee effects and stochasticity might be sufficient to account for Neanderthal extinction

The replacement of Neanderthals by Anatomically Modern Humans has typically been attributed to environmental pressure or a superiority of modern humans with respect to competition for resources. Here we present two independent models that suggest that no such heatedly debated factors might be needed to account for the demise of Neanderthals. Starting from the observation that Neanderthal populations already were small before the arrival of modern humans, the models implement three factors that conservation biology identifies as critical for a small population's persistence, namely inbreeding, Allee effects and stochasticity. Our results indicate that the disappearance of Neanderthals might have resided in the smallness of their population(s) alone: even if they had been identical to modern humans in their cognitive, social and cultural traits, and even in the absence of inter-specific competition, Neanderthals faced a considerable risk of extinction. Furthermore, we suggest that if modern humans contributed to the demise of Neanderthals, that contribution might have had nothing to do with resource competition, but rather with how the incoming populations geographically restructured the resident populations, in a way that reinforced Allee effects, and the effects of inbreeding and stochasticity.

Ecocultural range-expansion scenarios for the replacement or assimilation of Neanderthals by modern humans

Recent archaeological records no longer support a simple dichotomous characterization of the cultures/behaviors of Neanderthals and modern humans, but indicate much cultural/behavioral variability over time and space. Thus, in modeling the replacement or assimilation of Neanderthals by modern humans, it is of interest to consider cultural dynamics and their relation to demographic change. The ecocultural framework for the competition between hominid species allows their carrying capacities to depend on some measure of the levels of culture they possess. In the present study both population densities and the densities of skilled individuals in Neanderthals and modern humans are spatially distributed and subject to change by spatial diffusion, ecological competition, and cultural transmission within each species. We analyze the resulting range expansions in terms of the demographic, ecological and cultural parameters that determine how the carrying capacities relate to the local densities of skilled individuals in each species. Of special interest is the case of cognitive and intrinsic-demographic equivalence of the two species. The range expansion dynamics may consist of multiple wave fronts of different speeds, each of which originates from a traveling wave solution. Properties of these traveling wave solutions are mathematically derived. Depending on the parameters, these traveling waves can result in replacement of Neanderthals by modern humans, or assimilation of the former by the latter. In both the replacement and assimilation scenarios, the first wave of intrusive modern humans is characterized by a low population density and a low density of skilled individuals, with implications for archaeological visibility. The first invasion is due to weak interspecific competition. A second wave of invasion may be induced by cultural differences between moderns and Neanderthals. Spatially and temporally extended coexistence of the two species, which would have facilitated the transfer of genes from Neanderthal into modern humans and vice versa, is observed in the traveling waves, except when niche overlap between the two species is extremely high. Archaeological findings on the spatial and temporal distributions of the Initial Upper Palaeolithic and the Early Upper Palaeolithic and of the coexistence of Neanderthals and modern humans are discussed.

The effect of trauma on Neanderthal culture: A mathematical analysis

Traumatic lesions are often observed in ancient skeletal remains. Since ancient medical technology was immature, severely traumatized individuals may have frequently lost the physical ability for cultural skills that demand complex body movements. I develop a mathematical model to analyze the effect of trauma on cultural transmission and apply it to Neanderthal culture using Neanderthal fossil data. I estimate from the data that the proportion of adult individuals who suffered traumatic injuries before death was approximately 0.79-0.94, in which 0.37-0.52 were injured severely and 0.13-0.19 were injured before adulthood. Assuming that every severely traumatized individual and a quarter to a half of the other traumatized individuals lost the capacity for a cultural skill that demands complex control of the traumatized body part, I estimate that if an upper limb is associated with a cultural skill, each individual had to communicate closely with at least 1.5-2.6 individuals during adulthood to maintain the skill in Neanderthal society, and if a whole body is associated, at least 3.1-11.5 individuals were necessary. If cultural transmissions between experts and novices were inaccurate, or if low frequency skills easily disappeared from the population due to random drift, more communicable individuals were necessary. Since the community size of Neanderthals was very small, their high risk of injury may have inhibited the spread of technically difficult cultural skills in their society. It may be important to take this inhibition into consideration when we study Neanderthal culture and the replacement of Neanderthals by modern humans.

Competitive Exclusion and Axiomatic Set-Theory: De Morgan's Laws, Ecological Virtual Processes, Symmetries and Frozen Diversity

This work applies the competitive exclusion principle and the concept of potential competitors as simple axiomatic tools to generalized situations in ecology. These tools enable apparent competition and its dual counterpart to be explicitly evaluated in poorly understood ecological systems. Within this set-theory framework we explore theoretical symmetries and invariances, De Morgan's laws, frozen evolutionary diversity and virtual processes. In particular, we find that the exclusion principle compromises the geometrical growth of the number of species. By theoretical extending this principle, we can describe interspecific depredation in the dual case. This study also briefly considers the debated situation of intraspecific competition. The ecological consequences of our findings are discussed; particularly, the use of our framework to reinterpret coupled mathematical differential equations describing certain ecological processes.

Evidence for a (15)N positive excursion in terrestrial foodwebs at the Middle to Upper Palaeolithic transition in south-western France: Implications for early modern human palaeodiet and palaeoenvironment

The Middle to Upper Palaeolithic transition around 35,000 years ago coincides with the replacement of Neanderthals by anatomically modern humans in Europe. Several hypotheses have been suggested to explain this replacement, one of them being the ability of anatomically modern humans to broaden their dietary spectrum beyond the large ungulate prey that Neanderthals consumed exclusively. This scenario is notably based on higher nitrogen-15 amounts in early Upper Palaeolithic anatomically modern human bone collagen compared with late Neanderthals. In this paper, we document a clear increase of nitrogen-15 in bone collagen of terrestrial herbivores during the early Aurignacian associated with anatomically modern humans compared with the stratigraphically older Châtelperronian and late Mousterian fauna associated with Neanderthals. Carnivores such as wolves also exhibit a significant increase in nitrogen-15, which is similar to that documented for early anatomically modern humans compared with Neanderthals in Europe. A shift in nitrogen-15 at the base of the terrestrial foodweb is responsible for such a pattern, with a preserved foodweb structure before and after the Middle to Upper Palaeolithic transition in south-western France. Such an isotopic shift in the terrestrial ecosystem may be due to an increase in aridity during the time of deposition of the early Aurignacian layers. If it occurred across Europe, such a shift in nitrogen-15 in terrestrial foodwebs would be enough to explain the observed isotopic trend between late Neanderthals and early anatomically modern humans, without any significant change in the diet composition at the Middle to Upper Palaeolithic transition.

Survival of the scarcer

We investigate extinction dynamics in the paradigmatic model of two competing species A and B that reproduce (A→2A, B→2B), self-regulate by annihilation (2A→0, 2B→0), and compete (A+B→A, A+B→B). For a finite system that is in the well-mixed limit, a quasistationary state arises which describes coexistence of the two species. Because of discrete noise, both species eventually become extinct in time that is exponentially long in the quasistationary population size. For a sizable range of asymmetries in the growth and competition rates, the paradoxical situation arises in which the numerically disadvantaged species according to the deterministic rate equations survives much longer.

Neanderthals versus Modern Humans: Evidence for Resource Competition from Isotopic Modelling

During later MOIS3, in Europe two populations were present, autochthonous Neanderthals and modern humans. Ecological competition between these two populations has often been evoked but never demonstrated. Our aim is to establish whether resource competition occurred. In this paper, in order to examine the possibility of ecological competition between these two populations, 599 isotopic data were subjected to rigorous statistical treatment and analysis through mixing models. The aim of this paper was to compare dietary strategies of Neanderthals and modern humans over time. Our conclusions suggest that Neanderthals and modern humans shared dietary habits in the particular environmental context of MOIS3 characterised in Europe by climatic deterioration. In this environmental context, the resource competition between Neanderthals and modern humans may have accelerated the disappearance of the Neanderthal population.

Diffusion coefficient of modern humans outcompeting Neanderthals

A nonlinear mathematical model is used to describe Neanderthals extinction about 35,000 years before present. Using archaeological data, radiocarbon re-calibrate speed among others, we show that the diffusion coefficient describing Modern Humans spread corresponds to 1596 km(2)/yr. The model is well established since all archaeological parameters, including Neanderthal-Modern interaction coefficient, become estimated.

To what extent did Neanderthals and modern humans interact?

Neanderthals represent an extinct hominid lineage that existed in Europe and Asia for nearly 400,000 years. They thrived in these regions for much of this time, but declined in numbers and went extinct around 30,000 years ago. Interestingly, their disappearance occurred subsequent to the arrival of modern humans into these areas, which has prompted some to argue that Neanderthals were displaced by better suited and more adaptable modern humans. Still others have postulated that Neanderthals were assimilated into the gene pool of modern humans by admixture. Until relatively recently, conclusions about the relationships between Neanderthals and contemporary humans were based solely upon evidence left behind in the fossil and archaeological records. However, in the last decade, we have witnessed the introduction of metagenomic analyses, which have provided novel tools with which to study the levels of genetic interactions between this fascinating Homo lineage and modern humans. Were Neanderthals replaced by contemporary humans through dramatic extinction resulting from competition and/or hostility or through admixture? Were Neanderthals and modern humans two independent, genetically unique species or were they a single species, capable of producing fertile offspring? Here, we review the current anthropological, archaeological and genetic data, which shed some light on these questions and provide insight into the exact nature of the relationships between these two groups of humans.