Model Description
Exploring the dynamic feedbacks between biological and cultural evolutionary systems is critical to understanding the origins of modern human behavior. The authors present a population dynamics model using ordinary differential equations and agent based modeling to delineate the consequences of differing mobility strategies expressed as reproduction potential at the population level for Late Pleistocene hominins in Western Eurasia (i.e., modern Homo sapiens and Neanderthals). The model describes the interaction of two biologically distinct populations and assumes that when these populations interact they are able to interbreed and produce hybrid offspring. The model also assumes that all individuals have the same reproductive potential and can yield three possible phenotypes comprising a single locus, two-allele genetic model. The model demonstrates that when reproductive potential (r) is low, Neanderthals continue at their initial frequency. However, as r is increased, the Neanderthal population number drops precipitously over the same time period. The model suggests that the disappearance of Neanderthals could have resulted from absoprtion into a pan-Eurasian genome and cultural sphere rather than selective advantage.
$\begin{equation}
\frac{dN(i)}{d_t}=\sum_{j=1}^{6} P_ij(t)
\end{equation}$ |
| Total population dynamics - i.e. $N(t)$ is the total number of individuals at time $t$. |
$\begin{equation}
\frac{dN_1}{d_t}=(p_1f_1^2+p_5f_1f_3+\frac{p_3}{4}f_3^2)rN
\end{equation}$ |
| Population dynamics for Phenotype 1 |
$\begin{equation}
\frac{dN_2}{d_t}=(p_2f_2^2+p_6f_2f_3+\frac{p_3}{4}f_3^2)rN
\end{equation}$ |
| Population dynamics for Phenotype 2 |
$\begin{equation}
\frac{dN_3}{d_t}=(2p_4f_1f_2+p_5f_1f_3+p_6f_2f_3+\frac{p_3}{2}f_3^2)rN
\end{equation}$ |
| Population dynamics for Phenotype 3 |
#human genetic model # this is a super simple model used to capture the dyanamics # of three interbreeding popultions. It serves as a null model # as a point of comparison to more complext models. par p1=1,p2=1,p3=1,p4=1,p5=1,p6=1,r=0.01 N=N1+N2+N3 f1=N1/N f2=N2/N f3=N3/N N1' = (p1*f1*f1 + p5*f1*f3+ (p3*f3*f3)/4)*r*N N2' = (p2*f2*f2 + p6*f2*f3+ (p3*f3*f3)/4)*r*N N3' = (2*p4*f1*f2 + p5*f1*f3 + p6*f2*f3 + (p3*f3*f3)/2)*r*N @ bounds=1000000 init N1=0.7,N2=0.3,N3=0 aux fr1=f1 aux fr2=f2 aux fr3=f3
Dytchkowskyj D, Arizona State University.
. 2011. Modeling human ecodynamics and biocultural interactions in the late Pleistocene of western Eurasia. Human Ecology. 39(6)
