Wednesday, December 8, 2010

The Shape of the Neolithic Transition: Populations Under Space Competition

"An alloy of copper and tin first used in Britain towards the end of the 3rd millennium BC for tools, decoration, axes, daggers, swords and pins and giving its name to the period we now know as the Bronze Age. The two material were mixed in the quantities of 88% copper 12% tin and heated to around 1200 degrees centigrade before the molten metal was poured into clay or stone moulds. These were then broken open and the item polished, ground or sharpened to make the finished article. Link"


When I think of Neolithic pastoralists and farmers, one of the first things that comes to mind is their motivation.  What drove them forward and what environment did they encounter?  Did they arrive all at once or at first in a trickle.   Where they alone and if not, what kind of relationship did they have with the Mesolithic natives?

In that light, a new paper, which Razib flagged last week, advances the case for an already populated Europe:

Anisotropic dispersion, space competition and the slowdown of the Neolithic transition,
Neus Isern and Joaquim Fort

Link (open access)

The authors model the slowdown of the Neolithic advance into an increasingly populated Northern Europe in direction y:


Working from the diffusion equation, the authors develop an expression for the front speed of the northwest bound advance across Europe.  What the authors are really interested in is why the advance across Europe slowed as it moved northward.  The slowdown is expressed as:

 
y is the position in Europe, advancing from the Balkans to Frisia

c is the front is the front speed

cmax is the maximum possible front speed advancing into an unpopulated area

m(y) = M(y)/Mmax;
M(y) is the density of Mesolithic individuals at position y;
Mmax is the carrying capacity for Mesolithic populations

D is a diffusion coefficient

a is the initial growth rate of the Neolithic population

There is a particularly interesting aspect of the paper.  They don't know the shape of the Mesolithic population density M(y), so they try four test functions for m=M(y)/Mmax: a first order slope (m1), an exponential (m2), an inverted exponential (m3) and a function which approximates the normal distribution (m4).  Figure 2 in the paper shows these functions:


Substituting m(y) into the function for the slowdown c/cmax, the authors plot (Figure 3, below) the slowdown and compare it with observed front speeds calculated from archaeological data:


Note that the Figure 2 best fit function for the Mesolithic population distribution is m4, the approximation to the normal distribution.  The solutions for the slowdown also look like the Mesolithic population distribution functions, but are under compression at the front.  The best fit for the slowdown c/cmax also takes on the appearance of the normal distribution, but with frontal compression.

This same normal distribution has been observed in the Fertile Crescent West Asian, Southern European and Southwest Asian components, as I've demonstrated in Fertile Crescent Components Do the Wilkins Wakeley Model.

From the following plot, the "front" for the present day distribution of the "Southwest Asian" component appear to be between Armenia and Georgia.  Again, the distribution approximates a normal distribution but is under compression at its front.
1=Lezgin 2=Adygei 3=Georgian 4=Armenian 5=Turk 6=Assyrian 7=Cypriot 8=Syrian 9=Jordanian 10=Egyptian 11,13=blank 12=Saudi, 14=Ethiopian

For the "West Asian" component, the present day front is between Saudi Arabia and Ethiopia.
1=Lezgin 2=Adygei 3=Georgian 4=Armenian 5=Turk 6=Assyrian 7=Cypriot 8=Syrian 9=Jordanian 10=Egyptian 11,13=blank 12=Saudi, 14=Ethiopian

The Southern European component is diffusing out on multiple fronts.  Here we see a southern front in Saudi Arabia and a northern front on the northern side of the Caucasus.
1=Lezgin 2=Adygei 3=Georgian 4=Armenian 5=Turk 6=Assyrian 7=Cypriot 8=Syrian 9=Jordanian 10=Egyptian 11,13=blank 12=Saudi, 14=Ethiopian

The ADMIXTURE results are for present day populations that are under the influence of space competition.  The best fit European Mesolithic result in the referenced paper, five to eight thousand years ago, is also normal distribution like, which would indicate that there is some action at work that persuades populations under space competition to adopt a normal like distribution.

The Wilkins Wakeley paper suggests an answer: 

"Each individual produces a very large number of gametes, which are dispersed according to a normal distribution centered at the location of the individual and with variance 2-sigma squared.  Thus in each generation an effectively infinite number of gametes arrives at each location.  One of these gametes is selected at random to become the adult at that location in the next generation.  The distribution of the origins of those gametes is the correlation of the normal with a delta function at the individual's location.  Thus, the parent is normally distributed around the location of its offspring, with variance 2-sigma squared.

"Most continuous-space models in population genetics assume a uniform population density that would not actually be maintained by the proposed reproductive scheme.  A normal distribution of gametes without severe density regulation generates a population that is clumped together at certain locations and sparsely populated at others.  With its absolute density regulation at all locations, the model of reproduction here will immediately generate and maintain a population that is uniformly distributed across its habitat range."

What this suggests about the interface between Neolithic-Mesolithic populations is that their sum requirement for space was uniformly distributed and that each population was under the constraint of "severe density regulation."  Each population regulated the space between families, tribes and habitats in an even distribution and in so doing, distributed their gametes according to the normal distribution.

From the appearance of Figure 1, there is some clumping of Neolithic and Mesolithic populations.  Mesolithic populations appear to have held out in the British Isles, Alps, Western France, Frisia, and the Valley of the Vistula River. (The archaeological data appear suspect for Finland, Norway and Northern Russia.)  However, on average, there appears to have been enough density regulation in both the Mesolithic population and the Neolithic population to have resulted in approximately normally distributed populations.

The authors don't discuss the possibility that Mesolithic Hunters might originally have been more loosely distributed and not under the constraint of space competition.  Perhaps as the Neolithic advance moved forward, the mobile hunter Mesolithic population was pushed northward, and it became more dense and more regulated (evenly spaced).  The very old advance dates (greater than 7,500bp) in Northern Greece, Southern Italy, and scattered across Europe would suggest that for several thousand years, the advance into Europe was quite sporadic and unevenly distributed.  That would correspond with a more loosely distributed Mesolithic population.

As the two populations together became more densely concentrated, they would reach a state of dynamic equilibrium.  The population pressure behind the front of the Neolithic population would advance the front forward, with the retreating Mesolithic population maintaining its approximately normally distributed shape.  The Neolithic population would also be normally distributed at its center, but would have a frontally compressed edge.

As the battle for space became more intense among and between the two populations, it's clear that both populations sought a means to preserve themselves.  The Neolithic population developed weapons such as the copper axe, as well as more advanced methods of fortification.  The Mesolithic population appears to have headed for niches where Neolithic farming was not viable.

From the genetic record, we know that European Neolithic Farmers and Mesolithic populations eventually worked it out, but the process of intense space competition appears to have resulted in tremendous change, population displacements, technological advancements and sometimes, tribal warfare.

It's our friend the normal distribution that tells us that.

Tomorrow, I'll revisit what this paper suggests about normally distributed populations in the Fertile Crescent.