The edge of evolutionary dynamics

When the adaptive acceleration story hit the wires I started wondering if population size wasn't the only parameter that might have changed in the past 10,000 years. To make it short, perhaps a small-world network model is more much accurate now with the rise of complex societies (the complexity being contingent upon the parasitism of elites upon the marginal surplus productivity of the larger population sizes due to agriculture). I assume that in the hunter-gatherer world occurrences such as the burial of a Swiss man at Stonehenge in the British Isles 4,300 years ago were not unheard of; but, I suspect that they became appreciably more common after the rise of mass societies. Talking to a friend about these issues I stumbled upon a geometric analogy in relation to the evolutionary dynamics which I am conceptualizing. Imagine, if you will, a mutation which has a selection coefficient. That selection coefficient is contingent upon the population mean fitness. Once the mutation is fixed within a population obviously it does not confer elevated fitness in relation to the mean and the evolutionary action on that locus will cease (at least in the case of the mutant in question). Of course that mutant may still be increasing in frequency and be subject to positive directional selection in other populations as it spreads outward. Over time the the mutant allele may be characterized by a wave of advance as gene flow between demes results in the expansion of the radius across which the mutant allele is fixed. Along the edge of this radius selection will still be driving the frequency of the allele toward fixation, and the radius will obviously continue to increase in value. Assuming that the mutant is favored in all populations eventually one may envisage a point at which it is fixed in all populations. Then there will no longer be an edge along which positive selection can operate. If gene flow occurs via a process where the mutant allele crosses between adjacent demes the geometry of the wave of advance is obvious. But what if one imagines that on occasion gene flow "leap frogs" many demes so that the mutant allele is situated in a region far from the original wave of advance. Now there is a new edge and a new wave of advance! These long distance jumps by the mutant reduce the ratio between the interior and the edge. My hunch is that in a thinly populated world of factious tribes long distance jumps were rare because most gene flow was mediated via deme-to-deme transfer. With the rise of international institutions as well as spatially expansive political units most gene flow may still have remained deme-to-deme, but a non-trivial proportion might now have consisted of random scatterings across a vast radius defined by the furthest boundaries of diplomacy, trade and warfare. In pre-Imperial China during the life of Confucius many males of the lower gentry class made a habit of offering their services to any state willing to take them on (this was Confucius' own lot). Later, when the Chinese state employed scholar-bureaucrats as its representatives it was normal policy to station them far from their natal provinces so as to maximize objectivity through detachment from local affairs. Obviously this concept isn't limited to genes. In The Human Web macrohistorians Robert & William H. McNeill argue forcefully that the past 10,000 years has witnessed the rise of powerfully connected information networks. Tighter integration has allowed these networks to serve as more efficient conduits for the flow of information, resulting in more rapid cultural evolution as well as redundancy which dampens the impact of regressions (i.e., "Dark Ages").^1 It is perhaps a point of biographical wonder that Ramanujan rederived much of Western mathematics because of his isolation from the intellectual currents of the time. But from an economic perspective it seems likely that a more efficient utilization of his intellectual powers would have been to start upon the base of accumulated wisdom rather than having to reinvent the wheel.^2 In the end dynamics are dynamics. Though population transfers of Europeans to South Asia and East Asia are demographically trivial, genetically and intellectually they may have great impact. Tens of thousands of Europeans maybe all that is needed to let a hundred novel alleles bloom. It was all that was necessary to administer the British Raj and leave an indelible cultural stamp. A few dozen Christian believers maybe the spark which begins the process of the conversion of a substantial proportion of Chinese to that religion. Selection is a generic evolutionary process, it need not be limited to biological evolution, and it is almost certainly at work upon culture. 1 - During the Greek Dark Ages after the fall of Bronze Age civilization literacy was lost and had to be rediscovered. With a more robust network of with multiple nodes political collapse in on locus did not necessitate total extinction of a culture. For example, when the Western Roman Empire collapsed, and with it urban life and the literary aristocratic society, the East Roman Empire maintained continuity. 2 - On the other hand, William D. Hamilton notes that George Prices' work in evolutionary biology might have benefited from lack of exposure to previous models. In this way one could say that if the flow of information is too free then the intellectual adaptive landscape deterministically converges upon the local peak, instead of fortuitously stumbling upon the massif just beyond one's horizon.