They suggest that the similarity between the curves of biodiversity and human population probably comes from the fact that both are derived from the interference of the hyperbolic trend with cyclical and stochastic dynamics.

[21][22] Finally, Korotayev has demonstrated that the hyperbolic models of this type may be used to describe in a rather accurate way the overall growth of the planetary complexity of the Earth since 4 billion BC up to the present.

[25] He has also produced a number of mathematical models describing specifically long-term political-demographic dynamics of Egypt[26] and used them for a demographic structural analysis of the 2011 Egyptian Revolution.

Both studies focusing on specific historical societies and analyses of cross-cultural data have failed to find positive correlation between population density and incidence of warfare.

They have demonstrated that post-Soviet Russia experiences one of the world's highest prevalence of alcohol-related problems, which contributes to high mortality rates in this region.

[38] Korotayev and his colleagues have demonstrated that Protestantism has indeed influenced positively the capitalist development of respective social systems not so much through the "Protestant ethics" (as was suggested by Max Weber) but rather through the promotion of literacy.

Indeed, he shows that we have evidence for the systematic spread of major innovations (domesticated cereals, cattle, sheep, goats, horses, plow, wheel, copper, bronze, and later iron technology, and so on) throughout the whole North African – Eurasian Oikumene for a few millennia BCE.

By the end of the 1st millennium BCE we observe a belt of cultures, stretching from the Atlantic to the Pacific, with an astonishingly similar level of cultural complexity characterised by agricultural production of wheat and other specific cereals, the breeding of cattle, sheep, and goats; use of the plow, iron metallurgy, and wheeled transport; development of professional armies and cavalries deploying rather similar weapons; elaborate bureaucracies, and Axial Age ideologies, and so on – this list could be extended for pages.

A few millennia before, we would find another belt of societies strikingly similar in level and character of cultural complexity, stretching from the Balkans up to the Indus Valley outskirts.

[45] As is noted by Jack Goldstone, the "new view, carefully presented and rigorously modeled by Grinin and Korotayev, provides a richer and more nuanced version of the "Great Divergence," bridging many of the differences between the traditional and California viewpoints.

[47] Note also his research on Kondratiev waves in the world GDP dynamics that, employing spectral analysis, has confirmed their presence at an acceptable level of statistical significance.

[50] From a complexity perspective Korotayev's establishes a key point, that of the bifurcations of social and kinship organisation that coalesced historically around the differential practices of the major world religions.

Korotayev demonstrates the effects of breaking what might be seen as a ritual taboo of Murdockian comparison: Thou Shalt Not Code World Religion.

By doing so, Korotayev releases the Murdockian spell that lingers over the comparative approach in anthropology, and goes on to demonstrate the powerful effects of world religious communities — dating from what Jaspers calls the "Axial Age" (800–200 BCE) – on the preservation and differentiation of distinctive social and political structures in Eurasia.

Early theories explaining the determinants of postmarital residence (e.g., Lewis Henry Morgan, Edward Tylor, or George Peter Murdock) connected it with the sexual division of labour.

However, to the moment when Korotayev's research in this field began, cross-cultural tests of this hypothesis using worldwide samples had failed to find any significant relationship between these two variables.

If this polygyny factor is controlled (e. g., through a multiple regression model), division of labour turns out to be a significant predictor of postmarital residence.

[52] Korotayev was also one of the pioneers (together with his colleagues) of the study of correlation between spatial distributions of folklore-mythological motifs[53] and genetic markers,[54] as well as linguistic and sociostructural characteristics, and produced in this area significant results with respect to the deep history reconstruction.

[55] As is noticed by Julien d'Huy et al., "Korotayev and Khaltourina[56] showed statistical correlation between spatial distributions of mythological motifs and genetic markers, considerably above the 4,000 km...

He postulates that the traditionally accepted causes of the decline of unilineal descent organisation (statehood, class stratification, commercialisation) are less significant than deep Christianization.

He also theorises that the presence of unilineal descent groups correlates negatively with communal democracy and is especially strong for complex traditional societies.

[60] Korotayev has made a special contribution in this field by detecting principal trends in the evolution of Yemeni cultures through application of quantitative methods to the analysis of mass epigraphic sources in the Sabaic language.

[62] He was also the first to provide convincing evidence for the existence of matrilineal descent organisation in Pre-Islamic Arabia[63] and to suggest an adequate translation of the largest Qatabanic inscription, R 3566.

[64] Korotayev and his colleagues have also made significant contributions to the study of political-demographic dynamics in Subsaharan Africa, especially, the problems of the Tropical African countries' escape from the Malthusian trap.

They find that most sociopolitical systems of the Arabs reacted to the socioecological crisis by getting rid of the rigid supratribal political structures (kingdoms and chiefdoms) which started posing a real threat to their very survival.

At the beginning of the 7th century a tribe which would recognise themselves as subjects of some terrestrial supratribal political authority, a "king", risked to lose its honour.