SCUDEM III 2018 - Conflict Between Patrilineal Clans Differential Equations Modeling
Roughly 7,000 years ago the genetic record for humans indicates that there was a dramatic decrease in the
variation in Y chromosomes [2]. It appears that the number of people carrying the Y chromosome decreased
to one twentieth of their previous number. There is not an indication for a corresponding drop in the number
of people who do not carry the Y chromosomes.
A group of undergraduate students at Stanford University recently [1,2] hypothesized that the reason for the
sudden decrease in males is due to the development of patrilineal clans among humans, and the resulting
strife and wars between the clans impacted males at a much higher rate than females. The group developed a
mathematical model describing the genetic interactions that result from the hypothesized situation and
showed that the resulting genetic trends are consistent with the current genetic variations seen in both male
and female populations.
Assuming that the hypothesis is correct, develop a mathematical model describing conflict between
neighboring patrilineal clans that can be used to predict the resulting population dynamics including the
distribution of males and females in the human population. Based on your models under what conditions are
conflicts most intense? Was the decline of patrilineal clans inevitable or is it possible to reach an equilibrium
under such a social tradition?
One model for a group of two sets of males is given in the original paper [2]. The model assumes uniform
mixing of the different groups of males and only one group of females. Your model should not assume a
uniform pool of females, but include different groups of females associated with the clans. Additional
discussion on how to extend the model to more than two groups is expected.
[1] Collins, Nathan. 2018. Wars and clan structure may explain a strange biological event 7,000 years ago,
Stanford researchers find. Stanford University News Service. 30 May. https://news.stanford.edu/pressreleases/2018/05/30/war-clan-structubiological-event/.
Accessed 3 September 2018.
[2] Zeng, Tian Chen, Alan J. Aw, and Marcus W. Feldman. 2018. Cultural hitchhiking and competition
between patrilineal kin groups explain the post-Neolithic Y-chromosome bottleneck. Nature
Communications. Volume 9, Article number: 2077. https://www.nature.com/articles/s41467-018-04375-6.
Accessed 3 September 2018. Freely downloadable. This article is licensed under a Creative Commons
Attribution 4.0 International License.