Saturday, May 17, 2014

A thought on tribal membership

Consider a tribe in which one is a member if one goes through a membership ritual, or if one's mother was a member. Members can not leave the tribe,

Thus someone who has not themselves gone through the ritual is a member if and only if that person's mother was a member. If the mother did not gain membership through the ritual, then she is a member of the tribe if and only if her mother was a member. The relationship is recursive. All tribe members must themselves have gone through the membership ritual or must have a mother who can trace her maternal ancestors back to someone who did go through the membership ritual (or was an original member of the tribe when it was formed).

Thus anyone whose mother had a direct female line going back to a woman who went through the tribal membership ritual is a member of the tribe; anyone who has not him/herself gone through the ritual and does not have a mother who has an unbroken female line going back to a member is not a member.

Lets assume that the tribe has existed for 150 generations.
  • Everyone whose mother comes from a female line that at any point included a tribe member is a member.
  • Anyone whose mother's female line has a nom-member is not a member unless there was a subsequent woman member of that line who went through the membership ritual, or unless the person him/herself went through the ritual.
Thus, unless one's family history goes back to a woman in one's mother's direct female line who was known to have gone through the ritual, one can not say for sure that he/she is a member, unless that person him/herself has gone through the ritual. 

Equally, one who does not claim tribal membership can not be sure that he/she is not a member; some unknown many times great grandmother may have been a member, leaving her daughters members, and a continuous female line to one's own mother. Thus, unless one can trace one's mother's, mother's, mother's female line back 150 generations one can not be sure one is not a member of the tribe.

For those who can not trace their maternal line back to a woman who went through the membership ritual, they can not be sure that they are members of the tribe unless they can trace the maternal line back 150 generations assuring that each member in that line had a mother who was a member or had herself gone through the membership ritual.

World population has increased from a couple of hundred million at the beginning of the modern era to over 7 billion today of whom about half are female. Assuming that there were say one hundred million women in the year 1, on average each has 35 are female direct female descendants today. Of course, some of those original ladies will have many more descendants and some will not have any.

Assume that in 2000 years there are 80 generations of an average of 25 years per generation. On average, each women would have 1.044 daughters per generation who survived to have children. That is, 1.044 to the 80th power.)

If a specific woman 2000 years ago had girl descendants who averaged instead 1.1 such daughters, she would have today more than 2000 female descendants in the direct female line (that is who inherit her mitochondia) of fertile age. If the tribe described above included 100,000 such women, they would have 200 million such female descendants in the direct female line; thus there would be a about 400 million male and female current members of the tribe..

Of course there are tribes living today that we think of as having lived for thousands of years in the same general location, with fairly stable population size. One would assume that such a tribe would have roughly as many variants of mitochondria now as it had 2000 years ago.

My grandmothers had 12 and 13 children respectively, and one of my great grandmothers had 16. Clearly the potential exists in our species for a population explosion of one tribal group (Celtic in my case). Indeed, there are many more people in the world of Irish ancestry than there are Irish in Ireland.

If you assume a core population of Irish women 2000 years ago, there are probably more women today share their mitochondria who are citizens of other countries than there are in Ireland.

No comments: