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An Anthropological Application of Population Modeling Using Matrices. How Long Did It Take For Modern Humans To Migrate Out of Africa?. Rennie Ferguson Fall 2006. Homo sapiens. Originated in Africa 200-250,000 years ago Hunter-gatherers Nomads Agriculturists. Warfare?.

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an anthropological application of population modeling using matrices

An Anthropological Application of Population Modeling Using Matrices

How Long Did It Take For Modern Humans To Migrate Out of Africa?

Rennie Ferguson

Fall 2006

homo sapiens
Homo sapiens
  • Originated in Africa 200-250,000 years ago
  • Hunter-gatherers
      • Nomads
      • Agriculturists

Warfare?

h sapiens population
H. sapiens: Population
  • Ancestral population size
  • Ne=10,000-15,000 individuals
  • 45-240 individuals in a hunter-gatherer group
  • Average life span=35 years
but how did they get there
But how did they get there?

Out-of-Africa model

Multiregional model

Replaced

Interbred

but how did they get there5
But how did they get there?

Out-of-Africa model

Multiregional model

Replaced

Interbred

homo sapiens7
Homo sapiens

x1

x2

x7

x3

x6

x4

x5

x2

x3

slide8

Central Asia

Alaska

Europe

Siberia

Middle East

China

North America

Africa

A more comprehensive model…

South America

the model
The Model

Leave Dates

130,000 years ago

?

?

?

?

?

?

North America

South America

Middle East

Siberia

Africa

Asia

Alaska

60,000 years ago

25,000 years ago

130,000 years ago

100,000 years ago

15,000 years ago

13,500-13,000 years ago

12,000 (?) years ago

Entry Dates

7 zones
7 zones

Became 1,000,000 km2 in my calculations

slide11

r=growth rate

r=1.0015, or 0.15% per generation

e=fraction of x1 that move to x2

= Average size of hunter-gatherer group/ Total people

=142.5/ 10,000

=0.014 or 1.4% per generation

(later had to be modified to 0.14% per generation)

matrix model13
Matrix Model

n=time (measured in lifespans, where average lifespan=35 years)

africa middle east
AfricaMiddle East

Population of x2 must reach 10,000, since area of Middle East ≈ area of Northern Africa

When n=500, years=35x500=17,500 years

middle east asia
Middle EastAsia

Population of x3 must reach 420,000, since area of Asia ≈ 42x the area Middle East

When n=2500, years=35x2500=87,500 years

asia siberia
AsiaSiberia

Population of x4 must reach 100,000, since area of Siberia ≈ 10x the area Middle East

When n=155, years=35x155=5,425 years

siberia alaska
SiberiaAlaska

Population of x5 must reach 10,000, since area of Middle East ≈ area of Alaska

When n=80, years=35x80=2,800 years

alaska north america
AlaskaNorth America

We want the population of x6 to reach 245,000, since area of North America ≈ 24.5x area of Middle East.

However, it takes 2000 generations for x6=241,787.

So…something happens after arrival in Alaska that makes the model incorrect.

More people moving out of Siberia? (so a larger e?)

People living in larger groups?

North America not populated evenly?

Americas actually highly contested…

the model19
The Model

Leave Dates (computed with the model)

112,500 years ago

25,000 years ago

19,575 years ago

16,775 years ago

?

130,000 years ago

North America

South America

Middle East

Siberia

Africa

Asia

Alaska

60,000 years ago

25,000 years ago

130,000 years ago

100,000 years ago

15,000 years ago

12,000 (?) years ago

13,500-13,000 years ago

Entry Dates

conclusions
Conclusions
  • Considering level of detail, an accurate model for human population movement.
  • According to model, humans were entering North America (leaving Alaska) by 16,775 years ago.
  • Found that a mathematical model can aid in interpreting genetic and archaeological evidence.
      • Question of the Americas and entry into Alaska
  • Problems:
      • Doesn’t account for climate or geography
      • Assumes that entry of new zone only occurs when the population size is met
      • Doesn’t account for movement backwards
      • Doesn’t address movement from North America to South America
sources
Sources

Cohen, Mark Nathan. “Health and the Rise of Civilization” Review author: Henry Harpending. American Ethnologist, Vol. 17, No. 4. (Nov. 1990), pp. 799-800. Stable URL: http://links.jstor.org/sici?sici=00940496%28199011%2917 %3A4%3C799%3AHATROC%3E2.0.CO%3B2-Q (accessed 4 December 2006)

“Homo sapiens.” http://www.answers.com/topic/human (3 December 2006)

“Mitochondrial Eve”, http://en.wikipedia.org/wiki/Mitochondrial_Eve (30 October 2006)

“Multiregional hypothesis.” http://en.wikipedia.org/wiki/Multiregional_hypothesis (3 December 2006)

Nash, George. “Assessing rank and warfare-strategy in prehistoric hunter-gatherer society: A study of representational warrior figures on rock-art from the Spanish Levant, South-eastern Spain.” www.archaeologysafaris.co.uk/gn/violence.htm (3 December 2006)

“Recent single-origin hypothesis.” http://en.wikipedia.org/wiki/Out_of_Africa_theory (3 December 2006)

S. G. Webb. “The First Boat People”. From the series: Cambridge Studies in Biological and Evolutionary Anthropology. http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521856566&ss=exc

Stringer, Chris and Peter Andrews. The Complete World of Human Evolution. New York: Thames & Hudson, 2005.

Wall, Jeffrey D. “Estimating Ancestral Population Sizes and Divergence Times.” Genetics 163: p. 395-404. January 2003. http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1462435&blobtype=pdf (3 December 2006)