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 ,000 years ago Originated in Africa ,000 years ago Hunter-gatherers Hunter-gatherers Nomads Nomads Agriculturists Agriculturists Warfare?

H. sapiens: Population Ancestral population size N e =10,000-15,000 individuals individuals in a hunter-gatherer group Average life span=35 years

But how did they get there? Out-of-Africa modelMultiregional model Replaced Interbred

But how did they get there? Out-of-Africa modelMultiregional model Replaced Interbred

Homo sapiens

x1x1 x2 x3 x2x2 x3x3 x4x4 x5x5 x7x7 x6x6

Africa Middle East Europe Central Asia China Siberia Alaska North America South America A more comprehensive model…

The Model Africa Middle East Asia Siberia Alaska North America 100,000 years ago 60,000 years ago 25,000 years ago 15,000 years ago Entry Dates Leave Dates South America 130,000 years ago ?????? 13, ,000 years ago 12,000 (?) years ago 130,000 years ago

7 zones Became 1,000,000 km 2 in my calculations

r=growth rate r=1.0015, or 0.15% per generation e=fraction of x 1 that move to x 2 = 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 Model

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

Africa  Middle East Population of x 2 must reach 10,000, since area of Middle East ≈ area of Northern Africa When n=500, years=35x500=17,500 years

Middle East  Asia Population of x 3 must reach 420,000, since area of Asia ≈ 42x the area Middle East When n=2500, years=35x2500=87,500 years

Asia  Siberia Population of x 4 must reach 100,000, since area of Siberia ≈ 10x the area Middle East When n=155, years=35x155=5,425 years

Siberia  Alaska Population of x 5 must reach 10,000, since area of Middle East ≈ area of Alaska When n=80, years=35x80=2,800 years

Alaska  North America We want the population of x 6 to reach 245,000, since area of North America ≈ 24.5x area of Middle East. However, it takes 2000 generations for x 6 =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 Model Africa Middle East Asia Siberia Alaska North America 100,000 years ago 60,000 years ago 25,000 years ago 15,000 years ago 12,000 (?) years ago Entry Dates Leave Dates (computed with the model) South America 112,500 years ago 25,000 years ago 19,575 years ago 16,775 years ago ? 130,000 years ago 13, ,000 years ago 130,000 years ago

Conclusions Considering level of detail, an accurate model for human population movement. 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. 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. Found that a mathematical model can aid in interpreting genetic and archaeological evidence. Question of the Americas and entry into Alaska Question of the Americas and entry into Alaska Problems: Problems: Doesn’t account for climate or geography Doesn’t account for climate or geography Assumes that entry of new zone only occurs when the population size is met Assumes that entry of new zone only occurs when the population size is met Doesn’t account for movement backwards Doesn’t account for movement backwards Doesn’t address movement from North America to South America Doesn’t address movement from North America to South America

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