Branching processes in homogeneous and inhomogeneous environment

Branching processes in Branching processes in homogeneous and homogeneous and

inhomogeneous inhomogeneous environmentenvironment

VLADIMIR VATUTINVLADIMIR VATUTIN(Steklov Mathematical Instutute)(Steklov Mathematical Instutute)

Moscow, RussiaMoscow, Russia

Ivan the Terrible is killing his Ivan the Terrible is killing his son (Painter - Il’ya Repin)son (Painter - Il’ya Repin)

RURK DYNASTY (8??-1598)RURK DYNASTY (8??-1598)

Viking RURK

...

Ivan IV (The Terrible)

Fedor died in 1598

Ivan (killed by his father in 1581)

Dmitrii (died in 1591 of an epileptic fit)

ROMANOV-GOTTORP ROMANOV-GOTTORP DYNASTY (1613-1917)DYNASTY (1613-1917)

Peter I

Alexandr II

Mikhail Romanov

....

Catherine The Great

Alexei

Nikolay II

Alexandr III

Queen Victoria

(haemophilia)

PrincessAlice

PrincessAlix

ROMANOV-GOTTORP ROMANOV-GOTTORP DYNASTY (1613-1917)DYNASTY (1613-1917)

Peter I

Alexandr II

Mikhail Romanov

....

Catherine The Great

Alexei

Nikolay II

Alexandr III

Queen Victoria

(haemophilia)

PrincessAlice

PrincessAlix

Rasputin

T. R. Malthus T. R. Malthus : : An Essay on the Principle of An Essay on the Principle of Population as it Affects the Future of Population as it Affects the Future of

Society, 1798)Society, 1798)

379379 out of out of 487487 bourgeois families in bourgeois families in the city Berne extinct between the city Berne extinct between 1583 1583 and and 17831783

The proportion of extinct families is The proportion of extinct families is 379/487379/487, that is more than , that is more than 0.750.75 (!) in (!) in approximately approximately 66 generations generations

Mitochondrial DNAMitochondrial DNA Mitochondrial DNAMitochondrial DNA Nonfertilized egg includes up to 10000 Nonfertilized egg includes up to 10000

mitochondrial DNAmitochondrial DNA

37genes

EggNuclear

DNA

Sperm -50 mtDNA

..

..

Mitochondrial DNAMitochondrial DNA

Fertilized egg Fertilized egg

Mitochondrial Mitochondrial DNADNA

37genes

EggNuclear

DNA

Sperm -50 mtDNA

10000+50 mtDNA

Nuclear DNA

Distance to the most recent common Distance to the most recent common ancestor ancestor

TT=(the average time between =(the average time between mutations)X(mutations)X(totaltotal number of mutationsnumber of mutations)/2)/2

1

2

The time of the birth of the The time of the birth of the ““AmerindianAmerindian” Eve” Eve

Using molecular data that were obtained as part Using molecular data that were obtained as part of study on the mitochondrial variation observed of study on the mitochondrial variation observed in in AmerindianAmerindian populations in the US one can populations in the US one can conclude by the methods of branching processes conclude by the methods of branching processes that Americas were settled about 20,000 years that Americas were settled about 20,000 years ago. (ago. (March 2, 2001 issue of ScienceMarch 2, 2001 issue of Science).).

North Atlanitic Right WhaleNorth Atlanitic Right Whale