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Branching processes in homogeneous and inhomogeneous environment. VLADIMIR VATUTIN ( Steklov Mathematical Instutute ) Moscow, Russia. Ivan the Terrible is killing his son (Painter - Il’ya Repin). RURK DYNASTY (8??-1598). Viking RURK. Ivan IV (The Terrible). Ivan ( killed by - PowerPoint PPT Presentation
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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