Branching processes in homogeneous and inhomogeneous environment VLADIMIR VATUTIN (Steklov Mathematical Instutute) Moscow, Russia.

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Presentation transcript:

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) Fedor died in 1598 Ivan (killed by his father in 1581) Dmitrii (died in 1591 of an epileptic fit)

ROMANOV-GOTTORP DYNASTY ( ) Alexandr II Mikhail Romanov.... Catherine The Great Alexei Nikolay II Alexandr III

ROMANOV-GOTTORP DYNASTY ( ) Alexandr II Mikhail Romanov.... Catherine The Great Alexei Nikolay II Alexandr III Rasputin

T. R. Malthus : An Essay on the Principle of Population as it Affects the Future of Society, 1798) 379 out of 487 bourgeois families in the city Berne extinct between 1583 and out of 487 bourgeois families in the city Berne extinct between 1583 and 1783 The proportion of extinct families is 379/487, that is more than 0.75 (!) in approximately 6 generations The proportion of extinct families is 379/487, that is more than 0.75 (!) in approximately 6 generations

Mitochondrial DNA Mitochondrial DNA Mitochondrial DNA Nonfertilized egg includes up to mitochondrial DNA Nonfertilized egg includes up to mitochondrial DNA 37 genes Egg Nuclear DNA Sperm -50 mtDNA

.. Mitochondrial DNA Fertilized egg Fertilized egg Mitochondrial DNA Mitochondrial DNA 37 genes Egg Nuclear DNA Sperm -50 mtDNA mtDNA Nuclear DNA

Distance to the most recent common ancestor T=(the average time between mutations)X(total number of mutations)/2 1 2

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

North Atlanitic Right Whale