Probability, Population Genetics and Evolution

نویسندگان

  • Vincent Bansaye
  • Nick Barton
  • Julien Berestycki
  • Jean Bertoin
  • Matthias Birkner
چکیده

Branching process in random environment (BPRE) are a generalization of GaltonWatson processes where the reproduction law is picked randomly in an i.i.d manner in each generation. In the supercritical case, the population Zn either explodes (with a positive probability) or becomes extincted. We are interested in the event when the process Zn takes positive but bounded values for large times n. We are characterizing the asymptotic behavior of P (0 < Zn < k). We are also interested by the form of the tree of the population conditionally on Zn = k. We will describe the position of the MRCA (most recent common ancestor) in the linear fractional case and two regimes appear. Finally, we will derive the rate function for lower large deviations of BPRE.

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تاریخ انتشار 2012