ISSN:
1432-1416
Keywords:
Inbreeding
;
Regular Mating Systems
;
Markov Chains Martingales
;
Renewal Events
;
Graph of Finitely Presented Semigroups
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Summary A probabilistic and algebraic treatment of regular inbreeding systems is presented. Regular inbreeding systems can be thought of as graphs which have certain natural homogeneity properties. Random walks Xn and Yn are introduced on the nodes of the graphs; the event {Xn = Yn} is a renewal event by the homogeneity property. We show that in such regular inbreeding systems the population becomes genetically uniform if and only if the event {Xn = Yn} is recurrent, which happens if ∑ 1/ An diverges, where An is the number of ancestors n generations into the past. We give two counterexamples to show the converse is false in general, but we verify the converse in the case of the graphs of certain finitely presented semigroups.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00275714
