Volume 19, 2015
|Page(s)||172 - 193|
|Published online||19 August 2015|
Height and the total mass of the forest of genealogical trees of a large population with general competition
1 Department of Mathematics, Hanoi National University, 334
Nguyen Trai Str., Hanoï, Viêt Nam.
2 Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France.
Revised: 30 October 2013
Consider a continuous time branching process, which is integer or real valued (in the latter case it is called a continuous state branching process, and we restrict ourselves to the class of Feller branching diffusions) which models the time evolution of a population, to which we superimpose an interaction between the branches (which destroys the branching property). In the case of a large population, the interaction is of the type of a competition, which increases the individual death rate. We give precise conditions on the competition term, in order to decide whether the extinction time (which is also the height of the forest of genealogical trees) remains or not bounded as the ancestral population size tends to infinity, and similarly for the total mass of that forest of genealogical trees.
Mathematics Subject Classification: 60J80 / 60J85 / 92D25
Key words: Population with competition / extinction time / total mass of genealogical tree
© EDP Sciences, SMAI 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.