"On a continuous approach to fixation on graphs with large populations: the star as a paradigm"Souza, MaxWe consider the general birth-death (BD) and death-birth (DB) processes introduced by Kaveh et al. [3], in which two constant fitness, one for birth and another for death, describe the selection mechanism of the population. Here we allow more general ones, namely frequency-dependent fitness functions under the weak-selection regime. For the star graph, these approximations will be given by solutions of certain ODEs (or system of ODES). It should be emphasised that, although continuous approximations are provided, no infinite population limit is considered here -- these approximations are obtained in the same spirit of [1] albeit with quite different techniques. The general BD and DB processes contain, as special cases, the BD-* and DB-* (where * can be either B or D) processes described in [2] --- this class includes many examples of update rules used in the literature. This is joint work with Poly H. Silva. [1] F. A. C. C. Chalub and M. O. Souza, Fixation in large populations: a continuous view of a discrete problem, J Math Biol, 72(1-2):283--330 (2016). [2] C. Hadjichrysanthou, M. Broom, and J. Rychtá?, Evolutionary games on star graphs under various updating rules, Dyn Games Appl, 1:386 (2011). [3] K. Kaveh, N. L. Komarova, and M. Kohandel, The duality of spatial death–birth and birth–death processes and limitations of the isothermal theorem, Royal Society Open Science, 2 (2015). |
« back