Paper Info
Title
On Lambda-Fleming-Viot Processes With General Frequency-Dependent Selection
Abstract
We construct a multitype constant-size population model allowing for general selective interactions as well as extreme reproductive events. Our multidimensional model aims for the generality of adaptive dynamics and the tractability of population genetics. It generalises the idea of Krone and Neuhauser [39] and Gonzalez Casanova and Spano [29], who represented the selection by allowing individuals to sample several potential parents in the previous generation before choosing the 'strongest' one, by allowing individuals to use any rule to choose their parent. The type of the newborn can even not be one of the types of the potential parents, which allows modelling mutations. Via a large population limit, we obtain a generalisation of Lambda-Fleming-Viot processes, with a diffusion term and a general frequency-dependent selection, which allows for nontransitive interactions between the different types present in the population. We provide some properties of these processes related to extinction and fixation events, and give conditions for them to be realised as unique strong solutions of multidimensional stochastic differential equations with jumps. Finally, we illustrate the generality of our model with applications to some classical biological interactions. This framework provides a natural bridge between two of the most prominent modelling frameworks of biological evolution: population genetics and eco-evolutionary models.
Year
DOI
Venue
2020
10.1017/jpr.2020.55
JOURNAL OF APPLIED PROBABILITY
Keywords
DocType
Volume
Lambda-Fleming-Viot process, frequency-dependent selection, population genetics, ancestral process, multidimensional SDEs with jumps
Journal
57
Issue
ISSN
Citations 
4
0021-9002
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Adrián González Casanova100.34
Charline Smadi200.34