On Λ-Fleming–Viot processes with general frequency-dependent selection

2020 ◽  
Vol 57 (4) ◽  
pp. 1162-1197
Author(s):  
Adrian Gonzalez Casanova ◽  
Charline Smadi
Keyword(s):  
Population Genetics ◽  
Adaptive Dynamics ◽  
Large Population ◽  
Biological Evolution ◽  
Strong Solutions ◽  
Biological Interactions ◽  
Diffusion Term ◽  
Frequency Dependent ◽  
Frequency Dependent Selection ◽  
General Frequency

AbstractWe 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 González Casanova and Spanò [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 non-transitive 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.

Zufallspaarung mit teilweiser Selbstung unter verschiedenen Modellen von häufigkeitsabhängiger Selektion /Mixed Random Mating and Selfing with Different Models of Frequency-Dependent Selection

1978 ◽  
Vol 33 (9-10) ◽  
pp. 755-768 ◽  
Author(s):  
M. Hühn
Keyword(s):  
Genetic Polymorphisms ◽  
Population Genetic ◽  
Random Mating ◽  
Large Population ◽  
Decisive Role ◽  
Initial Population ◽  
Special Importance ◽  
Gene Frequencies ◽  
Frequency Dependent ◽  
Frequency Dependent Selection

Abstract Given a large population with mixed random mating and selfing (one locus-two alleles) different models of frequency-dependent selection were discussed - including a simple biometrical model for considering and analysing the competitive effects between neighbouring individuals in plant populations. For each model there were studied: changes in gene frequencies, population genetic equilibria, times until reaching these equilibria etc. - in dependence of the different parameters used: composition of the initial population, probability of selfing, selection-coefficients, competition-parameters.Apart from only few differing results it follows from the studies performed in these investigations, that the different composition of the initial population is of no particular importance as well for the gene frequencies p̂ at equilibrium as for the time t̂ until reaching these equilibria. This result is especially right for p̂.Different probabilities of selfing and different degrees of dominance in the selection coefficients are indeed of some influence on the existence and location of the population genetic equilibria, but here too we find an disproportionately stronger dependence with the time t̂ until reaching the equilibrium than with the gene frequency p̂ at equilibrium . The special importance of overdominance for the maintenance of genetic polymorphisms, which is well known in the case of non­ frequency-dependent selection (see: model 1 of the present studies) turn out to be of some other meaning in the models of frequency-dependent selection, which were analysed in the present paper: Depart from only few special situations (model 2 ; complete self-fertilization in models 5 and 6 ; extremely high probabilities of selfing in model 7) nontrivial equilibria are reached for all degrees of dominance. Therefore, the special importance of overdominance mentioned above, not proves right in the case of frequency-dependent selection.The investigations of the present paper have shown, that existence and location of the non­ trivial population genetic equilibria are determined not so much by degree of dominance and probability of selfing, but the equilibria are mainly determined by the model of the investigation used in the concerning studies.In the case of frequency-dependent selection, therefore, the explicit form of the fitness values as functions of the frequencies plays the decisive role in maintaining genetic polymorphisms.

Introduction

2011 ◽  
Author(s):  
Michael Doebeli
Keyword(s):  
Mathematical Modeling ◽  
Frequency Dependence ◽  
Biological Interactions ◽  
Heritable Variation ◽  
Evolutionary Trajectory ◽  
Frequency Dependent ◽  
Frequency Dependent Selection ◽  
Suitable Parameter ◽  
Space Frequency

This introductory chapter provides an overview of frequency-dependent selection—the phenomenon that the evolving population is part of the changing environment determining the evolutionary trajectory. Selection is frequency-dependent if the sign and magnitude of the correlations between heritable variation and reproductive variation change as a consequence of changes in the trait distribution that are themselves generated by such correlations. From the perspective of mathematical modeling, the realm of frequency dependence in evolution is larger than the realm of situations in which selection is not frequency dependent, because the absence of frequency dependence in a mathematical model of evolution essentially means that some parameters describing certain types of biological interactions are set to zero. Thus, in a suitable parameter space, frequency independence corresponds to the region around zero, while everything else corresponds to frequency dependence. In this way, frequency-dependent selection should therefore be considered the norm, not the exception, for evolutionary processes.

Adaptive Diversification (MPB-48)

2011 ◽  
Author(s):  
Michael Doebeli
Keyword(s):  
Evolutionary Biology ◽  
Biological Diversity ◽  
Adaptive Dynamics ◽  
Theoretical Treatment ◽  
Mathematical Framework ◽  
Evolutionary Branching ◽  
Rare Type ◽  
Frequency Dependent ◽  
Frequency Dependent Selection ◽  
Adaptive Diversification

Understanding the mechanisms driving biological diversity remains a central problem in ecology and evolutionary biology. Traditional explanations assume that differences in selection pressures lead to different adaptations in geographically separated locations. This book takes a different approach and explores adaptive diversification—diversification rooted in ecological interactions and frequency-dependent selection. In any ecosystem, birth and death rates of individuals are affected by interactions with other individuals. What is an advantageous phenotype therefore depends on the phenotype of other individuals, and it may often be best to be ecologically different from the majority phenotype. Such rare-type advantage is a hallmark of frequency-dependent selection and opens the scope for processes of diversification that require ecological contact rather than geographical isolation. This book investigates adaptive diversification using the mathematical framework of adaptive dynamics. Evolutionary branching is a paradigmatic feature of adaptive dynamics that serves as a basic metaphor for adaptive diversification, and the book explores the scope of evolutionary branching in many different ecological scenarios, including models of coevolution, cooperation, and cultural evolution. It also uses alternative modeling approaches. Stochastic, individual-based models are particularly useful for studying adaptive speciation in sexual populations, and partial differential equation models confirm the pervasiveness of adaptive diversification. Showing that frequency-dependent interactions are an important driver of biological diversity, the book provides a comprehensive theoretical treatment of adaptive diversification.

Frequency-Dependent Selection at the Payne Inversion in Drosophila melanogaster

Evolution ◽  
1973 ◽  
Vol 27 (4) ◽  
pp. 558 ◽  
Author(s):  
R. Nassar ◽  
H. J. Muhs ◽  
R. D. Cook
Keyword(s):  
Drosophila Melanogaster ◽  
Frequency Dependent ◽  
Frequency Dependent Selection
Sign in / Sign up

Export Citation Format

Share Document