Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection

2009 ◽  
Vol 76 (4) ◽  
pp. 292-298 ◽  
Author(s):  
Meredith V. Trotter ◽  
Hamish G. Spencer
2020 ◽  
Vol 57 (4) ◽  
pp. 1162-1197
Author(s):  
Adrian Gonzalez Casanova ◽  
Charline Smadi

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.


Evolution ◽  
1973 ◽  
Vol 27 (4) ◽  
pp. 558 ◽  
Author(s):  
R. Nassar ◽  
H. J. Muhs ◽  
R. D. Cook

2016 ◽  
Vol 2 (11) ◽  
pp. e1601335 ◽  
Author(s):  
Jorge F. Mejias ◽  
John D. Murray ◽  
Henry Kennedy ◽  
Xiao-Jing Wang

Interactions between top-down and bottom-up processes in the cerebral cortex hold the key to understanding attentional processes, predictive coding, executive control, and a gamut of other brain functions. However, the underlying circuit mechanism remains poorly understood and represents a major challenge in neuroscience. We approached this problem using a large-scale computational model of the primate cortex constrained by new directed and weighted connectivity data. In our model, the interplay between feedforward and feedback signaling depends on the cortical laminar structure and involves complex dynamics across multiple (intralaminar, interlaminar, interareal, and whole cortex) scales. The model was tested by reproducing, as well as providing insights into, a wide range of neurophysiological findings about frequency-dependent interactions between visual cortical areas, including the observation that feedforward pathways are associated with enhanced gamma (30 to 70 Hz) oscillations, whereas feedback projections selectively modulate alpha/low-beta (8 to 15 Hz) oscillations. Furthermore, the model reproduces a functional hierarchy based on frequency-dependent Granger causality analysis of interareal signaling, as reported in recent monkey and human experiments, and suggests a mechanism for the observed context-dependent hierarchy dynamics. Together, this work highlights the necessity of multiscale approaches and provides a modeling platform for studies of large-scale brain circuit dynamics and functions.


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