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pro vyhledávání: '"Baake, Ellen"'
We establish connections between the absorption probabilities of a class of birth-death processes with killing, and the stationary tail distributions of a related class of birth-death processes with catastrophes. Major ingredients of the proofs are a
Externí odkaz:
http://arxiv.org/abs/2407.08478
Autor:
Baake, Ellen, Baake, Michael
The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the context of m
Externí odkaz:
http://arxiv.org/abs/2406.09430
Autor:
Baake, Ellen, Baake, Michael
The embedding problem of Markov transition matrices into Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the well-known coupon collection pr
Externí odkaz:
http://arxiv.org/abs/2405.05203
Publikováno v:
Theor. Popul. Biol. 158 (2024), 60-75
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the distant past,
Externí odkaz:
http://arxiv.org/abs/2306.03512
Publikováno v:
Theor. Popul. Biol. 142 (2021) 46-56
Recently, the selection-recombination equation with a single selected site and an arbitrary number of neutral sites was solved by means of the ancestral selection-recombination graph. Here, we introduce a more accessible approach, namely the ancestra
Externí odkaz:
http://arxiv.org/abs/2101.10080
Publikováno v:
Stochastic Processes Appl. 160 (2023), 409-457
We study ancestral structures for the two-type Moran model with mutation and frequency-dependent selection under the nonlinear dominance or fittest-type-wins scheme. Under appropriate conditions, both lead, in distribution, to the same type-frequency
Externí odkaz:
http://arxiv.org/abs/2011.08888
Publikováno v:
J. Math. Biol. 82 (2021) 1-27
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of large num
Externí odkaz:
http://arxiv.org/abs/2004.08958
Autor:
Baake, Ellen, Wakolbinger, Anton
Publikováno v:
in: Probabilistic Structures in Evolution (E. Baake, A. Wakolbinger, eds.), EMS Press, Berlin, 2021, pp. 43-68
This chapter gives a synopsis of recent approaches to model and analyse the evolution of microbial populations under selection. The first part reviews two population genetic models of Lenski's long-term evolution experiment with Escherichia coli, whe
Externí odkaz:
http://arxiv.org/abs/2004.01011
Autor:
Baake, Ellen, Alberti, Frederic
Publikováno v:
Doc. Math. 26 (2021), pp. 743--793
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of reach; only
Externí odkaz:
http://arxiv.org/abs/2003.06831
Autor:
Baake, Ellen, Baake, Michael
Publikováno v:
in: Probabilistic Structures in Evolution (E. Baake, A. Wakolbinger, eds.), EMS Press, Berlin, 2021, pp. 365-382
Solving the recombination equation has been a long-standing challenge of \emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of \emph{stochastic} models
Externí odkaz:
http://arxiv.org/abs/2002.08658