Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Hummel, Sebastian"'
Population models usually come in pairs; one process describes forward evolution (e.g. type composition) and the other describes backward evolution (e.g. lines of descent). These processes are often linked by a formal relationship known as duality. I
Externí odkaz:
http://arxiv.org/abs/2407.01242
Autor:
Hummel, Sebastian, Jaffe, Adam Quinn
Consider all the possible ways of coupling together two Brownian motions with the same starting position but with different drifts onto the same probability space. It is known that there exist couplings which make these processes agree for some rando
Externí odkaz:
http://arxiv.org/abs/2309.16922
We derive stationary and fixation times for the multi-type $\Lambda$-Wright-Fisher process with and without the classic linear drift that models mutations. Our method relies on a grand coupling of the process realized through the so-called lookdown-c
Externí odkaz:
http://arxiv.org/abs/2308.09218
Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics
Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A li
Externí odkaz:
http://arxiv.org/abs/2307.06010
Mean-field interacting multi-type birth–death processes with a view to applications in phylodynamics
Publikováno v:
In Theoretical Population Biology October 2024 159:1-12
Our results characterize the long-term behavior for a broad class of $\Lambda$-Wright--Fisher processes with frequency-dependent and environmental selection. In particular, we reveal a rich variety of parameter-dependent behaviors and provide explici
Externí odkaz:
http://arxiv.org/abs/2112.10560
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:
Ann. Appl. Probab. 32 (3), 1499-1556 (2022)
$\Lambda$-Wright--Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate frequency-depende
Externí odkaz:
http://arxiv.org/abs/1903.06731
Publikováno v:
Ann. Appl. Probab. 32 (4) 2400-2447 (2022)
We consider the mutation--selection differential equation with pairwise interaction (or, equivalently, the diploid mutation--selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral
Externí odkaz:
http://arxiv.org/abs/1812.00872
Publikováno v:
J. Math. Biol. 77 (2018), 795-820
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes ancestral (r
Externí odkaz:
http://arxiv.org/abs/1710.04573