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Mutation-selection balance: ancestry, load, and maximum principle.
The results are applied to threshold phenomena caused by the interplay of selection and mutation (known as error thresholds) and lead to a clarification of concepts, as well as criteria for the existence of error thresholds.
Modelling the fast fluorescence rise of photosynthesis
Ising quantum chain is equivalent to a model of biological evolution
A problem of biochemical physics that may be mapped exactly onto a quantum chain is presented that can be solved without approximation and describes mutation and selection as going on in parallel.
Supercritical multitype branching processes: the ancestral types of typical individuals
For supercritical multitype Markov branching processes in continuous time, the evolution of types along those lineages that survive up to some time t is investigated, and almost-sure convergence theorems for both time and population averages of ancestral types are established.
Mutation-selection models solved exactly with methods of statistical mechanics.
The mean number of mutations, the mutation load, and the variance in fitness under mutation-selection balance are investigated, and some insight is yielded into the 'error threshold' phenomenon, which occurs in some, but not all, examples.
Biological evolution through mutation, selection, and drift: An introductory review
The terminology and recapitulate the basic models of population genetics, which describe the evolution of the composition of a population under the joint action of the various evolutionaryforces, specify the ingredients explicitly, namely, the various mutation models and fitness landscapes.
Ancestral processes with selection: Branching and Moran models
Analytical results of Fearnhead (2002) are used to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution inforward time.
Error propagation in reproduction of diploid organisms. A case study on single peaked landscapes.
Focussing on diploid generalizations of the well-established single peaked landscape, quantitative effects of dominance on error thresholds in infinite populations are found, as well as unexpected qualitative features like multiple equilibria.
Mutation and recombination with tight linkage
- E. Baake
- MathematicsJournal of mathematical biology
- 1 May 2001
Abstract. An exact solution of the mutation-recombination equation in continuous time is presented, with linear ordering of the sites and at most one mutation or crossover event taking place at every…
An asymptotic maximum principle for essentially linear evolution models
This work considers here a family of reversible matrices of asymptotic dimension Nd and identifies conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N.