Mutation-selection balance: Ancestry, load, and maximum principle

Hermisson J, Redner O, Wagner H, Baake E (2002)

Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Hermisson, Joachim; Redner, Oliver; Wagner, Holger; Baake, EllenUniBi
Abstract / Bemerkung
We analyze the equilibrium behavior of deterministic haploid mutation-selection models. To this end, both the forward and the time-reversed evolution processes are considered. The stationary state of the latter is called the ancestral distribution, which turns out as a key for the study of mutation-selection balance. We find that the ancestral genotype frequencies determine the sensitivity of the equilibrium mean fitness to changes in the corresponding fitness values and discuss implications for the evolution of mutational robustness. We further show that the difference between the ancestral and the population mean fitness, termed mutational loss,provides a measure for the sensitivity of the equilibrium mean fitness to changes in the mutation rate. The interrelation of the loss and the mutation load is discussed. For a class Of models in which the number of mutations in an individual is taken as the trait value, and fitness is a function of the trait, we use the ancestor formulation to derive a simple maximum principle, from which the mean and variance of fitness and the trait may be derived; the results are exact for a number of limiting cases, and otherwise yield approximations which are accurate for a wide range of parameters. These results are applied to threshold phenomena caused by the interplay of selection and mutation (known as error thresholds). They lead to a clarification of concepts, as well as criteria for the existence of error thresholds. (C) 2002 Elsevier Science (USA).
clonal reproduction; mutation load; statistical physics; mutational robustness; backward processes; epistasis; mutation-selection model; branching process; error threshold
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Hermisson J, Redner O, Wagner H, Baake E. Mutation-selection balance: Ancestry, load, and maximum principle. THEORETICAL POPULATION BIOLOGY. 2002;62(1):9-46.
Hermisson, J., Redner, O., Wagner, H., & Baake, E. (2002). Mutation-selection balance: Ancestry, load, and maximum principle. THEORETICAL POPULATION BIOLOGY, 62(1), 9-46.
Hermisson, Joachim, Redner, Oliver, Wagner, Holger, and Baake, Ellen. 2002. “Mutation-selection balance: Ancestry, load, and maximum principle”. THEORETICAL POPULATION BIOLOGY 62 (1): 9-46.
Hermisson, J., Redner, O., Wagner, H., and Baake, E. (2002). Mutation-selection balance: Ancestry, load, and maximum principle. THEORETICAL POPULATION BIOLOGY 62, 9-46.
Hermisson, J., et al., 2002. Mutation-selection balance: Ancestry, load, and maximum principle. THEORETICAL POPULATION BIOLOGY, 62(1), p 9-46.
J. Hermisson, et al., “Mutation-selection balance: Ancestry, load, and maximum principle”, THEORETICAL POPULATION BIOLOGY, vol. 62, 2002, pp. 9-46.
Hermisson, J., Redner, O., Wagner, H., Baake, E.: Mutation-selection balance: Ancestry, load, and maximum principle. THEORETICAL POPULATION BIOLOGY. 62, 9-46 (2002).
Hermisson, Joachim, Redner, Oliver, Wagner, Holger, and Baake, Ellen. “Mutation-selection balance: Ancestry, load, and maximum principle”. THEORETICAL POPULATION BIOLOGY 62.1 (2002): 9-46.

45 Zitationen in Europe PMC

Daten bereitgestellt von Europe PubMed Central.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages.
Bienvenu F, Akçay E, Legendre S, McCandlish DM., Theor Popul Biol 115(), 2017
PMID: 28476403
Noise-driven growth rate gain in clonal cellular populations.
Hashimoto M, Nozoe T, Nakaoka H, Okura R, Akiyoshi S, Kaneko K, Kussell E, Wakamoto Y., Proc Natl Acad Sci U S A 113(12), 2016
PMID: 26951676
Populations adapt to fluctuating selection using derived and ancestral allelic diversity.
Lin WH, Rocco MJ, Bertozzi-Villa A, Kussell E., Evolution 69(6), 2015
PMID: 25908222
Comparative transcriptome of wild type and selected strains of the microalgae Tisochrysis lutea provides insights into the genetic basis, lipid metabolism and the life cycle.
Carrier G, Garnier M, Le Cunff L, Bougaran G, Probert I, De Vargas C, Corre E, Cadoret JP, Saint-Jean B., PLoS One 9(1), 2014
PMID: 24489800
Evolution of functional diversification within quasispecies.
Colizzi ES, Hogeweg P., Genome Biol Evol 6(8), 2014
PMID: 25056399
Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.
Bratus AS, Novozhilov AS, Semenov YS., Math Biosci 256(), 2014
PMID: 25149562
On the behavior of the leading eigenvalue of Eigen's evolutionary matrices.
Semenov YS, Bratus AS, Novozhilov AS., Math Biosci 258(), 2014
PMID: 25445764
Genealogies of rapidly adapting populations.
Neher RA, Hallatschek O., Proc Natl Acad Sci U S A 110(2), 2013
PMID: 23269838
Virus replication as a phenotypic version of polynucleotide evolution.
Antoneli F, Bosco F, Castro D, Janini LM., Bull Math Biol 75(4), 2013
PMID: 23413154
Genomic mutation rates that neutralize adaptive evolution and natural selection.
Gerrish PJ, Colato A, Sniegowski PD., J R Soc Interface 10(85), 2013
PMID: 23720539
New approaches to source-sink metapopulations decoupling demography and dispersal.
Bansaye V, Lambert A., Theor Popul Biol 88(), 2013
PMID: 23792379
Optimal lineage principle for age-structured populations.
Wakamoto Y, Grosberg AY, Kussell E., Evolution 66(1), 2012
PMID: 22220869
The structure of genealogies in the presence of purifying selection: a fitness-class coalescent.
Walczak AM, Nicolaisen LE, Plotkin JB, Desai MM., Genetics 190(2), 2012
PMID: 22135349
The structure of allelic diversity in the presence of purifying selection.
Desai MM, Nicolaisen LE, Walczak AM, Plotkin JB., Theor Popul Biol 81(2), 2012
PMID: 22198521
Distortions in genealogies due to purifying selection.
Nicolaisen LE, Desai MM., Mol Biol Evol 29(11), 2012
PMID: 22729750
Individual histories and selection in heterogeneous populations.
Leibler S, Kussell E., Proc Natl Acad Sci U S A 107(29), 2010
PMID: 20616073
On the application of statistical physics to evolutionary biology.
Barton NH, Coe JB., J Theor Biol 259(2), 2009
PMID: 19348811
Phase diagram for the Eigen quasispecies theory with a truncated fitness landscape.
Saakian DB, Biebricher CK, Hu CK., Phys Rev E Stat Nonlin Soft Matter Phys 79(4 pt 1), 2009
PMID: 19518254
Robustness and epistasis in mutation-selection models.
Wolff A, Krug J., Phys Biol 6(3), 2009
PMID: 19411737
Modeling clonal expansion from M-FISH experiments.
Stolte T, Hösel V, Müller J, Speicher M., J Comput Biol 15(2), 2008
PMID: 18312152
Diploid biological evolution models with general smooth fitness landscapes and recombination.
Saakian DB, Kirakosyan Z, Hu CK., Phys Rev E Stat Nonlin Soft Matter Phys 77(6 pt 1), 2008
PMID: 18643300
Dynamics of the Eigen and the Crow-Kimura models for molecular evolution.
Saakian DB, Rozanova O, Akmetzhanov A., Phys Rev E Stat Nonlin Soft Matter Phys 78(4 pt 1), 2008
PMID: 18999456
Highly fit ancestors of a partly sexual haploid population.
Rouzine IM, Coffin JM., Theor Popul Biol 71(2), 2007
PMID: 17097121
Thermodynamics of neutral protein evolution.
Bloom JD, Raval A, Wilke CO., Genetics 175(1), 2007
PMID: 17110496
Error-threshold exists in fitness landscapes with lethal mutants.
Takeuchi N, Hogeweg P., BMC Evol Biol 7(), 2007
PMID: 17286853
Mutation model for nucleotide sequences based on crystal basis.
Minichini C, Sciarrino A., Biosystems 84(3), 2006
PMID: 16387418
Recombination and the evolution of mutational robustness.
Gardner A, Kalinka AT., J Theor Biol 241(4), 2006
PMID: 16487979
Polymer-population mapping and localization in the space of phenotypes.
Kussell E, Leibler S, Grosberg A., Phys Rev Lett 97(6), 2006
PMID: 17026205
An asymptotic maximum principle for essentially linear evolution models.
Baake E, Baake M, Bovier A, Klein M., J Math Biol 50(1), 2005
PMID: 15322822
The opportunity for canalization and the evolution of genetic networks.
Proulx SR, Phillips PC., Am Nat 165(2), 2005
PMID: 15729647
Unequal crossover dynamics in discrete and continuous time.
Redner O, Baake M., J Math Biol 49(2), 2004
PMID: 15293019
Aggregation of variables and system decomposition: Applications to fitness landscape analysis.
Shpak M, Stadler P, Wagner GP, Hermisson J., Theory Biosci 123(1), 2004
PMID: 18202879
Simon-Ando decomposability and fitness landscapes.
Shpak M, Stadler P, Wagner GP, Altenberg L., Theory Biosci 123(2), 2004
PMID: 18236097
Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme.
Saakian DB, Hu CK, Khachatryan H., Phys Rev E Stat Nonlin Soft Matter Phys 70(4 pt 1), 2004
PMID: 15600436
Perspective: Evolution and detection of genetic robustness.
de Visser JA, Hermisson J, Wagner GP, Ancel Meyers L, Bagheri-Chaichian H, Blanchard JL, Chao L, Cheverud JM, Elena SF, Fontana W, Gibson G, Hansen TF, Krakauer D, Lewontin RC, Ofria C, Rice SH, von Dassow G, Wagner A, Whitlock MC., Evolution 57(9), 2003
PMID: 14575319

62 References

Daten bereitgestellt von Europe PubMed Central.

Biological evolution through mutation, selection, and drift: an introductory review
Baake, 2000

Quantum mechanics versus classical probability in biological evolution
Baake, Phys. Rev. E 57(), 1998
Linkage and the limits to natural selection.
Barton NH., Genetics 140(2), 1995
PMID: 7498757
Viral quasi-species and recombination
Boerlijst, Proc. R. Soc. Lond. B 263(), 1996
Error thresholds on correlated fitness landscapes
Bonhoeffer, J. Theor. Biol. 164(), 1993
Mathematical properties of mutation–selection models
Bürger, Genetica 102/103(), 1998

Bürger, 2000
Mutation load and mutation-selection-balance in quantitative genetic traits.
Burger R, Hofbauer J., J Math Biol 32(3), 1994
PMID: 8182355
Mutation–selection balance and the evolutionary advantage of sex and recombination
Charlesworth, Genet. Res. Camb. 55(), 1990

Crow, 1970
The mutation load in Drosophila
Crow, 1983
Statistical mechanics and population biology
Demetrius, J. Stat. Phys. 30(), 1983
Polynucleotide evolution and branching processes.
Demetrius L, Schuster P, Sigmund K., Bull. Math. Biol. 47(2), 1985
PMID: 4027436
in Sequence space and quasispecies evolution
Eigen, 1988
The molecular quasi-species
Eigen, Adv. Chem. Phys. 75(), 1989

Ethier, 1986

Ewens, 1979
Error threshold in simple landscapes
Franz, J. Phys. A 30(), 1997
Fixation of clonal lineages under Muller's ratchet.
Gabriel W, Burger R., Evolution 54(4), 2000
PMID: 11005281
Gabriel W, Lynch M, Burger R., Evolution 47(6), 1993
PMID: 28567994

Gillespie, 1991
A mathematical theory of natural and artificial selection. Part V: selection and mutation
Haldane, Proc. Camb. Philos. Soc. 23(), 1927
Four-state quantum chain as a model of sequence evolution
Hermisson, J. Stat. Phys. 102(), 2001
Error thresholds and stationary mutant distributions in multi-locus diploid genetics models
Higgs, Genet. Res. Camb. 63(), 1994
The selection mutation equation.
Hofbauer J., J Math Biol 23(1), 1985
PMID: 4078498

Hofbauer, 1988
Smoothness within ruggedness: the role of neutrality in adaptation.
Huynen MA, Stadler PF, Fontana W., Proc. Natl. Acad. Sci. U.S.A. 93(1), 1996
PMID: 8552647

Jagers, 1975

Karlin, 1975

Karlin, 1981
Towards a general theory of adaptive walks on rugged landscapes.
Kauffman S, Levin S., J. Theor. Biol. 128(1), 1987
PMID: 3431131

Kauffman, 1993
A limit theorem for multidimensional Galton–Watson processes
Kesten, Ann. Math. Statist. 37(), 1966

Kimura, 1983
The mutational load with epistatic gene interactions in fitness.
Kimura M, Maruyama T., Genetics 54(6), 1966
PMID: 17248359
Deleterious mutations and the evolution of sexual reproduction.
Kondrashov AS., Nature 336(6198), 1988
PMID: 3057385
An exact correspondence between Eigen's evolution model and a two-dimensional Ising system
Leuthäusser, J. Chem. Phys. 84(), 1986
Statistical mechanics on Eigen's evolution model
Leuthäusser, J. Stat. Phys. 48(), 1987

Maynard, 1995
Global stability of genetic systems governed by mutation and selection. II
Moran, Math. Proc. Camb. Philos. Soc. 81(), 1977
A genetic model with mutation and selection
O'Brien, Math. Biosci. 73(), 1985
Evolution by nearly-neutral mutations.
Ohta T., Genetica 102-103(1-6), 1998
PMID: 9720273
A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population
Ohta, Genet. Res. 20(), 1973
Beyond the average: the evolutionary importance of gene interactions and variability of epistatic effects
Phillips, 2000
The evolution of mutation rates: separating causes from consequences.
Sniegowski PD, Gerrish PJ, Johnson T, Shaver A., Bioessays 22(12), 2000
PMID: 11084621
Self-replication with errors. A model for polynucleotide replication.
Swetina J, Schuster P., Biophys. Chem. 16(4), 1982
PMID: 7159681
Phylogenetic inference
Swofford, 1996
Wagner GP, Booth G, Bagheri-Chaichian H., Evolution 51(2), 1997
PMID: 28565347
What is the difference between models of error thresholds and Muller's ratchet
Wagner, J. Math. Biol. 32(), 1993
Ising quantum chain and sequence evolution
Wagner, J. Stat. Phys. 92(), 1998
Pleiotropy and the preservation of perfection.
Waxman D, Peck JR., Science 279(5354), 1998
PMID: 9508691
Model dependency of error thresholds: the role of fitness functions and contrasts between the finite and infinite sites models
Wiehe, Genet. Res. Camb. 69(), 1997

Wilkinson, 1965

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