Publications

(A) Harmonic Analysis

[1]      Bürger R:  Functions of translation type and functorial properties of Segal algebras I. Monatsh. Math. 90, 101-115 (1980)

[2]      Bürger R: Functions of translation type and functorial properties of Segal algebras II. Monatsh. Math. 92, 253-268 (1981)

[3]      Bürger R: Functions of translation type and Wiener's algebra.  Arch. Math. 36, 73-78 (1981)

[4]      Bürger R: Functions of translation type and solid Banach spaces of functions. Pacific J. Math. 100, 259-269 (1982)

[5]      Bürger R: Contributions to duality theory on groups and hypergroups. In: Topics in Modern Harmonic Analysis. Vol. II. (F. Ricci and G. Weiss, eds.), pp. 1055-1070. Roma: Istituto Nazionale di alta Matematico Francesco Severi (1983)
 

(B) Population Genetics and Mathematical Biology

[1]       Bürger R: On the evolution of dominance modifiers I. A nonlinear analysis.  J. Theor. Biol. 101, 585-598 (1983)

[2]       Bürger R: Nonlinear analysis of some models for the evolution of dominance. J. Math. Biol. 16, 269-280 (1983)

[3]       Bürger R: Dynamics of the classical genetic model for the evolution of dominance. Math. Biosci. 67, 125-143 (1983)

[4]       Wagner GP, Bürger R: On the evolution of dominance modifiers II. A non-equilibrium approach to genetic systems. J. Theor. Biol. 113, 475-500 (1985)

[5]       Bürger R: Dynamical models in quantitative genetics. In: Dynamics of  Macrosystems (J.P. Aubin, D. Saari and K. Sigmund, eds.), pp. 75-89. Lect. Notes in Economy and Math. Systems 257. Berlin-Heidelberg-New York: Springer Verlag (1985)

[6]       Bürger R: Constraints for the evolution of functionally coupled characters: A nonlinear analysis of a phenotypic model. Evolution 40, 182-193 (1986)

[7]       Bürger R: Evolutionary dynamics of functionally constrained phenotypic characters. IMA J. of Math. Appl. Med. Biol. 3, 265-287 (1986)

[8]       Bürger R: On the maintenance of genetic variation: Global analysis of Kimura's continuum-of-alleles model. J. Math. Biol. 24, 341-351 (1986)

[9]       Bürger R: Perturbations of positive semigroups and applications to population genetics. Math. Zeitschrift 197, 259-272 (1988)

[10]   Bürger R: The maintenance of genetic variation: A functional analytic approach to quantitative genetic models. In: Population Genetics and Evolution (G. de Jong,  ed.), pp. 63-72. Berlin-Heidelberg-New York: Springer Verlag (1988)

[11]   Bürger R: Mutation-selection balance and continuum-of-alleles models. Math. Biosci. 91, 67-83 (1988)

[12]   Bürger R, Wagner GP, Stettinger F: How much heritable variation can be maintained in finite populations by mutation-selection balance? Evolution 43, 1748-1766 (1989)

[13]   Bürger R: Linkage and the maintenance of heritable variation by mutation-selection balance. Genetics 121, 175-184 (1989)

[14]   Bürger R: Mutation-selection models in population genetics and evolutionary game theory. Acta Applicandae Mathematicae 14, 75-89 (1989)

[15]   Mayo O, Bürger R, Leach CR: The heritability of fitness: some single gene models. Theoret. Appl. Genetics 79, 278-284 (1990)

[16]   Mayo O, Leach CR, Bürger R: Quantitatively determined self-incompatibility II. Outcrossing in Borago officinalis. Theoret. Appl. Genetics 79: 427-430 (1990)

[17]   Bürger R: An Integro-differential equation from population genetics and perturbations of differentiable semigroups in Fréchet spaces. Proc. Royal Soc. Edinb. 118A, 63-73 (1991)

[18]   Bürger R: Unbounded one-parameter semigroups, Fréchet spaces and applications. In: Semigroup Theory and Evolution Equations (Ph. Clement et al., eds.), pp. 77-91. New York: M. Dekker (1991)

[19]   Gabriel W, Bürger R: Population extinction by mutational load and demographic stochasticity. In: Species Conservation: A Population Biological Approach (A. Seitz and V. Loeschke, eds.), pp. 49-60. Basel: Birkhäuser (1991)

[20]   Bürger R: Moments, cumulants, and polygenic dynamics. J. Math. Biol. 30, 199-213 (1991)

[21]   Gabriel W, Bürger R: Survival of small populations under demographic stochasticity. Theor. Popul. Biol. 41, 44-71 (1992)

[22]   Gabriel W, Bürger R: Aussterberisiko kleiner Populationen: Markov-Ketten und Monte-Carlo-Simulationen als komplementäre Ansätze. In: Fortschritte der Simulation in Medizin, Biologie and Ökologie (D.P.F. Möller and O. Richter, eds.), pp. 118-120. Informatik-Bericht 92/6. TU Clausthal (1992)

[23]   Bürger R: Predictions of the dynamics of a polygenic character under directional selection.  J. Theor. Biol. 162, 487-513 (1993)

[24]   Bomze IM, Bürger R: On the balance between mutation and frequency-dependent selection in evolutionary game dynamics. In: Evolution Equations, Control Theory, and Biomathematics (Ph. Clement and G. Lumer, eds.), pp. 11-23. New York: M. Dekker (1993)

[25]   Lynch M, Bürger R, Butcher D, Gabriel W: The mutational meltdown in asexual populations. J. Heredity 84, 339-344 (1993)

[26]   Gabriel W, Lynch M, Bürger R: Muller's ratchet and mutational meltdowns. Evolution 47, 1744-1757 (1993)

[27]   Bürger R, Hofbauer J: Mutation load and mutation-selection-balance in quantitative genetic traits. J. Math. Biol. 32, 193-218 (1994)

[28]   Gabriel W, Bürger R: Extinction risk by mutational meltdown: synergistic effects between population regulation and genetic drift. In: Conservation Genetics (V. Loeschke, J. Tomiuk, S. K. Jain, eds.), pp. 69-84. Birkhäuser: Basel (1994)

[29]   Bürger R, Lande R: On the distribution of the mean and variance of a quantitative trait under mutation-selection-drift balance. Genetics 138, 901-912 (1994)

[30]   Bürger R, Ewens WJ: Fixation probabilities of additive alleles in diploid populations. J. Math. Biol. 33, 557-575 (1995)

[31]   Bürger R, Lynch M: Evolution and extinction in a changing environment: a quantitative genetic analysis. Evolution 49, 151-163 (1995)

[32]   Lynch M, Conery J, Bürger R: Mutational meltdowns in sexual populations. Evolution 49, 1067-1080 (1995)

[33]   Lynch M, Conery J, Bürger R: Mutation accumulation and the extinction of small populations. Amer. Natur. 146, 489-518 (1995)

[34]   Bomze, IM, Bürger R: Stability by mutation in evolutionary games. Games and Economic Behavior 11, 146-172 (1995)

[35]   Bürger R, Bomze IM: Stationary distributions under mutation-selection balance: structure and properties. Adv. Appl. Prob. 28, 227-251 (1996)

[36]   Mayo O, Bürger R: The evolution of dominance: A theory whose time has passed? Biol. Rev. 27, 97-110 (1997)

[37]   Bürger R, Lynch M: Adaptation and extinction in changing environments. In: Stress, Adaptation, and Evolution (R. Bijlsma and V. Loeschke, eds.), pp. 209-239. Basel: Birkhäuser (1997)

[38]   Bürger R: Mathematical properties of mutation-selection models. Genetica 102/103, 279-298 (1998)

[39]   Bürger R, Gimelfarb A: Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection. Genetics 152, 807-820 (1999)

[40]   Bürger R: Evolution of genetic variability and the advantage of sex and recombination in changing environments. Genetics 153, 1055-1069 (1999)

[41]   Gabriel W, Bürger R: Fixation of clonal lineages under Muller's ratchet. Evolution 54, 1116-1125 (2000)

[42]   Bürger R: Additive genetic variation under intraspecific competition and stabilizing selection: A two-locus study. Theor. Popul. Biol. 61, 197-213 (2002), pdf

[43]   Bürger R, Gimelfarb A: Fluctuating environments and the role of mutation in maintaining quantitative genetic variation. Genetical Research 80, 31-46 (2002), pdf

[44]   Bürger R: On a genetic model of intraspecific competition and stabilizing selection. Amer. Natur. 160, 661-682 (2002), pdf

[45]   Willensdorfer M, Bürger R: The two-locus model of Gaussian stabilizing selection. Theor. Popul. Biol. 64, 101-117 (2003), pdf

[46]   Jones AG, Arnold SJ, Bürger R: Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift. Evolution 57, 1747-1760 (2003), pdf

[47]   Lorenz A, Fuchs J, Bürger R, Loidl J.: Chromosome pairing does not contribute to nuclear architecture in vegetative yeast cells. Eukaryotic Cell 2, 856-866 (2003).

[48]   Bürger R, Gimelfarb A.: The effects of intraspecific competition and stabilizing selection on an polygenic trait. Genetics 167, 1425-1443 (2004), pdf

[49]   Jones AG, Arnold SJ, Bürger R: Evolution and stability of the G-matrix on a  landscape with a moving optimum. Evolution 58, 1639-1654 (2004), pdf

[50]   Whitlock MC, Bürger R: Fixation of new mutations in small populations. In: Evolutionary Conservation Biology (R. Ferrière, U. Dieckmann, D. Couvet, eds), pp. 155-170. Cambridge: Univ. Press (2004), pdf

[51]   Bürger R, Krall C: Quantitative-genetic models and changing environments. In: Evolutionary Conservation Biology (R. Ferriere, U. Dieckmann, D. Couvet, eds), pp. 171-187. Cambridge: Univ. Press (2004), pdf

[52]   Bürger R: A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50: 355-396 (2005), pdf

[53]   Bürger R, Willensdorfer M, Nowak MA: Why are phenotypic mutation rates much higher than genotypic mutation rates? Genetics 172, 197-206 (2006), pdf (see also Research Highlights in Nature Reviews Genetics 7(3), p. 157)

[54]   Bürger R, Schneider K: Intraspecific competitive divergence and  convergence under assortative mating. Amer. Natur. 167, 190-205 (2006), pdf 

[55]   Schneider K, Bürger R: Does competitive divergence occur if mating is costly? J. Evol. Biol. 19, 570-588 (2006)

[56]   Bürger R, Schneider K, Willensdorfer M: The conditions for speciation through intraspecific competition.  Evolution 60, 2185-2206 (2006), pdf 

[57]   Jones AG, Arnold SJ, Bürger R: The mutation matrix and the evolution of evolvability. Evolution 61, 727-745 (2007), pdf

[58]   Willensdorfer M, Bürger R, Nowak MA: Phenotypic mutation rates and the abundance of abnormal proteins in yeast. PLoS Comput. Biol. 3(11), e203. doi:10.1371/journal.pcbi.0030203 (2007), pdf

[59]   Peischl S, Bürger R: Evolution of dominance under frequency-dependent intraspecific competition. J. Theor. Biol. 251, 210-226 (2008), pdf 

[60]   Bürger R, Bagheri HC Dominance and its evolution. In: SE Jorgensen & BD Fath (eds) Encyclopedia of Ecology, 1st edn., pp. 945-952. Oxford: Elsevier B.V. (2008), pdf

[61]   Arnold SJ, Bürger R, Hohenlohe PA, Ajie BC, Jones AG: Understanding the evolution and stability of the G-matrix. Evolution 62, 2451-2461 (2008), pdf

[62]   Manapat M, Ohtsuki H, Bürger R, Nowak MA: Originator dynamics. J. Theor. Biol. 256, 586-595 (2009), http://dx.doi.org/10.1016/j.jtbi.2008.10.006

[63]   Bürger R: Multilocus selection in subdivided populations I: Convergence properties for weak or strong migration. J. Math. Biol. 58, 939-978 (2009),  pdf,  doi:10.1007/s00285-008-0236-5

[64]   Bürger R: Multilocus selection in subdivided populations II: Maintenance of polymorphism under weak or strong migration. J. Math. Biol. 58, 979-997 (2009), pdf,  doi:10.1007/s00285-008-0237-4

[65]   Bürger R: Polymorphism in the two-locus Levene model with nonepistatic directional selection. Theor. Popul. Biol. 76, 214-228 (2009), pdf, doi:10.1016/j.tpb.2009.07.002

[66]   Bürger R: Evolution and polymorphism in the multilocus Levene model with no or weak epistasis. Theor. Popul. Biol. 78, 123-138 (2010), pdf, doi:10.1016/j.tpb.2010.06.002

[67]   Bolnick DI, Amarasekare P, Araujo M, Bürger R, Levine J, Novak M, Rudolf V, Schreiber S, Urban M, Vasseur D: Why intraspecific trait variation matters in ecology. Trends Ecol. Evol. 26, 183-192 (2011), http://dx.doi.org/10.1016/j.tree.2011.01.009

[68]   Schreiber S, Bürger R, Bolnick DI: The community effects of phenotypic and genetic variation within a predator population. Ecology 92, 1582-1593 (2011), doi:10.1890/10-2071.1

[69]   Bürger, R: Some mathematical models in evolutionary genetics. In: The Mathematics of Darwin’s Legacy (FACC Chalub & JF Rodrigues, eds), pp. 67-89. Birkhäuser, Basel (2011), pdf

[70]   Bürger R, Akerman A: The effects of linkage and gene flow on local adaptation: A two-locus continent-island model. Theor. Popul. Biol. 80, 272-288 (2011), pdf, doi:10.1016/j.tpb.2011.07.002; Erratum

[71]   Bank C, Bürger R, Hermisson J: The limits to parapatric speciation: Dobzhansky-Muller incompatibilities in a continent-island model. Genetics 191, 845–863 (2012), pdf,

[72]   Jones AG, Bürger R, Arnold SJ, Hohenlohe P, Uyeda JS: The effects of stochastic and episodic movement of the optimum on the evolution of the G-matrix and the response of the trait mean to selection. J. Evol. Biol. 25, 2210–2231 (2012), pdf, doi: 10.1111/j.1420-9101.2012.02598.x

[73]   Urban MC, Bürger R, Bolnick DI: Asymmetric selection and the evolution of extraordinary defences. Nat. Commun. 4:2085 (2013), pdf, doi: 10.1038/ncomms3085

[74]  Akerman A, Bürger R: The consequences of gene flow for local adaptation and differentiation: a two-locus two-deme model. J. Math. Biol. 68, 1135-1198 (2014), pdf, doi: 10.1007/s00285-013-0660-z

[75]  Geroldinger L, Bürger R: A two-locus model of spatially varying stabilizing or directional selection on a quantitative trait. Theor. Popul. Biol. 94, 10-41 (2014), pdf, doi:10.1016/j.tpb.2014.03.002

[76]  Akerman A, Bürger R: The consequences of dominance and gene flow for local adaptation and differentiation at two linked loci. Theor. Popul. Biol. 94, 42-61 (2014), pdf,  doi:10.1016/j.tpb.2014.04.001

[77]  Bürger R: A survey of migration-selection models in population genetics. Discrete Cont. Dyn. Syst. B 19, 883 - 959 (2014), pdf, doi: 10.3934/dcdsb.2014.19.883

[78]  Aeschbacher S, Bürger R: The effect of linkage on establishment and survival of locally beneficial mutations. Genetics 197, 317-336 (2014), pdf, doi:10.1534/genetics.114.163477

[79]  Jones AG, Bürger R, Arnold SJ: Epistasis and natural selection shape the mutational architecture of complex traits. Nat. Commun. 5:3709 (2014), pdf, doi: 10.1038/ncomms4709

[80]  Servedio M, Bürger R: The counterintuitive role of sexual selection in species maintenance and speciation. Proc. Natl. Acad. Sci. 111, 8113-8118 (2014), pdf, doi: 10.1073/pnas.1316484111

[81]  Geroldinger L, Bürger R: Clines in quantitative traits: The role of migration patterns and selection scenarios. Theor. Popul. Biol. 99, 43-66 (2015), pdf, Appendix B,  doi:10.1016/j.tpb.2014.10.006

[82]  Servedio M, Bürger R: The effects of sexual selection on trait divergence in a peripheral population with gene flow. Evolution 69, 2648–2661 (2015); pdf, doi:10.1111/evo.12762

[83]  Yeaman S, Aeschbacher S, Bürger R: The evolution of genomic islands by increased establishment probability of linked alleles. Molecular Ecology 25, 2542–2558 (2016), pdf, doi: 10.1111/mec.13611

[84]  Bürger, R: Two-locus clines on the real line with a step environment. Theor. Popul. Biol. 117, 1-22 (2017), pdf, 10.1016/j.tpb.2017.08.002

[85]  Pontz M, Hofbauer J, Bürger R: Evolutionary dynamics in the two-locus two-allele model with weak selection. J. Math. Biol. 76, 151–203 (2018), pdf, supplement, 10.1007/s00285-017-1140-7

[86]   Servedio M, Bürger R: The effects on parapatric divergence of linkage between preference and trait loci versus pleiotropy. Genes, 2018, 9(4), 217; https://doi.org/10.3390/genes9040217

[87]   Jones AG, Bürger R, Arnold SJ: The G-matrix simulator family: software for research and teaching. J. of Heredity 109, 825–829 (2018), https://doi.org/10.1093/jhered/esy054

[88]   Su L, Lam K-Y, Bürger R: Two-locus clines maintained by diffusion and recombination in a heterogeneous environment. J. Differential Equations 266, 7909-7947 (2019), https://doi.org/10.1016/j.jde.2018.12.022; https://arxiv.org/abs/1808.03665

[89]   Jones AG, Bürger R, Arnold SJ: The effects of epistasis and pleiotropy on genome-wide scans for adaptive outlier loci. J. of Heredity 110, 493-513 (2019), https://doi.org/10.1093/jhered/esz007

[90]   Patel S, Bürger R: Eco-evolutionary feedbacks between prey densities and linkage disequilibrium in the predator maintain diversity. Evolution 73, 1533-1548 (2019), https://doi.org/10.1111/evo.13785; bioRxiv: http://dx.doi.org/10.1101/523720

[91]   Bürger R: Multilocus population-genetic theory. Theor. Popul. Biol. 133, 40-48 (2020),  https://doi.org/10.1016/j.tpb.2019.09.004

[92]   Servedio M, Bürger R: The effectiveness of pseudomagic traits in promoting divergence and enhancing local adaptation. Evolution 74, 2438-2450 (2020), https://doi.org/10.1111/evo.14056

[93]   Svenson EI, Arnold SJ, Bürger R, Csilléry K, Draghi J, Henshaw JM, Jones AG, De Lisle S, Marques DA, McGuigan K, Simon MN & Runemark A: Correlational selection in the age of genomics. Nature Ecology & Evolution 5, 562-573 (2021), https://dx.doi.org/10.1038/s41559-021-01413-3

Pontz M, Bürger R: The effects of epistasis and linkage on the invasion of locally beneficial mutations and the evolution of genomic islands. Submitted (2021);

 

Monograph:

The Mathematical Theory of Selection, Recombination, and Mutation. Chichester: John Wiley & Sons (2000)

Click here for a PDF-file with corrections, updates, further developments, etc. Reports on further deficiencies are welcome.

 

Edited Proceedings:

   Stochastic Models in Biological Sciences (Eds.: R. Bürger, C. Maes, J. Miekisz). Banach Center Publications, Vol. 80, 276pp. Institute of Mathematics, Polish Academy of Sciences, Warzawa (2008)