Adaptive Dynamics Titles

ADAPTIVE DYNAMICS PAPERS

This page contains some references to the development and applications of adaptive dynamics, with a strong bias towards stochastic trait substitution sequences and evolutionary branching. The list is not exhaustive even in this narrow scope, and I take no responsibility for missing references. If you would like to have a paper included, please alert me at firstname.lastname@helsinki.fi. Since this page is also intended to help course students, I include a few publications outside the scope of adaptive dynamics which are useful in relation to the population dynamics of invading mutants, the connection to speciation models, etc.

Last updated: 17/11/2011 | Maintained by: Eva Kisdi

If you want to read just one paper:

Geritz, S. A. H., É. Kisdi, G. Meszéna, and J. A. J. Metz. 1998. Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12:35-57.

Adaptive dynamics framework of Geritz & Metz

Geritz, S. A. H., É. Kisdi, G. Meszéna, and J. A. J. Metz. 1998. Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12:35-57.

Geritz, S. A. H., J. A. J. Metz, É. Kisdi, and G. Meszéna. 1997. Dynamics of adaptation and evolutionary branching. Phys. Rev. Letters 78:2024-2027.

Metz, J. A. J., S. A. H. Geritz, G. Meszéna, F. J. A. Jacobs, and J. S. van Heerwaarden. 1996. Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. Pp. 183-231 in S. J. van Strien, and S. M. Verduyn Lunel, eds. Stochastic and spatial structures of dynamical systems. North Holland, Amsterdam, The Netherlands.

Eshel, I., U. Motro, and E. Sansone. 1997. Continuous stability and evolutionary convergence. J. theor. Biol. 185:333-343.

The first paper above gives a self-contained description of the adaptive dynamics framework and an illustrative example for how it can be used. The second paper is a short account specifically tailored for the interest of physicists; the third paper is more mathematical. Eshel et al. reached some of the results independently.

Geritz, S. A. H., É. Kisdi, G. Meszéna, and J. A. J. Metz. 2004. Adaptive dynamics of speciation: Ecological underpinnings. Pp. 54-75 in U. Dieckmann, M. Doebeli, J. A. J. Metz, and D. Tautz, eds. Adaptive speciation. Cambridge University Press. PDF

Kisdi É. & M. Gyllenberg. 2004. On some misconceptions about adaptive dynamics. TUCS Technical Report 624 (ISBN 952-12-1417-1)

Meszéna G., M. Gyllenberg, F. J. Jacobs & J. A. J. Metz. 2005. Link between population dynamics and dynamics of Darwinian evolution. Phys. Rev. Letters PRL 95, 078105.

Durinx M., J. A. J. Metz & G. Meszéna. 2008. Adaptive dynamics for physiologically structured population models. J. Math. Biol. 56: 673-742.

Kisdi É. & S. A. H. Geritz. 2010. Adaptive dynamics: A framework to model evolution in the ecological theatre. J. Math. Biol. (Perspectives in Mathematical Biology) 61: 165-169.

Metz J.A.J. 2011. Thoughts on the geometry of meso-evolution: Collecting mathematical elements for a postmodern synthesis. In: Fabio A. C. C. Chalub & José Francisco Rodrigues (eds): The Mathematics of Darwin's Legacy, Springer Verlag, pp. 193-232.

Target review:

Waxman D. and S. Gavrilets. 2005. 20 Questions on Adaptive Dynamics. J. evol. Biol. 18:1139-1154.

accompanied by 15 commentaries in JEB vol. 15(8); see Table of Contents

Books:

Dieckmann U., J. A. J. Metz, M. W. Sabelis & K. Sigmund (eds). 2002. Adaptive dynamics of infectious diseases: In pursuit of virulence management. Cambridge University Press, Cambridge

Dieckmann U., M. Doebeli, J. A. J. Metz & D. Tautz (eds). 2004. Adaptive speciation. Cambridge University Press, Cambridge

Dercole F. & S. Rinaldi. 2008. Analysis of evolutionary processes. Princeton University Press, Princeton

Evolutionary stability and convergence stability

Maynard Smith J. 1982. Evolution and the theory of games. Cambridge University Press

Eshel I. 1983. Evolutionary and continuous stability. J. theor. Biol. 103:99-111.

Taylor P.D. 1989. Evolutionary stability in one-parameter models under weak selection. Theor. Pop. Biol. 36:125-143.

Nowak M. 1990. An evolutionary stable strategy may be inaccessible. J.theor.Biol. 142:237-241.

Christiansen F. B. 1991. On conditions for evolutionary stability for a continuously varying character. Am. Nat. 138:37-50.

Abrams P. A., H. Matsuda & Y. Harada. 1993. Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol. 7:465-487..

Doebeli M. & I. Ispolatov. 2010. Continuously stable strategies as evolutionary branching points. J. theor. Biol. 266: 529-535..

The canonical equation. Convergence stability in more than one dimensions

Dieckmann U. & R. Law. 1996. The dynamical theory of coevolution: A derivation from stochastic ecological processes. J. Math. Biol. 34:579-612.

Matessi C. & Di Pasquale. 1996. Long-term evolution of multilocus traits. J. Math. Biol. 34:613-653.

Leimar O. Multidimensional convergence stability and the canonical adaptive dynamics. In: U. Dieckmann & J.A.J. Metz (eds): Elements of adaptive dynamics. Cambridge University Press, in press

Leimar O. 2001. Evolutionary change and Darwinian demons. Selection 2:65-72.

Leimar O. 2005. The evolution of phenotypic polymorphism: Randomized strategies versus evolutionary branching. Am. Nat. 165:669-681.

Leimar O. 2009. Multidimensional convergence stability. Evol. Ecol. Res. 11: 191-208.

Dercole F. & S. Rinaldi. 2008. Analysis of evolutionary processes. The adaptive dynamics approach and its applications. Princeton University Press, Princeton.

The paper of Dieckmann and Law contains the derivation of the canonical equation of mutation-limited evolution. Towards the end of their paper, Matessi and Di Pasquale give all generic two-dimensional evolutionary singularities (for two independently evolving traits or equivalently for two coevolving strategies) and investigate their absolute convergence. The papers of Leimar deal with strong convergence (convergence of nonindependent traits with any constant covariance matrix) as well as absolute convergence. The book of Dercole and Rinaldi discusses the canonical equation and evolutionary bifurcation theory along with many applications.

Champagnat N., R. Ferriere and G. Ben Arous. 2001. The canonical equation of adaptive dynamics: a mathematical view. Selection 2:73-84.

Champagnat N., R. Ferriere & S. Méléard. 2006. Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theor. Pop. Biol. 69:297-321.

Durinx M. & J. A. J. Metz. 2005. Multi-type branching processes and adaptive dynamics of structured populations. In: P. Haccou, P. Jagers & V. Vatutin: Branching processes: Variation, growth and extinction of populations. Cambridge Studies in Adaptive Dynamics 5, Cambridge University Press, pp. 266-277.

Durinx M., J. A. J. Metz & G. Meszéna. 2008. Adaptive dynamics for physiologically structured population models. J. Math. Biol. 56: 673-742.

Meleard S. & V. C. Tran. 2009. Trait substitution sequence process and canonical equation for age-structured populations. J. Math. Biol. 58: 881-921.

S. Meleard. 2011. Random modeling of adaptive dynamics and evolutionary branching. In: Fabio A. C. C. Chalub & José Francisco Rodrigues (eds): The Mathematics of Darwin's Legacy, Springer Verlag, pp. 175-192.

Other limiting approaches

Diekmann, O., P.-E. Jabin, S. Mischler & B. Perthame. 2005. The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach. Theor. Pop. Biol. 67:257-271. 7:198-202.

Cressman, R. & J. Hofbauer. 2005. Measure dynamics on a one-dimensional continuous trait space: Theoretical foundations for adaptive dynamics. Theor. Pop. Biol. 67:47-59.

Champagnat N., R. Ferriere & S. Méléard. 2006. Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theor. Pop. Biol. 69:297-321.

Champagnat N., R. Ferriere & S. Méléard. 2008. From individual stochastic processes to macroscopic models in adaptive evolution. Stochastic Models 24: 2-44.

Invasion dynamics

Metz, J. A. J., R. M. Nisbet & S. A. H. Geritz. 1992. How should we define 'fitness' for general ecological scenarios? TREE 7:198-202.

Metz J.A.J., A.M. de Roos. 1992. The role of physiologically structured population models within a general individual-based modeling perspective. In: D.L. DeAngelis & L.J. Gross (eds): Individual-based models and approaches in ecology, Chapman & Hall, New York

Caswell H. 1989. Matrix population models. Sinauer Associates, Sunderland.

Metz J. A. J. & O. Leimar. 2011. A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms. J. Biol. Dyn. 5: 163-190.

Gyllenberg M., and J. A. J. Metz. 2001. On fitness in structured metapopulations. Journal of Mathematical Biology 43:545-560.

Metz J. A. J., and M. Gyllenberg. 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of evolutionarily stable dispersal strategies. Proceedings of the Royal Society of London B 268:499-508.

Parvinen, K. 2006. Evolution of dispersal in a structured metapopulation model in discrete time. Bull. Math. Biol. 68:655-678. (see Appendix A)

Parvinen, K. & J. A. J. Metz. 2008. A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution. Theor. Pop. Biol. 73: 517-528.

Van Baalen M. & D. A. Rand. 1998. The unit of selection in viscous populations and the evolution of altruism. J. theor. Biol. 193:631-648. pair approximation in lattice models

Ferriere R. & M. Gatto. 1995. Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations. Theor.Pop. Biol. 48:126-171.

Kisdi É. & G. Meszéna. 1993. Density dependent life history evolution in fluctuating environments. In: J. Yoshimura & C. Clark (eds): Adaptation in a stochastic environment. Lecture Notes in Biomathematics, Springer-Verlag, Vol. 98 pp. 26-62. fitness in stochastic environments

Tuljapurkar S. 1989. An uncertain life: Demography in random environments. Theor. Pop. Biol. 35:227-294. structured populations in stochastic environments

Does invasion imply fixation?
Adaptive dynamics with multiple population dynamical attractors

Rand D. A., H. B. Wilson & J. M. McGlade. 1994. Dynamics and evolution: Evolutionarily stable attractors, invasion exponents and phenotype dynamics. Phil. Trans. R. Soc. Lond. B 343:261-283.

Geritz S. A. H., M. Gyllenberg, F. J. A. Jacobs & K. Parvinen. 2002. Invasion dynamics and attractor inheritance. J. Math. Biol. 44:548-560; also available as a TUCS preprint

Geritz S. A. H. 2005. Resident-invader dynamics and the coexistence of similar strategies. J. Math. Biol. 50:67-82.

Dercole F. & S. Rinaldi. 2008. Analysis of evolutionary processes. The adaptive dynamics approach and its applications. Princeton University Press, Princeton.

Evolutionary conservation biology

Johansson J. & U. Dieckmann. 2009. Evolutionary responses of communities to extinctions. Evol. Ecol. Res. 11: 561-588.

Evolutionary suicide

Gyllenberg M. & K. Parvinen. 2001. Necessary and sufficient conditions for evolutionary suicide. Bull. Math. Biol. 63:981-993

Gyllenberg M., K. Parvinen & U. Dieckmann. 2002. Evolutionary suicide and evolution of dispersal in structured metapopulations. J. Math. Biol. 45:79-105; IIASA Interim Report IR-00-056

Parvinen K. 2005. Evolutionary suicide. Acta Biotheoretica 53:241-264.

Function-valued traits

Parvinen K., U. Dieckmann & M. Heino. 2006. Function-valued adaptive dynamics and the calculus of variations. J. Math. Biol. 52:1-26.

Dieckmann U., M. Heino & K. Parvinen. 2006. The adaptive dynamics of function-valued traits. J. theor. Biol. 241:370-389.

Adaptive dynamics and optimization

Mylius S.D. & O. Diekmann. 1995. On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74: 218-224.

Metz J.A.J., S.D. Mylius & O. Diekmann. 2008. When Does Evolution Optimize? Evol. Ecol. Res. 10: 629-654.

For over a decade, this paper was available as the main part of the preprint
Metz J.A.J., S.D. Mylius & O. Diekmann. 1996. When Does Evolution Optimize? On the Relation Between Types of Density Dependence and Evolutionarily Stable Life History Parameters. IIASA Working Paper WP-96-004

Kisdi E. 1998. Frequency dependence versus optimization. TREE 13: 508.

G. Meszéna, É. Kisdi, U. Dieckmann, S.A.H. Geritz & J.A.J. Metz (2001): Evolutionary optimisation models and matrix games in the unified perspective of adaptive dynamics. Selection 2:193-210. PDF (Courtesy of Akadémiai Kiadó, Budapest)

Gyllenberg M., J.A.J. (Hans) Metz & R. Service. 2011. When do optimisation arguments make evolutionary sense? In: Fabio A. C. C. Chalub & José Francisco Rodrigues (eds): The Mathematics of Darwin's Legacy, Springer Verlag, pp. 233-268.

Adaptive dynamics and matrix games

Dieckmann U. & J. A. J. Metz. 2006. Surprising evolutionary predictions from enhanced ecological realism. Theor. Pop. Biol. 69:263-281.

Evolutionary bifurcation theory

Geritz S. A. H., E. van der Meijden & J. A. J. Metz. 1999. Evolutionary dynamics of seed size and seedling competitive ability. Theor. Pop. Biol. 55:324-343.
This paper provides a detailed bifurcation analysis of adaptive dynamics in a specific model, and also describes some bifurcation structures as well as the connection points between isoclines and the boundary of the area of coexistence in general.

Rueffler C., T. J. M. van Dooren & J. A. J. Metz. 2004. Adaptive walks on changing landscapes: Levins' approach extended. Theor. Pop. Biol. 65:165-178.

de Mazancourt C. & U. Dieckmann. 2004. Trade-off geometries and frequency-dependent selection. Am. Nat. 164:765-778.

Bowers R. G., A. Hoyle, A. White & M. Boots. 2005. The geometric theory of adaptive evolution: Trade-off and invasion plots. J. theor. Biol. 233:363-377.

Kisdi É. 2006. Trade-off geometries and the adaptive dynamics of two co-evolving species. Evol. Ecol. Res. 8: 959-973.

Dercole F. & S. Rinaldi. 2008. Analysis of evolutionary processes. The adaptive dynamics approach and its applications. Princeton University Press, Princeton.

Priklopil T. On invasion boundaries and the unprotected coexistence of two strategies. J. Math. Biol. in press, DOI 10.1007/s00285-011-0448-y.

The role of environmental dimensionality

Meszéna, G., and J. A. J. Metz. The role of effective environmental dimensionality. In: U. Dieckmann, and J. A. J. Metz (eds.): Elements of adaptive dynamics, Cambridge University Press, in press; see IIASA Interim Report IR-99-045

Metz J.A.J., Mylius S.D. & Diekmann O. 2008. When Does Evolution Optimize? Evol. Ecol. Res. 10: 629-654; see also IIASA Working Paper WP-96-004 (1996)

Evolution in finite populations

Proulx S. R. & T. Day. 2001. What can invasion analyses tell us about evolution under stochasticity in finite populations? Selection 2:1-16.

Rousset F. 2003. A minimal derivation of convergence stability measures. J. theor. Biol. 221:665-668.

Johansson J. & J. Ripa. 2006. Will sympatric speciation fail due to stochastic competitive exclusion? Am. Nat. 168:572-578.

Claessen D., J. Andersson, L. Persson & A. M. de Roos. 2007. Delayed evolutionary branching in small populations. Evol. Ecol. Res. 9:51-69.

Claessen D., J. Andersson, L. Persson & A. M. de Roos. 2008. The effect of population size and recombination on delayed evolution of polymorphism and speciation in sexual populations. Am. Nat. 172:E18-E34.

Johansson J., J. Ripa & N. Kucklander. 2010. The risk of competitive exclusion during evolutionary branching: Effects of resource variability, correlation and autocorrelation. Theor. Pop. Biol. 77: 95-104.

Szilágyi A. & G. Meszéna. 2010. Coexistence in a fluctuating environment by the effect of relative nonlinearity: A minimal model. J. theor. Biol. 267: 502-512.

Simulation methods

Dieckmann U., P. Marrow & R. Law. 1995. Evolutionary cycling in predator-prey interactions: Population dynamics and the Red Queen. J. theor. Biol. 176:91-102.

Geritz, S. A. H., É. Kisdi, G. Meszéna, and J. A. J. Metz. 1998. Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12:35-57.

Kisdi E. & S. A. H. Geritz. 1999. Adaptive dynamics in allele space: Evolution of genetic polymorphism by small mutations in a heterogeneous environment. Evolution 53:993-1008.

Adaptive dynamics of alleles in diploid populations

Kisdi E. & S. A. H. Geritz. 1999. Adaptive dynamics in allele space: Evolution of genetic polymorphism by small mutations in a heterogeneous environment. Evolution 53:993-1008.

Van Dooren T. J. M. 1999. The evolutionary ecology of dominance-recessivity. J. theor. Biol. 198:519-532.

see also a two locus - two allele population genetic model:
Peischl S. & R. Burger. 2008. Evolution of dominance under frequency-dependent intraspecific competition. J. theor. Biol. 251: 210-226.

Van Dooren T. J. M. 2000. The evolutionary dynamics of direct phenotypic overdominance: Emergence possible, loss probable. Evolution 54: 1899-1914.

Van Doorn S. & U. Dieckmann 2006. The long-term evolution of multi-locus traits under frequency-dependent disruptive selection. Evolution 60:2226-2238.

Proulx S. R. & P. C. Phillips. 2006. Allelic divergence precedes and promotes gene duplication. Evolution 60: 881-892.

Van Dooren T. J. M. 2006. Protected polymorphism and evolutionary stability in pleiotropic models with trait-specific dominance. Evolution 60: 1991-2003.

Phenotypic diversification without speciation

Maire N., M. Ackermann & M. Doebeli. 2001. Evolutionary branching and the evolution of anisogamy. Selection 2:119-132.

Bolnick D. I. & M. Doebeli. 2003. Sexual dimorphism and adaptive speciation: Two sides of the same ecological coin. Evolution 57:2433-2449.

Van Dooren T. J. M., M. Durinx & I. Demon. 2004. Sexual dimorphism or evolutionary branching? Evol. Ecol. Res. 6:857-871.

Leimar O. 2005. The evolution of phenotypic polymorphism: Randomized strategies versus evolutionary branching. Am. Nat. 165:669-681.

Matessi C. & A. Gimelfarb. 2006. Discrete polymorphisms due to disruptive selection on a continuous trait. I. The one-locus case. Theor. Pop. Biol. 69:283-295.

Rueffler C., T. J. M. van Dooren, O. Leimar & P. A. Abrams. 2006. Disruptive selection and then what? Trends Ecol. Evol. 21:238-245.

Durinx M. & T. J. M. van Dooren. 2009. Assortative mate choice and dominance modification: Alternative ways of removing heterozygote disadvantage. Evolution 63: 334-352.

Adaptive dynamics and multilocus / quantitative genetics

Loeschcke V. & F. B. Christiansen. 1984. Evolution and intraspecific exploitative competition. II. A two-locus model for additive gene effects. Theor. Pop. Biol. 26:228-264.

Taper M.L. and T.J. Case. 1992. Models of character displacement and the theoretical robustness of taxon cycles. Evolution 46: 317-333.

Abrams P.A., Y. Harada & H. Matsuda. 1993. On the relationship between quantitative genetic and ESS models. Evolution 47: 982-985.

Spichtig M. & T. J. Kawecki. 2004. The maintenance (or not) of polygenic variation by soft selection in heterogeneous environments. Am. Nat. 164:70-84. This paper demonstrates that polymorphism is maintained in many loci when the corresponding adaptive dynamics model has an evolutionary branching point, and also shows how the results change if several, but not infinitely many, loci affect the trait.

Bürger R. & A. Gimelfarb. 2004. The effects of intraspecific competition and stabilizing selection on a polygenic trait. Genetics 167: 1425-1443.

Bürger R. 2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50: 355-396.

Bürger R & K. Schneider. 2006. Intraspecific competitive divergence and convergence under assortative mating. Am. Nat. 167: 190-205.

Kopp M. & J. Hermisson. 2006. The evolution of genetic architecture under frequency-dependent disruptive selection. Evolution 60: 1537-1550.

Evolutionary branching vs sympatric speciation

Dieckmann U. & M. Doebeli. 1999. On the origin of species by sympatric speciation. Nature 400:354-357.

Geritz S. A. H. & E. Kisdi. 2000. Adaptive dynamics in diploid, sexual populations and the evolution of reproductive isolation. Proc. R. Soc. Lond. B 267:1671-1678.

Doebeli M. & U. Dieckmann. 2000. Evolutionary branching and sympatric speciation caused by different types of ecological interactions. Am. Nat. 156:S77-S101.

Drossel B. & A. McKane. 2000. Competitive speciation in quantitative genetic models. J. theor. Biol. 204:467-478.

Van Doorn G. S. & F. J. Weissing. 2001. Ecological versus sexual selection models of sympatric speciation: a synthesis. Selection 2:17-40.

Van Doorn G. S., P. C. Luttikhuizen & F. J. Weissing. 2001. Sexual selection at the protein level drives the extraordinary divergence of sex-related genes during sympatric speciation. Proc. R. Soc. Lond. B 268:2155-2161.

Matessi C., A. Gimelfarb & S. Gavrilets. 2001. Long term buildup of reproductive isolation promoted by disruptive selection: how far does it go? Selection 2:41-64.

Bolnick D. I. 2004. Waiting for sympatric speciation. Evolution 58:895-899.

Van Doorn G. S., U. Dieckmann & F. J. Weissing. 2004. Sympatric speciation by sexual selection: A critical reevaluation. Am. Nat. 163: 709-725.

Doebeli M. 2005. Adaptive speciation when assortative mating is based on female preference for male marker traits. J. evol. Biol. 18:1587-1600.

Polechova J. & N. H. Barton. 2005. Speciation through competition: A critical review. Evolution 59:1194-1210.

Bolnick D. I. 2006. Multi-species outcomes in a common model of sympatric speciation. J. theor. Biol. 241:734-744.

Schneider K. A. & R. Bürger. 2006. Does competitive divergence occur if assortative mating is costly? J. evol. Biol. 19:570-588.

Doebeli M., H. J. Blok, O. Leimar & U. Dieckmann. 2007. Multimodal pattern formation in phenotype distributions of sexual populations. Proc. R. Soc. Lond. B 274:347-357.

Pennings P. S., M. Kopp, G. Meszéna, U. Dieckmann & J. Hermisson. 2008. An analytically tractable model for competitive speciation. Am. Nat. 171: E44-E71.

Kopp, M. & J. Hermisson. 2008. Competitive speciation and costs of choosiness. J. evol. Biol. 21:1005-1023.

Ripa J. 2009. When is sympatric speciation truly adaptive? An analysis of the joint evolution of resourve utilization and assortative mating. Evol. Ecol. 23: 31-52.

Kisdi E. & T. Priklopil. 2011. Evolutionary branching of a magic trait. J. Math. Biol. 63: 361-397.

Evolutionary branching and speciation along environmental gradients

Doebeli M. & U. Dieckmann. 2003. Speciation along environmental gradients. Nature 421:259-264.

Mizera F. & G. Meszéna. 2003. Spatial niche packing, character displacement and adaptive speciation along an environmental gradient. Evol. Ecol. Res. 5:363-382.

Leimar O., M. Doebeli & U. Dieckmann. 2008. Evolution of phenotypic clusters through competition and local adaptation along an environmental gradient. Evolution 62: 807-822.

Heinz S. K., R. Mazzucco & U. Dieckmann. 2009. Speciation and the evolution of dispersal along environmental gradients. Evol. Ecol. 23: 53-70.

Ispolatov J. & M. Doebeli. 2009. Diversification along environmental gradients in spatially structured populations. Evol. Ecol. Res. 11: 295-304.

Payne J. L., R. Mazzucco & U. Dieckmann. 2009. The evolution of conditional dispersal and reproductive isolation along environmental gradients. J. theor. Biol. 273: 147-155.

How to deal with multilocus genetics

The papers listed here are of course outside the scope of adaptive dynamics, but they provide valuable background to multilocus genetic simulations that e.g. explore the connection between evolutionary branching and sympatric speciation, and they were included in a course given on adaptive dynamics.

Barton N. H. & M. Turelli. 1991. Natural and sexual selection on many loci. Genetics 127:229-255. The general theory of multilocus selection, and the quasi-linkage equilibrium approximation for weak selection

Kirkpatrick M. & M. R. Servedio. 1999. The reinforcement of mating preferences on an island. Genetics 151:865-884. A model that utilises the Barton-Turelli approach with quasi-linkage equilibrium. It may be easier to start with an example like this than with the general framework

Shpak M. & A. S. Kondrashov. 1999. Applicability of the hypergeometric phenotypic model to haploid and diploid populations. Evolution 53:600-604. phenotypic recursion based on the hypergeometric model

Applications (the list is not exhaustive!)

* indicates evolutionary branching.

Papers on the symmetric Lotka-Volterra competition model are listed separately (see below).
See also chapters in the book series Cambridge Studies in Adaptive Dynamics

1997-1998

* Meszéna, G., I. Czibula, and S. A. H. Geritz. 1997. Adaptive dynamics in a 2-patch environment: A toy model for allopatric and parapatric speciation. J. Biol. Syst. 5:265-284; also available as IIASA Interim Report IR-97-001

* Doebeli, M., and G. D. Ruxton. 1997. Evolution of dispersal rates in metapopulation models: Branching and cyclic dynamics in phenotype space. Evolution 51:1730-1741.

Law R. & U. Dieckmann. 1998. Symbiosis through exploitation and the merger of lineages in evolution. Proc. R. Soc. Lond. B 265:1245-1253.

Van Dooren T. J. M. & J. A. J. Metz. 1998. Delayed maturation in temporally structured populations with non-equilibrium dynamics. J. evol. Biol. 11:41-62.

1999

* Boots M. & Y. Haraguchi. 1999. The evolution of costly resistance in host-parasite systems. Am. Nat. 153:359-370.

* Geritz, S. A. H., E. van der Meijden, and J. A. J. Metz. 1999. Evolutionary dynamics of seed size and seedling competitive ability. Theor. Pop. Biol. 55:324-343.

* Kisdi, É. 1999. Evolutionary branching under asymmetric competition. J. theor. Biol. 197:149-162.

* Kisdi E. & S. A. H. Geritz. 1999. Adaptive dynamics in allele space: Evolution of genetic polymorphism by small mutations in a heterogeneous environment. Evolution 53:993-1008.

* Koella J. C. & M. Doebeli. 1999. Population dynamics and the e1volution of virulence in epidemiological models with discrete host generations. J. theor. Biol. 198: 461-475

* Jansen V. A. A. & G. S. E. E. Mulder. 1999. Evolving biodiversity. Ecology Letters 2:379-386.

Johst, K., M. Doebeli and R. Brandl. 1999. Evolution of complex dynamics in spatially structured populations. Proc. R. Soc. Lond. B 266:1147-1154.

* Parvinen, K. 1999. Evolution of migration in a metapopulation. Bull. Math. Biol. 61:531-550.

2000

* Day T. 2000. Competition and the effect of spatial resource heterogeneity on evolutionary diversification. Am. Nat. 155:790-803.

* Doebeli M. & U. Dieckmann. 2000. Evolutionary branching and sympatric speciation caused by different types of ecological interactions. Am. Nat. 156:S77-S101.

Levin S. A. & H. C. Muller-Landau. 2000. The evolution of dispersal and seed size in plant communities. Evol. Ecol. Res. 2:409-435.

2001

* Cheptou P.-O. & A. Mathias. 2001. Can varying inbreeding depression select for intermediary selfing rate? Am. Nat. 157:361-373

* Day T. 2001. Population structure inhibits evolutionary diversification under competition for resources. Genetica 112-113:71-86.

* De Jong T. & S. A. H. Geritz. 2001. The role of geitonogamy in the gradual evolution towards dioecy in cosexual plants. Selection 2:133-146. PDF (Courtesy of Akadémiai Kiadó, Budapest)

Gyllenberg M. & K. Parvinen. 2001. Necessary and sufficient conditions for evolutionary suicide. Bull. Math. Biol. 63:981-993

* Kisdi É. 2001. Long-term adaptive diversity in Levene-type models. Evol. Ecol. Res. 3:721-727.

* Kisdi É. & S. A. H. Geritz. 2001. Evolutionary disarmament in interspecific competition. Proc. R. Soc. Lond. B 268:2589-2594.

* Kisdi É., F. J. A. Jacobs and S. A. H. Geritz. 2001. Red Queen evolution by cycles of evolutionary branching and extinction. Selection 2:161-176. PDF (Courtesy of Akadémiai Kiadó, Budapest)

* Law R., J. L. Bronstein & R. Ferriere. 2001. On mutualists and exploiters: Plant-insect coevolution in pollinating seed-parasite systems. J. theor. Biol. 212:373-389.

* Maire N., M. Ackermann & M. Doebeli. 2001. Evolutionary branching and the evolution of anisogamy. Selection 2:119-132.

* Mathias, É. Kisdi & I. Olivieri. 2001. Divergent evolution of dispersal in a heterogeneous landscape. Evolution 55:246-259.

* Meszéna G. & E. Szathmáry. 2001. Adaptive dynamics of parabolic replicators. Selection 2:147-160. PDF (Courtesy of Akadémiai Kiadó, Budapest)

2002

Bowers R. G. & A. White. 2002. The adaptive dynamics of Lotka-Volterra systems with trade-offs. Math. Biosci. 175:67-81.

* Claessen D. & U. Dieckmann. 2002. Ontogenetic niche shifts and evolutionary branching in size-structured populations. Evol. Ecol. Res. 4:189-217.

* Day T., P. A. Abrams & J. M. Chase. 2002. The role of size-specific predation in the evolution and diversification of prey life histories. Evolution 56:877-887.

* Dercole F. & S. Rinaldi. 2002. Evolution of cannibalistic traits: Scenarios derived from adaptive dynamics. Theor. Pop. Biol. 62:365-374.

Dercole F., R. Ferriere & S. Rinaldi. 2002. Ecological bistability and evolutionary reversals under asymmetric competition. Evolution 56:1081-1090.

* Doebeli M. 2002. A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms. Popul. Ecol. 44:59-70.

* Ferdy J.-B., L. Depres. & B. Godelle. 2002. Evolution of mutualism between globeflowers and their pollinating flies. J. theor. Biol. 217: 219-234.

* Ferriere R., J. I. Bronstein, S. Rinaldi, R. Law & M. Gauduchon. 2002. Cheating and the evolutionary stability of mutualisms. Proc. R. Soc. Lond. B 269:773-780.

Gyllenberg M., K. Parvinen & U. Dieckmann. 2002. Evolutionary suicide and evolution of dispersal in structured metapopulations. J. Math. Biol. 45:79-105; IIASA Interim Report IR-00-056

Holland J. N. & D. L. DeAngelis. 2002. Ecological and evolutionary conditions for fruit abortion to regulate pollinating seed-eaters and increase plant reproduction. Theor. Pop. Biol. 61:251-263.

Loeuille N., M. Loreau & R. Ferriere. 2002. Consequences of plant-herbivore coevolution on the dynamics and functioning of ecosystems. J. theor. Biol. 217:369-381.

* Kisdi É. 2002. Dispersal: Risk spreading versus local adaptation. Am. Nat. 159:579-596.

* Mathias A. & É. Kisdi. 2002. Adaptive diversification of germination strategies. Proc. R. Soc. Lond. B 269:151-156.

* Parvinen K. 2002. Evolutionary branching of dispersal strategies in structured metapopulations. J. Math. Biol. 45:106-124; also available as a TUCS preprint

Pugliese A. 2002. On the evolutionary coexistence of parasite strains. Math. Biosci. 177-178:355-375.

2003

* Abrams P. A. 2003. Can adaptive evolution or behaviour lead to diversification of traits determining a trade-off between foraging gain and predation risk? Evol. Ecol. Res. 5:653-670.
This model exhibits evolutionary branching when evolution is slow as compared to population dynamics, but faster evolution results in cyclic behaviour rather than in diversification.

* Bowers R. G., A. White, M. Boots, S. A. H. Geritz & E. Kisdi. 2003. Evolutionary branching/speciation: Contrasting results from systems with explicit or emergent carrying capacities. Evol. Ecol. Res. 5:883-891.

* Dercole F. 2003. Remarks on branching-extinction evolutionary cycles. J. Math. Biol. 47:569-580.

* Dercole F., J.-O. Irisson & S. Rinaldi. 2003. Bifurcation analysis of a prey-predator coevolution model. SIAM J. Appl. Math. 63:1378-1391.

Le Galliard J.-F., R. Ferriere & U. Dieckmann. 2003. The adaptive dynamics of altruism in spatially heterogeneous populations. Evolution 57:1-17.

Mágori K., B. Oborny, U. Dieckmann & G. Meszéna. 2003. Cooperation and competition in heterogeneous environments: The evolution of resource sharing in clonal plants. Evol. Ecol. Res. 5:787-817.

Parvinen K., U. Dieckmann, M. Gyllenberg & J. A. J. Metz. 2003. Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity. J. evol. Biol. 16:143-153; IIASA Interim Report IR-00-035

* Schreiber S. J. & G. A. Tobiason. 2003. The evolution of resource use. J. Math. Biol. 47:56-78

* Van Dooren T. J. M. & O. Leimar. 2003. The evolution of environmental and genetic sex determination in fluctuating environments. Evolution 57:2667-2677.

* Vukics A., J. Asboth & G. Meszéna. 2003. Speciation in multidimensional evolutionary space. Phys. Rev. E 68:41903

2004

* Ackermann M. & M. Doebeli. 2004. Evolution of niche width and adaptive diversification. Evolution 58:2599-2612.

* Bonsall M. B., V. A. A. Jansen & M. P. Hassell. 2004. Life history trade-offs assemble ecological guilds. Science 306:111-114.

* Doebeli M., C. Hauert & T. Killingback. 2004. The evolutionary origin of cooperators and defectors. Science 306:859-862.

* Egas M., U. Dieckmann & M. W. Sabelis. 2004. Evolution restricts the coexistence of specialists and generalists: The role of trade-off structure. Am. Nat. 163:518-531.

* Gandon S. 2004. Evolution of multihost parasites. Evolution 58: 455-469.

* Gudelj I., F. van den Bosch & C. A. Gilligan 2004. Transmission rates and adaptive evolution of pathogens in sympatric heterogeneous plant populations. Proc. R. Soc. Lond. B 271: 2187-2194.

Ernande B. & U. Dieckmann. 2004. The evolution of phenotypic plasticity in spatially structured environments: Implications of intraspecific competition, plasticity costs and environmental characteristics. J. evol. Biol. 17:613-628.

* Friesen M. L., G. Saxer, M. Travisano & M. Doebeli. 2004. Experimental evidence for sympatric ecological diversification due to frequency-dependent competition in Escherichia coli. Evolution 58:245-260.

Kisdi É. 2004. Conditional dispersal under kin competition: Extension of the Hamilton-May model to brood size-dependent dispersal. Theor. Pop. Biol. 66:369-380.

* Parvinen K. & M. Egas. 2004. Dispersal and the evolution of specialisation in a two-habitat type metapopulation. Theor. Pop. Biol. 66:233-248.

2005

* Egas M., M. W Sabelis & U. Dieckmann. 2005. Evolution of specialization and ecological character displacement of herbivores along a gradient of plant quality. Evolution 59:507-520.

* Ferdy J.-B. & B. Godelle. 2005. Diversification of transmission modes and the evolution of mutualism. Am. Nat. 166:613-627.

Le Galliard J.-F., R. Ferriere & U. Dieckmann. 2005. Adaptive evolution of social traits: Origin, trajectories, and correlations of altruism and mobility. Am. Nat. 165:206-225.

* Mágori K., P. Szabó, F. Mizera & G. Meszéna. 2005. Adaptive dynamics on a lattice: Role of spatiality in competition, co-existence and evolutionary branching. Evol. Ecol. Res. 7:1-21.

* Troost T. A., B. W. Kooi & A. L. M. Kooijman. 2005. Ecological specialization of mixotrophic plankton in a mixed water column. Am. Nat. 166:E45-E61.

2006

* Hancock P. J. F. & N. F. Britton. 2006. Adaptive responses to spatial aggregation and habitat destruction in heterogeneous landscapes. Evol. Ecol. Res. 8:1349-1376.

* Ito H. & T. Ikegami. 2006. Food-web formation with recursive evolutionary branching. J. theor. Biol. 238: 1-10. This paper models the evolutionary dynamics with a diffusion equation, which is an alternative to the mutation-limited approach of adaptive dynamics. Diversification nevertheless occurs via a gradual process similar to evolutionary branching.

Kisdi, E. & S. Liu. 2006. Evolution of handling time can destroy the coexistence of cycling predators. J. evol. Biol. 19:49-58.

* Kooi B. W. & T. A. Troost. 2006. Advantage of storage in a fluctuating environment. Theor. Pop. Biol. 70: 527-541.

* Ma L. & S. A. Levin. 2006. The evolution of resource adaptation: How generalist and specialist consumers evolve. Bull. Math. Biol. 68: 1111-1123.

* Parvinen, K. 2006. Evolution of dispersal in a structured metapopulation model in discrete time. Bull. Math. Biol. 68: 655-678.

* Proulx S. R. & P. C. Phillips. 2006. Allelic divergence precedes and promotes gene duplication. Evolution 60: 881-892.

* Rueffler C., T. J. M. Van Dooren & J. A. J. Metz. 2006. The evolution of resource specialization through frequency-dependent and frequency-independent mechanisms. Am. Nat. 167: 81-93.

* Snyder R. E. 2006. Multiple risk reduction mechanisms: Can dormancy substitute for dispersal? Ecol. Letters 9: 1106-1114.

* Van Dooren T. J. M. 2006. Protected polymorphism and evolutionary stability in pleiotropic models with trait-specific dominance. Evolution 60: 1991-2003.

* Várkonyi P. L., G. Meszéna & G. Domokos. 2006. Emergence of asymmetry in evolution. Theor. Pop. Biol. 70: 63-75.

* White A., J. V. Greenman, T. G. Benton & M. Boots. 2006. Evolutionary behaviour in ecological systems with trade-offs and non-equilibrium population dynamics. Evol. Ecol. Res. 8:387-398.

2007

Broom M. & J. Rychtar. 2007. The evolution of a kleptoparasitic system under adaptive dynamics. J. Math. Biol. 54: 151–177.

* Geritz S. A. H., É. Kisdi & P. Yan. 2007. Evolutionary branching and long-term coexistence of cycling predators: Critical function analysis. Theor. Pop. Biol. 71: 424-435.

* Giafis A. & R. G. Bowers. 2007. The adaptive dynamics of the evolution of host resistance to indirectly transmitted microparasites. Math. Biosci. 210: 668-679.

* Hoyle A. & R. G. Bowers. 2007. When is evolutionary branching in predator–prey systems possible with an explicit carrying capacity? Math. Biosci. 210: 1-16.

* Ito H. C. & M. Shimada. 2007. Niche expansion: Coupled evolutionary branching of niche position and width. Evol. Ecol. Res. 9: 675-695.

* Ito H. C. & U. Dieckmann. 2007. A new mechanism for recurrent adaptive radiations. Am. Nat. 170: E96-E111.

Kamo M., A. Sasaki & M. Boots. 2007. The role of trade-off shapes in the evolution of parasites in spatial host populations: An approximate analytical approach. J. theor. Biol. 244: 588-596.

Mougi A. & K. Nishimura. 2007. Evolution of life-history traits collapses competitive coexistence. J. theor. Biol. 248: 552-559.

* Parvinen K. 2007. Evolutionary suicide in a discrete-time metapopulation model. Evol. Ecol. Res. 9: 619-633.

* Rueffler C., T. J. M. van Dooren & J. A. J. Metz. 2007. The interplay between behavior and morphology in the evolutionary dynamics of resource specialization. Am. Nat. 169: E34-E52.

* Svennungsen T. O. & O. H. Holen. 2007. The evolutionary stability of automimicry. Proc. R. Soc. Lond. B 274: 2055-2062.

* Szilágyi A. & G. Meszéna. 2007. Two-patch model of spatial niche segregation. Evol. Ecol., in press (DOI 10.1007/s10682-007-9212-6)

Troost T. A., B. W. Kooi & S. A. L. M. Kooijman. 2007. Bifurcation analysis can unify ecological and evolutionary aspects of ecosystems. Ecol. Mod. 204: 253-268.

* Wolf M., G. S. van Doorn, O. Leimar & F. J. Weissing. 2007. Life-history trade-offs favour the evolution of animal personalities. Nature 447: 581-584. See also Brief communications arising: Do animal personalities emerge? by F. Massol and P.-A. Crochet and reply by Wolf et al., Nature 451 (2008) pp. E8-E10.

2008

* Best A., A. White & M. Boots. 2008. Maintenance of host variation in tolerance to pathogens and parasites. Proc. Natl. Acad. Sci. 105: 20786-20791.

* Boldin B. & O. Diekmann. 2008. Superinfections can induce evolutionarily stable coexistence of pathogens. J. Math. Biol. 56: 635-672.

Gyllenberg M., E. Kisdi & M. Utz. 2008. Evolution of condition-dependent dispersal under kin competition. J. Math. Biol. 57: 285-307.

Heino M., K. Parvinen & U. Dieckmann. 2008. Evolution of foraging strategies on resource gradients. Evol. Ecol. Res. 10: 1131-1156.

* Nurmi T. & K. Parvinen. 2008. On the evolution of specialization with a mechanistic underpinning in structured metapopulations. Theor. Pop. Biol. 73: 222-243.

* Nurmi T., S. Geritz, K. Parvinen & M. Gyllenberg. 2008. Evolution of specialization in resource utilization in structured metapopulations. J. Biol. Dyn. 3: 297-322.

* Parvinen, K. & J. A. J. Metz. 2008. A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution. Theor. Pop. Biol. 73: 517-528.

* Troost T. A., B. W. Kooi & U. Dieckmann. 2008. Joint evolution of predator body size and prey-size preference. Evol. Ecol. 22: 771-799.

2009

* Best A., A. White & M. Boots. 2009. The implications of coevolutionary dynamics to host-parasite interactions. Am. Nat. 173: 779-791.

* Boldin B., S. A. H. Geritz & E. Kisdi. 2009. Superinfections and adaptive dynamics of pathogen virulence revisited: A critical function analysis. Evol. Ecol. Res. 11: 153-175.

Geritz, S. A. H., M. Gyllenberg & P. Ondracek. 2009. Evolution of density-dependent dispersal in a structured metapopulation. Math. Biosci. 219: 142-148.

Heino, M., K. Parvinen & U. Dieckmann. 2009. Evolution of foraging strategies on resource gradients. Evol. Ecol. Res. 10: 1131-1156.

Jones E. I., R. Ferriere & J. L. Bronstein. 2009. Eco-evolutionary dynamics of mutualists and exploiters. Am. Nat. 174: 780-794.

* Parvinen K. & G. Meszéna. 2009. Disturbance-generated niche-segregation in a structured metapopulation model. Evol. Ecol. Res. 11: 651-666.

* Rajon E., S. Venner & F. Menu. 2009. Spatially heterogeneous stochasticity and the adaptive diversification of dormancy. J. evol. Biol. 22: 2094-2103.

* Ravigne V., U. Dieckmann & I. Olivieri. 2009. Live where you thrive: Joint evolution of habitat choice and local adaptation facilitates specialization and promotes diversity. Am. Nat. 174: E141-E169.

* Svennungsen T. O. & E. Kisdi. 2009. Evolutionary branching of virulence in a single-infection model. J. theor. Biol. 257: 408-418.

Troost T. A., J. A. van Dam, B. W. Kooi & E. Tuenter. 2009. Seasonality, climate cycles and body size evolution. Math. Model. Nat. Phenom. 4: 135-155.

2010

* Alizon S. & B. Boldin. 2010. Within-host viral evolution in a heterogeneous environment: Insights into the HIV co-receptor switch. J. evol. Biol. 23: 2625–2635.

* Best A., A. White, E. Kisdi, J. Antonovics, M. A. Brockhurst & M. Boots. 2010. The evolution of parasite range. Am. Nat. 176: 63-71.

Cobey S., M. Pascual & U. Dieckmann. 2010. Ecological factors driving the long-term evolution of influenza's host range. Proc. R. Soc. B 277: 2803-2810.

* Debarre F. & S. Gandon. 2010. Evolution of specialization in a spatially continuous environment. J. evol. Biol. 23: 1090-1099.

Evans T., R. G. Bowers & M. Mortimer. 2010. Adaptive dynamics of temperate phages. Evol. Ecol. Res. 413-434.

* Friesen M. L. & A. Mathias. 2010. Mixed infections may promote diversification of mutualistic symbionts: why are there ineffective rhizobia? J. evol. Biol. 23: 323-334.

Kooi B. W. & J. van der Meer. 2010. Bifurcation theory, adaptive dynamics and DEB-structured populations of iteroparous species. Phil. Trans. Roy. Soc. 365: 3579-3590.

* Nilsson J. & J. Ripa. 2010. Adaptive branching in source-sink habitats. Evol. Ecol. 24: 479-489.

* Parvinen K. 2010. Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction. Proc. R. Soc. Lond. B in press (available online, doi:10.1098/rspb.2010.0191)

* Zu J., M. Mimura & J. Y. Wakano. 2010. The evolution of phenotypic traits in a predator-prey system subject to Allee effect. J. theor. Biol. 262: 528-543.

2011

* Aguilée R., B. de Becdelièvre, A. Lambert & D. Claessen. 2011. Under which conditions is character displacement a likely outcome of secondary contact? J. Biol. Dyn. 5: 135-146.

* Best A., S. Webb, A. White & M. Boots. 2011. Host resistance and coevolution in spatially structured populations. Proc. R. Soc. B 278: 2216-2222.

Gyllenberg M., E. Kisdi & M. Utz. 2011. Variability within families and the evolution of body-condition-dependent dispersal. J. Biol. Dyn. 5: 191-211.

Gyllenberg M., E. Kisdi & M. Utz. 2011. Body condition dependent dispersal in a heterogeneous environment. Theor. Pop. Biol. 79: 139-154.

* Herron M. D. & M. Doebeli. 2011. Adaptive diversification of a plastic trait in a predictably fluctuating environment. J. theor. Biol. 285: 58-68.

* Hoyle A., R. G. Bowers & A. White. 2011. Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics. Bull. Math. Biol. 73: 1154-1169.

* Johnstone R. A. & A. Manica. 2011. Evolution of personality differences in leadership. Proc. Natl. Acad Sci. USA 108: 8373-8378.

* Massol F., A. Duputie, P. David & P. Jarne. 2011. Asymmetric patch size distribution leads to disruptive selection on dispersal. Evolution 65: 490-500.

* Nurmi T. & K. Parvinen. 2011. Joint evolution of specialization and dispersal in structured metpopulations. J. theor. Biol. 275: 78-92.

* K. Parvinen. 2011. Adaptive Dynamics of Altruistic cooperation in a metapopulation: Evolutionary emergence of cooperators and defectors or evolutionary suicide? Bull. Math. Biol. 73: 2605–2626.

* Svardal H., C. Rueffler & J. Hermisson. 2011. Comparing environmental and genetic variance as adaptive response to fluctuating selection. Evolution 65: 2492-2513.

Papers on the symmetric Lotka-Volterra competition model

Christiansen F. B. & V. Loeschcke. 1980. Evolution and intraspecific exploitative competition I. One locus theory for small additive gene effects. Theor. Pop. Biol. 18:297-313.

Slatkin M. 1980. Ecological character displacement. Ecology 61:163-177.

Loeschcke V. & F. B. Christiansen. 1984. Evolution and intraspecific exploitative competition. II. A two-locus model for additive gene effects. Theor. Pop. Biol. 26:228-264.

Taper M.L. & T.J. Case. 1985. Quantitative genetic models for the coevolution of character displacement. Ecology 66:355-371.

Christiansen F. B. & V. Loeschcke. 1987. Evolution and intraspecific competition III. One-locus theory for small additive gene effects and multidimensional resource qualities. Theor. Pop. Biol. 31:33-46.

Doebeli M. 1996. An explicit genetic model for ecological character displacement. Ecology 77:510-520.

Dieckmann U. & M. Doebeli. 1999. On the origin of species by sympatric speciation. Nature 400:354-357.

Drossel B. & A. McKane. 1999. Ecological character displacement in quantitative genetic models. J. theor. Biol. 196:363-376.

Day T. 2000. Competition and the effect of spatial resource heterogeneity on evolutionary diversification. Am. Nat. 155:790-803.

Day T. 2001. Population structure inhibits evolutionary diversification under competition for resources. Genetica 112-113:71-86.

Doebeli M. & U. Dieckmann. 2003. Speciation along environmental gradients. Nature 421:259-264.

Mizera F. & G. Meszéna. 2003. Spatial niche packing, character displacement and adaptive speciation along an environmental gradient. Evol. Ecol. Res. 5:363-382.

Vukics A., J. Asboth & G. Meszéna. 2003. Speciation in multidimensional evolutionary space. Phys. Rev. E 68:41903

Ackermann M. & M. Doebeli. 2004. Evolution of niche width and adaptive diversification. Evolution 58:2599-2612.

Mágori K., P. Szabó, F. Mizera & G. Meszéna. 2005. Adaptive dynamics on a lattice: Role of spatiality in competition, co-existence and evolutionary branching. Evol. Ecol. Res. 7:1-21.

Baptestini E. M., M. A. M. de Augiar, D. I. Bolnick & M. S. Araujo. 2009. The shape of the competition and carrying capacity kernels affects the likelihood of disruptive selection. J. theor. Biol. 259: 5-11.

Doebeli M. & I. Ispolatov. 2010. Complexity and diversity. Science 328: 494-497.

Forerunners: Attracting fitness minima (in adaptive dynamics, evolutionary branching points) found in classic studies

Christiansen F. B. & V. Loeschcke. 1980. Evolution and intraspecific exploitative competition I. One locus theory for small additive gene effects. Theor. Pop. Biol. 18:297-313.

Hoekstra R. F. 1980. Why do organisms produce gametes of only two different sizes? Some theoretical aspects of the evolution of anisogamy. J. theor. Biol. 87:785-793.

van Tienderen P.H. & G. de Jong. 1986. Sex ratio under the haystack model: Polymorphism may occur. J. theor. Biol. 122:69-81.

Hofbauer J. & K. Sigmund. 1990. Adaptive dynamics and evolutionary stability. Appl. Math. Lett. 3(4):75-79.

Christiansen F. B. 1991. On conditions for evolutionary stability for a continuously varying character. Am. Nat. 138:37-50.

Cohen D. & S. A. Levin. 1991. Dispersal in patchy environments: The effects of temporal and spatial structure. Theor. Pop. Biol. 39:63-99.

Ludwig D., S. A. Levin. 1991. Evolutionary stability of plant communities and the maintenance of multiple dispersal types. Theor. Pop. Biol. 40:285-307.

Brown J. S. & N. B. Pavlovic. 1992. Evolution in heterogeneous environments: Effects of migration on habitat specialization. Evol. Ecol. 6:360-382.

Brown J. S. & T. L. Vincent. 1992. Organization of predator-prey communities as an evolutionary game. Evolution 46:1269-1283.

Abrams P. A., H. Matsuda & Y. Harada. 1993. Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol. 7:465-487.

Vincent T. L., Y. Cohen & J. S. Brown. 1993. Evolution via strategy dynamics. Theor. Pop. Biol. 44:149-176.

Law R., P. Marrow & U. Dieckmann. 1997. On evolution under asymmetric competition. Evol. Ecol. 11:485-501.

Marrow P., U. Dieckmann & R. Law. 1996. Evolutionary dynamics of predator-prey systems: An ecological perspective. J. Math. Biol. 34:556-578.

Other approaches to adaptive dynamics - a sample

Review: Abrams P. A. 2001. Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods. Ecology Letters 4:166-175.

Christiansen F. B. & V. Loeschcke. 1980. Evolution and intraspecific exploitative competition I. One locus theory for small additive gene effects. Theor. Pop. Biol. 18:297-313.

Eshel, I. 1996. On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution. J. Math. Biol. 34:485-510.

Hammerstein P. 1996. Darwinian adaptation, population genetics and the streetcar theory of evolution. J. Math. Biol. 34:511-532.

Abrams P. A., H. Matsuda & Y. Harada. 1993. Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol. 7:465-487.

Matsuda H. & P.A. Abrams. 1994. Timid consumers: Self-extinction due to adaptive change in foraging and anti-predator effort. Theor.Pop.Biol. 45:76-91

Matsuda H. & P.A. Abrams. 1994. Runaway evolution to self-extinction under asymmetrical competition. Evolution 48:1764-1772.

Abrams P.A. & H. Matsuda. 1994. The evolution of traits that determine ability in competitive contests. Evol. Ecol. 8:667-686

Abrams P. 1999. The adaptive dynamics of consumer choice. Am. Nat. 153:83-97.

Marrow P., R. Law & C. Cannings. 1992. The coevolution of predator-prey interactions: ESSs and Red Queen dynamics. Proc. R. Soc. Lond. B 250:133-141.

Dieckmann U., P. Marrow & R. Law. 1995. Evolutionary cycling in predator-prey interactions: Population dynamics and the Red Queen. J. theor. Biol. 176:91-102.

Marrow P., U. Dieckmann & R. Law. 1996. Evolutionary dynamics of predator-prey systems: An ecological perspective. J. Math. Biol. 34:556-578.

Law R., P. Marrow & U. Dieckmann. 1997. On evolution under asymmetric competition. Evol. Ecol. 11:485-501.

Taylor P. & T. Day. 1997. Evolutionary stability under the replicator and the gradient dynamics. Evol. Ecol. 11:579-590.

Brown J. S. & T. L. Vincent. 1987. Coevolution as an evolutionary game. Evolution 41:66-79.

Brown J. S. & T. L. Vincent. 1992. Organization of predator-prey communities as an evolutionary game. Evolution 46:1269-1283.

Vincent T. L., Y. Cohen & J. S. Brown. 1993. Evolution via strategy dynamics. Theor. Pop. Biol. 44:149-176.

Cohen Y., T. L. Vincent & J. S. Brown. 1999. A G-function approach to fitness minima, fitness maxima, evolutionarily stable strategies and adaptive landscapes. Evol. Ecol. Res. 1:923-942.

Vincent T. L. & J. S. Brown. 2001. Evolutionarily stable strategies in multistage biological systems. Selection 2:85-102.

Brown J. S., Y. Cohen & T. L. Vincent. 2007. Adaptive dynamics with vector-valued strategies. Evol. Ecol. Res. 9: 719-756.

Ripa J., L. Storlind, P. Lundberg & J. S. Brown. 2009. Niche co-evolution in consumer-resource dynamics. Evol. Ecol. Res. 11: 305-323.

Vincent T. L., T. L. S. Vincent & Y. Cohen. 2011. Darwinian dynamics and evolutionary game theory. J. Biol. Dyn. 5: 215-226.

Rael R. C., T. L. Vincent & J. M. Cushing. 2011. Competitive outcomes changed by evolution. J. Biol. Dyn. 5: 227-252.

Cohen Y. 2011. Evolutionary distributions: Producer-consumer pattern formation. J. Biol. Dyn. 5: 253-267.