ADAPTIVE
DYNAMICS PAPERS
This page
contains some references to the development and applications of adaptive dynamics,
with a strong bias towards the modelling framework based on stochastic trait
substitution sequences that involves evolutionary branching. The list is not
exhaustive even in this narrow scope, and I take no responsibility for
missing references. Since this page is also intended to help course students, I
include a few publications outside the scope of adaptive dynamics that are useful in relation to the population dynamics of invading
mutants, the connection to speciation models, etc.
Last
updated: 27/08/2004 | Maintained by: Eva Kisdi
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 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.
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.
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.
Champagnat N., R. Ferričre and G. Ben Arous. 2001. The
canonical equation of adaptive dynamics: a mathematical view. Selection
2:73-84.
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 covariance matrix) and absolute
convergence, respectively.
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.
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.
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 E. & 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
Dercole, F. 2002. Evolutionary dynamics through bifurcation analysis: Methods
and applications. PhD Thesis, Politecnico di Milano, chapter 3.
Geritz S. A. H. Resident-invader dynamics and the coexistence of similar
strategies. J. Math. Biol., in press.
Adaptive
dynamics and optimization
Metz
J.A.J., Mylius S.D. & Diekmann O. 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.
Adaptive
dynamics and matrix games
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)
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.
Jacobs F. & J. A. J. Metz. Bifurcation analysis
for adaptive dynamics based on Lotka-Volterra competition models. in prep.
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. 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
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.
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.
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.
Van Dooren T. J. M. 2000. The evolutionary dynamics of
direct phenotypic overdominance: Emergence possible, loss probable. Evolution
54: 1899-1914.
Adaptive
dynamics and multilocus / quantitative genetics
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., in press. 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.
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. & M. Doebeli. 2003. Sexual dimorphism
and adaptive speciation: Two sides of the same ecological coin. Evolution
57:2433-2449.
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.
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.
*
Parvinen, K. 1999. Evolution of migration in a
metapopulation. Bull. Math. Biol. 61:531-550.
* 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.
2000
* 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.
* Regoes R. R., M. A. Nowak & S. Bonhoeffer. 2000.
Evolution of virulence in a heterogeneous host population. Evolution 54:64-71.
2001
* Cheptou P.-O. & A. Mathias. 2001. Can varying
inbreeding depression select for intermediary selfing rate? Am. Nat.
157:361-373
* 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.
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
* 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.
2004
* 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.
* 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.
* 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.
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.
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.
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.
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
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. Research 1:923-942.
Vincent T. L. & J. S. Brown. 2001. Evolutionarily stable strategies in
multistage biological systems. Selection 2:85-102.