[Reference for hitchhikers]
Weissing, F. J., Edelaar, P., & Van Doorn, G. S. (2011). Adaptive speciation theory: a conceptual review. Behavioral ecology and sociobiology, 65, 461-480.
Spencer, H. G., & Feldman, M. W. (2005). Adaptive dynamics, game theory and evolutionary population genetics. Journal of Evolutionary Biology, 18(5), 1191-1193.
Diekmann, O. (2003). A beginner's guide to adaptive dynamics. Banach Center Publications, 63, 47-86.
Two or multi-dimensional trait space
Strongly or Absolutely convergence stability
[REF] Leimar, O. 2001. Evolutionary change and Darwinian demons. Selection, 2: 65–72.
Isoclinic stability
[REF] Kisdi, É. (2006). Trade-off geometries and the adaptive dynamics of two co-evolving species. Evolutionary Ecology Research, 8(6), 959-973.
Finite population
[Reference; stochastistic branching]
Wakano, J. Y., & Iwasa, Y. (2013). Evolutionary branching in a finite population: deterministic branching vs. stochastic branching. Genetics, 193(1), 229-241.
[Reference; delaed evolutionary branching]
Claessen, D., Andersson, J., Persson, L., & de Roos, A. M. (2007). Delayed evolutionary branching in small populations. Evolutionary Ecology Research, 9(1), 51-69.
Invasion fitness: The initial growth rate of rare mutants
A proxy for invasion fitness: the dimensionless basic reproduction ratio, the expected total number of offspring that a rare mutant individual will have in its lifetime
[Reference]
Brännström, Å., Johansson, J., & Von Festenberg, N. (2013). The hitchhiker’s guide to adaptive dynamics. Games, 4(3), 304-328.
Examples:
Suzuki, S. U., & Sasaki, A. (2019). Ecological and evolutionary stabilities of biotrophism, necrotrophism, and saprotrophism. The American Naturalist, 194(1), 90-103.
Suzuki, S. U., & Sasaki, A. (2011). How does the resistance threshold in spatially explicit epidemic dynamics depend on the basic reproductive ratio and spatial correlation of crop genotypes?. Journal of Theoretical Biology, 276(1), 117-125.
[Reference]
Van Dooren, T. J. M. (2005). The future of a mutation‐limited tool‐box. Journal of evolutionary biology, 18(5), 1158-1161.
[Reference]
Durinx, M., (Hans) Metz, J.A.J. & Meszéna, G. Adaptive dynamics for physiologically structured population models. J. Math. Biol. 56, 673–742 (2008). https://doi.org/10.1007/s00285-007-0134-2
[Reference; dimorphism]
Van Dooren, T. J., Durinx, M., & Demon, I. (2004). Sexual dimorphism or evolutionary branching?. Evolutionary Ecology Research, 6(6), 857-871.
van Doorn, G. S., & Weissing, F. J. (2002). Ecological versus sexual selection models of sympatric speciation: a synthesis. Selection, 2(1-2), 17-40.
[Reference]
van Doorn, G. S., Edelaar, P., & Weissing, F. J. (2009). On the origin of species by natural and sexual selection. Science, 326(5960), 1704-1707.
[Reference; linkage equilibrium]
Geritz, S.A.H., and Kisdi, É. (2000). Adaptive dynamics in diploid sexual populations and the evolution of reproductive isolation. Proceedings of the Royal Society of London B 267: 1671–1678
[Reference; linkage 'dis'–equilibrium]
van Doorn, G. S., & Weissing, F. J. (2002). Ecological versus sexual selection models of sympatric speciation: a synthesis. Selection, 2(1-2), 17-40.
[Reference; Community assembly]
Dieckmann, U., Brännström, Å., HilleRisLambers, R., Ito, H.C. (2007). The Adaptive Dynamics of Community Structure. In: Takeuchi, Y., Iwasa, Y., Sato, K. (eds) Mathematics for Ecology and Environmental Sciences. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34428-5_8
We use the replicator equation to understand processes of reaching evolutionary equilibrium.
We assume that ...
形質分布のモーメントの発展方程式との関係から、収束安定性や進化的安定性を調べる
[Reference]
Wakano, J.Y. & Lehmann, L. (2014) “Evolutionary branching in deme-structured populations.” J. Theor. Biol. 351: 83–95.
“Invasion means Fixation” の成立条件（変異型の野生型への初期侵入が置き換えまでをも意味するか否か）
[Reference]
Geritz, S. A., Gyllenberg, M., Jacobs, F. J., & Parvinen, K. (2002). Invasion dynamics and attractor inheritance. Journal of mathematical biology, 44, 548-560.
進化的分岐が起きた後の二型集団の進化ダイナミクス
進化的特異点の分類理論における多型の場合には進化的特異連合 (evolutionarily singular coalition) の理論への拡張
[Reference]
Geritz, S.A.H., Kisdi, ́E., Mesz ́ena, G. & Metz, J.A.J. (1998) “Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree.” Evol. Ecol. 12(1): 35–57.
H. Ito's homepage: http://beetle.starfree.jp/R_adaptive_dynamics.html
E. Kisdi's homepage: https://www.mv.helsinki.fi/home/kisdi/addyn.htm
[Reference]
Abrams, P. A. (2005). Adaptive Dynamics’ vs.‘adaptive dynamics. Journal of Evolutionary Biology, 18(5), 1162-1165.
Geritz, S. A. H., & Gyllenberg, M. (2005). Seven answers from adaptive dynamics. Journal of Evolutionary Biology, 18(5), 1174-1177.
Gourbiere, S., & Mallet, J. (2005). Has adaptive dynamics contributed to the understanding of adaptive and sympatric speciation?. Journal of evolutionary biology, 18(5), 1201-1204.
Waxman, D., & Gavrilets, S. (2005). 20 questions on adaptive dynamics. Journal of evolutionary biology, 18(5), 1139-1154.
Waxman, D., & Gavrilets, S. (2005). Issues of terminology, gradient dynamics and the ease of sympatric speciation in adaptive dynamics. Journal of Evolutionary Biology, 18(5), 1214-1219.
[Reference]
Asexual population (beyond one species):
Dieckmann, Ulf. 1995. Coevolutionary Dynamics of Stochastic Replicator Systems. Forschungszentrum Jülich.
Dieckmann, Ulf, and Richard Law. 1996. “The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes.” Journal of Mathematical Biology 34 (5–6): 579–612. https://doi.org/10.1007/BF02409751.
Dieckmann, Ulf, Paul Marrow, and Richard Law. 1995. “Evolutionary Cycling in Predator-Prey Interactions: Population Dynamics and the Red Queen.” Journal of Theoretical Biology 176 (1): 91–102. https://doi.org/10.1006/jtbi.1995.0179.
Doebeli, Michael, and Ulf Dieckmann. 2000. “Evolutionary Branching and Sympatric Speciation Caused by Different Types of Ecological Interactions.” The American Naturalist 156 (S4): S77–101.
Sexual population:
Ito, H. C., & Dieckmann, U. (2007). A new mechanism for recurrent adaptive radiations. The American Naturalist, 170(4), E96-E111.
[Reference]
Champagnat, Nicolas, R. Ferričre, and G. Ben Arous4. 2002. “The Canonical Equation of Adaptive Dynamics: A Mathematical View.” Selection 2 (1–2): 73–83.
Dieckmann, Ulf. 1995. Coevolutionary Dynamics of Stochastic Replicator Systems. Forschungszentrum Jülich.
Dieckmann, Ulf, and Richard Law. 1996. “The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes.” Journal of Mathematical Biology 34 (5–6): 579–612. https://doi.org/10.1007/BF02409751.
Dieckmann, Ulf, Paul Marrow, and Richard Law. 1995. “Evolutionary Cycling in Predator-Prey Interactions: Population Dynamics and the Red Queen.” Journal of Theoretical Biology 176 (1): 91–102. https://doi.org/10.1006/jtbi.1995.0179.
Doebeli, Michael. 2011. Adaptive Diversification. Princeton: Princeton University Press.
Doebeli, Michael, and Ulf Dieckmann. 2000a. “Evolutionary Branching and Sympatric Speciation Caused by Different Types of Ecological Interactions.” The American Naturalist 156 (S4): S77–101.
Hofbauer, Josef, and Karl Sigmund. 1990. “Adaptive Dynamics and Evolutionary Stability.” Applied Mathematics Letters 3 (4): 75–79.
Holsinger, Kent E. 1991. “Mass-Action Models of Plant Mating Systems: The Evolutionary Stability of Mixed Mating Systems.” The American Naturalist 138 (3): 606–22.
Kishi, Shigeki, and Takefumi Nakazawa. 2013. “Analysis of Species Coexistence Co-Mediated by Resource Competition and Reproductive Interference.” Population Ecology 55:305–13.
Kuno, Eizi. 1992. “Competitive Exclusion through Reproductive Interference.” Researches on Population Ecology 34:275–84.
Leimar, Olof. 2009. “Multidimensional Convergence Stability.” Evolutionary Ecology Research 11 (2): 191–208.
Metz, Johan AJ, Roger M Nisbet, and Stefan AH Geritz. 1992. “How Should We Define ‘Fitness’ for General Ecological Scenarios?” Trends in Ecology & Evolution 7 (6): 198–202.
Dieckmann, U., Brännström, Å., HilleRisLambers, R., & Ito, H. C. (2007). The adaptive dynamics of community structure. In Mathematics for ecology and environmental sciences (pp. 145-177). Berlin, Heidelberg: Springer Berlin Heidelberg.