3. Adaptive dynamics

What is adaptive dynamcis?

Convergence stability & Evolutionary stability

• 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.

Replicator equation

We use the replicator equation to understand processes of reaching evolutionary equilibrium.

We assume that ...

Limitation & Future works

• 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

[REF] 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）

[REF] 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

[REF] 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.

Reference

• Reference homepages

  • 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