Abstract
In this paper, with the method of adaptive dynamics and critical function analysis, we investigate the evolutionary diversification of prey species. We assume that prey species can evolve safer strategies such that it can reduce the predation risk, but this has a cost in terms of its reproduction. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for continuously stable strategy and evolutionary branching in the prey strategy. It is found that if the trade-off curve is globally concave, then the evolutionarily singular strategy is continuously stable. However, if the trade-off curve is concave-convex-concave and the prey's sensitivity to crowding is not strong, then the evolutionarily singular strategy may be an evolutionary branching point, near which the resident and mutant prey can coexist and diverge in their strategies. Second, we find that after branching has occurred in the prey strategy, if the trade-off curve is concave-convex-concave, the prey population will eventually evolve into two different types, which can coexist on the long-term evolutionary timescale. The algebraical analysis reveals that an attractive dimorphism will always be evolu...Continue Reading
References
Mar 29, 1968·Science·D Pimentel
Jan 1, 1996·Journal of Mathematical Biology·P MarrowR Law
Jan 1, 1996·Journal of Mathematical Biology·U Dieckmann, R Law
Mar 13, 1999·Journal of Theoretical Biology·E Kisdi
Jun 15, 1999·Theoretical Population Biology·S A GeritzJ A Metz
Jul 1, 1982·Journal of the History of Biology·C U Smith
Mar 13, 2002·Bio Systems·József Garay
Apr 27, 2002·Science·Peter R Grant, B Rosemary Grant
Apr 12, 2003·Bio Systems·Mark A Bedau, Norman H Packard
May 4, 2004·The American Naturalist·Martijn EgasMaurice W Sabelis
Jan 18, 2005·Journal of Theoretical Biology·Roger G BowersMichael Boots
Feb 1, 2005·Mathematical Biosciences·Andrew White, Roger G Bowers
Feb 5, 2005·Journal of Mathematical Biology·Stefan A H Geritz
Feb 9, 2005·Evolution; International Journal of Organic Evolution·Martin Ackermann, Michael Doebeli
May 13, 2005·Theoretical Population Biology·Odo DiekmannBenoît Perthame
Jan 18, 2006·Journal of Theoretical Biology·Wendi WangShinji Nakaoka
Feb 14, 2006·The American Naturalist·Claus RuefflerJohan A J Metz
Jul 13, 2006·Bulletin of Mathematical Biology·Junling Ma, Simon A Levin
May 1, 2007·Theoretical Population Biology·Stefan A H GeritzPing Yan
Nov 21, 2007·Journal of Theoretical Biology·Andrew HoyleMichael Boots
Dec 23, 2008·Journal of Theoretical Biology·Thomas O Svennungsen, Eva Kisdi
Sep 23, 2009·Journal of Theoretical Biology·Ross Cressman
Oct 27, 2009·Journal of Theoretical Biology·Jian ZuJoe Yuichiro Wakano
Jun 1, 1992·Trends in Ecology & Evolution·J A MetzS A Geritz
Mar 16, 2011·Mathematical Biosciences·Jian ZuMasayasu Mimura
Citations
Aug 13, 2013·Theoretical Population Biology·Jian Zu, Jinliang Wang
Apr 29, 2014·Acta Biotheoretica·Jian ZuJianqiang Du
Feb 5, 2016·Mathematical Biosciences·Xin WangLina Hao
Oct 17, 2017·Ecology·Elias EhrlichUrsula Gaedke
Apr 16, 2021·Bulletin of Mathematical Biology·Ao Li, Xingfu Zou