Abstract
Eco-coevolutionary theory predicts that predator-prey coevolution occurring on the time scale of ecological dynamics (e.g., changes in population abundances) can drive novel kinds of predator-prey cycles, e.g., cryptic cycles where one species cycles while the other remains effectively constant and clockwise cycles where peaks in predator density precede peaks in prey density. However, because this body of theory has focused on particular models and studied the different cycle types in isolation, it is unclear what biological characteristics (e.g., costs for offense or defense) determine when a particular cycle type will arise. In this study, I explore the kinds of predator-prey cycles that arise in a general eco-coevolutionary model where there is disruptive selection and the coevolutionary dynamics are fast relative to the ecological dynamics of the system. With a graphical tool created using the theory of fast-slow dynamical systems, I predict what kinds of cycles can arise in the model and how cycle type depends on the costs for prey defense and predator offense. Fast-slow dynamical systems theory requires a separation of time scales between the ecological and evolutionary processes; however, numerical simulations show that this tool can help predict how coevolution drives populations cycles in systems where the speeds of ecological and evolutionary dynamics are comparable. Thus, this work is a step forward in building a general eco-coevolutionary theory.
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References
Abrams PA (1992) Adaptive foraging by predators as a cause of predator-prey cycles. Evol Ecol 6:56–72
Abrams PA (2001) Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: an assessment of three methods. Ecol Lett 4:166–175
Abrams PA (2005) ‘Adaptive Dynamics’ vs. ‘adaptive dynamics’. J Evoutionary Biol 18:1162–1165
Abrams PA, Cressman R, Krivan V (2007) The role of behavioral dynamics in determining the patch distributions of interacting species. Am Nat 169:505–518
Abrams PA, Matsuda H (1997a) Fitness minimization and dynamic instability as a consequence of predator-prey coevolution. Evolutionary Ecol 11:1–20
Abrams PA, Matsuda H (1997b) Prey adaptation as a cause of predator-prey cycles. Evolution 51:1742–1750
Abrams PA, Matsuda H, Harada Y (1993) Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evolutionary Ecol 7:465–487
Arnold L, Jones CKRT, Mischaikow K, Raugel G (1995) Dynamical Systems, Springer Berlin/Heidelberg, vol 1609, chap. Geometric Singular Perturbation Theory, pp 44–118
Becks L, Ellner SP, Jones LE, Hairston NG Jr (2010) Reduction of adaptive genetic diversity radically alters eco-evolutionary community dynamics. Ecol Lett 13:989–997
Bohannan BJM, Lenski RE (1999) Effect of prey heterogeneity on the response of a model food chain to resource enrichment. Am Nat 153:73–82
Bohannan BJM, Lenski RE (2000) Linking genetic change to community evolution: insights from studies of bacteria and bacteriophage. Ecol Lett 3:362–377
Brodie III ED, Brodie ED Jr (1999) Costs of exploiting poisonous prey: Evolutionary trade-offs in a predator-prey arms race. Evolution 53:626–631
Bulmer MG (1975) Phase relations in the ten-year cycle. J Anim Ecol 44:609–621
Cortez MH (2011) Comparing the qualitatively different effects rapidly evolving and rapidly induced defences have on predator prey interactions. Ecol Lett 14:202–209
Cortez MH, Ellner SP (2010) Understanding rapid evolution in predator-prey interactions using the theory of fast-slow dynamical systems. Am Nat 176:E109–E127
Cortez MH, Weitz JS (2014) Coevolution can reverse predator—prey cycles. Proc Nat Acad Sci USA 111:7486–7491
Decole F, Ferrière R, Gragnani A, Rinaldi S (2006) Coevolution of slow-fast populations: evolutionary sliding, evolutionary pseudo-equilibria and complex Red Queen Dynamics. ProcRoyal Soc B 273:983–990
Deng B (2001) Food chain chaos due to junction-fold point. Chaos 11:514–525
Dieckmann U, Marrow P, Law R (1995) Evolutionary cycling in predator-prey interactions: population dynamics and the Red Queen. J Theor Biol 176:91–102
Edeline E, Ari TB, Vollestad LA, Winfield IJ, Fletcher JM, James JB, Stenseth NC (2008) Antagonistic selection from predators and pathogens alters food-web structure. Proc Nat Acad Sci USA 105:19792–19796
Elton CS, Nicholson M (1942) Fluctuations in numbers of the muskrat (Ondatra zibethica) in Canada. J Anim Ecol 11:96–126
Fussmann GF, Loreau M (2007) Eco-evolutionary dynamics of communities and ecosystems. Funct Ecol 21:465–477
Grant PR, Grant BR (2002) Unpredictable evolution in a 30-year study of Darwin’s finches. Science 296:707–711
Hairston NG Jr, Dillon TA (1990) Fluctuating selection and reponse in a population of freshwater copepods. Evolution 44:1796–1805
Hairston NG Jr, Lampert W, Caceres CE, Holtmeier CL, Weider LJ, Gaedke U, Fischer JM, Fox JA, Post DM (1999) Lake ecosystem: rapid evolution revealed by dormant eggs. Nature 401:446
Hairston NG Jr, Walton WE (1986) Rapid evolution of a life history trait. Proc Nat Acad Sci USA 83:4831–4833
Hall AR, Scanlan PD, Buckling A (2011a) Bacteria-phage coevolution and the emergence of generalist pathogens. Am Nat 177:44–53
Hall AR, Scanlan PD, Buckling A (2011b) Host parasite coevolutionary arms races give way to fluctuating selection. Ecol Lett 14:635–642
Heath DD, Heath JW, Bryden CA, Johnson RM, Fox CW (2003) Rapid evolution of egg size in captive salmon. Science 299:1738–1740
Horne MT (1970) Coevolution of Escherichia coli and bacteriophages in chemostat culture. Science 168:992–993
Jones LE, Becks L, Ellner SP, Hairston NG Jr, Yoshida T, Fussmann G (2009) Rapid contemporary evolution and clonal food web dynamics. Philos Trans Royal Soc B: Biol Sci 364:1579–1591
Jones LE (2007) Effects of rapid prey evolution on predator-prey cycles. J Math Biol 55:541–573
Khibnik AI, Kondrashov AS (1997) Three mechanisms of Red Queen dynamics. Philos Trans Royal Soc London B: Biol Sci 264:1049–1056
Kinnison MT, Hairston NG Jr (2007) Eco-evolutionary conservation biology: contemporary evolution and dynamics of persistence. Funct Ecol 21:444–454
Kr̆ivan V (2007) The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs. Am Nat 170:771–782
Lande R (1982) A quantitative genetic theory of life history evolution. Ecology 63:607–615
Lotka AJ (1934) Théorie analytique des associations biologiques, lre partie
Marrow P, Dieckmann U, Law R (1996) Evolutionary dynamics of predator-prey systems: an ecological perspective. J Math Biol 34:556–578
Mizoguchi K, Morita M, Fischer CR, Yoichi M, Tanji Y, Unno H (2003) Coevolution of bacteriophage PP01 and Escherichia coli O157:H7 in continuous culture. Appl Environ Microbiol 69:170–176
Mougi A (2012a) Predator prey coevolution driven by size selective predation can cause anti-synchronized and cryptic population dynamics. Theor Popul Biol 81:113–118
Mougi A (2012b) Unusual predator-prey dynamics under reciprocal phenotypic plasticity. J Theor Biol 305:96–102
Mougi A, Iwasa Y (2011) Unique coevolutionary dynamics in a predator-prey system. J Theor Biol 277:83–89
Palkovacs EP, Marshall MC, Lamphere BA, Lynch BR, Weese DJ, Fraser DF, Reznick DN, Pringle CM, Kinnison MT (2009) Experimental evaluation of evolution and coevolution as agents of ecosystem change in Trinidadian streams. Philos Trans Royal Soc London B: Biol Sci 364:1617–1628
Poggiale JC, Auger P, Cordoleani F, Nguyen-Huu T (2009) Study of a virus-bacteria interaction model in a chemostat: application of geometrical singular perturbation theory. Philos Trans Royal Soc A: Math, Phys Eng Sci 367:4685–4697
Reznick DN, Ghalambor CK, Crooks K (2008) Experimental studies of evolution in guppies: a model for understanding the evolutionary consequences of predator removal in natural communities. Mol Ecol 17:97–107
Reznick DN, Shaw FH, Rodd FH, Shaw RG (1997) Evaluation of the rate of evolution in natural populations of guppies (Poecilia reticulata). Science 275:1934–1937
Rinaldi S, Muratori S (1992) Slow-fast limit cycles in predator-prey models. Ecol Modell 61:287–308
Rosenzweig ML, MacArthur RH (1963) Graphical representation and stability conditions of predator-prey interactions. Am Nat 97:209–223
Volterra V (1926) Variazioni e fluttuazioni del numero dindividui in specie animali conviventi. Mem R Accad Naz dei Lincei 2:31– 113
Wei Y, Kirby A, Levin BR (2011) The population and evolutionary dynamics of Vibrio cholerae and its bacteriophage: conditions for maintaining phage-limited communities. Am Nat 178:715–728
Wei Y, Ocampo P, Levin BR (2010) An experimental study of the population and evolutionary dynamics of Vibrio cholerae O1 and the bacteriophage JSF4. Proc Royal Soc B 277:3247–3254
Yoshida T, Ellner SP, Jones LE, Bohannan BJM, Lenski RE, Hairston NG Jr (2007) Cryptic population dynamics: rapid evolution masks trophic interactions. PLoS Biol 5:1–12
Yoshida T, Jones LE, Ellner SP, Fussmann GF, Hairston NG Jr (2003) Rapid evolution drives ecological dynamics in a predator-prey system. Nature 424:303–306
Acknowledgments
I thank Peter Abrams and two anonymous reviewers for helpful comments on previous versions of the manuscript. MHC was supported by the National Science Foundation under Award No. DMS-1204401.
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Cortez, M.H. Coevolution-driven predator-prey cycles: predicting the characteristics of eco-coevolutionary cycles using fast-slow dynamical systems theory. Theor Ecol 8, 369–382 (2015). https://doi.org/10.1007/s12080-015-0256-x
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DOI: https://doi.org/10.1007/s12080-015-0256-x