1. Rapid Evolution and Predator-Prey Dynamics with Variable Cost of Defense Rebecca J. Dore, Stephen P. Ellner, Laura E. Jones, Cornell University

2. Outline Background and inspiration for current research - Rapid Prey Evolution in an Experimental System 1.“Strange” cycles 2. Genetic Variablity 3. Trade-offs 4. Variable Costs Present Model – The effect of genetic variability on stability of a predator-prey system Conclusions and Future Work

3. Experimental System Predator-prey microcosm with rotifers, Brachionus calyciflorus, cultured together with their algal prey, Chlorella vulgaris, in nitrogen limited, continuous flow-through chemostat systems. Algae and rotifers reproduce asexually, so evolutionary change occurs as a result of changes in the relative frequency of different algal prey types (clones).

4. Evolutionary dynamics between predator and prey “Evolutionary” cycling → long period, out-of-phase limit cycles Predatory rotifer (Brachionus calicyflorus) in red; algal prey (Chorella vulgaris) in green.

5. Model: multiple algal clones with tradeoff Predator avoidance vs. Ability to compete for nutrients Clone Frequency Time (Days) Long Cycles result of evolution of algal genotypes that cycles with the predator population (Schertzer et al. 2002)

6. Finding Distinct Algal Clones After many tries, 10 microsat loci in prey 7 pairs of strains distinguishable by PCR using just 1 locus 1 pair with growth/defense tradeoff Gene Mapper Spectral Reading on PCR products In trials with known clone proportions, relative peak height predicted clone frequencies very well (R2=0.96) Undefended Clone’s allele Defended Clone’s allele

7. In batch culture experiments, "defended" prey clone has much lower mortality when predators are present, slower population growth when predators are absent Ten minutes later… Defense = Survives Being Eaten 1 4 80 Rotifer r value

8. Genetic Results Clone frequencies changed as predicted: superior competitor initially dominant, but loses out as predator population grows.

9. Tradeoff between Defense and Fitness Cost Artificially selected algal populations in the presence or absence of grazing rotifers Measured Algal food value (i.e. rotifer population growth rate) Algal population growth rate under varying nutrient limitation (as a measure of competitive ability)

10. Algal Food Value Population growth of Brachionus calyciflorus (B )

11. Algal Population Growth Rate Under high nitrate concentrations no difference Under low nitrate (i.e. increased competition) grazed pop has lower growth rate → VARIABLE COST Yoshida et al. (2004) Proc. R. Soc. Lond. B

12. In Summary “Grazed” algae became lower in food value and heritably smaller than “non-grazed” algae. Population growth rate of grazed algae was heritably lower than non-grazed algae. Evolutionary Tradeoff between algal food value and competitive ability Cost is Variable

13. Outline Background and inspiration for current research - Rapid Prey Evolution in an Experimental System Present Model – The effect of genetic variability on stability of a predator-prey system Conclusions and Future Work

14. Questions A) What are the effects of genetic variability on stability and dynamics of a predator-prey system? B) How does the stability of the system change when we let the cost of prey defense vary with population size?

15. Effects of Genetic Variability Classically three types of dynamics have been observed: WITHOUT evolution: 1.One or both go extinct 2.Both exist at some steady-state equilibrium 3.Predator-prey cycles WITH evolution: 1.One or both go extinct. 2.Both exist at steady-state equilibrium 3.Red Queen Dynamics 4.co-existence with predator-prey cycles and trait cycling for the predator trait, but not the prey

16. Methods We compared two Models: 1) Fixed Cost - cost does not change with population size but rather, is some fixed constant. 2) Variable Cost - cost is density-dependent so that, as population size increases, cost increases. At low densities, defense is “free”. *Cost is defined as a decrease in fecundity

17. Fixed Cost Variable Cost Population Dynamics (N,x) = Prey density and defense (P,y) = Predator density and search efficiency

18. Trait Dynamics: Q.T. Model For a Rare Invader So V x → 0 when trait mean → 0 Fixed vs. Variable Cost will have different equations for

19. Fixed Cost Population Cycles Trait Cycles Black=prey, Red=predator Variable Cost Population Cycles Trait Cycles Black=prey, Red=predator Results

20. Bifurcation Diagram – shows the region where cycling can occur Prey Trait Cost Grazing

21. Conclusions Variable Cost appears to be more stabilizing than Fixed Cost Cycles are qualitatively different (shorter period, higher amplitude) when cost is variable.

22. Problems with Model Definition of trade-off curve Due to numerical errors, defined prey trade-off using a quadratic term (ax 2 ) so that x can not be negative. This leads to a marginal cost of zero at some point which means the prey never give up on defense. Jakobsen &Tang (2002) – colony forming Phaeocystis Multiples parameters Many possible outcomes for model depending on choice of active parameter.

23. Solutions? Definition of trade-off curve Redefine the prey trade-off curve as a linear term, ax, so that it is more biologically relevant. Use only the output from MATCONT where x > 0 Multiple parameters Solve the simplified predator-prey system without evolution to get parameters for cycling.

24. Variable vs. Fixed

25. Acknowledgements At Cornell University: Stephen Ellner, Nelson Hairston, Laura Jones At McGill University: Justin At Tokyo University: Take Yoshida Also thank you to Joe Tien at Fred Hutchinson Cancer Research Institute, Seattle