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Rapid Evolution and Predator-Prey Dynamics with Variable Cost of Defense

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Title: Rapid Evolution and Predator-Prey Dynamics with Variable Cost of Defense


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 anExperimental System
  • 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
tradeoffPredator avoidance vs. Ability to
compete for nutrients
Long Cycles result of evolution of algal
genotypes that cycles with the predator
population (Schertzer et al. 2002)
Clone Frequency
Time (Days)
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
(R20.96)
Undefended Clones allele
Defended Clones allele
7
In batch culture experiments, "defended" prey
clone has much lower mortality when predators
are present, slower population growth when
predators are absent
r value
Rotifer
1 4 80
Defense Survives Being Eaten
Ten minutes later
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 anExperimental 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
  • One or both go extinct
  • Both exist at some steady-state equilibrium
  • Predator-prey cycles
  • WITH evolution
  • One or both go extinct.
  • Both exist at steady-state equilibrium
  • Red Queen Dynamics
  • 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
Population Dynamics
(N,x) Prey density and defense (P,y) Predator
density and search efficiency
Fixed Cost
Variable Cost
18
Trait Dynamics Q.T. Model
For a Rare Invader
So Vx ? 0 when trait mean ? 0
Fixed vs. Variable Cost will have different
equations for
19
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 (ax2) 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 gt 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
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