Rapid Evolution and Predator-Prey
Dynamics with Variable Cost of
Defense
Rebecca J. Dore, Stephen P. Ellner,
Laura E. Jones, Cornell University
Outline
•
Background and inspiration for current
research - Rapid Prey Evolution in an
Experimental System
1.
2.
3.
4.
•
•
“Strange” cycles
Genetic Variablity
Trade-offs
Variable Costs
Present Model – The effect of genetic
variability on stability of a predator-prey system
Conclusions and Future Work
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).
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.
Long Cycles result of
evolution of algal genotypes
that cycles with the predator
population (Schertzer et al.
2002)
Clone Frequency
Model: multiple algal clones with tradeoff
Predator avoidance vs. Ability to compete
for nutrients
Time (Days)
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
Undefended
Clone’s allele
Defended
Clone’s allele
In trials with
known clone
proportions,
relative peak
height predicted
clone
frequencies very
well (R2=0.96)
1.5
1
r value
0.5
Rotifer
0
-0.5
11
4
4
-1
-1.5
80
80
Roti
In batch culture
experiments, "defended"
prey clone has
much
lower mortality
265r
395r
when
predators are
present, slower
population growth when
predators are absent
Defense = Survives Being Eaten
Ten
minutes
later…
Genetic Results
• Clone
frequencies
changed as
predicted:
superior
competitor
initially
dominant,
but loses
out as
predator
population
grows.
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)
0
Algal
0 1 2 Food
3 4 5Value
6 7 8
9
Population growth rate [day -1 ]
Population growth of Brachionus
calyciflorus
Days
2
1.5
(B)
(B
)
1
0.5
0
Grazed
Non-grazed
Algal Population Growth Rate
Population growth rate [day -1 ]
2.5
non-grazed
2.0
grazed
***
1.5
1.0
0.5
• Under high nitrate
concentrations no
difference
• Under low nitrate
(i.e. increased
competition)
grazed pop has
lower growth rate
0.0
1
4
Nitrate concentration [µmol l -1]
80
→ VARIABLE COST
Yoshida et al. (2004) Proc. R. Soc. Lond. B
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
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
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?
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
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
Population Dynamics
(N,x) = Prey density and defense
(P,y) = Predator density and search efficiency
Fixed Cost
P


( yx)
N
  r (1 
)  Ge
 ax  N
k
dt 
qN

dN
2
 ( yx) N
2 
   Ge
 ( d  cy )  P
dt 
qN

dP
Variable Cost
P


( yx)
N
  r (1 
)  Ge
 ax N  N
k
dt 
qN

dN
2
Trait Dynamics: Q.T. Model














dx   1 dN V
dt x N dt x














dy   1 dP V
dt y P dt y
For a Rare Invader
V x  Ax x
V y  Ay y
So Vx → 0 when trait mean → 0
Fixed vs. Variable Cost will have different equations for
dx
dt
Results
Fixed Cost
Population Cycles
Variable Cost
Population Cycles
Black=prey, Red=predator
Trait Cycles
Black=prey, Red=predator
Trait Cycles
Prey Trait Cost
Bifurcation Diagram – shows the region where
cycling can occur
Grazing
Conclusions
• Variable Cost appears to be more
stabilizing than Fixed Cost
• Cycles are qualitatively different (shorter
period, higher amplitude) when cost is
variable.
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.
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.
Variable
vs.
Fixed
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