Transcript Victim strikes back counterattacks of predatory mites by

Adaptive Dynamics
PhD Course Evolutionary Dynamics, 11 – 15 November 2012.
IBED – Population Biology | Groningen Graduate School Ecology and
Evolution
Overview of the Lectures
Tuesday evening:
Overview evolutionary ecology & intro Adaptive Dynamics;
Wednesday morning:
Intro Adaptive Dynamics cont. & Fitness function;
Exercises;
Wednesday afternoon:
AD, a closer look: mathematical recipes
Testing the theory: evolutionary branching in E. coli bacteria?
Reading - AD “polemics” in the literature;
Wednesday evening:
Adaptive Dynamics and speciation;
Thursday morning:
AD, a closer look: canonical equation
“Evolutionary Suicide”, “Resident strikes back” & attractor inheritance;
Discussion of AD “polemics” in the literature;
Structure of This First Lecture
–Motivation for evolutionary ecology.
–Introducing the (since the ’70s) traditional tools of evolutionary
ecology: Evolutionary Optimization and Evolutionary Game Theory;
and the main term ever since: ESS.
Motivation for Evolutionary Ecology
Evolutionary ecology comes naturally to population ecologists,
because:
… natural selection is (almost) unavoidably present in our base
populations.
… it provides us with expectations of the likely state of the (food
web) system (e.g., for life history traits or behavioural strategies).
… evolutionary dynamics and population dynamics feed back into
each other, and
… timescales of evolutionary change and population dynamics may
be of the same order of magnitude.
Example eco-evo-interaction
Predator-prey dynamics of
Chlorella algae and Branchionus
rotifers (freshwater lakes)
Example eco-evo-interaction
Predator-prey dynamics something’s off…
The cycles are out of phase…!
This means that the dynamics are
not driven by standard predatorprey interaction
Example eco-evo-interaction
Alternative explanation:
Evolution during the cycles…!
That is, rapid change in palatability in the prey population, which trades
off with competitive ability.
Multi-clone predator-prey dynamics (Yoshida et al. 2003, Nature)
Example eco-evo-interaction
Example eco-evo-interaction
Alternative explanation in words:
Predators increase in number, driving the abundance of palatable prey
down. Unpalatable prey clones take over and cause slowly decreasing
predator numbers, which in turn favours restoration of the palatable prey
clones because they are better competitors than the unpalatable ones,
which… etc.
“Evolution at the ecological time-scale”.
Traditional Tools in Evolutionary Ecology
1: Evolutionary Optimization Theory (since 1970s)
Example: optimal patch exploitation
2: Evolutionary Game Theory (since 1970s)
Example: the Hawk-Dove Game
3. Evolutionary Ecology and ESS (since 1980s)
Example: the Milker-Killer Dilemma
All use the term “Evolutionarily Stable Strategy”, or ESS:
a strategy that, when adopted by the whole population, cannot be
invaded (‘beaten’) by any (nearby) mutant strategy.
1. Evolutionary Optimization Theory
Developed in 1960s and ’70s.
Most popular in Life History Theory, where, e.g., a heated debate
has raged on whether evolution optimizes the instantaneous growth
rate (r) or the lifetime reproductive output (R0).
An example: optimal patch exploitation
Question: how should consumers distribute over patches?
Objective: maximize fitness of a consumer which depends on its
patch choice.
Assume: two types of patch; individuals are both “ideal” and “free”.
2. Evolutionary Game Theory
Introduced in evolutionary biology by John Maynard Smith, in 1973,
after pioneering work by Bill Hamilton in 1967.
Adapted from Game Theory as developed in Economics since the
1950s (Von Neumann & Morgenstern; John Nash, “A Beautiful
Mind”).
Standard example: the Hawk-Dove Game
Question: when should animals fight for food?
Objective: study interaction in pairs of individuals ‘fighting’ for food.
Assume: two types of strategy, Hawk and Dove.
Example: the Hawk-Dove Game I
‘Dove’ proposes to split the food item without fighting, but leaves it
to the other if that one starts to fight.
‘Hawk’ will fight over the food item, even at the cost of injury.
‘Pay-off matrix’ can be constructed for the four different
interactions:
vs Hawk
vs Dove
Hawk
0.5·V – C
V
Dove
0
0.5·V
Example: the Hawk-Dove Game II
What to do? What strategy to play?
This depends on the values of V and C, of course, but – in general
in games – also on the frequency of strategies in the population.
To solve this game, ask yourself what you should play to get the
highest pay-off in case you meet a Hawk and in case you meet a
Dove:
vs Hawk vs Dove
Hawk
0.5·V – C
V
Dove
0
0.5·V
Hawk is ESS when C < 0.5·V
3. Evolutionary Ecology and ESS
Optimization theory only works when fitness is independent of the
frequencies of strategies in the population.
Game theory by its nature has this frequency-dependent fitness,
but here density-dependence or population dynamics is not
included.
To illustrate that these dependences matter, an example from our
research: the Milker-Killer Dilemma
Question: when should predators disperse while exploiting prey?
Objective: study effect of dispersal rate on reproductive output.
Assume: prey population will be overexploited at some time.
Example: the Milker-Killer dilemma
P. persimilis
T. urticae
Observation: the predatory mite P. persimilis does not disperse
from a local prey population until all prey are exterminated.
Under which conditions should we expect this, as an ESS?
The Milker-Killer dilemma
(examples from Bas Pels, André de Roos & Maus Sabelis [2002], Am.Nat. 159:172-189)
Predators can produce more
offspring in a patch when
they use their prey prudently
(“Milkers”; dispersal rate m>0
while there are still prey to
eat)
… but this behaviour is
vulnerable to cheating
(“Killers”; NO dispersal while
there are still prey to eat)
μ=0