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Minus van Baalen (CNRS, UMR 7625 EcoEvo, Paris)
The Interaction Between
Evolution and Ecology
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Original Proposition
Introduction into Adaptive Dynamics
Application: Virulence Evolution
Application: Kin Selection, Cooperation, and Units of Adaptation
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Potential Topics
Synthetic Biology, Experimental Evolution
Mechanisms and Evolutionary Outcomes
Invasion Biology & Evolution
Genomics & Information Theory
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Evolution and Ecology
Population Genetics
Game Theory
Life History Theory
Community Ecology
Invasion
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Population Genetics
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Well-known standard case:
Sexual reproduction
Diploid genetics
Two alleles (dominant/recessive)
Variables: gene frequencies
Population Genetics
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Gene frequencies
time
gene
freq
uenc
ies
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Typical assumptions:
single population
simplified ecology
– most ecological aspects are subsumed in ‘frequency dependence’
more realistic cases difficult to analyse
– density dependence
– population interactions
Population Genetics
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Simple model
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example 2
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example 3
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Measures of increaseSubtle differences
λ rate of population increase– invasion continuous time : λ > 0– invasion discrete time : λ > 1
R0 basic reproduction ratio of individuals– invasion : R0 > 1
r net rate of reproduction of population– invasion : r > 0
s selection coefficient– increase in frequency : s > 0
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Much attention to
interaction among alleles and loci
– dominance
– modifiers
– conditions that favour polymorphism
– epistasis, linkage
– links with developmental biology
Population Genetics
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Little attention to
Interactions among individuals
– Population dynamics and ecology
– Behaviour
Population Genetics
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Phenotypic plasticity
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Phenotypic plasticity
A dominates
it depends…
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Gene frequencies
time
gene
freq
uenc
ies
We can select for redness but what about greenness???
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‘Evolution is change in gene frequencies’
‘That problem has been solved long ago’
‘The big problem is to explain speciation’
Population Genetics
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Game Theory
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First developments during 2nd World War
Then applied to Sociology
Why do individuals cooperate?
Applied to Behavioural Ecology
Interactions among individuals
Bill Hamilton John Maynard Smith
Game Theory
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John Maynard Smith
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Bill Hamilton
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Observation: fighting animals rarely kill
Why such restraint?
Hawk-Dove Game
Maynard Smith & Price 1971
Evolutionary Game Theory
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Individuals may choose among a range of strategies
Sometimes finding the optimum strategy is easy
Often, however, payoffs depend on what others do
Game Theory
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Hawk-Dove Game
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Calculation
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Graph
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If pH < p* (few Hawks) then play ‘Hawk’
If pH > p* (many Hawks) then play ‘Dove’
If pH = p* both ‘Hawk’ and ‘Dove’ do equally well
A resident strategy that plays ‘Hawk’ with probability p* cannot be beaten
Formalised in concept of ESS
Evolutionarily Stable Strategies
John Maynard Smith,Richard Dawkins
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Evolutionary Stability
If for all strategies J ≠ I
W(I|I) > W(J|I)
then strategy I is an ESS
If W(I|I) = W(J|I) then I is ESS if W(I|J) > W(J|J)
Maynard Smith & Price’s second condition.
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Caricature:
‘The fitness of an individual depends
on the strategies it adopts
(which can be either pure or mixed)
but also depends on the resident strategies
according to the payoff function’
Evolutionary Game Theory
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Problems
where do the strategies come from?
– Physiology?
– Developmental genetics?
– Behaviour?
– Life History Theory?
where does the payoff function come from?
Evolutionary Game Theory
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In many species, mothers can decide the sex of their offspring
Strategy = {% sons, % daughters}
Fischer in the 30s:
produce 50% daughters
Hamilton in the 60s:
depends on mating structure
biased sex ratios
Example: Sex Allocation
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In many spatially heterogeneous environments, individuals can decide where to go
Often, payoffs depend on where others go
Q1: where should you go ?
Q2 (knowing A1) where does everybody go?
Prediction: Ideal Free Distribution
nobody gains by moving to another place
Ex: Habitat Selection
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Where does the payoff function come from?
Fitness = Lifetime reproductive succces
If Fitness > 1 ⇒ Invasion
Life History Theory
Evolutionary Game Theory
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Population Genetics
mutant genotypes may generate new phenotypes
Game Theory
outcome of interaction depends on conditions
Life History Theory
rare mutants will try to optimize their strategies
Ecosystem Dynamics
invasion of rare species, density dependence
Important Insights
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Adaptive Dynamics
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Caricature
‘New mutants may appear
initially rare
whose invasion fitness
depends on the resident attractor’
Peter Hammerstein, Ilan Eshel, Hans Metz, David Rand, Geza Meszena,
Ulf Dieckmann,Stefan Geritz, Eva Kisdi.
Adaptive Dynamics
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summary
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Practical Method
monomorphic population trait a
resident dynamics
attractor
mutant invasion
pairwise invasibility plot (PIP)
Adaptive Dynamics
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Pairwise Invasibility Plot
resident trait
mut
ant
trai
t
+ +
–
–
positivemutantfitness
negativemutantfitness
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Pairwise Invasibility Plot
resident trait
mut
ant
trai
t+
+
–
–
Evolutionary Repeller
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Pairwise Invasibility Plot
resident trait
mut
ant
trai
t+
+
–
–
Garden of Eden
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Pairwise Invasibility Plot
resident trait
mut
ant
trai
t
+
+
–
––
–‘Branching point’
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Kisdi & Geritz
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Epidémiologie
β paramètre de transmissionµ mortalité de baseα mortalité induite, virulence
Individu↓
Population
dSdt
=[host reproduction]−µS−βSI
dIdt
=βSI− (µ+α)I
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Epidémiologie + Evolution
I souche residente, J souche mutante
dSdt
=[host reproduction]−µS−βSIdIdt
=βSI− (µ+α)I
= −β∗SJ
=dJdt
=β∗SJ− (µ+α∗)J
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« Dynamique adaptative »
• théorie des jeux dans un cadre écologique
• pour deriver la valeur sélective (fitness)+ en lieu de simplement supposer lʼexpression
• pour predire la réponse evolutive+ stratégies evolutivement stable+ branchement évolutif
Articles par Metz, Kisdi, Geritz, Law, Rand, Dieckmann…
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Lʼinvasion des mutants• Resident I en équilibre endemique
dI/dt = 0
• Le mutant J envahit sidJ/dt > 0
" " " " (quand il est rare, J << I)
• Invasion si R0
β∗Sµ+α∗ > 1
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R0 easy to calculate?
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Invasion
• Mutant J envahit siβ∗Sµ+α∗ > 1 =
βSµ+α
β∗
µ+α∗ >β
µ+α
La virulence optimale maximise β∗
µ+α∗
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ESS
• La séléction naturelle favorise les parasites – qui maximisent
– exploitent leurs hôtes dʼune façon optimale– les individus infectés, pas la population !
β∗
µ+α∗
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Une contrainte…tra
nsm
issio
n (β
*)
mortalité de l’hôte (µ + α∗)
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…implique un Trade-offtra
nsm
issio
n (β
*)
host mortality (µ + α∗)
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Epidémiologie + Evolution+ Intervention
I souche residente, J souche mutanteD modification de transmission
dSdt
=[host repr.]−µS−DβSI−Dβ∗SJ
dIdt
=DβSI− (µ+α)I
dJdt
=Dβ∗SJ− (µ+α∗)J
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Invasion
• Mutant J envahit si
β∗
µ+α∗ >β
µ+α
La virulence optimale maximise β∗
µ+α∗
Dβ∗Sµ+α∗ > 1 =
DβSµ+α
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• Les parasites maximisent
une quantité qui ne dépend pas de D!
Evolution
β∗
µ+α∗
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Conséquences
• La virulence dépend de la forme du trade-off– la rélation entre transmission et mortalité– déterminée par la physiologie de lʼhôte/
parasite• La virulence ne dépend pas de facteurs
externes+ à lʼexception du taux de mortalité de base– pas de rôle pour lʼépidémiologie
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Virulence Déterminée au…
niveau de la populationinteractions sociales, interactions ecologiques, compétition, ressources, santé publique
niveau de l’individuvirulence
niveau intra-hôtephysiologie, dynamique intra-hôte, choses moleculaires, médicaments, antibiotiques
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Conséquences
• Virulence depend de la forme du trade-off+ dépend de la physiologie de lʼhôte+ dynamique intra-hôte du parasite+ système immunitaire
– La virulence ne dépend pas de facteurs externes
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Le dilemme du parasite
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Le dilemme du parasite
• Un parasite peut– augmenter sa transmission, ou– prolonger la duration de lʼinfection– mais pas les deux en même temps
• ce dilemme est capturé par lʼanalyse graphique…
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…mais… la réalité ?
• dans le modèle :durée de lʼinfection = survie de lʼhôte
• souvent pas très réaliste :– infections terminées par le système
immunitaire (guérison)– compétition avec dʼautres parasites
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Infections multiples
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Infections multiples
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Infections multiples
• parasites partagent leurs hôtes• reduit transmission en long terme• favorise transmission en court terme• mène à une virulence augmentée
+ Eshel 1977 + Levin & Pimentel 1981+ Nowak & May 1994+ van Baalen & Sabelis 1995
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Modèles compétition intra-hôte• Superinfection
– la souche la plus virulente remplace les autres– (Levin & Pimentel 1981, Nowak & May 1994)
– chaque souche a une chance de gagner– Gandon et al. 2001, 2002)
• Coinfection– les souches coexistent à lʼintérieur de
lʼhôte– (Eshel 1977, van Baalen & Sabelis 1995)
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Superinfection
S
I J
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Superinfection
σ : Aggressivité intra-hôte
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Invasion
le mutant envahit si
fitness ≠ taux de reproduction de base !
β∗S +σβ∗Iµ+α∗+σβI
> 1
R0 =β∗S
µ+α∗
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`• virulence optimale maximise
• en contraste avec cas simple, dépend de plein de choses– densité hôtes saines,– densité hôtes infectés (avec souche
residente)– stratégie de la souche residente
β∗S +σβ∗Iµ+α∗+σβI
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Cas simple
• supposons σ constant• virulence optimale maximise
• presque comme résultat déjà obtenu, sauf que virulence dépend du ʻforce dʼinfectionʼ du resident (β*I )
βµ+α+σβ∗I
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Résumé
Modèle simple sans compétition intra-hôte : - pas de « virulence management »
Avec compétition intra-hôte :
- infection difficile → moins d’infections multiples
- moins d’infections multiples → virulence diminuéeEwald: « C’est ce que je dis tout le temps ! »
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Virulence & infections multiples
niveau populationnelinteractions sociales, interactions ecologiques, compétition, ressources, santé publique
niveau individuelinfectivité, mortalité, immunité, comportement, visites médicales, vaccination
niveau intra-hôtephysiologie, dynamique intra-hôte, aspects moléculaires, médication