François Massol - présentation MEE2013

Evolution of dispersal in
heterogeneous and
uncertain environments
François Massol
May 2013 – Models in Evolutionary Ecology, Montpellier

Pros and cons
kin competition
inbreeding avoidance
catastrophes
temporal variability
environmental
heterogeneity
cost of dispersal
Pros Cons
van Valen 1971; Balkau & Feldman 1973; Roff 1975;
Hamilton & May 1977; Bengtsson 1978

The larger picture
Patterns (direct):Processes:
kin competition
inbreeding
catastrophes
temp. variability
heterogeneity
cost of dispersal
dispersal ESS

The larger picture
kin competition
inbreeding
catastrophes
temp. variability
heterogeneity
cost of dispersal
dispersal ESS
polymorphism?

The larger picture
kin competition
inbreeding
catastrophes
temp. variability
heterogeneity
cost of dispersal
dispersal ESS
polymorphism?
association with
other traits

The larger picture
Patterns (indirect):
kin competition
inbreeding
catastrophes
temp. variability
heterogeneity
cost of dispersal
dispersal ESS
polymorphism?
association with
other traits
diversity
gene flow
…

Heterogeneity and variability
• Environments are temporally variable
organisms experience temporally variable habitats
• Environments are spatially heterogeneous
dispersing allows for different habitats among siblings

Measuring heterogeneity
First-order measure: proportion of type 1 patch, ρ

Measuring variability
φ = 0
φ > 0
φ < 0
time
time
time
temporal autocorrelation in patch state, φ

Questions
1. How can we model the evolution of dispersal
in uncertain heterogeneous environments?
2. Case study: the joint evolution of selfing and
dispersal when pollinator occurrence is
random
3. What happens when dispersal can be
informed?

Adaptive dynamics
Assumptions:
– phenotypic gambit
“The phenotypic gambit is to examine the evolutionary basis of a character as if the
very simplest genetic system controlled it: as if there were a haploid locus at which
each distinct strategy was represented by a distinct allele, as if the payoff rule gave
the number of offspring for each allele, and as if enough mutation occurred to
allow each strategy the chance to invade.” A. Grafen, in Krebs & Davies 1984
– rare mutations of small effects
Tools:
– expression for fitness (using matrices)
– selection gradient → convergence stability
– Hessian of mutant fitness → evolutionary stability

Perturbations, life cycle & the
evolution of dispersal
with Florence Débarre

How does environmental state change?

Life cycles
Ravigné et al., 2004

Life cycles
Looking at the evolution of local adaptation…
Ravigné et al., 2004

Life cycles
What if the order of events is different?
– selection gradient on dispersal rate may change
direction when reproduction, dispersal and
regulation happen in a different order (Johst &
Brandl 1997)
– the order of reproduction, dispersal and regulation
directly impact the evolution of local adaptation
traits (Ravigné et al. 2004)

A general model
Ingredients:
– 2 patch types (1 & 2; affect fecundity), infinity of
patches
– 4 life cycle events: reproduction, dispersal, regulation
& environmental change
– discrete, non-overlapping generations
– reproduction: result of local adaptation, not limiting
– regulation: local (but large populations)
– dispersal: global (no limitation by distance)
Massol (2013)

Classification of life cycles
extended from Massol (2013)
Levene soft selection
regime
Ravigné
type 3
Ravigné
type 3
Ravigné et al.’s
classification
Order of
events
Dempster hard
selection regime
D D D D D
D E E E
EEE
R R
RR RR
Simple life cycles Complex life cycles
Modelling
complexity
Simple life cycles

extended from Massol (2013)
Order of
events
D D D D D
D E E E
EEE
R R
RR RR
When dispersal is unconditional
Classes of equivalence for fitness
correspond to Ravigné et al.’s
To the really interested audience:
• E always commutes with regulation.
• With unconditional dispersal, E also commutes with dispersal.
Levene soft selection
regime
Ravigné
type 3
Ravigné
type 3
Ravigné et al.’s
classification
Dempster hard
selection regime

Evolution of dispersal
Massol & Débarre (in prep)
Order of
events
DE
R
DE
RD
E R
LeveneRavignéRavigné et al.’s
classification
Dempster

Order of
events
DE
R
DE
RD
E R
classification
Dempster
evolution towards
philopatry

Order of
events
DE
R
DE
RD
E R
classification
Dempster
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
dispersalrate(d)
temporal autocorrelation in patch state ( φ )
Branching

Order of
events
DE
R
DE
RD
E R
classification
Dempster
Zero dispersal when
Total dispersal when
Branching when
 
   
2
1/2
2 31
g
c
g g

 


 2c g 
0 

Order of
events
DE
R
DE
RD
E R
classification
Dempster
dispersalrate(d)
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
bistability

Order of
events
DE
R
DE
RD
E R
classification
Dempster
Zero dispersal when
or
Total dispersal when  2c g 
 
 
21/2
2 3 2
21/2
2 2 3
2
1 1 4 1
2 2
c
  
  
 
    
 
 
   
 
 
 
1/2
2 2 31/2
2 3 2 2
2
21/2
2 3
4 1
2 1 1 1 1
1
2 1
c
c c
c
c
 
  


 
 
     
 
 


DE
R
Ravigné
D
E R
Levene
DE
R
Dempster
Evolution towards total philopatry
Intermediate dispersal rates are possible
Branching happens for negatively autocorrelated
environments
Either total philopatry or total dispersal
Bistability can happen

Baker’s law revisited
with Pierre-Olivier Cheptou

Words from Baker (1955)
“With a self-compatible individual a single
propagule is sufficient to start a sexually
reproducing colony”
“Self-compatible flowering plants are usually
able to form seeds in the absence of visits from
specialised pollinating insects, which may be
absent from the new situation”

Baker’s law
Principle: selfing provides reproductive
assurance without pollination
Expectation: island species should be selfers
(verbal model)
Corollary belief: selfers disperse more

Self-fertilization & dispersal: two major traits
Modifications of these traits are expected to
greatly affect fitness
Their evolutions are often considered separately
in theoretical models

Classical selection pressures on self-fertilization:
– higher transmission rate (Fisher 1941)
– pollination uncertainty (Baker 1955)
– inbreeding depression (Lande & Schemske 1985)

Common selection pressures?
catastrophes
temp. variability
heterogeneity
dispersal rate ESS
pollination
uncertainty
selfing rate ESS
pollinator
dynamics

Infinite island model with large populations
Fluctuations in pollination, e
Inbreeding depression, δ
Migrant survival, q
Two traits under selection (s,d)
δ
q
d
1-e
1 - s
e
Cheptou & Massol (2009)

In terms of life cycles…
… with zero autocorrelation
(with autocorrelation: see Massol & Cheptou 2011)
DE
R
Ravigné

(1 )s  
(1 )
1
2
1
2
s
s
s  
 



1 d 
1 d 
d
d
q
q
/mutant residentw w
/mutant residentw w
reproduction dispersal regulation
e
1 e
W

Scenario I
dispersalrate(d)
selfing rate (s)
“dispersal/outcrossing” syndrome
*
*
0
1 (1 )
s
e
d
q e


 

Scenario II
dispersalrate(d)
selfing rate (s)
“no dispersal/selfing” syndrome
(may be mixed selfing)*
*
2
2 1
0
e
s
d
e  



Scenario III
dispersalrate(d)
Both syndromes exist (bistability)
2 ESS (evolutionary stable eq.)
1 evolutionary repellor (saddle)
selfing rate (s)

1. Three scenarios for evolutionary equilibria
2. Two syndromes for trait associations:
dispersal/outcrossing vs. no dispersal/partial selfing
goes against Baker’s law
3. Under scenario III (two ESS), bistability with
Ravigné life cycles

Understanding Baker’s law:
– need separating extrinsic (e.g. pollinators) vs.
intrinsic (e.g. mate density) determinants of pollen
limitation
– the asymmetry of dispersal (mainland/island vs.
metapopulation) dictates the reproductive value of
“island” populations
– with local regulation, evolution will not “optimize”
Massol & Cheptou (2011)

Informed dispersal in an uncertain
world
with Florence Débarre

Informed dispersal and life cycles
• Conditioning dispersal decision on patch “quality”
may decrease the indirect cost of dispersing
• First theoretical argument using two-patch
models (McPeek & Holt 1992)
• With almost static environments and bad cues,
dispersal is not conditioned on current perceived
patch quality (McNamara & Dall 2011)
→ bang-bang dispersal (all or nothing), with no
polymorphism (informed dispersal vs. polymorphism)

Informed dispersal
Perceived
environment
True
environment
Error ε
Emigration rate
strategy (ei)
Dispersal
strategy (di)
Statistical
expectation
 1 2 21d e e   
 2 1 11d e e   
after McNamara & Dall (2011)

Ravigné et al.’s
classification
Ravigné RavignéLevene
E E
E ER
R R RD
D
D D
Order of events

Information & life cycles
Ravigné et al.’s
classification
E E
E ER
R R RD
D
D D
Order of events
evolution towards
philopatry

Ravigné et al.’s
classification
E E
E ER
R R RD
D
D D
Order of events
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
dispersalrate(ei)
e1 (out of bad patches)
e2 (out of good patches)
Results with perfect cue

Ravigné et al.’s
classification
E E
E ER
R R RD
D
D D
Order of events
dispersalrate(ei)
Results with imperfect cue
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
branching

Ravigné et al.’s
classification
E E
E ER
R R RD
D
D D
Order of events
dispersalrate(ei)
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
branching
Results with
perfect cue

Ravigné et al.’s
classification
E E
E ER
R R RD
D
D D
Order of events
dispersalrate(ei)
Results with
imperfect cue
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
branching

Making sense of all of that…
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
dispersalrate(ei)
temporal autocorrelation in patch state ( φ )temporal autocorrelation in patch state ( φ )
be regulated where it’s
easy…
… & go find a better place
to reproduce
E
ER
RD D
Results with
perfect cue

Making sense of all of that…
dispersalrate(ei)
temporal autocorrelation in patch state ( φ )temporal autocorrelation in patch state ( φ )
be regulated where it’s
easy…
E
ER
RD D
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
… & go find a better place
to reproduce
Results with
imperfect cue

Informed dispersal and life cycles
Take-home messages:
– informed dispersal follows different rationales with
different life cycles
– disruptive selection can happen in an informed
dispersal model
Not shown here but true:
– bang-bang dispersal strategies happen for some
parameter values only, and are not often robust to
the cost of dispersal
– bistability can occur with certain life cycles

Final take-home messages
1. Environmental variability can affect the
evolution of dispersal in a variety of ways
2. The joint evolution of dispersal and other
traits (e.g. selfing) yields interesting, bistable
patterns that deserve more attention
3. Informed dispersal and dispersal
polymorphisms are not mutually exclusive

Discussion
• Evolution of dispersal: “mature topic”
• Combination of factors determining selection
• Feeds back on other traits (e.g. local
adaptation, selfing)
→ understanding the evolution of dispersal
might be key to understanding patterns
(diversity, functioning, resilience…) in spatially
structured models

Acknowledgements
Ongoning collaborations on this topic:
P.-O. Cheptou, P. David, F. Débarre, A. Duputié, P. Jarne, F. Laroche, T. Perrot
Any kind of help & comments:
J. Auld, N. Barton, J. C. Brock, M. Burd, J. Busch, V. Calcagno,
J. Chave, M. Daufresne, C. Eckert, D. Fairbairn, S. Gandon, I. Hanski,
J. Hermisson, K. Holsinger, J. Kelly, M. Leibold, R. Morteo,
N. Mouquet, I. Olivieri, M. Palaseanu-Lovejoy, O. Ronce, D. Schoen
Usual suspects:

François Massol - présentation MEE2013

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