Download - 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
Patterns (direct): Processes:
kin competition
inbreeding
catastrophes
temp. variability
heterogeneity
cost of dispersal
dispersal ESS
polymorphism?
The larger picture
Patterns (direct): Processes:
kin competition
inbreeding
catastrophes
temp. variability
heterogeneity
cost of dispersal
dispersal ESS
polymorphism?
association with other traits
The larger picture
Patterns (direct): Processes:
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?
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
E E E
R R
R R R R
Simple life cycles Complex life cycles Modelling complexity
Simple life cycles
Classification of life cycles extended from Massol (2013)
Order of events
D D D D D
D E E E
E E E
R R
R R R R
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
D E
R
D E
R D
E R
Levene Ravigné Ravigné et al.’s classification
Dempster
Evolution of dispersal Massol & Débarre (in prep)
Order of events
D E
R
D E
R D
E R
Levene Ravigné Ravigné et al.’s classification
Dempster
evolution towards philopatry
Evolution of dispersal Massol & Débarre (in prep)
Order of events
D E
R
D E
R D
E R
Levene Ravigné Ravigné et al.’s classification
Dempster
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
dis
pe
rsal
rat
e (
d )
temporal autocorrelation in patch state ( φ )
Bra
nch
ing
Evolution of dispersal Massol & Débarre (in prep)
Order of events
D E
R
D E
R D
E R
Levene Ravigné Ravigné et al.’s classification
Dempster
Zero dispersal when Total dispersal when Branching when
2
1/2
2 31
gc
g g
2c g
0
Evolution of dispersal Massol & Débarre (in prep)
Order of events
D E
R
D E
R D
E R
Levene Ravigné Ravigné et al.’s classification
Dempster
dis
pe
rsal
rat
e (
d )
temporal autocorrelation in patch state ( φ )
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
bis
tab
ility
Evolution of dispersal Massol & Débarre (in prep)
Order of events
D E
R
D E
R D
E R
Levene Ravigné Ravigné et al.’s classification
Dempster
Zero dispersal when or Total dispersal when 2c g
21/2
2 3 2
21/2
22 3
21 1 4 1
2 2c
1/2
2 2 31/2
2 3 2 2
2
21/2
2 3
4 12 1 1 1 1
1
2 1
cc c
c
c
Evolution of dispersal Massol & Débarre (in prep)
D E
R
Ravigné
D
E R
Levene
D E
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
Baker’s law revisited
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
Baker’s law revisited
Classical selection pressures on self-fertilization:
– higher transmission rate (Fisher 1941)
– pollination uncertainty (Baker 1955)
– inbreeding depression (Lande & Schemske 1985)
Baker’s law revisited
Common selection pressures?
catastrophes
temp. variability
heterogeneity
dispersal rate ESS
pollination uncertainty
selfing rate ESS
pollinator dynamics
Baker’s law revisited
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)
Baker’s law revisited Cheptou & Massol (2009)
In terms of life cycles…
… with zero autocorrelation
(with autocorrelation: see Massol & Cheptou 2011)
D E
R
Ravigné
Baker’s law revisited
(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
Cheptou & Massol (2009)
Baker’s law revisited
Scenario I
dis
pe
rsal
rat
e (
d)
selfing rate (s)
“dispersal/outcrossing” syndrome
*
*
0
1 (1 )
s
ed
q e
Cheptou & Massol (2009)
Baker’s law revisited
Scenario II
dis
pe
rsal
rat
e (
d)
selfing rate (s)
“no dispersal/selfing” syndrome
(may be mixed selfing) *
*
2
2 1
0
es
d
e
Cheptou & Massol (2009)
Baker’s law revisited
Scenario III
dis
pe
rsal
rat
e (
d)
Both syndromes exist (bistability) 2 ESS (evolutionary stable eq.) 1 evolutionary repellor (saddle)
selfing rate (s)
Cheptou & Massol (2009)
Baker’s law revisited
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
Cheptou & Massol (2009)
Baker’s law revisited
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)
Classification of life cycles
Ravigné et al.’s classification
Ravigné Ravigné Levene
E E
E E R
R R R D
D
D D
Order of events
Information & life cycles
Ravigné et al.’s classification
Ravigné Ravigné Levene
E E
E E R
R R R D
D
D D
Order of events
evolution towards philopatry
Massol & Débarre (in prep)
Information & life cycles
Ravigné et al.’s classification
Ravigné Ravigné Levene
E E
E E R
R R R D
D
D D
Order of events
Massol & Débarre (in prep)
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
dis
pe
rsal
rat
e (
ei )
temporal autocorrelation in patch state ( φ )
e1 (out of bad patches)
e2 (out of good patches)
Results with perfect cue
Information & life cycles
Ravigné et al.’s classification
Ravigné Ravigné Levene
E E
E E R
R R R D
D
D D
Order of events
Massol & Débarre (in prep)
dis
pe
rsal
rat
e (
ei )
temporal autocorrelation in patch state ( φ )
Results with imperfect cue
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
e2 (out of good patches)
bra
nch
ing
e1 (out of bad patches)
Information & life cycles
Ravigné et al.’s classification
Ravigné Ravigné Levene
E E
E E R
R R R D
D
D D
Order of events
Massol & Débarre (in prep)
dis
pe
rsal
rat
e (
ei )
temporal autocorrelation in patch state ( φ )
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
e2 (out of good patches)
e1 (out of bad patches)
bra
nch
ing
Results with perfect cue
Information & life cycles
Ravigné et al.’s classification
Ravigné Ravigné Levene
E E
E E R
R R R D
D
D D
Order of events
Massol & Débarre (in prep)
dis
pe
rsal
rat
e (
ei )
temporal autocorrelation in patch state ( φ )
Results with imperfect cue
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
e1 (out of bad patches) b
ran
chin
g
e2 (out of good patches)
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
dis
pe
rsal
rat
e (
ei )
temporal autocorrelation in patch state ( φ ) temporal autocorrelation in patch state ( φ )
e1 (out of bad patches)
e2 (out of good patches)
e2 (out of good patches)
e1 (out of bad patches)
Massol & Débarre (in prep)
be regulated where it’s easy…
… & go find a better place to reproduce
E
E R
R D D Results with perfect cue
Making sense of all of that… d
isp
ers
al r
ate
( e
i )
temporal autocorrelation in patch state ( φ ) temporal autocorrelation in patch state ( φ )
Massol & Débarre (in prep)
be regulated where it’s easy…
E
E R
R D D
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
e2 (out of good patches)
e1 (out of bad patches)
0.5 0.0 0.5 1.0
0.2
0.4
0.6
0.8
1.0
e1 (out of bad patches)
e2 (out of good patches)
… & 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
Massol & Débarre (in prep)
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: