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

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


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


Order of events

D E

R

D E

R D

E R


Dempster

evolution towards philopatry


Order of events

D E

R

D E

R D

E R


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


Order of events

D E

R

D E

R D

E R


Dempster

Zero dispersal when Total dispersal when Branching when

2

1/2

2 31

gc

g g

2c g

0


Order of events

D E

R

D E

R D

E R


Dempster

dis

pe

rsal

rat

e (

d )


0.5 0.0 0.5 1.0

0.2

0.4

0.6

0.8

1.0

bis

tab

ility


Order of events

D E

R

D E

R D

E R


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


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


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)

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


(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

dis

pe

rsal

rat

e (

d)

selfing rate (s)

“dispersal/outcrossing” syndrome

*

*

0

1 (1 )

s

ed

q e



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



Scenario III

dis

pe

rsal

rat

e (

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)

Classification of life cycles


Ravigné Ravigné Levene

E E

E E R

R R R D

D

D D

Order of events

Information & life cycles



E E

E E R

R R R D

D

D D

Order of events

evolution towards philopatry

Massol & Débarre (in prep)




E E

E E R

R R R D

D

D D

Order of events


0.5 0.0 0.5 1.0

0.2

0.4

0.6

0.8

1.0

dis

pe

rsal

rat

e (

ei )


e1 (out of bad patches)

e2 (out of good patches)

Results with perfect cue




E E

E E R

R R R D

D

D D

Order of events


dis

pe

rsal

rat

e (

ei )


Results with imperfect cue

0.5 0.0 0.5 1.0

0.2

0.4

0.6

0.8

1.0


bra

nch

ing





E E

E E R

R R R D

D

D D

Order of events


dis

pe

rsal

rat

e (

ei )


0.5 0.0 0.5 1.0

0.2

0.4

0.6

0.8

1.0



bra

nch

ing

Results with perfect cue




E E

E E R

R R R D

D

D D

Order of events


dis

pe

rsal

rat

e (

ei )



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


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 )






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 )


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



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


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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