Pollinator-Plant –Herbivore System

Evolution of Specialization in a

Pollinator-Plant –Herbivore System

Kylafis Grigoris, Georgelin Ewen,

Loeuille Nicolas

Evolution of Specialization according to existing theory

• Shape of trade-off function between specialization rates (e.g. Levins 1968, Kisdi 2001)

• Density-dependent mechanisms (e.g. local density regulation:

Rueffler et al 2004; Ravigne et al 2009)

i) Convergence Stable ii) Convergence Unstable (Reppelor)

: Singular Strategy

S_R1 S_R1

S_R2 S_R2

R₁ C

R₂

C R₁

C R₂ or

The Ecological Model

1

1 dM b m n P b m n1 1 m1 1 2 2 m2 2P cMM dm

M dt    

2

1 1

1 1 1 1 1

1

dP r m n M h n H

p m h

P dt   

1 2

2 2 2 2 2

2

dP r m n M h n H

p m h

P dt   

1

1 1 1 1 2 2 2 2

dH a h n P a h n P c H d

h h H h

H dt    

Graphical Representation of Stable M-H Coexistence

• Plants are limiting the growth function (ZNGI) of their Pollinator (M) and their Herbivore (H)

• The Pollinator exerts a (+) impact on Plants/ The Herbivore exerts a (-) impact on them

Plant 1 (P₁) Plant 2 (P 2)

R^* =

R f

P c m

m a f

a f dN

C = C_M

Plant 1 (P₁)

R^* =

R f

P c m

m a f

a f dN

C =

C_H

Plant 2 (P 2)

+ +

- -

Pollinator mostly limited by P_1, Stronger impact on P₁

Herbivore mostly limited by P₂ Stronger impact on P₂

Graphical Representation of Stable M-H Coexistence

• Two Stability Conditions (but not the only ones) : i) H and M are limited by a different plant species (P₂

and P₁, respectively )

ii) H and M exert the strongest impact on their most limiting plant resource

Plant 1 (P₁)

R^* =

R f

P c m

m a f

a f dN

C =

C_H

Plant 2 (P 2)

C_M

H+M

H H M

M : Stable

Equilibrium Point

Stable Interaction Configuration

Pollinator

Plant 1

Herbivore

Plant 2

: Strong Interaction

: Weak Interaction

+ +

- -

Question

How the rates of specialization of the H (h

, h

) affect the (co)evolution of the rates of

specialization of the M (m

, m

):

Scenario A: h

is High and h

is Low

Scenario B: h

is Low and h

is High

Single Evolution of the Pollinator

• Convergence stability of the singular strategy (m₁^*,m₂^*) depends on the following condition:

< 0

m₂

m₁ (rate of specialization on P₁)

: Singular Strategy (m₁^*,m₂^*)

* *

* 1 * 2

2 * 1 *

1 1

P P

P P

m m

Ao Sm

    

 

   

  

Trade-off Shape

(weak trade-off = negative value) Density-Dependent term

(rate of Specialization on P 2)

Single Evolution of the Pollinator under Scenario A (h

high/h

low)

Pollinator

Plant 1

Herbivore

Plant 2

Single Evolution of the Pollinator under Scenario A (h

high/h

low)

Pollinator

Plant 1

Herbivore

Plant 2

h₁ high

Single Evolution of the Pollinator under Scenario A (h

high/h

low)

Pollinator

Plant 1

Herbivore

Plant 2

h₁ high

An increase in m₁^*

* 1

0

1* P

m ^





Single Evolution of the Pollinator under Scenario A (h

high /h

low)

Pollinator

Plant 1

Herbivore

Plant 2

h₁ high

An increase in m₁^*

* 1

0

1* P m ^





* 1

0

2* P m ^





* *

1 1

* *

* 1 * 2 0

2 1

P P

P P

m m ^

 

  

Conclusion: Convergence Stability is

compromised  evolution of M towards a maximum rate of specialization on P₁ (i.e., max. m₁ and m₂=0 )

Single Evolution of the Pollinator under Scenario B (h

high/h

low)

Pollinator

Plant 1

Herbivore

Plant 2

Single Evolution of the Pollinator under Scenario B (h

high/h

low)

Pollinator

Plant 1

Herbivore

Plant 2

h₂ high

Single Evolution of the Pollinator under Scenario B (h

high/h

low)

Pollinator

Plant 1

Herbivore

Plant 2

h₂ high

An increase in m₁^*

* 1

0

1* P m ^





Single Evolution of the Pollinator under Scenario B (h

high/h

low)

Pollinator

Plant 1

Herbivore

Plant 2

h₂ high

An increase in m₁^*

* 1

0

1* P m ^





* 1

0

2* P m ^





P2*¶P 1*

¶m₁^* -P

1*¶P 2*

¶m₁^*

Conclusion: Convergence stability is weakly compromised or even reinforced  evolution of M towards intermediate rates of specialization on P₁ and on P₂ (i.e., Generalism)

Small (+) or even (-)

Conclusions

• Ecological stability of the M-P

-P

-H system requires a certain degree of specialization of M and H on P

and P

• The degree of specialization in the Herbivore affects the evolution of the degree of

specialization in the Pollinator (and vice versa)

via density-dependent mechanisms.