eötvös university, budapest · 2017. 12. 2. · boza, gergely international intitute for applied...

Boza, Gergely

International Intitute for Applied Systems Analysis

(IIASA) EEP, Laxenburg

Eötvös University, Budapest

[email protected]

[email protected]

mailto:[email protected]:[email protected]

• The evolution and stability of mutualism and cooperation

• Continuous reactive investment games

• Conditional, context-dependent cooperation

• Partner choice mechanisms

• Public Good Games with threshold effects

• Division of labor in collective actions

• Stability of microbiomes

• Quorum sensing

• Coexistence and cooperation in early replicator communities

I am interested in...

1.

service

service

benefit cost

cost benefit

2. Interacting individuals

Direct reciprocity

Reciprocity in humans: Economic exchanges

Reciprocity in humans: food sharing among hunter-gatheres

(Aché in Paraguay)

Reciprocity in animals: food sharing in vampire bats (Desmodus rotundus)

Reciprocity in plants, fungi, bacteria: nutritional mutualisms

Conditional mutualistic investments

Rhizobium etli

Analysis of the metabolic network • 387 reactions

• 371 metabolites

• 363 genes

Conditional mutualistic investments

Return

investment

Investment

t >1, iterative game

The model

, , 0 , ,( )t i j t i jC I C I

Investment in the 1st round

, , 0 1 , ,( ) [1 exp( )]t j i t j iB I B B I

, , , , , ,( ) ( )t i j t j i t i jp B I C I

iji uI ,,1

jitiijit pcuI ,,1,, Investment in the 1< rounds

It = α + c • payofft-1 α1 = α2= const. > 0

The evolution and stability of conditional investments

c1

c2

u

• c zero isocline

• u zero isocline

c

The evolution and stability of conditional and unconditional investments

Unconditional investment, u

Conditio

nal in

vestm

ent, c

(closely) monomorphic population

The investment cycle

IBM simulation results

0

20

40

60

80

100

0 20000 40000 60000 80000 100000 120000 140000

0

20

40

60

80

100

0 20000 40000 60000 80000 100000 120000 140000

0

20

40

60

80

100

0 2000 4000 6000 8000 10000 12000 14000

Time

Pa

yo

ff


Conditio

nal in

vestm

ent, c

Investment cycle phases

, ,

1

1( )

i i

J

i x i i j i x x

j

g x P xJ

Investment cycle and phase polymorphism


Co

nd

itio

na

l in

ve

stm

en

t, c

, ,

1

1( )

i i

J

i x i i j i x x

j

g x P xJ

0.1

0.001

1e-5

0

0 π/2 π 3π/2

Phase of the investment cycle

(φ)

Fre

quency o

f p

hase c

ate

gory


Conditio

nal in

vestm

ent, c

Investment cycle and phase polymorphism

Strategy diversity and phase polymorphism stabilizes cooperative investments

Species A

Species B

Introducing spatial population structure in interspecific reciprocal investment game

investments investments

Spatial bubbles and the dynamic spatial mosaic structure

Species A Species B

Spatial bubbles and invasion dynamics

R m

m R

coexistence

clu

ste

r 1.

clu

ste

r 2.

boundary

log u

log c

Summary

• Cooperative investments are unstable for medium levels of

reciprocity

• Above a threshold, evolution drives strategy pairs through

investment cycles temporarily

• Mutation-generated polymorphism of strategies leads to

phase diffusion along the investment cycle

• Strategy diversity (polymorphism) stabilizes investment

levels at the population level

• Spatial mosaic structure further promotes mutualism stability,

through a mechanism that is fundamentally different from the

role of space in intraspecies cooperation

Non-linear benefit functions

and threshold effects in nature

lions (Panthera leo)

from Packer et al. (1990)

and Stander (1992)



Harris’ Hawk (Parabuteo unicinctus)

from Bednarz (1988)

Brown-Necked Raven (Corvus ruficollis)

Yosef & Yosef (2009)



killer whales (Orcinus orca)

humpback whales (Megaptera novaengliae)

from Leighton et al. (2004)



from Hibbing et al. (2010)

The Threshold Public Good Game

Number of cooperators

Score

0

R

T

Threshold value (T)

D

C

Threshold Public Good Game

Threshold value (T)

Group size (N)

Cost of cooperation (C(x))

Benefit of cooperation (b)

focal CC CD DD

C b-c b-c -c

D b 0 0

partners

Well–mixed population

3

1

Individual willingness to cooperate (x) is a continuous, evolving trait.

x = 1 always cooperate

x = 0 always defect

2

following Bach et al. (2006)

x -axis

Polymorphic equlibria, bifurcation, hysteresis point

1

0

0.5

0 1 0.5

x

C(x)

C(x) – cost of cooperation

T (threshold value) =2

Stable fix points

Instable fix points

N (group size) = 3

4 5 6

7 9

Group size

s – steepness

(n - T) * (- s) P (x) =

1

1 + e

N= 5

T= 2 3 4 5

number of cooperators in the group

pro

bab

ilit

y o

f p

ub

lic

go

od

pro

du

ced

Hysteresis point and the sigmoid return function

Group cooperation and inter-group conflict

Population structure and multilevel selection

time

x a 0 1 1

x a 0 1 1

x a 0 1 1

x a 0 1 1

N =5

T = 3

(DD) (CC)

(CD) (CD;DC)

x – willingness to cooperate during cooperative hunting

a – willingness to cooperate during group defence

Summary

• Non-linear payoff functions are more suited for many

phenomena in nature

• Stable polymorphism, coexistence of cooperators and

defectors

• Spatial population structure promotes cooperation

• Division of labor in multi-public good games

• Context dependent cooperation (cooperators vs. laggards)

assuming intra-group cooperation and inter-group conflict

• Not all non-cooperators are in fact „full” cheaters

Spread of beneficial and parasitic microorganisms in host mediated microbiomes

Non-linear dosage-effect function of antibiotics

from Hibbing et al. (2010)

Leaf-cutter ant microbiome

Env, Env, Env, Env, Env, Int, Env,

pr/24

i i j i i i i i it t t t t t t tj nn

DA A A A A A A t

x

Int, Int, Env, Int, Int, i i i i i i i i

t t t t t tA A A A A t

A+R+ A+R+

0 pr AR( ) ir r r t c

Dynamics of the antibiotics in the environment

Intracellular dynamics of the antibiotics

Reproduction rate of the producer (A+R+)

Reproduction rate of parasite (A-R-)

A-B- A-B- Int,

0 pr ( ) ( , , ) i

ir r r t T A

Modelling antibiotics producing bacteria

Antibiotics producing vs parasitic bacteria

A+R+

A-R-

Individuals Antibiotics

Antibiotics producing vs parasitic bacteria

[email protected]

[email protected]
mailto:[email protected]:[email protected]

eötvös university, budapest · 2017. 12. 2. · boza, gergely international intitute for applied...

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