EVOLUTION OF DECEIT ASA SECOND-LINE DEFENSE:

Ht+1 = Hter-aPt

Pt+1= Ht(1-e-aPt)

A QUESTION POSED:

Could a mutant fake marker invade ofpopulation of “honest” caterpillars?

REFINE QUESTION

Could a mutant fake marker invade ofpopulation of “honest” caterpillars thatemploy hiding as a first line ofdefense?

SCENARIO

Parasitoid

Host

Detection

Acceptance

Hiding

False-marking

THE CHROMOSOME:2 loci, 4 alleles

Hide

• High• Medium• Low• No

False Mark

• Strong• Medium• Weak• None

THE CHROMOSOME

A binary string that represents thephenotype that expresses a specificstrategy:e.g. 1 1 0 01 1 translates into good hider0 0 translates into no mark

AN EXAMPLE

• Strategy 0010 has a value of 2i.e. 0*1 + 1*2 + 0*4 + 0*8

• Strategy 1001 has a value of 9 i.e.1*1 + 0*2 + 0*4 + 1*8

SIMULATION

• Deterministic• Some proportion of hosts are found

based upon relative hiding value• Some proportion of found hosts

are attacked based upon markstrength and wasp rules

UNLIKE PREY-

Hosts don’t disappear after attackbut they may change identity

FITNESS IS DETERMINEDBY:

• Escape from parasitoids• Cost of defense

Hiding≥ false-mark

THREE SCENARIOS:

Parasitoids are hard wired (frequencyindependent)

Parasitoids are flexibleParasitoid’s flexibility evolves

STARTING POPULATION

S M W N S M W N S M W N S M W N0.0

0.1

0.2

0.3

FREQ

UENC

Y

MARK

HIDE HIGH MEDIUM LOW NO

S: STRONGM: MEDIUMW: WEAKN: NONE

FREQUENCY INDEPENDENT

S M W N S M W N S M W N S M W N0.0

0.1

0.2

0.3

0.4

0.5

0.6

FREQ

UENC

Y

MARK

H IDE HIGH MEDIUM LOW NO

S: STRONGM: MEDIUMW: WEAKN: NONE

PARASITOID ACCEPTANCEPLASTICITY

• Within generation as number of“parasitized” hosts increases

• Among generations as fake markerphenotypes change in frequency

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Proportion of "Parasitized" Hosts

Ten

den

cy t

o

"Su

perp

ara

siti

ze"

PLASTIC PARASITES

S M W N S M W N S M W N S M W N0.0

0.1

0.2

0.3

0.4

0.5

FREQ

UENC

Y

S: STRONGM: MEDIUMW: WEAKN: NONE

MARK

H IDE HIGH MEDIUM LOW NO

THE NEW GA

• Actually two GA’s, one for the hostpopulation and one for the parasitoidpopulation

• The parasitoid chromosome has one genefor sensitivity to mark strength and anotherfor sensitivity to mark frequency in theenvironment

PARASITES EVOLVE

FIT(p) =a Hfh + Ffhop, n + Dfdop, d

n=1

N

ÂÊ Ë Á ˆ

¯

1+ a Hto

+Fop,n

n=1

N

Âto

+F 1 - op, n( )

n=1

N

Âtr

+Dop, d

n=1

N

Âto

+D 1- op, d( )

n=1

N

Âtr

Ê

Ë

Á Á Á

ˆ

¯

˜ ˜

PARASITOID’S PAYOFF

ACCEPT• FIT(a | p) = fp -to

• FIT(a | h) = fh - to

REJECT• FIT = -tr

PARASITES EVOLVE

1 2 3 4 5 6 7 80

100

200

Genotypes (sensitivity >>)

Frequ

ency

fp = 0.1fhtr = 0.1 to

fp = 0.6 fhtr = 0.6 to

x mark = 4.9

x mark = 2.5

AN INSIGHT

False marking as a second line ofdefense only spreads through theprey population under limitedcircumstances

(our test is conservative!)

HOST DYNAMICSgn t + 1( ) = gn t( ) 1 - m( )

where m = gnan1

gnn =1

N

 aT

rmT

bn,sÊ Ë

ˆ ¯ q

where an = hide genotype n, mT

= fraction of marked hosts in population T,

bn = false - mark genotype n,r = parasitoid responses = parasitoid response shape pararameterq = proportion of hosts encountered per epoch