EVOLUTION OF DECEIT AS A SECOND-LINE DEFENSEggbaker/reference/modeling/week3/GA.2.pdf · EVOLUTION...
Transcript of EVOLUTION OF DECEIT AS A SECOND-LINE DEFENSEggbaker/reference/modeling/week3/GA.2.pdf · EVOLUTION...
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