Cooperation: Interests overlap

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Cooperation Interests overlap Mate choice and
mating systems Interests diverge Interests
conflict
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War of Attrition or the Waiting Game
Question How much time do you spend waiting for
females to arrive?
Answer It depends on how long other males are
waiting...
Too short ... longer waiting males claims all
late arriving females But if all males wait a
long time, it pays to leave early and claim
females arriving at new cowpats
Male Dung flies guard fresh cowpats
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Winners are decided simply by a contest involving
waiting (or displaying) for different amounts of
time War of Attrition
Imagine two males, A and B, that wait time XA and
XB, respectively, and assume XA gt XB, that is
male A wins the contest
Payoff to A V cB Payoff to B - cB
where V value of the resource and c is the
cost associated with waiting
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Payoff to A V cB Payoff to B - cB
Obviously B would have done better if XB gt XA,
so.... if XA 10 sec, then XB should be 10.1
sec, but if XB 10.1 sec, then XA should be
10.2........
Choose a random waiting time in other words, be
unpredictable
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ESS Distribution of waiting times as a function
of resource value
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Define two strategies HAWK and DOVE
HAWK Always fight to injure or kill their
opponents at a potential risk of
injury to themselves
DOVE Display as if to fight, but never engage
in a fight
Payoffs Winner 50 Injury -100 Loser
0 Display -10
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Payoffs Winner 50 Injury -100 Loser
0 Display -10
Payoff matrix

• Hawk meets Hawk
• Half the encounters an individual wins
• and half it loses and sustains injury

Payoff (1/2)?50 (1/2)?(-100)
Hawk
Dove
-25
Hawk
Dove
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Payoffs Winner 50 Injury -100 Loser
0 Display -10
Payoff matrix

• Hawk meets Dove
• Hawk beats Dove Always
• Dove always immediately retreat when encountering
  Hawk

Payoff (1)?50
Hawk
Dove
-25
50
Hawk
Dove
10
Payoffs Winner 50 Injury -100 Loser
0 Display -10
Payoff matrix

• Dove meets Hawk
• Dove loses to Hawk - Always

Payoff (1)?(0)
Hawk
Dove
-25
50
Hawk
Dove
0
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Payoffs Winner 50 Injury -100 Loser
0 Display -10
Payoff matrix

• Dove meets Dove
• There is always a display and half the
• encounters an individual wins

Payoff (1/2)?(50-10) (1/2)?(0-10)
Hawk
Dove
-25
50
Hawk
Dove
0
15
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Hawk
Dove
What is the ESS?
-25
50
Hawk
h frequency of Hawks (1-h) frequency of
Doves
Mean Hawk Payoff -25(h) 50(1-h) Mean Dove
payoff 0(h) 15(1-h)
Dove
0
15
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The Speckled Wood Butterfly treats patches of
sunlight as territories and immediately set up
shop when they come upon one
If an intruder arrives it immediately retreats
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In lions too, ownership of females in estrus
appears to be decided on who gets there first.
Fights are very rare, and a bourgeois-like
strategy holds, probably b/c fights are
potentially very costly and the benefits low
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In nature, contests are much more complex than
simple Hawk, Dove, Bourgeois strategies
The value of conceptualizing these games is to
make clear the best fighting strategy of an
individual depends on the strategies of others
a Game
The ESS depends on the relative pay-offs in the
game (how individuals value resources and pay
costs), and thus it highlights what kinds of data
we need to gather

• Other points theoretical treatment highlights
• Avoidance of serious fights
• Respect for ownership

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We want to continue these themes
today, Specifically, (1) Individuals often
differ in their fighting ability (2)
Assessment of fighting ability often follows
ritualized behaviors/displays (3)
Differences in Resource Value (inherently or thru
individual differences)
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Males reproductive success depends on fighting
ability the strongest stags maintain harems and
huge rep. success
But at a cost almost all males suffer small
injuries, 20-30 become permanently injured,
e.g., broken leg, blinded by antler
These risks are minimized by opponents assessing
each others fighting potential so as to attempt
to fights the fights that can be won.
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Ritualized Red Deer assessment of opponents
strength
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Ritualized contests of strength in Copperheads
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Dall sheep, Buffalo, and other ungulates assess
strength thru head-on clashes
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• What we can conclude from these examples and
  others
• Displays used in assessment appear to be reliable
  signals of size and strength,
• e.g., vocal displays, pushing and shoving
• Display also must involve some degree of
  cooperation after all it should pay for
• both individuals to avoid a fight if at all
  possible and they have a common interest in
• obtaining info about each other
• (3) Contests often proceed through a set pattern
  of assessment i.e., ritualized

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The Sequential Assessment Model (Enquist and
Leimar)
Assessment is analogous to statistical
sampling...One bout contains random error and
so to increase the accuracy of assessment
requires repeated estimations involving contests
that become increasingly dangerous
When you realize your opponents strength exceeds
yours Give up
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a - Lateral Orientation, fins erect b
Tail-beating c Frontal Orientation d Biting
e Mouth Wrestling f Loser gives up and
signals by changing color, fins down
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Individuals may give-up after any stage,but as
size differences decreases individual aggression
escalates through the series
20 min contests between evenly matched rivals
Brief matches between asymmetric rivals
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We want to continue these themes
today, Specifically, (1) Individuals often
differ in their fighting ability (2)
Assessment of fighting ability often follows
ritualized behaviors/displays (3)
Differences in Resource Value (inherently or thru
individual differences)
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When do we expect to see contests settled by
arbitrary convention of ownership (?) as opposed
to real differences in fighting ability?
Asymmetric war of Attrition
Bourgeois strategy No specified relationship
between ownership and fighting ability,
its an arbitrary
convention However, what if animals could
control their risk along a continuum,
adjusting for differences in strength and how
they value the resource?
If thats the case, Bourgeois is no longer an ESS
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V resource value (benefit) K rate of accruing
costs correlated to fighting ability
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Steven Austads work on Bowl-and-Doily Spiders
(Frontinella pyramitela)
Once mature, males feed very little and spend
most of their time looking for females. They only
live 3 days as mature males.
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Male copulation Rapid diminishing returns
Leads to Asymmetry in the value of the female to
resident and intruder males
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War of Attrition Hawk-Dove Hawk-Dove-Bourgeois
Sequential Assessment Asymmetric War of Attrition
War of Attrition Hawk-Dove Hawk-Dove-Bourgeois
Sequential Assessment Asymmetric War of Attrition
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Badges of Status The size of the black bib in
male house sparrows signals dominance rank
and eliminates undo fighting between males
Captain
Lieutenant
Private
Sergeant
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Summary

1. Its a Gameactually several types of games
2. Simple everything else equal Games become more
   complicated
3. No one wants to fight, but everyone wants to
   winESS will be a balance between these two