1. Chapter 17: Signal costs and constraints
Lecture #19
Chapter 17: Signal costs and constraints
Chapter 19: Game theory
4/14/11

2. For Tuesday
Put up a draft of your wiki introduction. This should explain what your topic is, what organisms you might be focusing on and why it is important for communication.
Make links or headers for the three sections that will follow in coming weeks

3. In the interest of time We will skip Chapter 18 : Signal design
(Chapter 20: Signal honesty??)
Final exam Q (Katie M - 18)
You now get a free pick of chapters

4. Today
Sender
Costs and constraints
Receiver
Evolutionary game theory

5. Tradeoffs between correct detection and false alarms
Want to maximize Phit and minimize Pfalse alarm
Can send more discreet signals
Can better discriminate signals
Will depend on costs to senders vs receivers
Two kinds of males

6. Signaling costs Signaling only occurs if
Benefits > Costs
What are some of the possible costs?

7. Sender signaling costs
Conspicuousness to predators / parasites
Energetic costs of signaling
Time lost
Conflict with original function

8. Sender costs 1. Conspicuousness
Visual
Auditory
Chemical

9. 1a. Visual conspicuousness - guppies
Variation in coloration

10. 1a. Visual conspicuousness
Females prefer to mate with brightest males
These males are also more conspicuous to predators (female uses color to indicate male health)
If more predators, males can not afford to be as colorful
Variation in guppy colors btn populations with different predators
Alternate balance of natural and sexual selection

11. Visual systems of guppies and predators
COLORS are those used by guppies in populations with those predators
Private wavelengths are seen by guppies but not by predators
Note: killifish is minimal predator

12. 1b. Auditory conspicuousness -
Parasitic female fly finds calling male cricket
Lays eggs which ultimately kill cricket

13. 1b. Auditory conspicuousness
Behavioral choice: play two songs from opposite speakers
See how many of female crickets vs females flies approach
Female crickets and female flies have same preference for high chirp rates

14. Female fly ear tuned to crickets

15. Redwing blackbird: female calls while sitting on nest
Cost: Female calls while sit on nest have higher predation
Female calls at a nest result in more predation. Depradate = plunder

16. Redwing blackbird: female calls while sitting on nest
Cost: Female calls while sit on nest have higher predation
Benefit: Male defends nests more with calling females
Male crow will attack a stuffed crow more if there are female calls at nest. No difference if nest or not with crow only. So it is the call that makes the difference

17. Redwing blackbird: female calls while sitting on nest
Cost: Female calls while sit on nest have higher predation
Females must answer a male call to get benefit. Just giving chits does not help.
Overall net gain
Chit or teer helps if it is given in answer to a male call. If no initial male call, then no advantage of chits or teers.
Successful means raised fledglings.

18. Sender cost 2. Energetic costs for visual signals
2 sec long signal may repeat every 10 sec for several hours
Displaying costs twice the energy of not displaying
Fig 23.9

19. Energetic costs for auditory signals
Gray treefrogs need more O2 when call at faster rates
This is true for Carolina wrens as well
Treefrogs O2 consumption when calling is even faster than O2 comsumption during forced exercise
Wren comsuption is given as multiples of O2 consumption at resting metabolism

20. Sender cost 3. Time lost
Time signaling is time not doing something else
Foraging
Parental care
Resting
In lekking species, maintain / defend territory so no time for foraging
Compensate w/ large body size

21. Sender cost 4. Conflict with original function
Tails provide lift during take off and serve as rudder to steady flight
Elaborate tails have increased drag
Folded tails are used during signaling. Spread tails used to fly. Gray areas generate lift and white areas generate drag.
Area contributes to lift
Area gives drag

22. Sender constraints Phylogenetic constraints
Constraints on sender learning

23. Sender constraint 1. Phylogenetic constraints
Can’t make a structure if don’t have genes to make it
Mammals don’t stridulate
Insects don’t use vocal cords
Can map on very broad phylogeny to see gains and losses of sensory modalities

24. Phylogenetic constraints

25. Body size constraint on auditory frequency
Frogs
Birds
Each point is a different species. Shown is the fundamental frequency of the call, though frequencies can vary over a wide range

26. Sender cost 2. Constraints on sender learning
Brain size can constrain learning
HVC= higher vocal center
Contrasts are between
species
genera
families
This uses phylogenetic independent contrasts between pairs of species that differ in HVC volume to see what corresponding difference in song repertoire is +

27. How do they know this isn’t just a difference in exposure during sensitive period?
Marsh wrens
Normal repertoire size
Repertoire size after expose to 200 songs NY 50 40
California
150
100
California wrens have larger HVC nuclei

28. Receiver costs Vulnerability to predation Time lost
More time spent assessing senders = more costs
Time lost
May need to survey signal for extended time to determine sender condition (repeatability or longevity of signal)
Female sage grouse visit 6-10 males on 3 separate mornings, viewing each 10 minutes!

29. Receiver constraints Phylogenetics Transmission constraint Visual
Auditory
Chemical
Transmission constraint

30. Receiver phylogenetic constraints
Table 17.2

31. Visual resolution is better for larger body size
Smaller angle means tinier objects can be distinguished so resolution is better

32. Auditory receivers Type of ear determines frequency range
Body size determines ability to use arrival times to locate sender

33. Transmission constraints for each modality
Media
Range
Localiz-ability
Temporal rates
Complexity
Duration
Visual
Light
Lower ++
Auditory
No vacuum
Largest +
Chemical
Currents
Moderate -
Slow
Low
Electric
Water
Tactile

34. Transmission constraints
Table 17.3

35. Evolutionary game theory
Part III of book
No longer assume communication is for benefit of both sender and receiver
New factors to consider
Deceit, conflict, subterfuge
Can receivers force senders to be honest?
Can senders manipulate receivers?

36. Taking organisms into account
Before, the environment set the optimal signal
If now include other organisms in the environment, how does that complicate optimality?
Behavioral choice of sender or receiver may change context
Sender and receiver may have dissimilar interests
Optimality may cycle through different possibilities
Or it may stabilize

37. Game theory from economics

38. Evolutionary game theory
Each individual can have different strategies
Make choice based on strategy that opponent might use
Game will stabilize if animals in different roles find the best overall response to all other roles

39. Evolutionarily stable strategy (ESS)
Each role has its own ESS
Will not be displaced over time
Depends on strategies of other roles
A role can have several ESSs
Often two alternative ESSs
Sender gives honest signals and receiver is attentive and responds to signals
Sender cheats and lies and receiver ignores or discounts signals
Which ESS you get may depend on chance history

40. ESS theory Predicts alternative strategies
May differ considerably from optimality based on modalities and environment
May not be intuitive
Classify games by a few criteria
Gives simplifying assumptions
Assumptions help know if particular ESS is possible in nature

41. Classifying evolutionary games
Type of strategy set
Role symmetry
Payoff frequency dependence
Sequential dependence

42. 1. Type of strategy set
Set of strategies - list of alternative behaviors or anatomical structures an animal can adopt in a particular role
Discreet
Continuous
Number of behaviors / strategies
- If only one then is pure strategy
Mixed strategies
Can be genetic polymorphism where different individuals have genes causing one or another strategy
Can be behavioral in which single individual can switch between strategies

43. 2. Role symmetry Symmetrical game Asymmetrical game
Single role: Each has same strategy set so equal chance of winning w/ same strategy
e.g. two male baboons competing for a sleeping site by exchanging vocalizations
Asymmetrical game
Multiple roles: Each role has different strategies, different probability of winning, different payoffs
e.g. male vs female; young vs old
Sender vs receiver

44. 3. Payoff frequency dependence
Depends on number of opponents
Contest - between two opponents
This holds as long as meet one opponent at a time so each interaction occurs only btn 2 individuals
Scramble - more than two (playing against the field)

45. 3. Contest example Two chicks in nest
If neither begs, equal chance to be fed
If one begs but other not, begging chick gets all food
If both beg, equal chance to be fed
So outcome only depends on what other chick in nest does

46. 3. Scramble example T chicks in nest (T>2) If N beg and T-N do not
Chance begger gets worm is 1/N
So depends on how many of chicks beg - frequency dependent

47. 4. Sequential dependence
Do sequential decisions influence each other
If each outcome is independent of any other one, then treat each as separate game
If outcome depends on previous choice, then entire sequence is one game
Each decision is bout within larger game
Dynamic game
May be evolutionarily stable policy (rule of thumb to find optimal strategy)

48. 4. example Two crickets periodically try to take over same hole
If no way to recognize individuals, then each attempt is independent
If do recognize opponents, what happens this time may depend on if won or lost last time

49. Combinations of game criteria
Strategies
Discreet Continuous
Game
Symmetric Asymmetric
# opponents
Contest Scramble
Interactions
Independent Dependent

50. Some evolutionary games
Discreet symmetric contests
Hawk vs dove
Take game
Give game
Discreet asymmetric contests
Continuous contest
Asymmetric scramble

51. Discreet symmetric contests
Discreet strategies
Symmetric opponents (only 1 role)
Contest between 2 individuals
No sequential dependence
Simplest version
Two individuals each with same two strategies
Four possible payoffs

52. Simplest version: two players with two strategies
Four possible payoffs to focal individual
Opposing individual
Strategy 1
Strategy 2
PO11
PO12
PO21
PO22
PO12 is payoff for focal individual when it uses strategy 1 and opponent uses strategy 2
Focal individual

53. Put dot where best strategy is
If PO11>PO21 and PO12 > PO22
Opposing individual
Strategy 1
Strategy 2
PO11
PO12
PO21
PO22
PO12 is payoff for focal individual when it uses strategy 1 and opponent uses strategy 2
Focal individual

54. Put dot where best strategy is
If PO11>PO21 and PO12 > PO22
Opposing individual
Strategy 1
Strategy 2
PO12 is payoff for focal individual when it uses strategy 1 and opponent uses strategy 2
Focal individual

55. Four possible combinations
Both of these suggest one strategy that is pure ESS for focal player. Should be only strategy for that role.

56. Four possible combinations
Best to have strategy that differs from that of opponent
If all start strategy 1, if mutant gets strategy 2, it will win and so grow in frequency. If get too many strategy 2, it’s advantage is lost and so will decrease. So end up with mixture of strategies 1 and 2. Ratio depends on payoffs. This f could be that f individuals always use strategy 1 and (1-f) use strategy 2. Or it could be that individuals use strategy 1 f of the time and strategy 2 (1-f) of time. In reality, behavioral polymorphisms are more likely

57. Four possible combinations
Last case - it is best to have same strategy s opponent
Two ESSs, either all use strategy 1 or all use 2.
Will be one other stable ESS at f same as for case 3, but this is unstable point. Any increase in strategy 1 will drive all to strategy 1 and any increase in strategy 2 will make all strategy 2.
So there is always at least 1 ESS for discreet symmetric contest

58. Discreet symmetrical contest: Hawk vs dove
Population has two strategies to obtain a resource (food, mate, roost)
Fight - hawk
Display peacefully - dove
Discreet: two strategies fight or display
Symmetrical: all individuals equal
Contest: only two players
Contests are independent - no memory effect
Note: this does not mean this world is made up of hawks and doves. Rather each individual can choose to act like hawk or like a dove

59. Payoffs Hawk vs hawk - fight to see who wins
Hawk vs dove - dove runs away
Dove vs dove - display to see who wins

60. Payoffs Hawk vs hawk - always fight Hawk vs dove - dove runs away
Winner gets +V (wins commodity)
Loser gets -D (defeat, injuries)
Since any hawk wins 1/2 time payoff to each hawk is 1/2 (V + -D) = (V-D)/2
Hawk vs dove - dove runs away
Hawk wins and gets +V
Dove gets 0
Dove vs dove - display to see who wins
Winner gets +V Loser gets 0
Since dove wins 1/2 time, payoff to each is V/2

61. So compare payoffs and put dot where greatest

62. So compare payoffs and put dot where greatest
Two choices on left
if V > D then acting like a hawk is ESS
V = what victor gets
D = costs of defeat
So as what you win gets small compared to the cost of fighting, you shouldn’t risk a fight. So often beneficial not to fight and using signals to avoid this fight might be favored

63. So compare payoffs and put dot where greatest
if V < D then ESS is stable mixture with f=V/D frequency of hawks and 1-V/D frequency of doves
As V gets smaller, more animals should settle things peacefully
So as what you win gets small compared to the cost of fighting, you shouldn’t risk a fight. So often beneficial not to fight and using signals to avoid this fight might be favored

64. Example of hawk vs dove