1. Ch 14 end: Value of information Ch 15: Signal coding 4/7/11
Lecture 17
Ch 14 end: Value of information
Ch 15: Signal coding
4/7/11

2. Key ideas from last time
Communication : occurs between sender and receiver for benefit of both
Information is used by receiver to answer questions. Each question has signal set
Value of information is fitness payoff with information minus payoff without info
Amount of information transferred depends on new probability estimate that condition is true after receive info

3. Receiver updating
Receivers update prior estimates based on information received
New estimate gets better as receive more and more signals

4. Male bird song Healthy male sings fast 30% of time
50% %
Healthy Sick
30%
40%
70%
Fast song Slow
Healthy male sings fast 30% of time
Sick male sings fast 40% of time
What does this mean?? If receive signal S1, then either C1 is true and sent signal S1 or C2 is true and sent signal S1. New estimate that C1 is true is ratio that C1 is true and S1 sent to sum of C1 is true and S1 sent plus C2 is true and S1 sent.

5. Plot song distribution for healthy and sick males
0.7
0.3
Healthy
Sick
Fraction of songs
0.6
0.4
Slow Fast
Song speed

6. Signals can also be continuous

7. Payoff matrices For female trying to pick a healthy mate Male healthy
Male sick
Accept as mate
Hit
False alarm (penalty)
Reject as mate
Miss
Correctly reject

8. With continuous distributions, females have more complex decisions
Need to figure out threshold song speed at which to accept males

9. With continuous distributions, females have more complex decisions
Need to figure out threshold song speed to accept males
Maximize correct acceptance = hit and correct reject
Minimize mate with sick (false alarm) as well as good matings missed

10. Optimal wc (critical song speed) determined by payoffs for each condition
Healthy male
Sick male
Fast song
R11
R12
Slow song
R21
R22

11. Consider tradeoffs between correct detection and false alarms
Think about Phit versus Pfalse alarm
Hit = mate with healthy male
False alarm = mate with sick male

12. If distributions have same width (variance) what happens as means shift
If overlap then just as many good matings as bad so hits = false alarms
If healthy sing faster, then hits > false alarms
If large difference in means then
hits>>false alarms
Hit = mating with healthy individual
False alarm = mating with sick

13. If distributions have same width (variance) what happens as means shift
If have same mean then just as many good matings as bad
hits = false alarms
If healthy sing faster, then hits > false alarms
If large difference in means then
hits>>false alarms
Hit = mating with healthy individual
False alarm = mating with sick

14. As means shift, indicates receiver can better discriminate between healthy and sick
Receiver operating characteristics (ROC)
Distance from line is the receiver sensitivity, d’
It is like Q
How signal correlates with
condition
Sensitivity reflects both amount of information female receives and the value of that information
d’=0 d’
Hit = mating with healthy individual
False alarm = mating with sick d’

15. Costs to receiver
Up to now, assume that receiver gathers as much info as can and costs are fixed
But likely there are more costs to gather more information and info of more value
Increase information’s value
Q = correlation between received signal and
condition
 discreet signals
d’ = receiver sensitivity, ability to discriminate
between conditions
 continuous signals

16. Costs versus benefits, continuous signals
Want benefit to be most different from costs Difference between benefits and cost curve is the value of information
Here costs are shown to increase linearly, though they may increase more rapidly than that. So intermediate d’ will be optimal and give greatest value of info.

17. Swallows Bank swallow Barn swallow Cliff swallow Roughwing
Bank and cliff swallows put babies in large creches with 100 other babies. Adults feed only their chicks so need to be able to recognize them. Barn and roughwing swallows keep babies separate with pair of parents. Beecher found that cliff and bank swallows can better recognize their young. Songs are more variable in those species so young can also be told apart
Roughwing

18. Spectrogram of chick calls
Each cluster of calls is calls from 4 individuals from that species. There is more variation in bank and cliff swallows (colonial breeders) than barn or rough-wing swallows. Beecher suggests that bank and cliff swallows provide 8.7 and 10.2 bits of info while barn 4.6 and rough-wing Info = payoff with and w/o signal
Fig 14A

19. Ch 15: Coding Coding schemes and signal repertoires
Coding scheme of sender can influence receivers’ coding rules
Different communication questions require different coding schemes with different costs

20. Signal coding
Sender provides signal to receiver to tell which of alternative conditions is true C1 C2 C3 S1
P(S1|C1)
P(S1|C2)
P(S1|C3) S2
P(S2|C1)
P(S2|C2)
P(S2|C3) S3
P(S3|C1)
P(S3|C2)
P(S3|C3)
P(S1|C1) probability that signal S1 will be sent when condition C1 is true

21. Signal coding
Sender provides signal to receiver to tell which of alternative conditions is true
Healthy
Sick
Juvenile
Fast
0.7
0.4
0.02
Slow
0.3
0.6
0.05
Peeps
0.0
0.93

22. Coding rules No coding - all signals equally likely
Perfect coding - only 1 signal per condition
Specific - 1 signal per condition
Unique - 1 condition per signal
Neither

23. Signal coding Is this perfect coding? Specific? Unique? Healthy Sick
Juvenile
Fast
0.7
0.4
0.02
Slow
0.3
0.6
0.05
Peeps
0.0
0.93
Specific has one signal per condition
Unique has one condition per signal

24. Codes require signal diversity
Variation
Modify signal elements
Sound:
Light:
Odors:
Electrical:

25. Codes require signal diversity
Variation
Modify signal elements
Sound: frequency, amplitude, duration
Light: color, size, location
Smells: composition, concentration, ratios
Electrical: frequency, amplitude, duration
Modify temporal pattern
Use in combinations
Often use clusters of signals - stereotyped sets
Use in larger chains
Chains may have rules by which they can be strung together. These hierarchical rules form syntax of language

26. Codes require signal diversity
Note is continuous trace. Songs include 1-4 note types in fixed sequences (syllable, s) which are repeated in trills (t)
Swamp sparrow

27. Trill of swamp sparrow

28. Song sparrow variation
Sparrow Sparrow 2 - neighbor
Males sing song types with these shared between neighbors

29. Song sparrow - more diverse notes in song (note complexes)

30. May be very few signals used
Swish from rubbing wings, coos, and pops from popping sacs on chest. Timing of these elements is highly conserved, varying only 1-2% Different males only vary 2-4% between each other

31. Video

32. Signal set answers one question Answer can be variable or discreet
Frequency
Continuous - parasite load or size of opponent
Separate bands (readiness to flee, dominant low and subdom high)
Discrete (male vs female)
Discrete alternatives - predator nearby (hawk, snake, leopard, mammal)
condition

33. Condition might be variable but gets mapped onto discreet signal
Categorization limits costs by making sender generate fewer signals, but lose information
There is some error due to propagation that makes perceived signals be broader
Cry of chick
Parental response
Hunger of chick

34. Condition and signal are variable
Degree of fin erection
Degree of confidence win fight
Perceived fin erection
Iconic means there is a rule used to map signal onto condition
Two fish both want territory. Use general rule to convert fin height to confidence and determination to fight. Might prevent fight if one is more likely to win

35. Coding schemes Discreet conditions (sex)
Might emit several calls for the same state - this redundancy helps receiver not make mistakes
Or might only need to distinguish one individual (baby) from all others so binary task of receiver
Might use same signals in variety of contexts to answer different questions. Receiver needs to know context as well.
Can be mix of these different coding schemes
Discreet conditions (sex)

36. How do we infer sender coding schemes??
Discrete conditions and signals
Contingency table
Discrete conditions and continuous signals
Discriminant function analysis
Continuous signals and uncertain conditions
Clustering or principle component analysis
Test whether particular variable can predict the signals and so is what is being coded

37. How do we infer receiver coding?
Start with sender coding
Behavioral tests to see if receiver responds differently
Determine which condition is associated with each category

38. Signal function and coding
Different questions require different code complexities
Binary questions - only 2 answers
Manifold questions - many answers

39. Binary questions Only two conditions Binary recognition
Sex (male vs female)
Mating status (mated or not)
Use cheapest signal that can - highly heritable
Binary recognition
Mate vs not mate
Offspring vs not offspring
More complex coding - requires template matching

40. Examples Member of bird flock House finch, chickadees
Acquire flock specific call - senders
Receivers have template to recognize just their flocks call

41. Juvenile bat calls for parent
Stay constant from very young age
Similar within family but different between
Comparison with age
Comparison btn families
Bat 1 and 2 from same family. Bat 3 and 4 from different family
How do all bats in same family learn same call? How does parent learn call. Does it come from parent?? Does 1st to cry set template for others?
Scherrer and Wilkinson suggest these calls are heritable!!!

42. Binary questions Binary comparison
Two opponents in a fight - compare one to another
Is individual healthy - compare to threshold
Common during mating
If male meets threshold then female will mate

43. Manifold questions Large number of possible answers
If conditions can be ordered, signals are also ordered
If can’t be ordered then gets quite complicated

44. Iconic agonistic signals
Map pattern onto aggressiveness using a rule

45. Bee dances to inform direction and distance to food source
Direction of dance tells direction of food relative to sun
Amount of waggles tells distance to food
These are iconic rules where dance is mapped onto distance and direction
Rule is heritable within hive
If group bees from different hives, will fly wrong distance since different rule to convert waggle rate to distance

46. Compound signal coding - answer several questions at same time
Combinational mapping
Take all combos and give each a unique signal
Parameter mapping
Each parameter is assigned one question
species identify - pulse rate
body size - frequency
female mate selection - call rates and amplitude
Hierarchical mapping
Difference in mean signal - group
Variation about mean - individual

47. Tamarin group calls
Individuals within group share some aspects of call but have variation to distinguish them.

48. Repertoire size Signal repertoire
# of questions asked - functional diversity
# of signals / question = variant diversity
All signals for all questions = signal repertoire
Is there a limit to signal repertoire?
30-40 signals in some taxa
But can be variation btn individuals and btn taxa

49. Dabbling ducks Species similar in function of calls and displays
Differ in number of courtship displays
Mallards (A-H) 8 displays
Pintail (I-J) 2 displays
Mallard
Preening B) down-up C) head up tail up w/ burp call D) grunt whistle E) nod-swimming F) back of head G) head pumping H) bridle display after mating
Pintail only tail up burp call and head up tailup

50. Expanding repertoire size
Expand possible limits for one of signal parameters
Add more singal parameters
Reduce variability of parameter so can distinguish more variants of that parameter
Not clear if there really are limits to repertoire space
Need sender to be able to expand variation AND receiver to be able to perceive this increased variation