animal communication
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III. Function, b. Information & DecisionsIII. Function, b. Information & Decisions
QuestionQuestion posed by female: Is this male healthy or sick? posed by female: Is this male healthy or sick?
Signals assigned to the same question are a Signals assigned to the same question are a signal set signal set (e.g. in this example, both song & dance signal health)(e.g. in this example, both song & dance signal health)
Alternative answers: male is healthy; male is sick….these are the Alternative answers: male is healthy; male is sick….these are the conditionsconditions
Sender has a Sender has a codecode that correlates the signal with the conditions: that correlates the signal with the conditions:• Songs are fast in healthy males, slow in sick malesSongs are fast in healthy males, slow in sick males• Dance is vigorous in healthy males, not in sick malesDance is vigorous in healthy males, not in sick males
All signals pooled across all questions and signal sets is the All signals pooled across all questions and signal sets is the signal repertoiresignal repertoire; size depends on the number of questions ; size depends on the number of questions asked and the number of possible answersasked and the number of possible answers
QUESTIONSQUESTIONS ALTERNATIVEALTERNATIVE ALTERNATIVE ALTERNATIVE CONDITIONSCONDITIONS SIGNALS SIGNALS
UnlikelyUnlikely Crest fully raisedCrest fully raised
Will opponent Will opponent attack?attack?
50:5050:50 Crest partially Crest partially raisedraised
LikelyLikely Crest downCrest down
Will this Will this opponent opponent escalate?escalate?
YesYes Loud callLoud call
NoNo Soft callSoft call
Example:Example: Territorial defense Territorial defense
III. Function, b. Information & DecisionsIII. Function, b. Information & Decisions
There are two basic kinds of information that can be There are two basic kinds of information that can be transferred by signals:transferred by signals:
Confirmation of Conditions: Confirmation of Conditions: Signals confirm which of several Signals confirm which of several alternatives suspected by the alternatives suspected by the Receiver is currently trueReceiver is currently true
Novel Facts: Novel Facts: Signals are used to Signals are used to share some fact unsuspected by share some fact unsuspected by the Receiver the Receiver
III. Function, b. Information & DecisionsIII. Function, b. Information & Decisions
Two kinds of information can be transferred by signals:Two kinds of information can be transferred by signals:
• Communication by most animals is of the second type Communication by most animals is of the second type of Scenario: receivers “know” the likely alternatives, of Scenario: receivers “know” the likely alternatives, either through learning or genetic biases or both, and either through learning or genetic biases or both, and signals largely serve to confirm which among these signals largely serve to confirm which among these alternatives is currently truealternatives is currently true
• Where novel alternatives do turn up, these are usually Where novel alternatives do turn up, these are usually assigned to one of the existing alternatives (e.g. one assigned to one of the existing alternatives (e.g. one more type of predator)more type of predator)
III. Function, b. Information & DecisionsIII. Function, b. Information & Decisions
Information as Probabilities:Information as Probabilities:
• If the alternatives to some question are already If the alternatives to some question are already known, then what must change with the provision of known, then what must change with the provision of information are the relative probabilities that each information are the relative probabilities that each alternative might be truealternative might be true
• We say the probabilities are We say the probabilities are updated updated with the with the provision of informationprovision of information
For example, you may start your day estimating a For example, you may start your day estimating a 1x101x10-5 -5 % chance of being killed by a terrorist attack, % chance of being killed by a terrorist attack, but increase that to 1.1x10but increase that to 1.1x10-5 -5 % after seeing the % after seeing the “orange” DHS alert“orange” DHS alert
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions1. Information as Probabilities1. Information as Probabilities
Information as Probabilities:Information as Probabilities:
• So today we’ll be talking about how receivers use So today we’ll be talking about how receivers use information encoded in signals to update their information encoded in signals to update their estimated probabilities that certain conditions are estimated probabilities that certain conditions are true, and thereby make decisionstrue, and thereby make decisions
• These decisions determine the benefits that both These decisions determine the benefits that both receivers and sender gain by communicatingreceivers and sender gain by communicating
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions1. Information as Probabilities1. Information as Probabilities
ExampleExample: The receiver (you) want to know whether you are going : The receiver (you) want to know whether you are going to like the new movie by a favorite director to like the new movie by a favorite director
Your priors are the percentage of movies by that director that you Your priors are the percentage of movies by that director that you previously liked (72%)previously liked (72%)
When you read a positive movie review in the paper (the signal), When you read a positive movie review in the paper (the signal), you update your probability estimates with this new you update your probability estimates with this new information… information… How do you update your estimate?How do you update your estimate?
C1 = C1 = Love itLove it
C2 = C2 = Hate itHate it
C1 Probability
C2 Probability
C1 Probability
C2 Probability
PPprior prior = 0.72= 0.72 1- 1- PPprior prior
PPupdated updated = ??= ?? 1- 1- PPupdatedupdated
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions1. Information as Probabilities1. Information as Probabilities
The reliability of signals can be The reliability of signals can be mapped on a mapped on a coding matrixcoding matrix
A A perfect signalperfect signal is never wrong is never wrong
When it is received, one needle When it is received, one needle goes to 1.0 probability and the goes to 1.0 probability and the other to 0:other to 0:
C1 Probability
C2 Probability
PPupdated updated = 1.0= 1.0 1- 1- PPupdatedupdated
C1 C2
S1
S2
Condition:Condition:
Sig
nal
:S
ign
al:
1.01.0 00
00 1.01.0
C1
C1 = C1 = Love itLove it
C2 = C2 = Hate itHate it
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions1. Information as Probabilities1. Information as Probabilities
C1 Probability
C2 Probability
An An imperfect signalimperfect signal is only correct is only correct some fraction X% of the timesome fraction X% of the time
Each signal moves the needles only Each signal moves the needles only part way towards 0 or 1part way towards 0 or 1
This is much more common in This is much more common in animal communicationanimal communication
C1 C2
S1
S2
Condition:Condition:
Sig
nal
:S
ign
al:
0.70.7 0.10.1
0.30.3 0.90.9
C1
C1 = C1 = Love itLove it
C2 = C2 = Hate itHate it
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions1. Information as Probabilities1. Information as Probabilities
C1 Probability
C2 Probability
Imperfect SignalsImperfect Signals: If you read more movie reviews, each gives : If you read more movie reviews, each gives new information, but each has a smaller effect on your new information, but each has a smaller effect on your opinion (diminishing returns to continued reading of reviews)opinion (diminishing returns to continued reading of reviews)
C1 = C1 = Love itLove it
C2 = C2 = Hate itHate it
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions1. Information as Probabilities1. Information as Probabilities
Since the change in probabilities with receipt of a given signal Since the change in probabilities with receipt of a given signal depends on the prior probability, we need to take prior depends on the prior probability, we need to take prior probabilities into account when we measure the probabilities into account when we measure the amount of amount of informationinformation the signal provides to the Receiver the signal provides to the Receiver
So we use the So we use the base 2 logarithm of the base 2 logarithm of the ratioratio of updated to of updated to prior probability estimates.prior probability estimates. Why?Why?
We use logarithms because they give the same absolute value We use logarithms because they give the same absolute value regardless of which direction the estimate changes, with a regardless of which direction the estimate changes, with a sign indicating the direction:sign indicating the direction:
e.g. loge.g. log22(0.9/0.1) = 3.17 and log(0.9/0.1) = 3.17 and log22(0.1/0.9) = –3.17(0.1/0.9) = –3.17
Why do we use base 2 logs?Why do we use base 2 logs?
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
It is easiest to think of information as the answers to specific It is easiest to think of information as the answers to specific questionsquestions
Binary QuestionsBinary Questions: The simplest type of question has only two : The simplest type of question has only two possible answers: yes or no, A or B, male or female, etc.possible answers: yes or no, A or B, male or female, etc.
Complex QuestionsComplex Questions: Any complex question with a finite : Any complex question with a finite number of possible answers can be broken down into a number of possible answers can be broken down into a series of binary questionsseries of binary questions
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
E.g. Cuckoo Eggs: E.g. Cuckoo Eggs: One egg in the nest is a cuckoo egg. How One egg in the nest is a cuckoo egg. How many binary questions do you have to ask to find it?many binary questions do you have to ask to find it?
Number of Number of AlternativesAlternatives
Number of Binary Number of Binary QuestionsQuestions
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
General Case: General Case: If If MM is the number of alternative answers to a is the number of alternative answers to a complex question, and complex question, and HH is the number of binary questions is the number of binary questions that need to be asked to find which alternative is true, thenthat need to be asked to find which alternative is true, then
M = 2M = 2HH
One One bitbit is the information required to answer a binary question is the information required to answer a binary question It takes It takes HH bits to answer a question with bits to answer a question with MM alternative answers alternative answers
Number of Number of Alternatives Alternatives (M)(M) 22 44 88 1616
Number of Binary Number of Binary Questions Questions (H)(H) 11 22 33 44
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
General Case: General Case: If M = 2If M = 2HH, then if follows that, then if follows that
H = logH = log2 2 MM
WhereWhere HH is the number of bits to answer a question, and is the number of bits to answer a question, and M M is is the number of alternative answers (conditions)the number of alternative answers (conditions)
• ...you can compute ...you can compute loglog2 2 M M on your calculator without using on your calculator without using base 2 logs by calculating base 2 logs by calculating ln(M)/ln(2)ln(M)/ln(2) or or loglog1010M/logM/log101022
• ...a value of M that is not an integer power of 2 is OK: thus ...a value of M that is not an integer power of 2 is OK: thus loglog223 = 1.583 = 1.58
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
So that’s how we quantify information; how does this relate to So that’s how we quantify information; how does this relate to probability estimates?probability estimates?
As you saw before, we measure the amount of information the As you saw before, we measure the amount of information the signal provides to the Receiver as the signal provides to the Receiver as the base 2 logarithm of the base 2 logarithm of the ratio of updated to prior probability estimatesratio of updated to prior probability estimates
Now, we formalize that in an equation:Now, we formalize that in an equation:
The amount of information in bits The amount of information in bits transferred by a signaltransferred by a signal about the about the likelihood of a particular answer likelihood of a particular answer AA to a question to a question
prior
updatedT AP
APH
)(
)(log
typrobabliliprior
yprobabilit updatedlog 22
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
Perfect Signals: Perfect Signals: After receipt of a perfect signal, the numerator After receipt of a perfect signal, the numerator in the amount of information expression, in the amount of information expression, P(A)P(A)updatedupdated goes to goes to
either 0 or 1either 0 or 1
If A is the answer that is now If A is the answer that is now knownknown to be true, the amount of to be true, the amount of information provided by the signal about information provided by the signal about AA is is
HHTT = log = log22(1/P(A)(1/P(A)priorprior) = – log) = – log22(P(A)(P(A)priorprior))
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
Wants to play: 0.2Wants to play: 0.2Wants food: 0.4Wants food: 0.4Amorous: 0.2Amorous: 0.2Fearful: 0.1Fearful: 0.1Aggressive: 0.1Aggressive: 0.1
HHTT play signal = play signal =
I. What is Information? I. What is Information? B. The Amount of InformationB. The Amount of Information
If you have these priors (PIf you have these priors (P00) )
for the 5 possible moods of for the 5 possible moods of your dog: your dog:
If you receive a “play signal”, which is a If you receive a “play signal”, which is a perfect signal, how much information perfect signal, how much information does it give youdoes it give you??
Imperfect Signals: Imperfect Signals: P(A)P(A)updatedupdated never goes to 1.0 after receipt of never goes to 1.0 after receipt of
an imperfect signal. Instead, we are left with an imperfect signal. Instead, we are left with
which can be rewritten aswhich can be rewritten as
Which is the same as Which is the same as
HHTT = H = Hpriorprior – H – Hupdatedupdated
prior
updatedT AP
APH
)(
)(log2
))((log())((log 22 updatedpriorT APAPH
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
HH as uncertainty: as uncertainty: HHTT = H = Hpriorprior – H – Hupdatedupdated
The first term, The first term, HHpriorprior = –log = –log22(P(A)(P(A)priorprior),), is the amount of information in is the amount of information in
bits required to remove bits required to remove ALLALL of our prior uncertainty about of our prior uncertainty about whether whether AA was true was true beforebefore the signal the signal
The 2The 2ndnd term, term, HHupdatedupdated = –log = –log22(P(A)(P(A)updatedupdated)), is the amount of information , is the amount of information
in bits required to remove in bits required to remove ALLALL uncertainty about whether uncertainty about whether AA is is true true afterafter receipt of the signal receipt of the signal
The difference between these two terms, HThe difference between these two terms, HTT, is the amount of initial , is the amount of initial
uncertainty about whether A was true that was removed by the uncertainty about whether A was true that was removed by the signalsignal
It is the amount of information transferred through communicationIt is the amount of information transferred through communication
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
ExampleExample: Suppose : Suppose P(A)P(A)priorprior = 0.5 = 0.5
how does how does HHTT change with different values of change with different values of P(A)P(A)updatedupdated??
P(A)P(A)updated updated 0.60.6 0.70.7 0.80.8 0.90.9 1.01.0
HHTT
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
Information theory was developed by Information theory was developed by Claude ShannonClaude Shannon to find fundamental to find fundamental limits on compressing and reliably storing and communicating datalimits on compressing and reliably storing and communicating data
Shannon entropyShannon entropy is a measure of the uncertainty associated with a random is a measure of the uncertainty associated with a random variable; quantifies the info contained in a message (in bits).variable; quantifies the info contained in a message (in bits).
How is information theory used?How is information theory used? We aren’t usually privy to what animals We aren’t usually privy to what animals are are tryingtrying to say...how many options are available, their priors are, etc. to say...how many options are available, their priors are, etc.
So while conceptually useful, the classic information theory we just learned is So while conceptually useful, the classic information theory we just learned is difficult to apply directly in animal communication. Many statistics have difficult to apply directly in animal communication. Many statistics have been built on this foundation, however, which are also conceptually been built on this foundation, however, which are also conceptually useful, and more tractable to useuseful, and more tractable to use
Markov Chain ModelsMarkov Chain Models of syntax are one example. of syntax are one example. Signal Detection Signal Detection TheoryTheory is an information-theoretic framework, which uses a statistical is an information-theoretic framework, which uses a statistical approach, similar to Type I and Type II errors in statistics (Wiley, approach, similar to Type I and Type II errors in statistics (Wiley, Adv. Adv. Study Behav. Study Behav. 2006). 2006).
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
Signal Detection Theory Signal Detection Theory (Acoustics)(Acoustics)
Each curve is a probability density Each curve is a probability density function (PDF) of for the outputs of a function (PDF) of for the outputs of a perceptual channel with and w/out the perceptual channel with and w/out the signal; The threshold is where signal; The threshold is where response occursresponse occurs
Signal detection theory predicts how Signal detection theory predicts how animals should increase the animals should increase the separation of the background vs. separation of the background vs. signal+background PDFs (i.e.signal+background PDFs (i.e. signal- signal-to-noise ratioto-noise ratio), e.g.:), e.g.:•Increase repetition rateIncrease repetition rate•Use diff freqs than backgroundUse diff freqs than background•Use diff amplitude modulationUse diff amplitude modulation•Use longer signals Use longer signals
III. Function, a. Info & DecisionsIII. Function, a. Info & Decisions2. The Amount of Information2. The Amount of Information
Another example of how information theory is used:Another example of how information theory is used:
Zipf’s statisticZipf’s statistic evaluates the signal composition or ‘structure’ of a evaluates the signal composition or ‘structure’ of a repertoire by examining the frequency of use of signals in repertoire by examining the frequency of use of signals in relationship to their ranks (i.e. first, second, third versus most-to-relationship to their ranks (i.e. first, second, third versus most-to-least frequent)(McCowan, et al. 1999)least frequent)(McCowan, et al. 1999)
• Measures the potential capacity for info transfer at the repertoire level by Measures the potential capacity for info transfer at the repertoire level by examining the ‘optimal’ amount of diversity and redundancy necessary examining the ‘optimal’ amount of diversity and redundancy necessary for communication transfer across a ‘noisy’ channel (i.e. all complex for communication transfer across a ‘noisy’ channel (i.e. all complex audio signals will require some redundancy)audio signals will require some redundancy)
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions2. The Amount of Information2. The Amount of Information
LogLog1010 Rank of use Rank of use
Adult dolphin Adult dolphin whistleswhistles
Log
Log 101
0 Fre
quen
cy F
requ
ency <1mo. old dolphin <1mo. old dolphin
whistleswhistles
Now we’ll discuss how the Now we’ll discuss how the ideal receiverideal receiver uses information to uses information to update his/her probability estimates (i.e. calculate pupdate his/her probability estimates (i.e. calculate pupdatedupdated))
Example: Example: Suppose the Receiver needs to know whether condition Suppose the Receiver needs to know whether condition CC11 or condition or condition CC22 is currently true is currently true
There are two signals, There are two signals, SS11 and and SS22 that can be used to provide that can be used to provide
information about this questioninformation about this question
We can summarize the coding rules for this system by constructing a We can summarize the coding rules for this system by constructing a coding matrixcoding matrix with the conditional probabilities in the cells with the conditional probabilities in the cells
CC11 CC22
SS22
Condition:Condition:
Sig
na
l:S
ign
al:E.g. conditional probability E.g. conditional probability P(SP(S11|C|C11)) is is
the probability that signal 1 occurs when the probability that signal 1 occurs when condition 1 is truecondition 1 is true
P(SP(S11|C|C11))
P(SP(S22|C|C11)) P(SP(S22|C|C22))
P(SP(S11|C|C22))SS11
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions3. Encoding Information3. Encoding Information
A Receiver’s task is to combine A Receiver’s task is to combine prior probabilitiesprior probabilities, knowledge , knowledge of the of the coding matrixcoding matrix, and receipt of a particular , and receipt of a particular signalsignal to to produce new produce new updatedupdated probabilities of the alternatives probabilities of the alternatives
There are many ways to update, but no mechanism of There are many ways to update, but no mechanism of updating can be more accurate than updating can be more accurate than Bayesian updating; Bayesian updating; it’s the it’s the theoreticaltheoretical upper limit upper limit
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions4. Making Decisions
Basic Logic: Basic Logic: First, assemble the priors and coding matrixFirst, assemble the priors and coding matrix
Baye’s Theorem states that the Baye’s Theorem states that the updatedupdated probability that probability that CC11 is is true after receipt of signal true after receipt of signal SS11 is: is:
p(Sp(S11|C|C11)) p(Sp(S11|C|C22))
p(Sp(S22|C|C11)) p(Sp(S22|C|C22))
C1 C2
S1
S2
Condition:Condition:
Sig
nal
:S
ign
al:
Priors:Priors: p(Cp(C11)) p(Cp(C22))
Note that all the numbers we Note that all the numbers we need to solve this are in our need to solve this are in our coding matrixcoding matrix
)|()()|()(
)|()()|(
212111
11111 CSpCpCSpCp
CSpCpSCp
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
p(C1 | S1) p(C1)p(S1 |C1)
p(C1)p(S1 |C1) p(C2)p(S1 |C2)
The numerator is the prob that we would see CThe numerator is the prob that we would see C11 and S and S11 together together
The denominator is the prob that we would see CThe denominator is the prob that we would see C11 and S and S11 together together
plus the prob we would see Splus the prob we would see S11 and C and C22 together; thus the together; thus the
denominator is the overall fraction of time we might see an Sdenominator is the overall fraction of time we might see an S1 1
signalsignal
The best estimate of the updated probability is thus the fraction of The best estimate of the updated probability is thus the fraction of time that we observe an Stime that we observe an S11 signal and it co-occurs with C signal and it co-occurs with C11
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
Example:Example:
• Suppose females of a bird species use the rate of Suppose females of a bird species use the rate of male songs to assess the health of potential matesmale songs to assess the health of potential mates
• Healthy males tend to sing Fast songs and sick ones Healthy males tend to sing Fast songs and sick ones tend to sing Slow songstend to sing Slow songs
• Suppose the two types of males are Suppose the two types of males are almostalmost equally equally common common (52% healthy, 48% sick)(52% healthy, 48% sick)
• Suppose also that coding is not perfect: Good males Suppose also that coding is not perfect: Good males sing Fast songs 70% of the time, whereas Bad males sing Fast songs 70% of the time, whereas Bad males sing Slow songs 60% of the timesing Slow songs 60% of the time
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
Example: Example: We first assemble the information available before We first assemble the information available before receipt of a signalreceipt of a signal
A female assumes any male has a 52% chance of being Good A female assumes any male has a 52% chance of being Good before she hears any songsbefore she hears any songs
GoodGood BadBad
FastFast
SlowSlow
0.520.52 0.480.48
Probability Good
0.700.70
0.300.30
0.400.40
0.600.60
Condition:Condition:
Sig
nal
:S
ign
al:
Priors:Priors:
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
Example: Example: After receipt of a Fast song, that estimate goes to:After receipt of a Fast song, that estimate goes to:
……IfIf that song had been Slow, her estimate would have been: that song had been Slow, her estimate would have been:
)|( FastGoodp
GoodGood BadBad
FastFast
SlowSlow
0.520.52 0.480.48
Probability Good
0.700.70
0.300.30
0.400.40
0.600.60
Condition:Condition:
Sig
nal
:S
ign
al:
Priors:Priors:
)|( SlowGoodp
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
p(G
oo
d)
p(G
oo
d)
1.00
0.5# Songs Sampled# Songs Sampled
Example: Example: After receipt of a Fast song, that estimate goes to:After receipt of a Fast song, that estimate goes to:
GoodGood BadBad
FastFast
SlowSlow
0.520.52 0.480.48
0.700.70
0.300.30
0.400.40
0.600.60
Condition:Condition:
Sig
nal
:S
ign
al:
Priors:Priors:
Sequential updating: Sequential updating: If the female is finished listening, then If the female is finished listening, then 0.655 is her final estimate. But if she’s going to keep listening, 0.655 is her final estimate. But if she’s going to keep listening, she now updates her priors to the new values she has obtainedshe now updates her priors to the new values she has obtained
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
)|( FastGoodp
Example: Example: Suppose 2Suppose 2ndnd song is also Fast: song is also Fast:
And she again updates her priors by replacing them with the most And she again updates her priors by replacing them with the most recent updated probabilitiesrecent updated probabilities
p(G
oo
d)
p(G
oo
d)
1.00
0.5# Songs Sampled# Songs Sampled
GoodGood BadBad
FastFast
SlowSlow
0.6550.655 0.3450.345
0.700.70
0.300.30
0.400.40
0.600.60
Condition:Condition:
Sig
nal
:S
ign
al:
Priors:Priors:
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
)|( FastGoodp
Example: Example: Suppose 3Suppose 3ndnd song is Slow: song is Slow:
p(G
oo
d)
p(G
oo
d)
1.00
0.5# Songs Sampled# Songs Sampled
GoodGood BadBad
FastFast
SlowSlow
0.700.70
0.300.30
0.400.40
0.600.60
Condition:Condition:
Sig
nal
:S
ign
al:
Priors:Priors: 0.7660.766 0.2340.234
She updates to the new probabilities and uses these as the next She updates to the new probabilities and uses these as the next prior probabilities…prior probabilities…
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
0.6210.621 0.3790.379
)|( SlowGoodp
p(G
oo
d)
p(G
oo
d)
1.00
0.5# Songs Sampled# Songs Sampled
GoodGood BadBad
FastFast
SlowSlow
0.700.70
0.300.30
0.400.40
0.600.60
Condition:Condition:
Sig
nal
:S
ign
al:
Priors:Priors: 0.6210.621 0.3790.379
Example: Example: Suppose 4Suppose 4thth song is Fast: song is Fast:
And so on…And so on…
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
)|( FastGoodp
Bad Male Bad Male TrajectoryTrajectory
p(G
oo
d)
p(G
oo
d)
1.00
0.5
# Songs Sampled# Songs Sampled
Good Male Good Male TrajectoryTrajectory
Fast SongsFast SongsSlow SongsSlow Songs
Example: Sequential SamplingExample: Sequential Sampling: Although the trajectory is : Although the trajectory is jagged (and different every time), the general trend if a male is jagged (and different every time), the general trend if a male is truly Good will be up, and if he is Bad, down. The Truth will truly Good will be up, and if he is Bad, down. The Truth will come out…. come out….
0.0
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
1.00
0.5
Example: Sequential SamplingExample: Sequential Sampling: Note that in general, the change : Note that in general, the change in probabilities, in probabilities, pp, for each successive song is smaller than for , for each successive song is smaller than for earlier songsearlier songs
What does this mean for the amount of information transmitted?What does this mean for the amount of information transmitted?
p(G
oo
d)
p(G
oo
d)
# Songs Sampled# Songs Sampled0.0
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
1.00
0.5
More accurate codeMore accurate code
Less accurate codeLess accurate code
Example: Sequential SamplingExample: Sequential Sampling: Finally, note that less accurate : Finally, note that less accurate coding matrices will cause the cumulative estimate to take longer coding matrices will cause the cumulative estimate to take longer to asymptote to the extreme:to asymptote to the extreme:
What does this mean for the amount of information transmitted?What does this mean for the amount of information transmitted?
p(G
oo
d)
p(G
oo
d)
# Songs Sampled# Songs Sampled0.0
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
Do Animals use Bayesian updating?Do Animals use Bayesian updating?
Sequential assessment of signals and cues is very common, from Sequential assessment of signals and cues is very common, from primates to honeybees; Bayesian updating is an optimal strategy primates to honeybees; Bayesian updating is an optimal strategy for sequential updating if:for sequential updating if:
• Animals have reasonable prior probabilities about likelihood of Animals have reasonable prior probabilities about likelihood of alternative conditions, and accuracy of coding schemealternative conditions, and accuracy of coding scheme
• Animals have time to assess signals and cues sequentiallyAnimals have time to assess signals and cues sequentially• Animals have the neural capacity to store the informationAnimals have the neural capacity to store the information
Some animals use short cuts and rules of thumb for updating which Some animals use short cuts and rules of thumb for updating which may be quite good. Bayesian updating is the best possible, but may be quite good. Bayesian updating is the best possible, but that’s not always the optimal thing to do… that’s not always the optimal thing to do… Even so, Even so, understanding BU is important because it defines the upper understanding BU is important because it defines the upper limit of what’s possible for comparison!limit of what’s possible for comparison!
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
Mate searching by female satin bowerbirds:Mate searching by female satin bowerbirds:
Al Uy found that females visit multiple males at their bowers during the Al Uy found that females visit multiple males at their bowers during the mating season and they visit each male multiple times (sequential mating season and they visit each male multiple times (sequential updating) before mating with one maleupdating) before mating with one male
Fits predictions of a Best-of-n model with Bayesian updating Fits predictions of a Best-of-n model with Bayesian updating (Luttbeg 1996)(Luttbeg 1996)
Females visit males at their bowers to Females visit males at their bowers to assess their signals (bower, decs)assess their signals (bower, decs)
Males mate with multiple femalesMales mate with multiple females
How should females find the best male?How should females find the best male?
Alternative hypotheses: Alternative hypotheses:
ThresholdThreshold vs. vs. Best-of-n modelsBest-of-n models
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
Older (more experienced) females often went straight back to the best Older (more experienced) females often went straight back to the best male in the population each year without shoppingmale in the population each year without shopping
When he died, they were all forced to start shopping again…When he died, they were all forced to start shopping again…
When females find a high-quality male, they When females find a high-quality male, they shop less the next year and often mate with shop less the next year and often mate with him again (they re-affirm prior estimates him again (they re-affirm prior estimates and re-mate if he’s still good)and re-mate if he’s still good)
Females who mated with a bad male, will Females who mated with a bad male, will avoid him the following year and find a avoid him the following year and find a better matebetter mate
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions4. Making Decisions, i. Bayesian Updating4. Making Decisions, i. Bayesian Updating
Mate searching by female satin bowerbirds:Mate searching by female satin bowerbirds:
(Uy et al. 200, 2001)(Uy et al. 200, 2001)
Benefits of CommunicationBenefits of Communication: : • Animals know the potential answers to most questions but Animals know the potential answers to most questions but
may be unsure which answer is currently truemay be unsure which answer is currently true• Senders can provide information that helps Receivers Senders can provide information that helps Receivers
improve their probability estimates for each alternativeimprove their probability estimates for each alternative• Receivers can improve estimates further by sampling Receivers can improve estimates further by sampling
successively and/or only attending to accurate signals successively and/or only attending to accurate signals
Costs of CommunicationCosts of Communication: : • Providing more accurate signals or sampling successively Providing more accurate signals or sampling successively
increases the costs of communication for both partiesincreases the costs of communication for both parties• How far does an imperfect signal have to change a prior How far does an imperfect signal have to change a prior
probability before it is worth the costs of sending and probability before it is worth the costs of sending and receiving it? receiving it? This is an optimization problemThis is an optimization problem
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions5. Take Home Messages5. Take Home Messages
Optimal InformationOptimal Information: :
• It never really pays to try to send or seek perfect It never really pays to try to send or seek perfect information through signalsinformation through signals
• Instead, animals are likely to establish some intermediate Instead, animals are likely to establish some intermediate compromise in which they sometimes err compromise in which they sometimes err
• Errors in communication are not evidence of faulty Errors in communication are not evidence of faulty evolution but the reasonable application of good economicsevolution but the reasonable application of good economics
• Optimality Optimality ≠ perfection!≠ perfection!
III. Function, b. Info & DecisionsIII. Function, b. Info & Decisions5. Take Home Messages5. Take Home Messages
Early ethological approach:Early ethological approach: Because signals evolve from intentions, Because signals evolve from intentions, preparatory movements, physiological precursors, etc… they preparatory movements, physiological precursors, etc… they reliably predict what sender will do next because sender can’t help reliably predict what sender will do next because sender can’t help it (they are constrained to be honest). Often ignored conflict it (they are constrained to be honest). Often ignored conflict entirely, and viewed communication as an altruistic exchange of entirely, and viewed communication as an altruistic exchange of informationinformation
Dawkins/Krebs arms race and early game models:Dawkins/Krebs arms race and early game models: Senders should Senders should try to trick, mislead, and manipulate receivers into giving responses try to trick, mislead, and manipulate receivers into giving responses benefiting sender, and receivers should become mind-readers benefiting sender, and receivers should become mind-readers trying to discount false signalstrying to discount false signals
Zahavi Handicaps:Zahavi Handicaps: Receivers only pay attention to signals that Receivers only pay attention to signals that impose a cost (handicap) on senders, which makes it costly to impose a cost (handicap) on senders, which makes it costly to send dishonest or exaggerated signalssend dishonest or exaggerated signals
III. Function, c. Honesty in AdvertisingIII. Function, c. Honesty in Advertising
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,2. Current Thinking2. Current Thinking
There are several dozen game-theoretic models of communication There are several dozen game-theoretic models of communication when there is a conflict of interest between the sender and when there is a conflict of interest between the sender and receiver, each depicting a different signaling context receiver, each depicting a different signaling context
Common theme:Common theme: There must be some type of There must be some type of cost or constraint cost or constraint imposed on imposed on senderssenders to guarantee honesty, but this cost is to guarantee honesty, but this cost is different for each model or contextdifferent for each model or context
We’ll discuss 3 categories of costs in communication:We’ll discuss 3 categories of costs in communication:
A. A. Necessary costsNecessary costsB. B. Incidental costsIncidental costsC.C. ConstraintsConstraints
Both senders and receiver may pay these costs, but it is the cost to Both senders and receiver may pay these costs, but it is the cost to the senders which we use to categorize the signals. Costs to the senders which we use to categorize the signals. Costs to
receivers are also important, because they select for “mind-readers” receivers are also important, because they select for “mind-readers” who only respond to honest signals.who only respond to honest signals.
A. Necessary Costs:A. Necessary Costs: Costs paid up front, Costs paid up front, do notdo not depend depend on receiver response, includes:on receiver response, includes:
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,1. Costs1. Costs
• Prior investment by sender in special structures, coloration, Prior investment by sender in special structures, coloration, organs, brain circuitry, etc.organs, brain circuitry, etc.
• Immediate costs sustained by sender while communicating Immediate costs sustained by sender while communicating such as time lost, energetic expenditure, and predation risksuch as time lost, energetic expenditure, and predation risk
• Receivers also pay some necessary costs (assessment costs, Receivers also pay some necessary costs (assessment costs, possible brain and sensory costs, etc.), which favors receivers possible brain and sensory costs, etc.), which favors receivers who only pay attention to honest signals (i.e. “mind-readers”).who only pay attention to honest signals (i.e. “mind-readers”).
B. Incidental Costs: B. Incidental Costs: Decreases in magnitude of payoffs to Decreases in magnitude of payoffs to either the sender or receiver; either the sender or receiver; doesdoes depend on receiver depend on receiver responseresponse
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,1. Costs1. Costs
• Costs to the Costs to the sendersender: if the receiver punishes the sender for : if the receiver punishes the sender for sending the signal (e.g. badges of status), this selects for honest sending the signal (e.g. badges of status), this selects for honest signals.signals.
• ReceiversReceivers can also pay incidental costs: If sender deceives the can also pay incidental costs: If sender deceives the receiver into acting against the receiver’s interests (sender receiver into acting against the receiver’s interests (sender deceit, bluff, exaggeration, withholding information). These costs deceit, bluff, exaggeration, withholding information). These costs select for receivers who only pay attention to honest signals (i.e. select for receivers who only pay attention to honest signals (i.e. “mind-readers”).“mind-readers”).
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,1. Costs1. Costs
C. Constraints:C. Constraints: limits on communication imposed by limits on communication imposed by environment, phylogenetic history and physicsenvironment, phylogenetic history and physics
Examples:Examples: Frequency and amplitude are limited by body size, Frequency and amplitude are limited by body size, brain size limits learning of songs, etc.brain size limits learning of songs, etc.
These aren’t always These aren’t always costlycostly to signalers, but they prevent to signalers, but they prevent cheating because overcoming the constraints (if that’s even cheating because overcoming the constraints (if that’s even possible), would require costs too large to bearpossible), would require costs too large to bear
Doing so, we end up with Doing so, we end up with three types of signalsthree types of signals::
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals3. Types of Signals
Type of cost affects the signal form, i.e. whether the signal is Type of cost affects the signal form, i.e. whether the signal is arbitrary or linked to the signal “message” (e.g. “I am big”)arbitrary or linked to the signal “message” (e.g. “I am big”)
Approach: Approach: classify and name signalsclassify and name signals by the type of cost by the type of costthat guarantees honestythat guarantees honesty
Note: this is yet another area with many different terms and frameworks!Note: this is yet another area with many different terms and frameworks!
A.A. Quality handicap signalsQuality handicap signals
B.B. Index signalsIndex signals
C.C. Costly Conventional signalsCostly Conventional signals
Zahavi (1975, 1977) Zahavi (1975, 1977) proposed that signals need costs to maintain proposed that signals need costs to maintain honesty, and that we should see that animals honesty, and that we should see that animals pay for their pay for their ornaments with fitness costsornaments with fitness costs (e.g. they use up some of what (e.g. they use up some of what they’re advertising)they’re advertising)
Idea not given much credence until 1990, when Grafen created a Idea not given much credence until 1990, when Grafen created a plausible game theory model showing that it works. plausible game theory model showing that it works. Recent work Recent work by Getty makes the story much more complicated!by Getty makes the story much more complicated!
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, A. Quality Handicaps3. Types of Signals, A. Quality Handicaps
Maynard Smith and Harper (1995) discuss how there is a minimum Maynard Smith and Harper (1995) discuss how there is a minimum “efficacy cost” that must be paid to send the signal; handicap signals “efficacy cost” that must be paid to send the signal; handicap signals are “Cost-added signals”, where there are “Cost-added signals”, where there is extra cost paid beyond efficacy cost is extra cost paid beyond efficacy cost to ensure honesty to ensure honesty (this is often forgotten (this is often forgotten in measures of handicap costs)in measures of handicap costs)
CostCost:: necessary costs (signal production costs, predation) necessary costs (signal production costs, predation)
Key featureKey feature:: Poor quality individuals pay a higher cost to Poor quality individuals pay a higher cost to produce a given level or intensity of display compared to high produce a given level or intensity of display compared to high quality individuals (condition-dependent handicap model)quality individuals (condition-dependent handicap model)
Signal formSignal form:: graded and linked to that aspect of quality that the graded and linked to that aspect of quality that the receiver wants to know (signal "uses up" the quality feature of receiver wants to know (signal "uses up" the quality feature of interest).interest).
InformationInformation:: Condition, health, vigor, fighting ability Condition, health, vigor, fighting ability
ContextsContexts:: mate attraction, some agonistic interactions mate attraction, some agonistic interactions
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, A. Quality Handicaps3. Types of Signals, A. Quality Handicaps
1.1. Displaying is costly, reducing Displaying is costly, reducing survival of displayersurvival of displayer
2.2. High-quality male pays lower High-quality male pays lower cost than low-quality malecost than low-quality male
3.3. Females more likely to mate Females more likely to mate with high-investing malewith high-investing male
4.4. Female preference for given Female preference for given display level is not different for display level is not different for high and low quality maleshigh and low quality males
Assumptions:Assumptions:
Grafen 1990 model of mate qualityGrafen 1990 model of mate qualityasymmetric continuous-strategy scrambleasymmetric continuous-strategy scramble
CostCost
oror
BenefitBenefit
Display intensityDisplay intensity
Solution:Solution: At ESS, high-quality males display at a higher intensity than low- At ESS, high-quality males display at a higher intensity than low-quality males, so display intensity is an indicator of male quality or condition. quality males, so display intensity is an indicator of male quality or condition. (Males in better condition may be better parents, or have better genes, etc)(Males in better condition may be better parents, or have better genes, etc)
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, A. Quality Handicaps3. Types of Signals, A. Quality Handicaps
Widowbirds (Malte Andersson, 1982)Widowbirds (Malte Andersson, 1982)
Nes
ting
fem
ales
Nes
ting
fem
ales
Costly graduated tailCostly graduated tail
From BBC From BBC Life of BirdsLife of Birds
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, A. Quality Handicaps3. Types of Signals, A. Quality Handicaps
Carotenoid plumage color in house finches:Carotenoid plumage color in house finches: costly to collect costly to collect and/or costly to use for plumageand/or costly to use for plumage
(Geoffrey Hill 1990, 1991)(Geoffrey Hill 1990, 1991)
Fee
ding
rat
e F
eedi
ng r
ate
by m
ale
by m
ale
Redder males provide moreRedder males provide more
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, A. Quality Handicaps3. Types of Signals, A. Quality Handicaps
Coloration may be heritableColoration may be heritable
Stabilizing costStabilizing cost: physical or physiological constraints: physical or physiological constraints
Key featureKey feature: Signal is physically constrained to be unbluffable : Signal is physically constrained to be unbluffable and honestand honest
Signal formSignal form: inextricably linked to information revealed by signal: inextricably linked to information revealed by signal
InformationInformation: body size, age, pointing: body size, age, pointing
ContextContext: agonistic, mate attraction, predator-prey: agonistic, mate attraction, predator-prey
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, B. Index Signals3. Types of Signals, B. Index Signals
1.1. Form of signal should Form of signal should be linked or associated be linked or associated with some type of with some type of physical or physiological physical or physiological constraintconstraint
2.2. Higher intensity signal Higher intensity signal variants should be more variants should be more effective but not more effective but not more costly to producecostly to produce
Assumptions:Assumptions:
Graphical representation of index signal with continuous state Graphical representation of index signal with continuous state and signal size:and signal size:
SignalSignal
sizesize
oror
intensityintensity
Sender attributeSender attribute
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, B. Index Signals3. Types of Signals, B. Index Signals
Examples: body size indicators, pointers, amplifiersExamples: body size indicators, pointers, amplifiers
Abdomen size is a condition index in the Abdomen size is a condition index in the jumping spider; triangle is an amplifierjumping spider; triangle is an amplifier
gaze direction and pointing signalsgaze direction and pointing signals
Snout-vent length (mm)Snout-vent length (mm)
Fun
dam
enta
l cal
l F
unda
men
tal c
all
freq
uenc
y (k
Hz)
freq
uenc
y (k
Hz)
Call frequency in toads is an Call frequency in toads is an index for body sizeindex for body size
Pointing at Pointing at nest sitenest site
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, B. Index Signals3. Types of Signals, B. Index Signals
Ritualized pushing/pulling contestsRitualized pushing/pulling contests
Young bull elephantsYoung bull elephants
BisonBison Dempsey fishDempsey fish
Elephant seal pupsElephant seal pups
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, B. Index Signals3. Types of Signals, B. Index Signals
Time after feedingTime after feeding
Hue
ran
kH
ue r
ank
% s
atur
atio
n%
sat
urat
ion
In some species, young nestlings exhibit red mouth In some species, young nestlings exhibit red mouth flush, hue and saturation of color increases with hungerflush, hue and saturation of color increases with hunger
• LikelyLikely explanation: Physiologically constrained explanation: Physiologically constrained
(Kilner 1997)(Kilner 1997)
before flush before flush after flushafter flush
Nestlings increase begging as hunger increases (visual and vocal signal)Nestlings increase begging as hunger increases (visual and vocal signal)
Parents respond by increasing their provisioning rateParents respond by increasing their provisioning rate
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, B. Index Signals3. Types of Signals, B. Index Signals
Notification of Detection Signals: Notification of Detection Signals: California Ground California Ground squirrels perform tail-flagging displays to predatory snakessquirrels perform tail-flagging displays to predatory snakes
Adults not in danger from snakes but Adults not in danger from snakes but young in burrows in serious dangeryoung in burrows in serious danger
Parent tail-flag to drive snakes awayParent tail-flag to drive snakes away
Rattlers have IR-sensitive pit organs; Rattlers have IR-sensitive pit organs; GS’s produce an IR signal to GS’s produce an IR signal to emphasize tail movementemphasize tail movement
Gopher snakes are not IR-sensitive, Gopher snakes are not IR-sensitive, and GS’s don’t use IRand GS’s don’t use IR
Aaron Rundus, UCD grad student in Aaron Rundus, UCD grad student in Animal Behavior & Don OwingsAnimal Behavior & Don Owings
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, B. Index Signals3. Types of Signals, B. Index Signals
Notification of Detection Signals: Notification of Detection Signals: California Ground California Ground squirrels perform tail-flagging displays to predatory snakessquirrels perform tail-flagging displays to predatory snakes
If snake is not deterred, these If snake is not deterred, these bad-ass squirrels attack…bad-ass squirrels attack…
When rattlers rattle, GS’s can When rattlers rattle, GS’s can determine threat level (cue?)determine threat level (cue?)
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, B. Index Signals3. Types of Signals, B. Index Signals
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types, C. Costly Conventional Signals3. Types, C. Costly Conventional Signals
CostCost:: Stabilizing cost is Stabilizing cost is incidental incidental (receiver retaliation)(receiver retaliation)
Key featureKey feature:: Retaliation rule: receivers "test" senders giving a Retaliation rule: receivers "test" senders giving a signal of similar size to their own (they dominate senders giving signal of similar size to their own (they dominate senders giving smaller signals, and retreat from senders giving larger signals); smaller signals, and retreat from senders giving larger signals); cheaters get caught because when they’re tested, they can’t cheaters get caught because when they’re tested, they can’t back it up. Cost of signal is thus higher for weak individuals. back it up. Cost of signal is thus higher for weak individuals.
Signal formSignal form:: Arbitrary ( Arbitrary (symbolicsymbolic) and antithetical, discrete or graded) and antithetical, discrete or graded
InformationInformation:: condition, fighting ability, motivation to escalate condition, fighting ability, motivation to escalate
ContextContext: : Agonistic interactions, cannot evolve Agonistic interactions, cannot evolve solelysolely for mating for mating
• Size of patch is strongly correlated with Size of patch is strongly correlated with dominance rankdominance rank
• Males with experimentally enlarged Males with experimentally enlarged patches were attacked more oftenpatches were attacked more often
1.21.2
1.01.0
.8.8
.6.6
.4.4
.2.2
00
ControlsControls Experimentally Experimentally enlarged enlarged patchespatches
(Møller 1987)(Møller 1987)
What kind of cost?What kind of cost? Sender Incidental costs Sender Incidental costs
Agg
ress
ive
enco
unte
rs
Agg
ress
ive
enco
unte
rs
per
15 m
inpe
r 15
min
Conventional signals not used Conventional signals not used solelysolely for female choice only; Why?for female choice only; Why?
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types, C. Costly Conventional Signals3. Types, C. Costly Conventional Signals
Do animals ever lie, bluff, or cheat?Do animals ever lie, bluff, or cheat?
Although prior models imply that cheating is rare, there are Although prior models imply that cheating is rare, there are some clear examples of occasional dishonesty and bluffing in some clear examples of occasional dishonesty and bluffing in otherwise “honest signals”otherwise “honest signals”
A mixture of honest signals and low levels of bluff may be A mixture of honest signals and low levels of bluff may be common. Possible reasons:common. Possible reasons:
• Perceptual errors by receivers may allow some cheaters Perceptual errors by receivers may allow some cheaters to escape detectionto escape detection
• Co-evolving sender/receiver systems have not reached Co-evolving sender/receiver systems have not reached an equilibriuman equilibrium
• It may be to costly for receivers to get perfect information It may be to costly for receivers to get perfect information (how much cheating to allow is an optimization problem)(how much cheating to allow is an optimization problem)
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,4. Cheating4. Cheating
Tolerating deceit: Tolerating deceit: PhotinusPhotinus and and PhoturisPhoturis fireflies fireflies
PhotinusPhotinus
PhoturisPhoturis
Male Male PhotinusPhotinus flash in species-specific flash in species-specific patterns; females flash back, and males patterns; females flash back, and males approach to mateapproach to mate
PhoturisPhoturis mimic the response flash of mimic the response flash of females, then eat the males = deceitfemales, then eat the males = deceit
Why do males respond to the female Why do males respond to the female signals?signals?
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,4. Cheating4. Cheating
Tolerating deceit: Tolerating deceit: PhotinusPhotinus and and PhoturisPhoturis fireflies fireflies
PhotinusPhotinus
PhoturisPhoturis
Males can’t find females without the Males can’t find females without the signals, so the benefit of responding to signals, so the benefit of responding to the signals is largethe signals is large
PhoturisPhoturis only eat males in 10-15% of only eat males in 10-15% of attempts, so cost is small attempts, so cost is small on averageon average
So it is optimal for male So it is optimal for male PhotinusPhotinus to to respond to female signals even though respond to female signals even though they occasionally get eatenthey occasionally get eaten
Optimality Optimality ≠ Perfection!!≠ Perfection!!
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,4. Cheating4. Cheating
Tolerating exploitation: Tolerating exploitation: Tungara frogs & bats (Ryan 1982)Tungara frogs & bats (Ryan 1982)
Female Tungara frogs prefer males Female Tungara frogs prefer males that produce a “chuck” callthat produce a “chuck” call
Bats can use the chuck to localize the Bats can use the chuck to localize the males (quick onset, broadband)males (quick onset, broadband)
It is optimum for males to produce the It is optimum for males to produce the calls, despite the risk of exploitation by calls, despite the risk of exploitation by bats (benefits outweigh costs)bats (benefits outweigh costs)
Males chuck less when females Males chuck less when females absent; some males let other males absent; some males let other males chuck, then intercept femaleschuck, then intercept females
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,4. Cheating4. Cheating
When there is a conflict of interests between the When there is a conflict of interests between the sender and receiver:sender and receiver:
Most signals seem to be Most signals seem to be relativelyrelatively accurate and honest accurate and honest due to receiver selection for costly signals, but a low level due to receiver selection for costly signals, but a low level of inaccuracy and cheating is probably commonof inaccuracy and cheating is probably common
When there is very little to no conflict of interests When there is very little to no conflict of interests between the sender and receiver:between the sender and receiver:
Honesty is easier to maintain, since both parties benefit Honesty is easier to maintain, since both parties benefit from honestyfrom honesty
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,4. Cheating4. Cheating
(Dawkins and Guilford, 1994)(Dawkins and Guilford, 1994)
• Male bluehead wrasse increase the Male bluehead wrasse increase the rate of fin movement as they approach rate of fin movement as they approach spawningspawning
• Spots on fins ‘amplify’ movementSpots on fins ‘amplify’ movement
• Rate of movement gives information Rate of movement gives information about the male’s ‘intention’ to spawnabout the male’s ‘intention’ to spawn
• Male and female both benefit from Male and female both benefit from coordinating spawningcoordinating spawning
Low-costLow-cost signals occur with low conflict of interest signals occur with low conflict of interest
If little to no conflict, no-cost conventional signals are stable, and If little to no conflict, no-cost conventional signals are stable, and everyone benefits by following the ruleseveryone benefits by following the rules
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,5. Communication with low conflict5. Communication with low conflict
SIGNAL TYPESIGNAL TYPE COSTCOST SIGNAL DESIGNSIGNAL DESIGN INFORMATIONINFORMATION
Quality Quality handicaphandicap
Necessary Necessary costs: costs: production, production, time, predationtime, predation
Graded display, Graded display, intensity correlated intensity correlated with sender qualitywith sender quality
Health, condition, Health, condition, stamina, fighting abilitystamina, fighting ability
IndexIndexPhysiological Physiological and physical and physical constraintsconstraints
Discrete or graded, Discrete or graded, form linked to sender form linked to sender attributesattributes
Body size, strength, Body size, strength, age, natal area, age, natal area, pointingpointing
Costly Costly ConventionalConventional
Incidental Incidental Costs: Receiver Costs: Receiver retaliationretaliation
Arbitrary form, Arbitrary form, discrete or graded discrete or graded signalsignal
Motivation, willingness Motivation, willingness to escalate or fighting to escalate or fighting abilityability
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, D. Summary3. Types of Signals, D. Summary
What maintains honesty in human advertising?What maintains honesty in human advertising?
III. Function, c. Honesty in Advertising,III. Function, c. Honesty in Advertising,3. Types of Signals, D. Summary3. Types of Signals, D. Summary
1. Honest signaling:1. Honest signaling: Getty (TREE, 2006) argues that handicaps Getty (TREE, 2006) argues that handicaps are (unfortunately) not as simple as Grafen says. Bergstrom are (unfortunately) not as simple as Grafen says. Bergstrom et al. (et al. (PRSPRS, 2002) show that in some circumstances, low-cost , 2002) show that in some circumstances, low-cost honest signals are possible. Also, lots of empirical work honest signals are possible. Also, lots of empirical work measuring costs...measuring costs...
2. Sensory Drive: 2. Sensory Drive: How does sensory drive shape signals? Can How does sensory drive shape signals? Can this contribute to reproductive isolation & speciation this contribute to reproductive isolation & speciation (Boughman, (Boughman, TREETREE 2002)? 2002)?
3. Noise Impacts:3. Noise Impacts: How does anthropogenic noise affect animal How does anthropogenic noise affect animal communication and thus fitness? (Rabin et al., communication and thus fitness? (Rabin et al., J Comp PsychJ Comp Psych 2003; Warren et al., 2003; Warren et al., Animal BehaviorAnimal Behavior 2006; Patricelli and 2006; Patricelli and Blickley, Blickley, AukAuk 2006) 2006)
III. Function, d. Current Areas of ResearchIII. Function, d. Current Areas of Research
4. Brood Parasitism:4. Brood Parasitism: The arms race between hosts and The arms race between hosts and parasites. Can these arms races lead to speciation? How do parasites. Can these arms races lead to speciation? How do parasites dupe hosts? How do hosts evolve resistance? parasites dupe hosts? How do hosts evolve resistance? (Davies, Kilner, Hauber) (Davies, Kilner, Hauber)
5. Sexual Selection:5. Sexual Selection: What do male signals indicate (e.g. What do male signals indicate (e.g. parasite resistance)? How do traits and prefs evolve (Kokko parasite resistance)? How do traits and prefs evolve (Kokko et al., et al., ARESARES 2006)? Can divergent sexual selection in 2006)? Can divergent sexual selection in isolated populations lead to speciation (Panhuis et al. 2001)?isolated populations lead to speciation (Panhuis et al. 2001)?
6. Multimodal signals / multiple signals: 6. Multimodal signals / multiple signals: Why multiple signals Why multiple signals for the what seems to be the same question? Are they actually for the what seems to be the same question? Are they actually different questions? Are there different receivers (Andersson different questions? Are there different receivers (Andersson et al., AmNat 2002; Coleman et al., et al., AmNat 2002; Coleman et al., Nature Nature 2004)? Is it driven 2004)? Is it driven by efficacy needs (Hebets & Papaj, by efficacy needs (Hebets & Papaj, BES BES 2005)?2005)?
III. Function, d. Current Areas of ResearchIII. Function, d. Current Areas of Research
7. Bird Song: 7. Bird Song: How are songs in a repertoire used in interactions How are songs in a repertoire used in interactions (e.g. song matching)? How are songs learned? How do local (e.g. song matching)? How are songs learned? How do local dialects arise? Do dialects contribute to reproductive isolation dialects arise? Do dialects contribute to reproductive isolation among populations? among populations?
8. Receiver Perceptual systems: 8. Receiver Perceptual systems: How do biases in the How do biases in the sensory and perceptual systems of receivers shape signals? sensory and perceptual systems of receivers shape signals? E.g. How does perception shape comparisons (Bateson & E.g. How does perception shape comparisons (Bateson & Healy Healy TREETREE 2005; Hebets & Papaj, 2005; Hebets & Papaj, BESBES 2005; Ten Cate et 2005; Ten Cate et al., al., Current BiolCurrent Biol 2006)... 2006)...and of course squirrels with IR tails!and of course squirrels with IR tails!
9. Referential/Representational Signals: 9. Referential/Representational Signals: Are signals truly Are signals truly referential to the external world or just the internal state of the referential to the external world or just the internal state of the animal (e.g. fear)? Do they evoke mental representations in animal (e.g. fear)? Do they evoke mental representations in receivers? (Evans & Evans receivers? (Evans & Evans Biol Letters Biol Letters 2006)2006)
III. Function, d. Current Areas of ResearchIII. Function, d. Current Areas of Research
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