dechaume-moncharmont | mee 2013 | decision rules in mate choice: how much choice do we (really)...
DESCRIPTION
TRANSCRIPT
1
Decision rules in mate choice:how much choice do we (really) have?
23 mai 2013
F.-X. Dechaume-Moncharmont
Equipe écologie évolutiveUMR CNRS 6282 Biogéosciences
Université de BourgogneDijon, France
Darwin 1871; Andersson 1994; Gibson & Langen 1996
mate choice: a major evolution force
♀
♂
♂♂
♂?
Matthias Galipaud Galipaud et al. (2013) Animal Behaviour
searching, sampling, choice ?
♀
♂
♂♂
♂?
male’s quality
best males are rare
directional preference
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
2
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
3
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
� optimal stopping
Goal: maximizing the probability of finding the best candidate
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
52
45
17
85
41
45
65
67
19
56
88
56
51
46
56
66
63
56
36
18
55
36
32
50
47
67
48
1
62
64
48
9
51
54
48
76
78
52
70
47
51
35
22
33
57
21
53
23
81
63
56
38
61
39
Lindley DV. 1961. Applied Statistics 10:39–51
Stein W et al. 2003. European Journal of Operational Research 151:140-52
n / e ≈ 37 %
� optimal stopping
secretary problemjob search gamemarriage problemgame of googol
Martin Gardner. 1960. Scientific American
Anthony Janetos
> 370 citations
Janetos AC. 1980. Strategies of female mate choice: a theoretical analysis. Behavioral Ecology and Sociobiology 7:107-112
decision rules: (1) threshold decision
(2) best-of-n
threshold
♀
♂♂
♂
♂
with or without last-chance
4
best-of-n
♀
♂♂
♂
♂
best-of-3
male’s quality
µ = 10σ = 1
random
E (
qual
ity o
f the
par
tner
)
quality of the best male among n(increasing function with n)
Barney LuttbegOklahoma State Univ.
Luttbeg B. 2002. Assessing the robustness and optimality of alternativedecision rules with varying assumptions. Animal Behaviour 63:805-814.
Strong hypothesis: once mated, males are immediately available for another copulation! � no competition among females?� irrelevant for monogamous species
Janetos 1980, Real 1990, Wiegmann et al. 1996, Luttbeg 2002, …
most mate-choice models suffer froma severe problem of self-consistency
but see :- Collins & McNamara 1993- Ramsey 2008- Bleu et al. 2012
I. Mate searching and decision rules
Thomas Brom
scramble competition
♀ ♂
♂
♂
♂♀best-of-2
best-of-3
5
frequency dependence � game theory
♀♂
♂♀best-of-2
best-of-3
individual based simulations
linux clusterCCUB - CRI uB
♂
m males
f females
µ = 10σ = 1
directional preference
Baya weavers (Tisserin Baya )
Ploceus philippinus
Pomatoschistus minutus
one-sided choice
Cyathopharynx furcifer
satin bowerbird (Jardinier satiné) Ptilonorhynchus violaceus
ESS(no mutant can outperform the resident strategy)
evolutionary stable strategy (ESS)
mea
n th
resh
old
number of generation
10 000 simulations
best-of-nasynchronous(Poisson process)
synchronous
msex-ratio =
m + f ♂♀
6
threshold
last chanceno last chance
msex-ratio =
m + f ♂♀
David RamseyUniv. of Limerick
Ramsey, D. M. 2008. A large population job search game with discrete time.European Journal of Operational Research 188:586-602.
Theorem. Suppose the values of the jobs initially available havea continuous distribution and α > 1, then the unique subgameperfect Nash equilibrium strategy is to accept any job.
nb of searchers 1α = = - 1
nb of jobs sex-ratio
job search game
« I married the first man I ever kissed. When I tell this to my children they just about throw up »
« Falling in love can be seen as a powerfull stopping rule that ends the current search for partner (at least temporarily). »
(Gigerenzer & Todd 1999)
random
best-of-n (async.)
threshold
effect of mu ?perspective effect
(Janetos 1980)
µ = 10
σ = 1
µ = 1
µ = 3
µ = 10
µ = 20
7
+ : sex-ratio = 0.6∆ : sex-ratio = 0.5
o : sex-ratio = 0.45
threshold
best-of-n
distribution of males’ qualitychoice with errors
(Houston 1997)
λ controls the weight given to errors on male choice
1p =
1 + exp [ -λ(W – Wc) ]
perfect assessment
blurry discrimination
(trivial) take-home message
due to opportunity costs, in case of scramble competition, whatever the quality of the chairs, you can’t afford to be picky!
experimental validations
heuristics v.s. ESS
self-referent preferences
follow-up
multiple cues
mutual mate choiceII. Priority heuristic
Clément Petit
8
Darwin’s pro-con list on getting married
July 1838 (29 years old)
Emma WedgwoodCharles Darwin
Darwin’s pro-con list on getting married
Marry
Children (if it Please God) — Constantcompanion, (& friend in old age) who willfeel interested in one — Object to bebeloved & played with — better than a doganyhow. — Home, & someone to take careof house — Charms of music & femalechit-chat — These things good for one'shealth — but terrible loss of time — MyGod, it is intolerable to think of spendingones whole life, like a neuter bee, working,working, & nothing after all — No, no won'tdo — Imagine living all one's day solitarilyin smoky dirty London House — Onlypicture to yourself a nice soft wife on a sofawith good fire, & books & music perhaps —Compare this vision with the dingy reality ofGrt. Marlbro' St.
Marry — Marry — Marry Q.E.D.
Not Marry
No children, (no second life), no one tocare for one in old age — What is the useof working without sympathy from near &dear friends — Who are near & dearfriends to the old, except relatives —Freedom to go where one liked — Choiceof Society & little of it — Conversation ofclever men at clubs — Not forced to visitrelatives, & to bend in every trifle — Tohave the expense & anxiety of children —perhaps quarelling — Loss of time —cannot read in the Evenings — Fatness &idleness — Anxiety & responsibility — Lessmoney for books — If many children forcedto gain one's bread — (But then it is verybad for ones health to work too much) —Perhaps my wife wont like London; thenthe sentence is banishment & degradationinto indolent, idle fool
weighted sum :2 cues: A and B
lexicographic rule (priority heuristic)
Brandstätter, E., Gigerenzer, G., and Hertwig, R. 2006. The priority heuristic: Making choices without trade-offs. Psychological Review 113:409-432.
(Nuttall & Keenleyside 1993)
lexicographic rule (priority heuristic)
εA
9
lexicographic rule (priority heuristic)
strategy prioritize
« A »
strategyprioritize
« B »
εA
εB
lexicographic rule (priority heuristic)
strategy prioritize
« A »
strategyprioritize
« B »
εA
εB
wA
wB
fitness difference between strategy « A » and strategy « B »
w = 0.5 wA + 0.5 wB
∆W = W (prioritize « A ») - W (prioritize « B »)
fitness difference between strategy « A » and strategy « B »
strategy prioritize « A » wins
w = 0.5 wA + 0.5 wB
A
Bstrategy prioritize « B » wins
∆W
92% of the best choice with weighted sums
fitness gain for strategy prioritize « A »
10
conclusions
scramble competition and opportunity costs could severely impairs choosiness
processes of sampling and/or choice (and not only the resulting pattern) deserves considerable attention fundings:
- ANR blanc « Monogamix »- Institut Universitaire de France (IUF)- UMR CNRS Biogéosciences
acknowledgements: - Matthias Galipaud, Thomas Brom, Clément Petit- Frank Cézilly, Loïc Bollache, Thierry Rigaud (univ. de Bourgogne)- John McNamara ,Tim Fawcett (Univ. of Bristol)- Alexandre Courtiol (Berlin), François Rousset, Loïc Etienne (ISEM) - P.-A. Zitt (Institut de Mathématiques de Bourgogne)