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![Page 1: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/1.jpg)
Sexual Selection II
The use of models
![Page 2: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/2.jpg)
Preliminary points
• My lecture presentations appear in PowerPoint and PDF formats at http://users.ox.ac.uk/~grafen/lectpres/
• A general reading list appears shortly on a slide (which is therefore online - see above)
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General References• C. Darwin (1871) The Descent of Man and Selection in
Relation to Sex. Republished in 1981 by Princeton University Press. (Extracts in M.Ridley (1987) The Essential Darwin. Unwin Hyman.)
• Andersson, M (1994) Sexual Selection. Princeton University Press
• Dawkins, MS (1995) Unravelling Animal Behaviour, 2nd edn. Chapter 6.
• Krebs, JR & Davies, NB (1993) An introduction to Behavioural Ecology, 3rd edn. Blackwell Scientific.
• Ridley, M (1996) Evolution, 2nd edn. Blackwell Science. Section 11.4. (pp 296-307)
![Page 5: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/5.jpg)
Andersson (1994)
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Why do models matter? An example:
• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
![Page 7: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/7.jpg)
Why do models matter? An example:
• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
![Page 8: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/8.jpg)
This slide and the three following slides show the whole treatment of Fisher’s runaway process in the 1958 edition of Fisher’s Genetical Theory of Natural Selection. The idea was first proposed by Fisher in a paper in 1915.
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and that was that. No equations, just words. An extraordinary and wonderful idea about self-reinforcement of preferences, placed within a context of other selective forces and phases of selection.
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• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
Why do models matter? An example:
![Page 13: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/13.jpg)
• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
Why do models matter? An example:
![Page 14: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/14.jpg)
Before Lande’s model...
• O’Donald (a former student of Fisher’s) had made various models that seemed to show the idea did not work, or worked partially and only in rather unusual circumstances
• Population geneticists were reluctant to accept that a verbal argument could make sense
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Lande’s model
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Zygotes
10 20 30 40Male Trait
0.02
0.04
0.06
0.08
0.1
0.12
RelativeFrequency
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Zygotes, are subject to differential viability so the Survivors have a lower mean.
10 20 30 40Male Trait
0.02
0.04
0.06
0.08
0.1
0.12
RelativeFrequency
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Zygotes, are subject to differential viability so the Survivors have a lower mean.But females mate preferentially with higher-valued males,
10 20 30 40Male Trait
0.02
0.04
0.06
0.08
0.1
0.12
RelativeFrequency
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Zygotes, are subject to differential viability so the Survivors have a lower mean.But females mate preferentially with higher-valued males, so the Successful Gametes have a higher mean than survivors,but in this case, not sufficiently to offset the effect of viability
10 20 30 40Male Trait
0.02
0.04
0.06
0.08
0.1
0.12
RelativeFrequency
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Zygotes, are subject to differential viability so the Survivors have a lower mean.But females mate preferentially with higher-valued males, so the Successful Gametes have a higher mean than survivors,which here more than offsets the effect of viability
10 20 30 40Male Trait
0.02
0.04
0.06
0.08
0.1
0.12
RelativeFrequency
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Zygotes, are subject to differential viability so the Survivors have a lower mean.But females mate preferentially with higher-valued males, so the Successful Gametes have a higher mean than survivors,which here more than offsets the effect of viability(Equilibrium if the blue and red lines are the same)
10 20 30 40Male Trait
0.02
0.04
0.06
0.08
0.1
0.12
RelativeFrequency
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Zygotes, are subject to differential viability so the Survivors have a lower mean.But females mate preferentially with higher-valued males, so the Successful Gametes have a higher mean than survivors,which here more than offsets the effect of viability(Equilibrium if the blue and red lines are the same)
10 20 30 40Male Trait
0.02
0.04
0.06
0.08
0.1
0.12
RelativeFrequency But what about selection on females?
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Selection on female preference happens only
• when there is a genetic correlation between the two traits, and
• there is selection on the male trait
Thus an equilibrium (no change) occurs whenever
• there is no selection on the male trait
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Mean male trait
Mean preferredtrait
Line of neutral equilibrium
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Mean male trait
Line of neutral equilibrium
Mean preferredtrait
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Mean male trait
Line of neutral equilibrium
Lines of motion
Mean preferredtrait
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Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Mean preferredtrait
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Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Mean preferredtrait
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Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Mean preferredtrait
![Page 30: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/30.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Mean preferredtrait
![Page 31: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/31.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Mean preferredtrait
![Page 32: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/32.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Mean preferredtrait
![Page 33: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/33.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Mean preferredtrait
![Page 34: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/34.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion whengenetic covariance is weak
Weak genetic covariance leads to a line of stable equilibria,which is a formal version of Fisher’s eventual balance between natural and sexual selection
Mean preferredtrait
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Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Mean preferredtrait
![Page 36: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/36.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Mean preferredtrait
![Page 37: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/37.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Mean preferredtrait
![Page 38: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/38.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Mean preferredtrait
![Page 39: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/39.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Mean preferredtrait
![Page 40: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/40.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Mean preferredtrait
![Page 41: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/41.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Mean preferredtrait
![Page 42: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/42.jpg)
Mean preferredtrait
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
![Page 43: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/43.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Strong genetic covariance leads to a line of unstable equilibria
Mean preferredtrait
![Page 44: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/44.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Strong genetic covariance leads to a line of unstable equilibriawhich is a formal version of Fisher’s runaway process
Mean preferredtrait
![Page 45: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/45.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motionwith strong genetic covariance
Strong genetic covariance leads to a line of unstable equilibriawhich is a formal version of Fisher’s runaway process
Mean preferredtrait
![Page 46: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/46.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion
To get both the runaway and the eventual stability, we need to bend the line
Mean preferredtrait
![Page 47: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/47.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion
To get both the runaway and the eventual stability, we need to bend the line
Mean preferredtrait
![Page 48: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/48.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion
To get both the runaway and the eventual stability, we need to bend the line
Mean preferredtrait
![Page 49: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/49.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion
To get both the runaway and the eventual stability, we need to bend the line
Mean preferredtrait
![Page 50: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/50.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion
To get both the runaway and the eventual stability, we need to bend the line
Mean preferredtrait
![Page 51: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/51.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion
To get both the runaway and the eventual stability, we need to bend the line
Mean preferredtrait
![Page 52: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/52.jpg)
Mean male trait
Line of neutral equilibrium
Lines of motion
To get both the runaway and the eventual stability, we need to bend the line, which is an informal extension of the model.
Mean preferredtrait
![Page 53: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/53.jpg)
Making the model
• takes all the biology out of the idea...
• ... but, despite what you may first think, this is a good idea! Because...
• it shows the argument is complete in itself
![Page 54: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/54.jpg)
• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
Why do models matter? An example:
![Page 55: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/55.jpg)
• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
Why do models matter? An example:
![Page 56: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/56.jpg)
The model captures
• runaway (i.e. exponential motion)
• balance between natural and sexual selection
• (though formally only in different versions of the model - the extension to both is informal)
• the crucial role of genetic covariance
![Page 57: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/57.jpg)
• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
Why do models matter? An example:
![Page 58: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/58.jpg)
The model does not capture
• the evolution of choosiness in Fisher’s “first phase”
• Fisher’s “cutting away at the roots of the process” by reduced male survival
![Page 59: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/59.jpg)
The model’s narrow effects:• to persuade biologists that Fisher’s idea
was right (in the sense of internally consistent)
• and so to make the study of sexual selection more respectable
• to put linkage disequilibrium centre-stage in thought about sexual selection
• to make explicit the crucial assumption that female choice was costless
![Page 60: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/60.jpg)
The model omits, as Fisher did,
• the costs of choice
• the possibility of disentangling the observed trait and the naturally selected trait
• (which lead on to handicap models)
![Page 61: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/61.jpg)
• Idea: Fisher’s runaway process
• Model: Lande’s model
• Which bits– does the model capture?– does the model miss out?
• How does the model clarify, extend, develop?
Why do models matter? An example:
![Page 62: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/62.jpg)
How does the model mislead?
• Many biologists believed that linkage disequilibrium was the essence of sexual selection (as argued by Steven Arnold)
• (whereas I think a single-locus model of Fisherian self-reinforcing preferences would work)
• The handicap models show this to be wrong
![Page 63: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/63.jpg)
Two other formal ideas
• Hamilton/Zuk– (1982, Science 218:384-387)
• Handicaps & Signalling– Zahavi (1975, J. Theor. Biol. 53: 205-214
and 1977, ibid, 67: 603-605)– Grafen (1990, J. Theor. Biol. 144: 473-516
& 517-546)
![Page 64: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/64.jpg)
Sexual Selection
• is a major part of evolutionary biology today
• is as interesting and controversial as it has ever been
• is the subject of empirical and theoretical studies that inform and inspire each other
![Page 65: Sexual Selection II The use of models. Preliminary points My lecture presentations appear in PowerPoint and PDF formats at grafen/lectpres](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d425503460f94a1d04d/html5/thumbnails/65.jpg)
Sexual Selection
• is a major part of evolutionary biology today
• is as interesting and controversial as it has ever been
• is the subject of empirical and theoretical studies that inform and inspire each other