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Sexual Selection II The use of models
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Preliminary points My lecture presentations appear in PowerPoint and PDF formats at 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 (pp )
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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?
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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?
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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
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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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?
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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?
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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 Relative Frequency 0.12 0.1 0.08 0.06 0.04 0.02 Male Trait 10
20 30 40 Zygotes
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Zygotes, are subject to differential viability so
Relative Frequency 0.12 0.1 0.08 0.06 0.04 0.02 Male Trait 10 20 30 40 Zygotes, are subject to differential viability so the Survivors have a lower mean.
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Zygotes, are subject to differential viability so
Relative Frequency 0.12 0.1 0.08 0.06 0.04 0.02 Male Trait 10 20 30 40 Zygotes, are subject to differential viability so the Survivors have a lower mean. But females mate preferentially with higher-valued males,
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Zygotes, are subject to differential viability so
Relative Frequency 0.12 0.1 0.08 0.06 0.04 0.02 Male Trait 10 20 30 40 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
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Zygotes, are subject to differential viability so
Relative Frequency 0.12 0.1 0.08 0.06 0.04 0.02 Male Trait 10 20 30 40 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
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Zygotes, are subject to differential viability so
Relative Frequency 0.12 0.1 0.08 0.06 0.04 0.02 Male Trait 10 20 30 40 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)
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Zygotes, are subject to differential viability so
Relative Frequency But what about selection on females? 0.12 0.1 0.08 0.06 0.04 0.02 Male Trait 10 20 30 40 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)
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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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Line of neutral equilibrium Mean preferred trait Mean male trait
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Line of neutral equilibrium Mean preferred trait Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion when genetic covariance is weak Mean male trait 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
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait Strong genetic covariance leads to a line of unstable equilibria
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait Strong genetic covariance leads to a line of unstable equilibria which is a formal version of Fisher’s runaway process
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Line of neutral equilibrium Mean preferred trait Lines of motion with strong genetic covariance Mean male trait Strong genetic covariance leads to a line of unstable equilibria which is a formal version of Fisher’s runaway process
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait To get both the runaway and the eventual stability, we need to bend the line
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait To get both the runaway and the eventual stability, we need to bend the line
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait To get both the runaway and the eventual stability, we need to bend the line
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait To get both the runaway and the eventual stability, we need to bend the line
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait To get both the runaway and the eventual stability, we need to bend the line
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait To get both the runaway and the eventual stability, we need to bend the line
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Line of neutral equilibrium Mean preferred trait Lines of motion Mean male trait To get both the runaway and the eventual stability, we need to bend the line, which is an informal extension of the model.
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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
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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?
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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?
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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
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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?
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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
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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
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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)
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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?
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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
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Two other formal ideas Hamilton/Zuk Handicaps & Signalling
(1982, Science 218: ) Handicaps & Signalling Zahavi (1975, J. Theor. Biol. 53: and 1977, ibid, 67: ) Grafen (1990, J. Theor. Biol. 144: & )
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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
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and is a LOT more fun than statistics!
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 and is a LOT more fun than statistics!
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