Modelling environmental effects on the variance of male sexual ornament exaggeration - PowerPoint PPT Presentation

Loading...

PPT – Modelling environmental effects on the variance of male sexual ornament exaggeration PowerPoint presentation | free to view - id: 15785-NjBhO



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Modelling environmental effects on the variance of male sexual ornament exaggeration

Description:

... Anole, Spectacled Parrotfish, Lamborghini courtesy of Wikipedia, www. ... Lamborghini with girls courtesy of Robert S. Hatrak II, www.hatrak.smugmug.com ... – PowerPoint PPT presentation

Number of Views:170
Avg rating:3.0/5.0
Slides: 29
Provided by: Office20093
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Modelling environmental effects on the variance of male sexual ornament exaggeration


1
Modelling environmental effects on the variance
of male sexual ornament exaggeration
  • Sam Tazzyman
  • Supervised by Prof. Andrew Pomiankowski and Prof.
    Rob Seymour

2
Sexual selection - a recap
  • Since girls put more resources in to each choice,
    they have to pick wisely
  • Since boys put less resources in to each choice,
    they can spread it around
  • Thus girls choose, boys are chosen

3
How is a girl to choose?
  • To impress the ladies, males have sexual
    ornaments
  • The more exaggerated the ornament, the more
    attractive the male
  • There are a huge variety of such ornaments in the
    natural world

4
Stalk-eyed flies
  • My model is based upon stalk-eyed flies
  • Males have big eye spans as a sexual
    characteristic
  • Females also have eye stalks, but they are
    smaller
  • In good environments, a males eye stalks will be
    even bigger
  • I work on averages over whole populations

5
The model
  • My model incorporates the handicap principle, in
    that the size of a males ornament is partially
    dependent on his viability
  • Mean ornament size and mean preference are
    allowed to evolve to equilibria

6
Varying variance
  • Experiments show that in poor environments, the
    size of the males eye-stalks relative to their
    body size varies much more
  • In good environments it varies less
  • Why should this be so?

David, P., Bjorksten, T., Fowler, K. and
Pomiankowski, A. 2000 Condition-dependent
signalling of genetic variation in stalk-eyed
flies. Nature (letter) 406, 186-188.
7
Varying variance
  • Each line represents the mean relative eye span
    of a group of full-siblings
  • Genetic variance increases with stress

Good
Poor
David, P., Bjorksten, T., Fowler, K. and
Pomiankowski, A. 2000 Condition-dependent
signalling of genetic variation in stalk-eyed
flies. Nature (letter) 406, 186-188.
8
The maths
  • There are lots of variables in the model
  • Concentrate upon t and v, and their product
    utv
  • ? t and ?t are fixed, since the distribution of
    t is at equilibrium and is normal

9
The maths
  • The distribution of v is more complicated

10
The maths
  • The parameter q?g
  • ? is the environmental quality experienced by the
    individual
  • g is the individuals genetic quality
  • Both log-normally distributed
  • Thus q also log-normally distributed

11
The maths
  • So whats the distribution of v?
  • Recall from before that
  • q log-normally distributed

12
The maths
  • We know the distributions of t and of v
  • We can find the distribution of utv
  • This directly affects the distribution of
    ornament sizes
  • If this distribution varies more, ornament size
    varies more

13
The maths
  • The variance ?u2 of u cannot be explicitly found,
    and nor can the variance ?v2 of v
  • ?u2 will be dependent upon the values of
    ?t2,?t,?v2 and ?v
  • ?v2 and ?v are in turn dependent upon the values
    of ?q2 and ?q

14
The maths
  • q is a measure of quality environmental and
    genetic
  • I interpret an increase in ?q with no change in
    ?q2 as an improvement in environmental conditions
  • Thus I plot changes in ?u2 with changing ?q

15
The biology
  • Does this strange curve make sense?

16
The biology
  • Section 1 - dystopia
  • In this region
  • Resources almost zero
  • v0 for all individuals
  • ?u2 thus very small

17
The biology
  • Section 2 - increase in variance of viability
  • In this region
  • Resources still quite scarce
  • v spreads throughout the range due to variation
    in g
  • ?u2 thus increases to a maximum

18
The biology
  • Section 3 - decrease in variance of viability
  • In this region
  • Resources increasingly available
  • More and more individuals have v1
  • ?u2 thus decreases to a local minimum

19
The biology
  • Section 4 - the dash to utopia
  • In this region
  • v increasing very slightly at a similar rate for
    everyone
  • ?u2 increases to asymptote at ?t2, the
    underlying genetic variance in t

20
Mimicking the experiment
  • Using the model, it is simple to produce results
    similar to those seen in the experiment

21
Mimicking the experiment
22
But…
  • Recall the asymptote at ?t2
  • Increasing the ?t2-value will produce
    qualitative differences

23
So…
  • There is a threshold in the relationship between
    ?t2 and ?v2
  • Unfortunately this is again not analytically
    discoverable

24
Thus…
Depending on the underlying conditions of the
population
25
What does this mean?
  • These underlying conditions arent directly
    expressible mathematically due to the complicated
    formulation of v
  • Imprecisely, whether a population is above or
    below the threshold will depend on the variance
    in viability compared to the variance in tail
    size genetics

26
The future?
  • A different (analytically solvable) formulation
    for v?
  • Different underlying assumptions? (t not normal,
    or not at equilibrium?)
  • Experiments to try and find a population
    increasing in variance as environment improves?

27
References
  • Papers
  • David, P., Bjorksten, T., Fowler, K. and
    Pomiankowski, A. 2000 Condition-dependent
    signalling of genetic variation in stalk-eyed
    flies. Nature (letter) 406, 186-188.
  • Iwasa, Y. and Pomiankowski, A. 1994 The evolution
    of mate preferences for multiple sexual
    ornaments. Evolution 48, 853-867.
  • Photos
  • Stalk-eyed fly 1, All Peafowl photos, Lesser Bird
    of Paradise, Carolina Anole, Spectacled
    Parrotfish, Lamborghini courtesy of Wikipedia,
    www.wikipedia,org
  • Mandrill courtesy of the Pi Pacific Institute for
    Mathematical Sciences, www.pims.math.ca
  • Rhino beetle courtesy of Faunapolis,
    www.faunapolis.org
  • Lamborghini with girls courtesy of Robert S.
    Hatrak II, www.hatrak.smugmug.com
  • Stalk-eyed fly 2 and mating flies courtesy of
    Stalk-eyed fly research group, UCL,
    www.ucl.ac.uk/ucbhkof

28
Thats all, folks!
About PowerShow.com