Evolution of

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DISPERSAL Conference. Paris 6/7 Dec 2007
Evolution of Condition-Dependent Dispersal under
Kin-Competition Margarete Utz (Éva Kisdi, Mats
Gyllenberg) Biomathematics Research
Group Department of Mathematics and
Statistics University of Helsinki
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Motivation

• Do strong or weak individuals disperse?
• strength / body condition competitive ability
• (and survival during dispersal)
• weak dispersers social dominance
  hypothesis
• strong dispersers

?
!
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Model Assumptions

• Extension of model by Hamilton and May (1977)
• Large metapopulation (number of patches ? 8)
• 1 (female) adult per patch
• Annual, semelparous species
• Constant fecundity large number of offspring (?
  8)
• Kin competition fraction of offspring disperse
  globally
• Patches of varying environmental quality
• Offspring body condition patch quality (no
  maternal effect)
• Dispersal cost decreases with body condition
• Local competition competitive ability increases
  with body condition
• Random reassignment of patch qualities

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Dispersal Strategy
resident strategy dispersal probability
p(z) mutant pm(z) calculate best reply
pm(z) to given strategy p(z) ESS best reply to
itself

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Marginal Value Theorem
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Slope of Best Reply
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Example 1 Weighted Lottery
weight function
simple exchange ratio between strong and weak
individuals in every patch effective number of
non-dispersers
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Example 2 Stronger of 2 Wins
in every patch condition-independent
mortality reduces number of competitors to 2
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Example 3 Strongest of Random Number Wins
k Poi(0.5) truncated P00.61, P10.31,
P20.08, P(k3)0 P00.66, P10.33,
P(k2)0 P00.47, P10.23, P20.3, P(k3)0 k
Poi(2.5) truncated P(k7)0
in every patch condition-independent
mortality reduces competitors to random number
k
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Example 4 Weighted Fair Lottery
µ0.1
small fraction µ of patches fair
lottery fraction 1-µ weighted lottery
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Example 5 Stronger of 5 Wins
in every patch condition-independent
mortality reduces number of competitors to 5
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Conclusions

• We can now explain dispersal of strong
  individuals!
• strong individuals
• high competitive ability high
  dispersal probability
• Second order derivatives shape the best reply!

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Future Work

• Offspring quality distribution
• activates social dominance hypothesis
• Which individuals within a family disperse?
• Trade-off
• mothers fecundity offspring body
  condition
• Environmental patch qualities are constant over
  years
• Do weaklings disperse more and strong
  individuals less?
• propensity of immigrating into a patch better
  than natal patch

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DISPERSAL Conference. Paris 6/7 Dec 2007
Thank you!
Thank you!