Patterns of multiallelic polymorphyism maintained by migration and selection

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Patterns of multiallelic polymorphyism maintained
by migration and selection

• Anthony DOrazio
• Andre De Laire
• Richard Gejji
• Namyong Lee
• Ellen Peterson

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Whats Our Problem?

• Assume 2 patches in an environment with 3 alleles
  present. The fitnesses of these alleles are
  related by
• random starting frequencies If no migration
  winner
• If migration presume A1 A3 survive

A1 A3
When does A2 survive? When do all three types
survive?
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Biological Relevance

• Ambystoma maculatum or the spotted salamander
• Egg masses are either distinctly clear,
  distinctly white or some intermediate.
• Genetic trait
• Differential predation on these masses by
  tadpoles
• Color laid in different ponds appears to
  correspond to frog concentrations.
• However, not much data on the intermediate form
  and it appears to be rarer than the other two.

Ruth, B.C. Dunson, W.A. Rowe, C.L. Hedges,
S.B. (1993). A molecular and functional
evaluation of the egg mass color polymorphism of
the spotted salamander, Ambystoma maculatum
Journal of Herpetology. 27 306-314 Petranka,
J.W. Rushlow, A.W Hopey, M.E. (1998).
Predation by tadpoles of Rana sulvatica on
embryos of Ambystoma maculatum Implications of
ecological role reversals by Rana (predator) and
Ambystoma (prey) Herpetologica. 54 1-13
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Discrete Time and Space Model

• Selection rule for allele Ai in patch l pi,l
  p i,l (?i,l / ?l)
• Frequency of allele Ai in patch k the next
  generation assuming migration pi,l

• Assume
• If

Frequ.
Frequ.
Probability you migrate
Probability you migrate
Get the first by making the generalist fitness
very close to one of the specialists in that patch
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• If

Graph on left when sums are very close. Graph on
right when the summation for allele 2 is
increased a bit
Occurs when the fitness of allele 2 in one of the
patches is very close to that of the specialist
there and the sums are almost equivalent
Conclusions System is dynamic. Appear to get
small ranges of migration for which coexistence
of all three possible but points are
unstable/chaotic. Generalists at high migration
rates depends on total fitness as well as fitness
in each patch. If a specialist survives it is
often the one that is in closest competition with
the generalist assuming the S matrices for the
specialists are not symmetric
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4 Alleles, 3 patches3 Specialists 1 Generalist

• Expect The 3 Specialists will survive
• Specific Case All 4 Alleles survive (at specific
  ? value)
• 2 of the specialists are only well fit in that
  specific patch
• Other two alleles about average in the patches
• Average of the generalist is greater than all of
  the specialist, each specialist has the same
  average

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4 Alleles, 3 patches3 Specialists 1 Generalist
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4 Alleles, 3 patches2 specialists 2 generalists

• 1 specialist 2 generalists survive
• Least fit specialist dies out
• two generalists have the same fitness in each of
  the patches, average fitness is greater than
  either of the specialists average fitness
• Two generalists have the same fitness in one of
  the patches, each of the other two patches one is
  very close to the specialist in that patch
• Most fit generalist dominates all of the patches

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1 Specialist 2 Generalists Survive
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2 specialists 1 generalist Generalist closest
to the fitness of a specialist in a patch survives
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Ideas Future Explorations

• Relativity of specialness
• Number of instances such that coexistence occurs
• Compare ODE model (DSCT) to PDE model (CSCT)

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