Can Hamilton’s rule be violated?

  1. Matthijs van Veelen  Is a corresponding author
  1. University of Amsterdam, The Netherlands
11 figures and 1 additional file

Figures

The value of coefficients βse and βsi may depend on the specification chosen.

If xco is included (as in specification II), these values will be different from when xco is not included (specification I). Including an interaction term (III) or a quadratic term (IV) will also make …

https://doi.org/10.7554/eLife.41901.002
Within each panel, the fitness functions are depicted in the upper part.

In panels A, B and C the bottom part depicts population structure profiles of mutant co-operators at p=0 (blue) and of mutant defectors at p=1 (red). In panel D the bottom part depicts the …

https://doi.org/10.7554/eLife.41901.003
Dynamics for two 2-player games.

Every point in the simplex represents a population state (f0,f1,f2). The left down corner is (1,0,0), which has only groups with 0 co-operators; the right down corner is (0,0,1), which has only groups with 2

https://doi.org/10.7554/eLife.41901.004
A road map for empirical tests of Hamilton’s rule.

The three synergy conditions are that πC(i)πC(1)+(i1)[ πD(1)πD(0) ] for all i=1,...,n, that πD(i)πD(n1)(ni1)[ πC(n)πC(n1) ] for all i=0,...,n1, and that π¯C(p)π¯D(p) increases with p.

https://doi.org/10.7554/eLife.41901.005
Appendix 1—figure 1
Population structure profiles u_ (blue) for co-operator invaders at p0, and u¯ (red) for defector invaders at p1.

Defectors at p0 only find themselves in groups with 0 defectors, co-operators at p1 only find themselves in groups with n co-operators (not depicted in the figures). In the lower panel mutants …

https://doi.org/10.7554/eLife.41901.008
Appendix 1—figure 2
The population structure profiles are depicted in the lower half of the figure, the payoffs in the upper half.
https://doi.org/10.7554/eLife.41901.009
Appendix 1—figure 3
The population structure profiles are depicted in the lower half of the figure, the payoffs in the upper half.
https://doi.org/10.7554/eLife.41901.010
Appendix 1—figure 4
The population structure profiles are depicted in the lower half of the figure, the payoffs in the upper half.
https://doi.org/10.7554/eLife.41901.011
Appendix 1—figure 5
The previous figures depicted u_, which is the population structure profile at p=0, and u¯, which is the population structure profile at p=1.

The payoffs co-operators get, when they find themselves in groups according to u_ would be compared to the payoffs defectors get when they are in a group of defectors only in order to determine …

https://doi.org/10.7554/eLife.41901.012
Appendix 1—figure 6
The πD according to the regression method coincides the true πD at p0 (top panel, red), but the πC according to the regression method (dotted blue) differs from the true πC (solid blue).

The πD and πC according to the regression method coincide with each other at p=0.5 (middle panel, dotted lines) but do not coincide with the true πD (solid red) and πC (solid blue). The πC according to …

https://doi.org/10.7554/eLife.41901.013
Appendix 1—figure 7
With parameters α=12, β=2 and γ=0.4, the equilibrium frequency of co-operators, at which π¯C(p)=π¯D(p), is p=0.465.

Inclusive fitness there is 14(1.82)(0.4)0.0550. Section X specifies the fp(x) for this example.

https://doi.org/10.7554/eLife.41901.014

Additional files

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