Hanna Kokko and Graeme D. Ruxton. 2000. Breeding suppression and predator-prey dynamics: errata. Ecology 81:1178.

Errata

Corrections to Kokko and Ruxton (2000, Ecology 81:252-260).
Ecological Archives E081-012.

Copyright

Kokko and Ruxton (2000) present a model of adaptive changes in population dynamics. The equations 2a-b used for fitness should read

V_X = S_X(X,Y,m_X) + m_X s_x(X,Y,m_X) (2a)

V_Y = S_Y(X,Y,m_Y) + m_Y s_y(X,Y,m_Y) (2b)

The original equations incorrectly scaled the reproductive value increase that parents obtain by producing offspring by 1/2. While this is true for each offspring in a diploid species, the equations 2a-b refer to female-to-female reproduction only. Since (assuming a 1:1 primary sex ratio) the production of females is associated with production of an equal number of males, the fitness benefit from each brood doubles, thus canceling the diploidy scaling. The corrected equations above match Fisher’s (1930) formulation where only same-sex offspring add to the parent’s fitness, unscaled by relatedness. In a treatment that explicitly includes both sexes, sex-specific reproductive values would have to include genetic relatedness (e.g. Taylor 1988).

This correction removes the factors 2 and 0.5 from equations 4-5. Maximizing V_X and V_Y will, under the correction, always tend to increase rather than decrease population growth rates (though we also note that this may again be violated in an age-structured model where parents may have higher reproductive values than new recruits). The main conclusions of the paper, concerning the range of possible effects on dynamics, however are not altered by the corrected equations. The shape of the new density dependence can still vary in ways that either promote or destroy population stability (Figure 1). Therefore, while parameter values at which specific examples are generated will differ from those presented in Kokko and Ruxton (2000), equivalent examples can be generated. As an example, Figure 2 shows an analogous example to Figure 4 of Kokko and Ruxton (2000), showing predator-induced oscillations.

Literature Cited

Fisher, R.A. 1930. The Genetical Theory of Natural Selection. 1st ed. Clarendon Press, Oxford.

Kokko, H., and G. D. Ruxton. 2000. Breeding suppression and predator-prey dynamics. Ecology 81:252-260.

Taylor, P.D. 1988. Inclusive fitness models with two sexes. Theoretical Population Biology 34:145-168.

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