Evol Ecol Res 16: 631-647 (2014) Full PDF if your library subscribes.
Environmental variation does not always promote plasticity:
evolutionarily realized reaction norm for costly plasticity
Atsushi Yamauchi1 and Daisuke Takahashi1,2
1Center for Ecological Research, Kyoto University, Otsu, Japan and 2Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden
Correspondence: A. Yamauchi, Center for Ecological Research, Kyoto University, Hirano 2-509-3, Otsu 520-2113, Japan.
Question: How does environmental variability influence evolutionarily realized phenotypic plasticity?
Mathematical method: Optimization in a spatially fluctuating environment.
Key assumptions: Either the maintenance cost of plasticity results from the amount of phenotypic response, or it results from the slope of the reaction norm. And there are two alternative types of state-specific benefit functions: either the benefit is maximal at an intermediate phenotype, or it is a monotonically increasing function of phenotype.
Conclusion: Organisms may not respond to rare environmental states. In this case, environmental variability suppresses two indices of phenotypic plasticity, i.e. the range of plasticity and the maximum slope of the reaction norm.
Keywords: environmental fluctuation, model, optimization, phenotypic plasticity.
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