Bulletin of Mathematical Biology

, Volume 73, Issue 5, pp 1052–1081 | Cite as

Evolution Stabilises the Synchronising Dynamics of Poikilotherm Life Cycles

Original Article


Temperature is the most significant factor controlling developmental timing of most temperate poikilotherms. In the face of climate change, a crucial question is how will poikilothermic organisms evolve when faced with changing thermal environments? In this paper, we integrate models for developmental timing and quantitative genetics. A simple model for determining developmental milestones (emergence times, egg hatch) is introduced, and the general quantitative genetic recursion for the mean value of developmental parameters presented. Evolutionary steps proportional to the difference between current median parameters and parameters currently selected for depend on the fitness, which is assumed to depend on emergence density. Asymptotic states of the joint model are determined, which turn out to be neutrally stable (marginal) fixed points in the developmental model by itself, and an associated stable emergence distribution is also described. An asymptotic convergence analysis is presented for idealized circumstances, indicating basic stability criteria. Numerical studies show that the stability analysis is quite conservative, with basins of attraction to the asymptotic states that are much larger than expected. It is shown that frequency-dependent selection drives oscillatory dynamics and that the asymptotic states balance the asymmetry of the emergence distribution and the fitness function.


Quantitative genetics Frequency dependent selection Evolution of phenology Developmental rate curves 


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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK
  2. 2.Department of Mathematics and StatisticsUtah State UniversityLoganUSA

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