Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Response of Poikilotherms to Extreme Temperature Events
Rebecca C. Tyson, Garrett Culos

Last modified: 2014-03-28


Mean temperature, the frequency of extreme climatic events, and temperature variability, are all projected to increase as a result of the current trends in climate change. In order to maximize our ability to mitigate the negative effects of climate change, it is important that we study the effects of extreme temperature events, and temperature variability. For populations whose development is temperature-dependent, these temperature variations can have strong effects on development and population dynamics. While small scale effects can be understood through experimental manipulations in the laboratory, population-level effects are more difficult to determine.


Temperature change has been shown to shift tree lines towards higher altitudes, and affect the home-range of many biological systems, such as the expansion of red fox northward and the parallel retreat of the arctic fox. Although the effects of shifting range boundaries and isotherms are being actively studied, temperature variability has been given much less attention. Nonetheless, even without large increases in temperature, increased variability in climatic conditions can have a strong effect on species survival. Increased variability in precipitation is likely to have hastened the extinction of two well known butterfly populations while variability in temperature has been demonstrated to have an effect on the extinction time of long-lived shorebirds. For Zooplankton, temperature variability has a major effect on its growth rates and generation times.


In this paper, we focus on poikilotherms, organisms whose development rate throughout each life stage is dictated by environmental temperature. Moreover, the different life stages of an organism, often separated by different morphologies, can develop at different rates over different temperature ranges. The developmental rates of an organism can be related to a host of processes including voltinism (number of generations per year), as well as the fecundity and mortality of the organism. The intrinsically non-linear relationship between ambient temperature and development is difficult to analyze without a mathematical model. Modeling with mathematics provides a relatively inexpensive alternative to field and/or laboratory studies, and a single model can be used as a basis for testing a wide variety of extreme temperature events superimposed on any plausible baseline annual temperature profile.


We investigate a temperature driven model to simulate and analyze the generational effects of thermal perturbations on poikilotherms, where thermal perturbations include increases in mean annual temperature, increases in daily and annual temperature swings, and extreme temperature events. Using information about the temperature-dependent developmental rates (inverse developmental times) for each life stage, we can analyze the stability of the organism's life-cycle under different thermal perturbations. The model is based on the G-function (generation function) model developed by Powell (Powell & Logan (2005) Theoretical Population Biology 67(3):161-79).




climate change, development rate, mathematical model, poikilotherm, G-function analysis