[Start playing with the R Shiny app or download the source files from my GitHub to run it locally in RStudio]
This interactive model—developed with Chris Johnson—projects the population dynamics a simple organism that has two temperature-sensitive life stages, a juvenile and an adult. We might choose such a model for organisms like frogs (tadpoles/adults), insects (larvae/adults), or other poikilothermic ectotherm. The model assumes that each stage has an optimal temperature for its various life history functions. Adult reproduction rates are highest at 20°C, dropping sharply and symmetrically at lower or higher temperatures. Development is slow at low temperatures, peaks around 21-22°C, and drops to zero around 30°C. Finally, mortality for both stages increases with increasing temperature, but does so more rapidly for adults.
The model takes the form of a system of differential equations, shown in the “Model description” tab. Users have the opportunity to move a temperature slider to explore how the densities of juveniles and adults are projected to change as a function of temperature. The key insights are that:
life history trade-offs mean that optimizing one demographic rate inevitably moves other rates off their optima
juveniles and adults have different “values” for total population density
the equilibrium stage structure is highly sensitive to temperature
populations can crash well within the physiological temperature limits of individuals
Recommended reading:
Johnson, C. A., Coutinho, R. M., Berlin, E., Dolphin, K. E., Heyer, J., Kim, B., Leung, A., Sabellon, J. L. and Amarasekare, P. (2016), Effects of temperature and resource variation on insect population dynamics: the bordered plant bug as a case study. Functional Ecology 30:1122–1131. doi: 10.1111⁄1365-2435.12583 link