An index to measure the effects of temperature change on trophic interactions

Experimental studies document the fact that environmental temperature changes can affect the timing of interactions in many consumer-resource systems through altered, or shifted, phenologies of the species involved. We develop a simple mathematical model that shows one method to measure, quantitatively, the magnitude of the shift. Under different temperature regimes we compute the intersection of two regions in a joint phenology space: the region where temporal interactions can occur and the region where particular-sized predators consume particular-sized prey. The area of the intersection provides a numerical value for measuring the effective interaction. A comparison of the areas for different temperature histories defines an index, or yardstick, for quantitatively assessing the effects of temperature variations on phenological shifts.