The intrinsic growth rate as a predictor of population viability under climate warming.

1. Lately, there has been interest in using the intrinsic growth rate (rm) to predict the effects of climate warming on ectotherm population viability. However, because rm is calculated using the Euler-Lotka equation, its reliability in predicting population persistence depends on whether ectotherm populations can achieve a stable age/stage distribution in thermally variable environments. Here, we investigate this issue using a mathematical framework that incorporates mechanistic descriptions of temperature effects on vital rates into a stage-structured population model that realistically captures the temperature-induced variability in developmental delays that characterize ectotherm life cycles. 2. We find that populations experiencing seasonal temperature variation converge to a stage distribution whose intra-annual pattern remains invariant across years. As a result, the mean annual per capita growth rate also remains constant between years. The key insight is the mechanism that allows populations converge to a stationary stage distribution. Temperature effects on the biochemical processes (e.g. enzyme kinetics, hormonal regulation) that underlie life-history traits (reproduction, development and mortality) exhibit well-defined thermodynamical properties (e.g. changes in entropy and enthalpy) that lead to predictable outcomes (e.g. reduction in reaction rates or hormonal action at temperature extremes). As a result, life-history traits exhibit a systematic and predictable response to seasonal temperature variation. This in turn leads to temporally predictable temperature responses of the stage distribution and the per capita growth rate. 3. When climate warming causes an increase in the mean annual temperature and/or the amplitude of seasonal fluctuations, the population model predicts the mean annual per capita growth rate to decline to zero within 100 years when warming is slow relative to the developmental period of the organism (0.03-0.05°C per year) and to become negative, causing population extinction, well before 100 years when warming is fast (e.g. 0.1°C per year). The Euler-Lotka equation predicts a slower decrease in rm when warming is slow and a longer persistence time when warming is fast, with the deviation between the two metrics increasing with increasing developmental period. These results suggest that predictions of ectotherm population viability based on rm may be valid only for species with short developmental delays, and even then, only over short time-scales and under slow warming regimes.