Modeling the Effects of Constant and Variable Temperatures on the Vital Rates of an Age-, Stage-, and Sex-Structured...

We present a general and flexible mathematical model (called SANDY) that can be used to describe many biological phenomena, including the phenology of arthropods. In this paper, we demonstrate how the model can be fitted to vital rates (i.e., rates associated with development, survival, hatching, and oviposition) of the two-spotted spider mite (Tetranychus urticae (Koch)) exposed to different constant temperatures ranging from 15°C to 37.5°C. SANDY was incorporated into an age-, stage- and sex-structured dynamic model, which was fitted to cohort life-tables of T. urticae conducted at five constant temperatures (15, 20, 25, 30, and 35°C). Age- and temperature-dependent vital rates for the three main stages (eggs, immatures, and adults) constituting the life-cycle of mites were adequately described by the SANDY model. The modeling approach allows for simulating the growth of a population in a variable environment. We compared the predicted net reproductive rate (R0) and intrinsic rate of natural increase (rm) at fluctuating temperatures with empirical values obtained from life-table experiments conducted at temperatures that changed with a daily amplitude (±0, ±3, ±6, ±9, and ±12°C) around an average of 22°C. Results show that R0 decreases with increasing amplitude, while rm is more robust to variable temperatures. An advantage of SANDY is that the same simple mathematical expression can be applied to describe all the vital rates. Besides, the approach is not confined to modeling the influence of a single factor on population growth but allows for incorporating the combined effect of several limiting factors, provided that the combined effect of the factors is multiplicative.