Integration of thermal time and hydrotime models to describe the development and growth of temperate earthworms

• We modelled temperate earthworm response to temperature (T) and water potential (Ψ).
• A thermal time model was used for growth and cocoon development responses to T.
• As Ψ and T were shown to interact, the current hydrothermal time was not suitable.
• A thermal time model including the effect of water potential was proposed.
• In this model, thermal time is constant while cardinal temperatures varies with Ψ.

Thermal time and hydrotime models have been developed to predict the development of various organisms with life traits regulated by temperature and humidity. They consider development rate to increase linearly with temperature or water availability above a base temperature or water potential. The objective of this work was to integrate concepts from thermal time and hydrotime models to describe the combined effects of temperature and water potential on development and growth of temperate earthworms. The model was calibrated with experimental data from the scientific literature. When water potential conditions were favourable for earthworms, the thermal time model suggested a linear increase in cocoon development and growth with increasing temperature between the base temperature (Tb) and the optimal temperature (To) followed by a linear decline in these parameters between To and the ceiling temperature (Tc). The model predicted Tb values of 4.3 °C and 2.5 °C, To values of 21.2 °C and 17.6 °C, and Tc values of 38.1 °C and 25.8 °C for cocoon development and growth, respectively. Development and growth rates were maximal at optimal temperatures To of 21.2 and 17.6 °C, respectively. Cocoon development rate and growth rate increased linearly between Tb and To. Above To, development and growth rates decreased linearly until Tc, at which both rates are null. For anecic species, Tc was found to be 38.1 and 25.8 °C for cocoon development and growth, respectively. At constant temperature, cocoon development and growth decreased linearly with water potential, as described by the hydrotime model. Base water potential (the water potential at which life history parameter values are zero) was found to be close to very wet conditions for growth (−23 and −10 kPa for juveniles and adults, respectively) and cocoon production (−32 kPa). The integrated model incorporated the effect of water potential into the thermal time model. Water potential modified the three cardinal temperatures (Tb, To and Tc) for growth and the growth rate at To, but not the slopes of the relationships between growth rate and temperature. Thus, increasing water potential reduced the temperature range at which earthworm growth was possible and the maximum growth at the optimal temperature. No data was available to validate this model for cocoon development.