Incorporating variability in simulations of seasonally forced phenology using integral projection models.

Devin W Goodsman,Richard S Middleton,Nate G Mcdowell,Brian H Aukema,Chonggang Xu

doi:10.1002/ece3.3590

Abstract

Phenology models are becoming increasingly important tools to accurately predict how climate change will impact the life histories of organisms. We propose a class of integral projection phenology models derived from stochastic individual‐based models of insect development and demography. Our derivation, which is based on the rate summation concept, produces integral projection models that capture the effect of phenotypic rate variability on insect phenology, but which are typically more computationally frugal than equivalent individual‐based phenology models. We demonstrate our approach using a temperature‐dependent model of the demography of the mountain pine beetle (Dendroctonus ponderosae Hopkins), an insect that kills mature pine trees. This work illustrates how a wide range of stochastic phenology models can be reformulated as integral projection models. Due to their computational efficiency, these integral projection models are suitable for deployment in large‐scale simulations, such as studies of altered pest distributions under climate change.

Highlights

Climate change is influencing the phenology of insects and plants with temperature-dependent development rates (Bentz et al, 2010; Cleland, Chuine, Menzel, Mooney, & Schwartz, 2007; Régnière, St-Amant, & Duval, 2012)
Scientists have developed a range of temperature-d ependent phenology models to understand and predict how phenology will change under a warmer climate including degree-day models (Tobin, Nagarkatti, Loeb, & Saunders, 2008), cohort-based models (Logan, 1988), individual-based models (Régnière, Bentz, Powell, & St-Amant, 2015; Régnière & Powell, 2013; Régnière, St-Amant, et al, 2012), and models based on partial differential equations such as the McKendrick–von Foerster equation and its extensions
We demonstrate the utility of stage- and age-structured integral projection models for accommodating phenotypic variation in rate parameters using a temperature-dependent model of mountain pine beetle (Dendroctonus ponderosae Hopkins) phenology and mortality

Summary

Introduction

Climate change is influencing the phenology of insects and plants with temperature-dependent development rates (Bentz et al, 2010; Cleland, Chuine, Menzel, Mooney, & Schwartz, 2007; Régnière, St-Amant, & Duval, 2012). Scientists have developed a range of temperature-d ependent phenology models to understand and predict how phenology will change under a warmer climate including degree-day models (Tobin, Nagarkatti, Loeb, & Saunders, 2008), cohort-based models (Logan, 1988), individual-based models (Régnière, Bentz, Powell, & St-Amant, 2015; Régnière & Powell, 2013; Régnière, St-Amant, et al, 2012), and models based on partial differential equations such as the McKendrick–von Foerster equation and its extensions (von Foerster, 1959; Gilbert, Powell, Logan, & Bentz, 2004; McKendrick, 1926). The development rate multiplied by the time interval (approximate level of development accrued in the time interval) at each time step is cumulatively summed over a time series of varying temperatures experienced by an organism. Popular degree-day-based phenology models that are commonly used to model crop and crop pest phenology (Herms, 2004; Sharratt, Sheaffer, & Baker, 1989) are a subtype of rate summation models in which daily temperatures above the lower temperature threshold are summed over a relevant number of days and specific phenological

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