Effects of temperature on development, survival and reproduction of insects: Experimental design, data analysis and modeling
Graphical abstract
Highlights
► Methodology for analysis of development, reproduction, survival thermal responses. ► From individuals observed under controlled but not necessarily constant temperatures. ► Using censored data and temperature transfer treatments at near-threshold extremes. ► Parsing variance into individual (intrinsic) and lack-of-fit (extrinsic) components. ► By maximum likelihood (examples include all life stages of mountain pine beetle).
Introduction
The physiological responses of organisms to temperature have had considerable attention in the scientific literature for more than a century. Recently, debate focused on a Metabolic Theory of Ecology (MTE) where temperature and body weight are the fundamental determinants of the rates at which life’s central processes occur: metabolism, development, reproduction, population growth, species diversity and even ecosystem processes (Brown et al., 2004). Discussion centers around the existence of a Universal Temperature Dependence (UTD), in the form of the exponential Arrhenius equation where r is some rate, b0 is a proportionality constant that varies between processes and taxa, E ≈ 0.6 to 0.7 eVK−1 is a near-constant activation energy, and k = 8.6173 × 10−5 eVK−1 is the Boltzmann constant relating energy to temperature, K (°K). Arguments have centered on the validity and universality of the UTD (Clarke, 2006, Clarke and Fraser, 2004, Huey and Kingsolver, 2011) and the constancy and ecological correlates of its main parameter E (Dell et al., 2011, Irlich et al., 2009). The UTD provides an adequate description of biological rate responses over a limited range of temperatures but over the range of temperatures to which poikilotherms such as insects are exposed, responses to temperature are unimodal (Sharpe and DeMichele, 1977, Knies and Kingsolver, 2010). Consequently, the breadth of temperature range, thresholds and optimum temperatures at which this unimodality is expressed, as well as their variability are critical (Angilletta et al., 2002, de Jong and van der Have, 2009, Dixon et al., 2009).
For cold-blooded organisms, including insects, the relationships between ambient temperature and development, survival and reproduction scale up from daily or even hourly effects on individuals to seasonal patterns of phenology (Schwartz, 1998, Visser and Both, 2005), population dynamics (Logan et al., 2006, Yang and Rudolf, 2010), and species distributions including the expanding interest in responses to climate change (Bentz et al., 2010, Kramer et al., 2000, Powell and Logan, 2005, Régnière and Logan, 2003, Sparks and Carey, 1995). Models that aim to predict the effects of temperature on the outcomes of these processes must account for the nonlinear nature of the thermal responses involved (Régnière and Logan, 2003, Schaalge and van der Vaart, 1988, Smerage, 1988), as well as the intraspecific and intrapopulation variability in these responses.
The intrinsic variability of developmental rates among individuals within populations (sensu Yurk and Powell, 2010) influences the observed distribution of phenological events in those populations. Thermal responses are often asymmetrically distributed and as such they can alter the timing of life stages (Gilbert et al., 2004) and its demographic consequences (Bellows, 1986, Powell and Bentz, 2009). From mathematical descriptions of these distributions, simulation models can generate age or stage frequencies including survival and reproduction over time in response to temperature input regimes. The most commonly used model categories are distributed delays (Manetsch, 1976), cohort-based (Sharpe et al., 1977), and individual-based (Cooke and Régnière, 1996, DeAngelis and Gross, 1992, Grimm, 2008).
Three issues in the design and analysis of temperature response experiments used to estimate parameters of phenology models are: (1) analysis of development times or their inverse, development rates (Kramer et al., 1991); (2) estimation of development times at temperatures near thresholds (extremes) where excessive mortality or developmental abnormalities such as the inability to hatch from an egg may occur; and (3) the relationship between individual variation and average developmental rates (Régnière, 1984, Wagner et al., 1984) and reproductive responses (Régnière, 1983).
In this paper, we propose a formal methodological framework within which to design experiments and analyze data on insect development, survival and reproduction responses estimated from individuals observed living in controlled, but not necessarily constant, temperatures. Our framework allows: (1) the use of censored data, where observations are interrupted after a certain time; (2) parsing of variance contributions between individual (intrinsic) and lack-of-fit; and (3) more precise estimation of thresholds by the transfer of individuals between extreme and moderate temperatures. It expands, simplifies and unifies the analysis of laboratory data parameterizing the thermal responses of insects in particular and poikilotherms in general. We demonstrate this approach using simulated data, data from the literature on the eastern spruce budworm Choristoneura fumiferana (Clem.), the spruce budmoth Zeiraphera canadensis Nutuua and Freeman (Lepidoptera: Tortricidae), the melon fly Bactrocera cucurbitae (Coquilett) (Diptera: Tephritidae), as well as new data from the mountain pine beetle Dendroctonus ponderosae Hopkins (Coleoptera: Curculionidae, Scolytinae) and the western spruce budworm C. occidentalis Freeman (Lepidoptera: Tortricidae).
Section snippets
Rate-summation models of insect development
The development rates of insects are rarely measured directly. Instead, they are calculated as the inverse of observed development time, such as the number of days between oviposition and hatch or between successive larval moults, and are expressed as proportions of total stage duration per unit of time. Development time and rate are related by:where τ(T,A) represents the modeled average time required to complete the life stage at temperature T, and A is a vector of parameter
Simulated dataset
To illustrate the analytical approach and test the efficacy of censoring and temperature transfer treatments on improving the quality of the thermal response functions obtained, we used a simulated dataset. First, we generated a “true” thermal response using Eq. (A6) with A = {Tb = 5, Δb = 0.1, Tm = 33, Δm = 3, ω = 0.13, ψ = 0.01}, σδ = 0.15 and συ = 0.1. This function includes explicitly two developmental thresholds and their respective boundary regions (Tb, Δb: lower; Tm, Δm: upper). At temperatures T = {4, 8,
Simulated dataset
The maximum likelihood estimation algorithm converged easily in all cases to provide very good parameter estimates to Eq. (A7) for both the censored and the temperature-transfer datasets (Fig. 1a and b; Table 2). Both methods resulted in much higher survival in the low-temperature treatments than if individuals had been allowed to complete their development without censoring or temperature transfers (Fig. 1c). There was not much difference in the quality of development rate estimates at
Discussion and conclusions
Process-based phenology models for poikilotherms will have greater utility if they incorporate the entire biological consequences of physiological responses to temperature and use sufficient data to provide unbiased estimates of parameters. Improvements are particularly evident when simulating processes that occur at near-threshold temperatures where developmental responses are strongly nonlinear and measurements difficult to obtain. However, critical phenological events in the life history of
Acknowledgements
We thank Matt Hansen, Lynn Rasmussen and Jim Vandygriff for their assistance with mountain pine beetle phloem sandwich construction and phenology data collection. The USDA Forest Service (Rocky Mountain Research Station), Canadian Forest Service, Alberta Sustainable Development Department, the Ontario and Manitoba Ministries of Natural Resources, and Saskatchewan Environment provided funding for this research.
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