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Modeling temperature‐dependent development rate and phenology in insects: review of major developments, challenges, and future directions

Corresponding Author

UMR EGCE, Univ. Paris Sud, CNRS, IRD, Univ. Paris Saclay, Gif‐sur‐Yvette, France

Correspondence: François Rebaudo, IRD – UMR 247 EGCE, 1 Avenue de la Terrasse, bât. 13, BP 1, 91198 Gif‐sur‐Yvette Cedex, France. E‐mail: francois.rebaudo@ird.fr Search for more papers by this author

Victor‐Badre Rabhi

Lic. Sciences de la Vie 2, Université Cergy‐Pontoise, Cergy Pontoise, France

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François Rebaudo

Corresponding Author

E-mail address: francois.rebaudo@ird.fr

http://orcid.org/0000-0002-3672-0101

UMR EGCE, Univ. Paris Sud, CNRS, IRD, Univ. Paris Saclay, Gif‐sur‐Yvette, France

Victor‐Badre Rabhi

Lic. Sciences de la Vie 2, Université Cergy‐Pontoise, Cergy Pontoise, France

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First published: 05 July 2018

https://doi.org/10.1111/eea.12693

Citations: 18

Abstract

The study of insect responses to temperature has a long tradition in science, starting from Réaumur's work on caterpillars in the 18th century. In 1932, Ernst Janisch wrote: ‘The problem is (and will be more and more in the future) one of the most important ones in entomology […]’. Almost 90 years after this paper, its prediction still holds true, with a sustained interest of the scientific community for the study of insect responses to temperature, especially in the context of climate change. We present a review of the major developments in the field of insect development responses to temperature and analyze the growing importance of modeling approaches in the literature using a bibliographic analysis. We discuss recent advances and future directions for phenology‐modeling based on temperature‐dependent development rate. Finally, we highlight the need for a change of paradigm toward a system‐based approach in order to overcome current challenges and to predict insect phenology more accurately, with direct implications in agriculture, conservation biology, and epidemiology.

Introduction

Temperature is the main driver of key functions of insects, including survival, reproduction, movement, and development. Among these, development is of particular importance in applied entomology as it is an essential component for building phenological models (Golizadeh & Zalucki, 2012). Phenological models can be used to predict emergence times (Bentz et al., 1991), distribution (Fand et al., 2014), outbreaks (Delatte et al., 2009), and voltinism (Kroschel et al., 2013), with implications for pest management, epidemiology, forensic science, mass insect rearing, and conservation plans (Roy et al., 2002; Kontodimas et al., 2004; Moore & Remais, 2014; Chuine & Régnière, 2017). Temperature‐dependent development in insects is often represented using the inverse of development time, that is, the development rate. The development rate in insects starts from a critical thermal minimum (CTmin) and increases slowly as temperature increases. It reaches a temperature range where development rate is almost linear, then continues growing up to an optimal level (Topt), to finally decrease rapidly to a critical thermal maximum (CTmax). If the almost linear phase of the development is extended, it crosses the abscissa at a temperature called base temperature (Tbase; Figure 1A). Many models have been developed to meet the challenge of characterizing insect responses to temperature over the last century (Figure 1B), with considerable interest still prevailing in the entomological community to characterize the relationship between temperature and development rate using thermal performance curves (Damos & Savopoulou‐Soultani, 2012; Chuine & Régnière, 2017). Recent advances have highlighted the importance of thermal performance curves in ecology and entomology, as long as their inherent assumptions are acknowledged (Sinclair et al., 2016). The scope of this review is not to present and detail the various models available for understanding and predicting temperature‐dependent development rate – see Damos & Savopoulou‐Soultani (2012), Shi et al. (2015), Mirhosseini et al. (2017), and Quinn (2017) for that purpose – but to document how the different approaches have evolved over time, in order to explain why so many models are available, and to identify current and future challenges.

**Figure 1**
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Relationship between temperature and development rate in insects. (A) Theoretical thermal performance curve with the critical thermal minimum (CTmin), maximum (CTmax), optimal (Topt), and base temperature (Tbase). (B, C) Some of the models quantifying the relationship between temperature and development rate adjusted to *Stethorus punctillum* Weise (Coleoptera: Coccinellidae) dataset (‘+’) for eggs from Table 3 in Roy et al. (2002) using the devRate R package. Models adjusted (B) without and (C) with Topt and CTmax estimation.

The first section describes efforts to characterize thermal thresholds of insect development and thermal performance curves. The second section reviews the literature to analyze the past and current trends, and the third section reviews recent advances and proposes future directions.

Thermal thresholds and thermal performance curves

Early science on thermal limits

In the early 1900s, the relationship between insect development and temperature was brought to light as a potential factor to control their development. Cold resistance was studied as a way of controlling hibernating insects by Bachmetjew (1900), followed by Sacharov (1930), whereas others, notably Payne (1929), pointed out the importance of relative humidity, and thus the importance of other factors in insect development. Temperature was recognized as the main driver for insect development. At this time, scientists had already highlighted individual variation within a population as well as the problem of intensity vs. quantity in low‐temperature exposure; see Uvarov (1931) for a review, and Block et al. (1990), Sinclair et al. (2003), Denlinger & Lee (2010), and Lee & Denlinger (1991) for more recent advances on insect strategies to cope with low temperatures. The literature on the upper temperature limit was much more extensive at the beginning of the 20th century, with general agreement on the considerable individual variation in resistance to high temperature within a population of the same species, and on the importance of relative humidity (Uvarov, 1931). Although these studies did not try to establish thermal performance curves, they constituted the base for future studies, and key elements of insect responses to temperature were already noted: (1) the role of exposure to extreme temperatures of differing intensity and quantity, (2) the importance of cofactors such as relative humidity, and (3) the critical importance of individual variation within a population.

Toward thermal performance curves

Insect development was studied using rearing units at various temperatures, so as to define upper and lower critical thermal thresholds for development (CTmin and CTmax; see Figure 1A), using thermal performance curves. Upper and lower critical thermal thresholds for development were already seen as stage‐dependent, influenced by other factors, and subject to variation within a population and between generations (Uvarov, 1931). Most studies used constant temperatures, although the majority of insects experience fluctuating temperatures in their natural environment (Howe, 1967). This may be due to experimental constraints (Greenspan et al., 2016) or to the complexity of insect responses to fluctuating temperatures (Colinet et al., 2015), together with early studies reporting no difference in development rate (Champlain & Butler, 1967; Fye et al., 1969; but see Cloudsley‐Thompson, 1953; Archer & Strong, 1975; Egwuatu & Taylor, 1977). Relative humidity also fluctuates in space and time, and its influence on development rate has been largely acknowledged (Tochen et al., 2016), as has its interaction with temperature (Chen et al., 2015). As is the case for temperature, most studies used a constant optimal relative humidity, without incorporation of a relative humidity parameter in thermal performance curves; but see Godfrey & Holtzer (1991) for a phenological model taking into account relative humidity.

The most popular thermal performance curve is based on the theory of a thermal constant developed for botany (i.e., the completion of a development stage requires an accumulation of energy measured in day‐degrees above the lower development threshold). It allowed a characterization of the relationship between development rate and temperature to be made in the early 20th century, together with its limitations at low and high temperatures (Prochnow, 1908). The so‐called straight velocity line gained a broad following with the often cited paper by Campbell et al. (1974) on aphids and their parasites. The nonlinearity of organism responses to temperature is acknowledged; however, and according to this study, high temperatures would not be normally experienced by organisms in their natural range. If this is often the case when considering degree days, it does not apply to degree hours where temperatures occasionally go beyond the zone of linearity (Howell & Neven, 2000). At the other extreme, the temperature threshold would not be directly measurable because of considerable mortality at low temperature, which justifies the use of the straight line equation and extrapolation (see Figure 1A and the base temperature Tbase). The apparent nonlinearity at low temperature would be due to other factors, such as genetic variation between individuals (Campbell et al., 1974). This hypothesis has driven the study of aphid clones (Lamb, 1992), where nonlinearity at low temperatures was comparable to the level observed on other study models, so that the genetic hypothesis was not supported by the aphid data. The critical study concluded that the lower developmental threshold could not be calculated through a linear regression extrapolation. Despite these limitations, the straight‐line equation is the most popular model used in most phenological models aimed at predicting insect development (Jarošík et al., 2011), and despite the uncertainties influencing degree day model output results in practice (Bergant & Trdan, 2006). Beyond these limitations, this model provides two interesting metrics to compare insects, the base temperature (Tbase) and the thermal constant (reciprocal of the slope) that can be used in meta‐analysis to compare insects and contextualize results (Jarošík et al., 2015).

The sigmoid response was an alternative to the linear response in the early development of thermal performance curves. The van ‘t Hoff and Arrhenius equations (van ‘t Hoff, 1884; Arrhenius, 1889, 1915) were developed for chemical reactions at the end of the 19th century, proposing a sigmoid response, which was disregarded at the time in characterizing insect development (Uvarov, 1931). The sigmoid response to temperature gained popularity after the work of Davidson using a sigmoid curve developed for population growth literature (Pearl & Reed, 1920) and truncated to the right in order to avoid deviance from empirical results, at the temperature for which the development occurs at the fastest rate (i.e., peak temperature) (Davidson, 1944). Yet, this model did not allow the determination of the upper and lower critical thermal thresholds for development (CTmax and CTmin). Another approach, using the reciprocal of the exponential curve, was proposed as an alternative equation with a better fit to empirical data (Janisch, 1932), grounded on the law of mass action that follows the exponential law, and more in accordance with the theoretical curve described by Prochnow (1908). Again, this model did not allow the upper and lower critical thermal thresholds for development to be determined.

The goal of new mathematical models was to accurately represent insect responses to temperature. From here, the development of mathematical models to characterize the relationship between temperature and insect development followed two schools of thought: biophysical models or those based on theoretical mechanistic assumptions regarding organism physiology, and models based on equations best describing the empirical data, without a true mechanistic basis (statistical models).

Biophysical vs. statistical models

A major step in the development of biophysical models was made with the work by Sharpe & DeMichele (1977), which proposed a thermodynamic model based on enzymatic reaction, from the combination of a linear response in mid‐temperature and a nonlinear response at both high and low temperatures, with thermodynamic constants to characterize the enzymatic response of organisms to temperature. The model is based on Erying's and Arrhenius’ equations (Eyring & Stearn, 1939). The general applicability of the model was tested over a wide range of organisms, including bacteria, insects, and plants. In 1981, Schoolfield et al. (1981) revised the Sharpe and DeMichele model, arguing that it was poorly suited for nonlinear regression. This new formulation facilitates nonlinear regression techniques, whereas there was no change in the theory of the model. This event marked a shift in the search for new models: the goal was now to obtain a model that still accurately described the empirical datasets, but with a focus on model applicability. Despite criticism of the biophysical approach originated by Sharpe and DeMichèle (Lamb, 1992), the thermodynamic model was also modified by Ikemoto (2005), to ease the nonlinear least‐square method to fit empirical data. Although a considerable literature cites these mechanistic developments, few studies actually used these models. This is probably because, despite the effort to facilitate the fit to empirical data, a greater effort is needed in both laboratory experiments and the fitting process.

Among statistical models (i.e., models without mechanistic basis), Stinner et al. (1974) proposed a sigmoid curve inverted after the optimum temperature. Although the authors recognized that the symmetry assumption is not always appropriate, the error is supposed to be negligible, given mortality rates at high temperatures (Stinner et al., 1974). This assumption is, however, questionable; the thermal performance curve is nonlinear and asymmetric. The consequence is that a change in the temperature range induces a different response if the change is positive or negative, especially around the optimal temperature for development where the curve is concave, a feature known as Jensen inequality (Denny, 2017). The same is true of the work by Taylor (1981), proposing a Gaussian curve truncated to the right (lethal effect of exposure to high temperature) to fit development rate for insects, while recognizing that symmetry near the optimum was not always appropriate. In contrast, two nonlinear models, known as Logan‐6 and Logan‐10, applied on Tetranychus mcdanieli McGregor (Trombidiformes: Tetranychidae), and validated using various datasets were developed (Logan et al., 1976). The justification for this development was a better description of the two phases of insect responses to temperature: (1) an increasing slope toward an optimum and (2) a rapid decrease after optimum temperature for insect development–see also the model proposed by Wang et al. (1982) and Figure 2A. Arguing that the Logan model approaches zero asymptotically, and thus fails to allow the lower threshold of development to be defined, scientists developed a model combining a Holling type III sigmoid equation with an exponential equation (Hilbert & Logan, 1983) or by introducing an intercept parameter (Lactin et al., 1995; Figure 2B).

**Figure 2**
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Thermal performance curves for insects using the (A) Logan‐10, (B) Lactin‐2, and (C) Briere‐2 model, using the devRate R package and experimental datasets from the literature database for *Lobesia botrana* Denis & Schiffermüller (Lepidoptera: Tortricidae), *Maruca vitrata* Fabricius (Lepidoptera: Crambidae), *Spodoptera cosmioides* Walker (Lepidoptera: Noctuidae), *Platynota idaeusalis* Walker (Lepidoptera: Tortricidae), *Helicoverpa zea* Boddie (Lepidoptera: Noctuidae), and *Diaphania nitidalis* Stoll (Lepidoptera: Crambidae).

If the characterization of a lower and upper threshold has been the motivation for the development of new models (Logan et al., 1976; Hilbert & Logan, 1983; Lactin et al., 1995), it has been at the cost of model complexity. Thus, efforts were made to develop models reducing the number of parameters (e.g., Briere model; Figure 2C), while keeping key model characteristics: (1) the asymmetry in development rate with a sharp decline above optimal temperature of development, and (2) the characterization of a lower and upper threshold of development (Briere et al., 1999; Shi et al., 2015). Despite these advances and Lamb's evidence on nonlinearity and the development of simplified models (above), to date the straight‐line equation is still the most used in papers (Quinn, 2017; Rebaudo et al., 2017), even if it is biased at extreme temperatures.

Bibliographic analysis and trends

To contextualize the importance of the relationship between temperature and development rate in insects and more generally in arthropods and to determine trends in the field, we explored the literature from 1940 to 2017, with an emphasis on the period from 1990 to 2017. Only papers directly addressing arthropod responses to temperature were selected, with a major emphasis on insects. The bibliographic database includes all the references used by Nietschke et al. (2007) on insect response to temperature models covering 1972–2004, references used by Irlich et al. (2009) from 1900 to 2006, those by Jarošík et al. (2011) for the developmental database on phenology models, those of the review of functions for modeling temperature development of arthropods by Quinn (2017) up to 2014, the references on the University of California Agriculture and Natural Resources website on the Statewide Integrated Pest Management Program (http://ipm.ucanr.edu/MODELS/), and a manual selection of papers from a search through PubMed for keywords ‘temperature’, ‘development’, and ‘rate’ from 2006 to 2016, with an additional effort through Google Scholar up to 2017. The bibliographic database is therefore not exhaustive and does not reflect the number of papers published every year, but rather the bibliographic research effort for each considered year. We limited the bibliographic analysis to papers from 1975 to 2017 in order to have a number of papers per year with abstracts and full content allowing statistical analyses and focused on papers from 1990 to 2017 to document the trends over the last decades. The bibliographic database contains 2 275 references (see Supporting Information S1), from which we could retrieve 1 828 papers with abstracts and full content.

The references originated from 420 journals, with Environmental Entomology, Journal of Economic Entomology, Entomologia Experimentalis et Applicata, Journal of Applied Entomology, Annals of the Entomological Society of America, and Applied Entomology and Zoology journals contributing most papers in the database from 1990 to 2017. New journals gained importance in recent years, such as PLoS ONE or Florida Entomologist, and others published fewer papers on the topic, such as Environmental Entomology (Figure 3). We analyzed the abstract content by computing the occurrence of each word in each paper abstract per year, correcting the occurrences by the number of papers per year and by the trend in abstract length found to be larger in recent years (linear regression; F_1,1827 = 286, P<2.2e‐16; R² = 0.135). Although the abstract may not always be representative of the methods or context of utilization, we hypothesized that scientific trends could be defined on that basis – see Carmel et al. (2013) for an example of abstract‐based classification of articles. We then analyzed the resulting word frequencies using regular expressions on selected topics. The first topic was selected to document the evolution of the thermal constant theory generally expressed in degree days. The regular expression used matched all words containing ‘degree’ and associated with a notion of duration such as ‘day(s)’ or ‘hour(s)’ (Figure 4A). The second topic refers to the usage of models over time, reflecting the importance given to the modeling process or model choice (here the regular expression matched all words containing ‘model’; Figure 4B). We then computed word frequencies from the entire paper contents per year to retrieve information about model usage by extracting the occurrences of models according to author names and fitted polynomial models to document trends in model usage over time (Figure 4C).

**Figure 3**
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Most frequent journals in the bibliographic database of papers addressing the relationship between temperature and development rate. The y‐axis in all panels indicates the number of papers. The x‐axis for A, B, and C indicates publication titles (A) from 2010 to 2017, (B) from 1990 to 2017, and (C) from 1975 to 2017. (D) Each column represents a year and numbers above the bars correspond to the total number of articles (publication titles). Publication titles are ordered according to the occurrence of papers for each year.

**Figure 4**
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Mean frequency of (A, B) use of keywords in abstracts with 90% confidence intervals (dashed lines), and (C) mentions of models from 1975 to 2017, fitted using polynomial models. Each panel corresponds to a use of keywords relating to a concept with (A) ‘degree days’ and (B) ‘model’.

The use of keywords relating to the thermal constant concept in abstracts increases from 1975 to 1990 (an average of almost one repetition per abstract in 1990) and decreases from 1990 to 2017 (polynomial regression; F_3,38 = 22.89, P = 1.24e‐08; R² = 0.62). This trend may be attributed to the attempts to build predictive models on the basis of the straight‐line equation, followed by substitution with nonlinear models. In accordance with the growing number of models in the literature, the topic around models grew significantly from 1975 to 2017 (polynomial regression; F_3,38 = 13.67, P = 3.37e‐06; R² = 0.48). This trend continues today despite little recent model development, supporting the view that model choice and usage are still topical and the growing importance of modeling techniques. Model usage over time (Figure 4C) allows us to indicate which models are most used (or referred to). We find the linear (Campbell et al., 1974) and the Logan (Logan et al., 1976) models in approximately one‐third of the papers since 2000. Other models are found less frequently, but the rapid adoption of the Briere (Briere et al., 1999) and Lactin (Lactin et al., 1995) models are notable.

Recent advances and future directions

Choosing a model given uncertainties regarding development rate at extreme temperatures

The characterization of the relationship between temperature and development rate is still a challenge, notably because of mortality at extreme temperatures and interindividual variation within the same species (Régnière et al., 2012), which makes model choice constrained by uncertainty. In the review of the various performance functions modeling temperature‐dependent development of arthropods, Quinn (2017) revealed that model choice is of critical importance because of the significant differences between model predictions (see also Shi et al., 2015; and Figure 1B‐D). In Quinn's (2017) study, although no function type was described as standing out from the rest, considering and comparing various functions in regard to the available datasets should lead to better predictions. The thermal performance curve approach was built out of uncertainties regarding the underlying mechanisms in insects, and the relationship between temperature and development in these models should be considered in regard to their associated assumptions (Sinclair et al., 2016). Some initiatives, such as the ILCYM (Insect Life Cycle Modeling) software for insect pests (Tonnang et al., 2013), the ArthroThermoModel software (Mirhosseini et al., 2017), or the R package devRate for arthropods (Rebaudo et al., 2017; R Core Team, 2018; Rebaudo & Struelens, 2018) may be a way out of selecting the previously fitted model in the literature on a similar species without considering alternatives, a practice that should be avoided (Quinn, 2017). Choosing between models on the basis of criteria such as Akaike's Information Criterion (AIC) may be an intuitive choice, but must be used with caution as each criterion has its advantages and disadvantages (e.g., AIC favors more complex models, which could lead to an overfitting of the data), and combination of various methods should be preferred (Angilletta, 2006). Model choice should also be guided by biological and ecological knowledge and observed data of the insects (Zahiri et al., 2010), especially when the mechanisms beyond insect thermal responses remain partially characterized, and their basis suggested to be both physiological and ecological (Dixon et al., 2009).

Integrating interindividual differences in development rate models and the shift toward integrated life cycle modeling

Most phenological models are based on the average rate of development, although we have known for a century that differences between individuals and between stages in the same species may be considerable. Integrating variation in insect responses – that is, plasticity and genetic diversity (de Jong & van der Have, 2008) – is the next critical step, especially at low and high temperatures, given the uncertainties of model predictions, and because the underlying mechanisms of this variation are not well understood (Chown, 2001; Schulte et al., 2011; Sinclair et al., 2012; Sgrò et al., 2016). Variation in responses can be found among populations established in different locations as a result of isolation by distance and selection to local condition (Sinclair et al., 2012), which can be artificially reproduced (Gilbert & Raworth, 1996), even if they may differ from naturally occurring adaptations (Kellermann et al., 2015). The first challenge is to integrate into models existing variation within populations and to characterize insect responses to temperature beyond an average curve with standard errors for parameter estimates. This may require a shift in the way models are used to represent thermal performance, from an average curve to density surface, where a temperature would match a density of development rates, within individual‐based models in which simulated individuals would have their own development rate (Crespo‐Pérez et al., 2015; Régnière et al., 2015). The second challenge is to integrate existing variation between populations – that is, geographic variation in insect responses, see Chuine & Régnière (2017) – into phenological models for better predictions at the regional scale.

Integrating dormancy, microclimate, and geographical variation

Climate is characterized by seasonality. A consequence of seasonality is the induction of dormancy in insects that can be triggered by temperature and photoperiod (Kutcherov et al., 2015). This delay in development in response to environmental conditions (i.e., diapause) has profound consequences in phenological models studying development predictions. Although in some cases, diapause induction has been found not to vary geographically (Kutcherov et al., 2015), most insects exhibit geographical variation in their traits because of both plasticity to local conditions and genetic diversity. As a consequence, modeling studies require different parameterization and large databases to estimate these parameters (Chuine & Régnière, 2017), which is often impracticable. Moreover, there is often a mismatch between the measured temperature and the temperature experienced by insects (Howe, 1967; Régnière & Turgeon, 1989; Faye et al., 2016), with consequences for predicted insect performances (Rebaudo et al., 2016; Faye et al., 2017). Transposition to field conditions remains a challenge to apply laboratory‐based models (Schulte et al., 2011; Sgrò et al., 2016). A solution may be to build thermal performance curves (or thermal performance density surfaces to integrate interindividual differences) on the basis of field observations rather than laboratory experiments or to use thermal performance curves obtained from fluctuating temperatures similar to those which insects experience in the field (Dallwitz, 1984; Jones et al., 2016). Even if the effect of fluctuating temperatures is not always significant on the development rate at some temperatures, there is evidence that it plays a central role in insect development and should be accounted for in field predictive models (Colinet et al., 2015).

Integrating multiple factors and their interactions

Other factors such as photoperiod, diet, relative humidity, rearing density, sex, and all the interactions between these factors have significant influence on development rate in insects (Uvarov, 1931), and thus represent another layer of complexity in the characterization of insect development. Numerous studies have indicated the effect of these factors, but few consider them simultaneously (Couret, 2013; Couret & Benedict, 2014). Large‐scale experiments would be required to quantify the effect of interacting factors on insect development rate, together with more complex models taking into account the fluctuating and multifactorial environment experienced by insects (Régnière et al., 2012; Crespo‐Pérez et al., 2013; Koussoroplis et al., 2017). An additional layer of complexity is the integration of trophic interactions and phenological synchrony (e.g., with host plants), of particular importance for accurate model predictions in a context of climate change (Mwalusepo et al., 2015).

Future directions

Future directions should take into account the dynamic nature of spatial and temporal change in environmental factors affecting development rate in insects. This may require a change of paradigm: from a pest‐centered approach to a system‐centered, combined with a transdisciplinary approach (Coll & Wajnberg, 2017). The analysis of trends and recent advances in temperature‐dependent development rate in insects highlights the need for datasets accounting for interindividual differences together with fluctuating temperatures in space and time and associated with a population genetic differentiation along geographical gradients (Chuine & Régnière, 2017). If thermal performance curves are central to characterize temperature‐dependent development rate, more complex models are needed, and spatially explicit individual‐based models may have a central role in future developments.

Conclusion

There are most certainly more than 3 000 papers directly addressing temperature‐dependent development rate characterization in the literature. We selected the most influential ones to bring out the major scientific advances, while highlighting century‐old challenges that remain unfulfilled and propose future directions. Among these challenges, model choice has received much attention, although no consensus has been found. The central role of fluctuating temperatures has been acknowledged but not systematically integrated into experimental studies. Furthermore, the integration of individual variability within a population of the same species and the multifactorial dependence of development rate has been disregarded. Finally, integrating microclimate and geographic genetic variation remains a challenge. The bibliographic analysis demonstrated that the shift toward nonlinear models and the increasing importance given to the modeling process is topical. Yet, in the context of climate change and the need to develop models that accurately describe the impact of future temperatures on insect development, it is critical to use new modeling approaches that could account for the complex nature of the environment experienced by insects. In this regard, a transdisciplinary system‐based approach using spatially explicit individual‐based models is promising.

Acknowledgements

We wish to thank Quentin Struelens for his contribution to the bibliographic database.

Supporting Information

References

Angilletta MJ (2006) Estimating and comparing thermal performance curves. Journal of Thermal Biology 31: 541– 545.
Crossref Web of Science®Google Scholar
Archer T & Strong R (1975) Comparative studies on the biologies of six species of Trogoderma: T. glabrum. Annals of the Entomological Society of America 68: 105– 114.
Crossref Web of Science®Google Scholar
Arrhenius S (1889) Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren. Zeitschrift für physikalische Chemie 4: 226– 248.
Crossref Google Scholar
Arrhenius S (1915) Quantitative Laws in Biological Chemistry. Bell, London, UK.
Google Scholar
Bachmetjew P (1900) Freezing of body fluids in insects. Zeitschrift für wissenschaftlichen Zoologie 67: 529– 550.
Google Scholar
Bentz BJ, Logan JA & Amman GD (1991) Temperature‐dependent development of the mountain pine beetle (Coleoptera: Scolytidae) and simulation of its phenology. Canadian Entomologist 123: 1083– 1094.
Crossref Web of Science®Google Scholar
Bergant K & Trdan S (2006) How reliable are thermal constants for insect development when estimated from laboratory experiments? Entomologia Experimentalis et Applicata 120: 251– 256.
Wiley Online Library Web of Science®Google Scholar
Block W, Baust J, Franks F, Johnston I & Bale J (1990) Cold tolerance of insects and other arthropods [and discussion]. Philosophical Transactions of the Royal Society of London B 326: 613– 633.
Crossref Web of Science®Google Scholar
Briere J‐F, Pracros P, Le Roux A‐Y & Pierre J‐S (1999) A novel rate model of temperature‐dependent development for arthropods. Environmental Entomology 28: 22– 29.
Crossref Web of Science®Google Scholar
Campbell A, Frazer B, Gilbert N, Gutierrez A & Mackauer M (1974) Temperature requirements of some aphids and their parasites. Journal of Animal Ecology 11: 431– 438.
Crossref Web of Science®Google Scholar
Carmel Y, Kent R, Bar‐Massada A, Blank L, Liberzon J et al. (2013) Trends in ecological research during the last three decades – a systematic review. PLoS ONE 8: e59813.
Crossref CAS PubMed Web of Science®Google Scholar
Champlain RA & Butler GD (1967) Temperature effects on development of the egg and nymphal stages of Lygus hesperus (Hemiptera: Miridae). Annals of the Entomological Society of America 60: 519– 521.
Crossref Web of Science®Google Scholar
Chen HS, Yang L, Haung LF, Wang WL, Hu Y et al. (2015) Temperature‐ and relative humidity‐dependent life history traits of Phenacoccus solenopsis (Hemiptera: Pseudococcidae) on Hibiscus rosa‐sinensis (Malvales: Malvaceae). Environmental Entomology 44: 1230.
Crossref CAS PubMed Web of Science®Google Scholar
Chown SL (2001) Physiological variation in insects: hierarchical levels and implications. Journal of Insect Physiology 47: 649– 660.
Crossref CAS PubMed Web of Science®Google Scholar
Chuine I & Régnière J (2017) Process‐based models of phenology for plants and animals. Annual Review of Ecology, Evolution, and Systematics 48: 159– 182.
Crossref Web of Science®Google Scholar
Cloudsley‐Thompson J (1953) The significance of fluctuating temperatures on the physiology and ecology of insects. Entomologist 86: 183– 189.
Google Scholar
Colinet H, Sinclair BJ, Vernon P & Renault D (2015) Insects in fluctuating thermal environments. Annual Review of Entomology 60: 123– 140.
Crossref CAS PubMed Web of Science®Google Scholar
Coll M & Wajnberg E (2017) Environmental Pest Management: Challenges for Agronomists, Ecologists, Economists and Policymakers. John Wiley & Sons, Chichester, UK.
Wiley Online Library Google Scholar
Couret J (2013) Meta‐analysis of factors affecting ontogenetic development rate in the Culex pipiens (Diptera: Culicidae) complex. Environmental Entomology 42: 614– 626.
Crossref CAS PubMed Web of Science®Google Scholar
Couret J & Benedict MQ (2014) A meta‐analysis of the factors influencing development rate variation in Aedes aegypti (Diptera: Culicidae). BMC Ecology 14: 3.
Crossref PubMed Web of Science®Google Scholar
Crespo‐Pérez V, Dangles O, Régnière J & Chuine I (2013) Modeling temperature‐dependent survival with small datasets: insights from tropical mountain agricultural pests. Bulletin of Entomological Research 103: 336– 343.
Crossref PubMed Web of Science®Google Scholar
Crespo‐Pérez V, Régnière J, Chuine I, Rebaudo F & Dangles O (2015) Changes in the distribution of multispecies pest assemblages affect levels of crop damage in warming tropical Andes. Global Change Biology 21: 82– 96.
Wiley Online Library PubMed Web of Science®Google Scholar
Dallwitz R (1984) The influence of constant and fluctuating temperatures on development rate and survival of pupae of the Australian sheep blowfly Lucilia cuprina. Entomologia Experimentalis et Applicata 36: 89– 95.
Wiley Online Library Web of Science®Google Scholar
Damos P & Savopoulou‐Soultani M (2012) Temperature‐driven models for insect development and vital thermal requirements. Psyche 2012: 123405.
Crossref Google Scholar
Davidson J (1944) On the relationship between temperature and rate of development of insects at constant temperatures. Journal of Animal Ecology 13: 26– 38.
Crossref Web of Science®Google Scholar
Delatte H, Gimonneau G, Triboire A & Fontenille D (2009) Influence of temperature on immature development, survival, longevity, fecundity, and gonotrophic cycles of Aedes albopictus, vector of chikungunya and dengue in the Indian Ocean. Journal of Medical Entomology 46: 33– 41.
Crossref CAS PubMed Web of Science®Google Scholar
Denlinger DL & Lee RE Jr (2010) Low Temperature Biology of Insects. Cambridge University Press, Cambridge, UK.
Crossref Google Scholar
Denny M (2017) The fallacy of the average: on the ubiquity, utility and continuing novelty of Jensen's inequality. Journal of Experimental Biology 220: 139– 146.
Crossref PubMed Web of Science®Google Scholar
Dixon AF, Honěk A, Keil P, Kotela MAA, Šizling AL & Jarošík V (2009) Relationship between the minimum and maximum temperature thresholds for development in insects. Functional Ecology 23: 257– 264.
Wiley Online Library Web of Science®Google Scholar
Egwuatu R & Taylor TA (1977) The effects of constant and fluctuating temperatures on the development of Acanthomia tomentosicollis Stål (Hemiptera, Coreidae). Journal of Natural History 11: 601– 608.
Crossref Web of Science®Google Scholar
Eyring H & Stearn AE (1939) The application of the theory of absolute reaction rates to proteins. Chemical Reviews 24: 253– 270.
Crossref CAS Web of Science®Google Scholar
Fand BB, Tonnang HEZ, Kumar M, Bal SK, Singh NP et al. (2014) Predicting the impact of climate change on regional and seasonal abundance of the mealybug Phenacoccus solenopsis Tinsley (Hemiptera: Pseudococcidae) using temperature‐driven phenology model linked to GIS. Ecological Modelling 288: 62– 78.
Crossref Web of Science®Google Scholar
Faye E, Rebaudo F, Yánez‐Cajo D, Cauvy‐Fraunié S & Dangles O (2016) A toolbox for studying thermal heterogeneity across spatial scales: from unmanned aerial vehicle imagery to landscape metrics. Methods in Ecology and Evolution 7: 437– 446.
Wiley Online Library Web of Science®Google Scholar
Faye E, Rebaudo F, Carpio C, Herrera M & Dangles O (2017) Does heterogeneity in crop canopy microclimates matter for pests? Evidence from aerial high‐resolution thermography. Agriculture, Ecosystems & Environment 246: 124– 133.
Crossref Web of Science®Google Scholar
Fye R, Patana R & McAda W (1969) Developmental periods for boll weevils reared at several constant and fluctuating temperatures. Journal of Economic Entomology 62: 1402– 1405.
Crossref Web of Science®Google Scholar
Gilbert N & Raworth D (1996) Forum: insects and temperature – a general theory. Canadian Entomologist 128: 1– 13.
Crossref Web of Science®Google Scholar
Godfrey LD & Holtzer TO (1991) Influence of temperature and humidity on European corn borer (Lepidoptera: Pyralidae) egg hatchability. Environmental Entomology 20: 8– 14.
Crossref Web of Science®Google Scholar
Golizadeh A & Zalucki MP (2012) Estimating temperature‐dependent developmental rates of potato tuberworm, Phthorimaea operculella (Lepidoptera: Gelechiidae). Insect Science 19: 609– 620.
Wiley Online Library Web of Science®Google Scholar
Greenspan SE, Morris W, Warburton R, Edwards L, Duffy R et al. (2016) Low‐cost fluctuating‐temperature chamber for experimental ecology. Methods in Ecology and Evolution 7: 1567– 1574.
Wiley Online Library Web of Science®Google Scholar
Hilbert D & Logan J (1983) Empirical model of nymphal development for the migratory grasshopper, Melanoplus sanguinipes (Orthoptera: Acrididae). Environmental Entomology 12: 1– 5.
Crossref Web of Science®Google Scholar
van ‘t Hoff JH (1884) Etudes de Dynamique Chimique. Frederik Muller, Amsterdam, The Netherlands.
Google Scholar
Howe R (1967) Temperature effects on embryonic development in insects. Annual Review of Entomology 12: 15– 42.
Crossref CAS PubMed Web of Science®Google Scholar
Howell JF & Neven LG (2000) Physiological development time and zero development temperature of the codling moth (Lepidoptera: Tortricidae). Environmental Entomology 29: 766– 772.
Crossref Web of Science®Google Scholar
Ikemoto T (2005) Intrinsic optimum temperature for development of insects and mites. Environmental Entomology 34: 1377– 1387.
Crossref Web of Science®Google Scholar
Irlich UM, Terblanche JS, Blackburn TM & Chown SL (2009) Insect rate‐temperature relationships: environmental variation and the metabolic theory of ecology. American Naturalist 174: 819– 835.
Crossref PubMed Web of Science®Google Scholar
Janisch E (1932) The influence of temperature on the life‐history of insects. Transactions of the Royal Entomological Society of London 80: 137– 168.
Wiley Online Library Google Scholar
Jarošík V, Honěk A, Magarey RD & Skuhrovec J (2011) Developmental database for phenology models: related insect and mite species have similar thermal requirements. Journal of Economic Entomology 104: 1870– 1876.
Crossref PubMed Web of Science®Google Scholar
Jarošík V, Kenis M, Honěk A, Skuhrovec J & Pyšek P (2015) Invasive insects differ from non‐invasive in their thermal requirements. PLoS ONE 10: e0131072.
Crossref PubMed Web of Science®Google Scholar
Jones VP, Horton DR, Mills NJ, Unruh TR, Miliczky E et al. (2016) Using plant volatile traps to develop phenology models for natural enemies: an example using Chrysopa nigricornis (Burmeister) (Neuroptera: Chrysopidae). Biological Control 102: 77– 84.
Crossref Web of Science®Google Scholar
de Jong G & van der Have TM (2008) Temperature dependence of development rate, growth rate and size: from biophysics to adaptation. Phenotypic Plasticity of Insects: Mechanisms and Consequences (ed. by D Whitman & TN Ananthakrishnan), pp. 461– 526. Science Publishers, Enfield, NH, USA.
Google Scholar
Kellermann V, Hoffmann AA, Kristensen TN, Moghadam NN & Loeschcke V (2015) Experimental evolution under fluctuating thermal conditions does not reproduce patterns of adaptive clinal differentiation in Drosophila melanogaster. American Naturalist 186: 582– 593.
Crossref PubMed Web of Science®Google Scholar
Kontodimas DC, Eliopoulos PA, Stathas GJ & Economou LP (2004) Comparative temperature‐dependent development of Nephus includens (Kirsch) and Nephus bisignatus (Boheman) (Coleoptera: Coccinellidae) preying on Planococcus citri (Risso) (Homoptera: Pseudococcidae): evaluation of a linear and various nonlinear models using specific criteria. Environmental Entomology 33: 1– 11.
Crossref Web of Science®Google Scholar
Koussoroplis A, Pincebourde S & Wacker A (2017) Understanding and predicting physiological performance of organisms in fluctuating and multifactorial environments. Ecological Monographs 87: 178– 197.
Wiley Online Library Web of Science®Google Scholar
Kroschel J, Sporleder M, Tonnang HEZ, Juarez H, Carhuapoma P et al. (2013) Predicting climate‐change‐caused changes in global temperature on potato tuber moth Phthorimaea operculella (Zeller) distribution and abundance using phenology modeling and GIS mapping. Agricultural and Forest Meteorology 170: 228– 241.
Crossref Web of Science®Google Scholar
Kutcherov D, Saulich A, Lopatina E & Ryzhkova M (2015) Stable and variable life‐history responses to temperature and photoperiod in the beet webworm, Loxostege sticticalis. Entomologia Experimentalis et Applicata 154: 228– 241.
Wiley Online Library Web of Science®Google Scholar
Lactin DJ, Holliday N, Johnson D & Craigen R (1995) Improved rate model of temperature‐dependent development by arthropods. Environmental Entomology 24: 68– 75.
Crossref Web of Science®Google Scholar
Lamb R (1992) Developmental rate of Acyrthosiphon pisum (Homoptera: Aphididae) at low temperatures: implications for estimating rate parameters for insects. Environmental Entomology 21: 10– 19.
Crossref Web of Science®Google Scholar
Lee RE & Denlinger DL (1991) Insects at Low Temperature. Chapman and Hall, New York, NY, USA.
Crossref Google Scholar
Logan JA, Wollkind DJ, Hoyt SC & Tanigoshi LK (1976) An analytic model for description of temperature dependent rate phenomena in arthropods. Environmental Entomology 5: 1133– 1140.
Crossref Web of Science®Google Scholar
Mirhosseini MA, Fathipour Y & Reddy GVP (2017) Arthropod development's response to temperature: a review and new software for modeling. Annals of the Entomological Society of America 110: 507– 520.
Crossref Web of Science®Google Scholar
Moore JL & Remais JV (2014) Developmental models for estimating ecological responses to environmental variability: structural, parametric, and experimental issues. Acta Biotheoretica 62: 69– 90.
Crossref PubMed Web of Science®Google Scholar
Mwalusepo S, Tonnang HEZ, Massawe ES, Okuku GO, Khadioli N et al. (2015) Predicting the impact of temperature change on the future distribution of maize stem borers and their natural enemies along East African mountain gradients using phenology models. PLoS ONE 10: e0130427.
Crossref PubMed Web of Science®Google Scholar
Nietschke BS, Magarey RD, Borchert DM, Calvin DD & Jones E (2007) A developmental database to support insect phenology models. Crop Protection 26: 1444– 1448.
Crossref Web of Science®Google Scholar
Payne NM (1929) Absolute humidity as a factor in insect cold hardiness with a note on the effect of nutrition on cold hardiness. Annals of the Entomological Society of America 22: 601– 620.
Crossref CAS Google Scholar
Pearl R & Reed LJ (1920) On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proceedings of the National Academy of Sciences of the USA 6: 275– 288.
Crossref CAS PubMed Web of Science®Google Scholar
Prochnow O (1908) Die Abhängigkeit der Entwicklungs‐ und Reaktionsgeschwindigkeit bei Pflanzen und poikilothermen Tieren von der Tempertur. Friedrich‐Wilhelms‐Universität, Berlin, Germany.
Google Scholar
Quinn BK (2017) A critical review of the use and performance of different function types for modeling temperature‐dependent development of arthropod larvae. Journal of Thermal Biology 63: 65– 77.
Crossref PubMed Web of Science®Google Scholar
R Core Team (2018) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
Google Scholar
Rebaudo F & Struelens Q (2018) devRate: quantify relationship between developmental rate and temperature in ectotherms, package version 0.1.6 R CRAN. Available at: https://CRAN.R-project.org/package=devRate (accessed on 25 January 2018).
Google Scholar
Rebaudo F, Faye E & Dangles O (2016) Microclimate data improve predictions of insect abundance models based on calibrated spatiotemporal temperatures. Frontiers in Physiology 7: 139.
Crossref PubMed Web of Science®Google Scholar
Rebaudo F, Struelens Q & Dangles O (2017) Modeling temperature‐dependent development rate and phenology in arthropods: the devRate package for R. Methods in Ecology and Evolution 9: 1144– 1150.
Wiley Online Library Web of Science®Google Scholar
Régnière J & Turgeon JJ (1989) Temperature‐dependent development of Zeiraphera canadensis and simulation of its phenology. Entomologia Experimentalis et Applicata 50: 185– 193.
Wiley Online Library Web of Science®Google Scholar
Régnière J, Powell J, Bentz B & Nealis V (2012) Effects of temperature on development, survival and reproduction of insects: experimental design, data analysis and modeling. Journal of Insect Physiology 58: 634– 647.
Crossref CAS PubMed Web of Science®Google Scholar
Régnière J, Bentz BJ, Powell JA & St‐Amant R (2015) Individual‐based modeling: mountain pine beetle seasonal biology in response to climate. Simulation Modeling of Forest Landscape Disturbances (ed. by AH Perera, BR Sturtevant & LJ Buse), pp. 135– 164. Springer, Dordrecht, The Netherlands.
Crossref Google Scholar
Roy M, Brodeur J & Cloutier C (2002) Relationship between temperature and developmental rate of Stethorus punctillum (Coleoptera: Coccinellidae) and its prey Tetranychus mcdanieli (Acarina: Tetranychidae). Environmental Entomology 31: 177– 187.
Crossref PubMed Web of Science®Google Scholar
Sacharov N (1930) Studies in cold resistance of insects. Ecology 11: 505– 517.
Wiley Online Library CAS Web of Science®Google Scholar
Schoolfield R, Sharpe P & Magnuson C (1981) Non‐linear regression of biological temperature‐dependent rate models based on absolute reaction‐rate theory. Journal of Theoretical Biology 88: 719– 731.
Crossref CAS PubMed Web of Science®Google Scholar
Schulte PM, Healy TM & Fangue NA (2011) Thermal performance curves, phenotypic plasticity, and the time scales of temperature exposure. Integrative and Comparative Biology 51: 691– 702.
Crossref PubMed Web of Science®Google Scholar
Sgrò CM, Terblanche JS & Hoffmann AA (2016) What can plasticity contribute to insect responses to climate change? Annual Review of Entomology 61: 433– 451.
Crossref CAS PubMed Web of Science®Google Scholar
Sharpe PJ & DeMichele DW (1977) Reaction kinetics of poikilotherm development. Journal of Theoretical Biology 64: 649– 670.
Crossref CAS PubMed Web of Science®Google Scholar
Shi P‐J, Reddy GVP, Chen L & Ge F (2015) Comparison of thermal performance equations in describing temperature‐dependent developmental rates of insects: (I) Empirical models. Annals of the Entomological Society of America 109: 211– 215.
Crossref Web of Science®Google Scholar
Sinclair BJ, Vernon P, Klok JC & Chown SL (2003) Insects at low temperatures: an ecological perspective. Trends in Ecology & Evolution 18: 257– 262.
Crossref Web of Science®Google Scholar
Sinclair BJ, Williams CM & Terblanche JS (2012) Variation in thermal performance among insect populations. Physiological and Biochemical Zoology 85: 594– 606.
Crossref PubMed Web of Science®Google Scholar
Sinclair BJ, Marshall KE, Sewell MA, Levesque DL, Willett CS et al. (2016) Can we predict ectotherm responses to climate change using thermal performance curves and body temperatures? Ecology Letters 19: 1372– 1385.
Wiley Online Library PubMed Web of Science®Google Scholar
Stinner R, Gutierrez A & Butler G (1974) An algorithm for temperature‐dependent growth rate simulation. Canadian Entomologist 106: 519– 524.
Crossref Web of Science®Google Scholar
Taylor F (1981) Ecology and evolution of physiological time in insects. American Naturalist 117: 1– 23.
Crossref Web of Science®Google Scholar
Tochen S, Woltz JM, Dalton DT, Lee JC, Wiman NG & Walton VM (2016) Humidity affects populations of Drosophila suzukii (Diptera: Drosophilidae) in blueberry. Journal of Applied Entomology 140: 47– 57.
Wiley Online Library Web of Science®Google Scholar
Tonnang E, Carhuapoma JH, Gonzales J, Sporleder M, Simon R & Kroschel J (2013) ILCYM‐Insect Life Cycle Modeling. A Software Package for Developing Temperature‐Based Insect Phenology Models with Applications for Regional and Global Analysis of Insect Population and Mapping. International Potato Center (CIP), Lima, Peru.
Google Scholar
Uvarov BP (1931) Insects and climate. Ecological Entomology 79: 1– 232.
Wiley Online Library Google Scholar
Wang R, Lan Z & Ding Y (1982) Studies on mathematical models of the relationship between insect development and temperature. Acta Ecologica Sinica 2: 47– 57.
CAS Google Scholar
Zahiri B, Fathipour Y, Khanjani M, Moharramipour S & Zalucki M (2010) Preimaginal development response to constant temperatures in Hypera postica (Coleoptera: Curculionidae): picking the best model. Environmental Entomology 39: 177– 189.
Crossref PubMed Web of Science®Google Scholar

Citing Literature

Number of times cited according to CrossRef: 18

Sung-Soo Yoon, Myung-Hyun Kim, Jinu Eo, Young-Ju Song, Temperature-dependent development models and phenology of Hydrochara affinis, Environmental Biology Research, 10.11626/KJEB.2020.38.2.222, 38, 2, (222-230), (2020).
Crossref
Ciarán P. Pollard, Christine T. Griffin, Rafael de Andrade Moral, Catriona Duffy, Julien Chuche, Michael T. Gaffney, Reamonn M. Fealy, Rowan Fealy, phenModel: A temperature-dependent phenology/voltinism model for a herbivorous insect incorporating facultative diapause and budburst, Ecological Modelling, 10.1016/j.ecolmodel.2019.108910, 416, (108910), (2020).
Crossref
Christelle Suppo, Audrey Bras, Christelle Robinet, A temperature- and photoperiod-driven model reveals complex temporal population dynamics of the invasive box tree moth in Europe, Ecological Modelling, 10.1016/j.ecolmodel.2020.109229, 432, (109229), (2020).
Crossref
Leonel Stazione, Fabian M. Norry, Federico H. Gomez, Pablo Sambucetti, Heat knockdown resistance and chill‐coma recovery as correlated responses to selection on mating success at high temperature in Drosophila buzzatii, Ecology and Evolution, 10.1002/ece3.6032, 10, 4, (1998-2006), (2020).
Wiley Online Library
Luca Rossini, Mario Contarini, Maurizio Severini, Stefano Speranza, Reformulation of the Distributed Delay Model to describe insect pest populations using count variables, Ecological Modelling, 10.1016/j.ecolmodel.2020.109286, 436, (109286), (2020).
Crossref
Ítala Tainy Barreto Francisco dos Santos, Heloisa Safira Santos Pinheiro, Júlio César Melo Poderoso, Vancleber Batista dos Santos, Thiago Xavier Chagas, Genésio Tâmara Ribeiro, Morphometry of the reproductive system of the predator Podisus nigrispinus (Dallas, 1851) (Hemiptera, Pentatomidae) when submitted to different temperatures, Ciência Rural, 10.1590/0103-8478cr20190899, 50, 12, (2020).
Crossref
Fábio Sampaio, Flávia S Krechemer, Cesar A Marchioro, Temperature‐dependent development models describing the effects of temperature on the development of Spodoptera eridania, Pest Management Science, 10.1002/ps.6101, 0, 0, (2020).
Wiley Online Library
François Rebaudo, Romain Benoist, Low-cost automatic temperature monitoring system with alerts for laboratory rearing units, MethodsX, 10.1016/j.mex.2019.09.013, (2019).
Crossref
Corentin Iltis, Philippe Louâpre, Karolina Pecharová, Denis Thiéry, Sébastien Zito, Benjamin Bois, Jérôme Moreau, Are life-history traits equally affected by global warming? A case study combining a multi-trait approach with fine-grain climate modeling, Journal of Insect Physiology, 10.1016/j.jinsphys.2019.103916, (103916), (2019).
Crossref
Maxime Damien, Kévin Tougeron, Prey-predator phenological mismatch under climate change, Current Opinion in Insect Science, 10.1016/j.cois.2019.07.002, (2019).
Crossref
H Jactel, J Koricheva, B Castagneyrol, Responses of forest insect pests to climate change: not so simple, Current Opinion in Insect Science, 10.1016/j.cois.2019.07.010, (2019).
Crossref
Kelsey A McCalla, Mehmet Keçeci, Ivan Milosavljević, David A Ratkowsky, Mark S Hoddle, The Influence of Temperature Variation on Life History Parameters and Thermal Performance Curves of Tamarixia radiata (Hymenoptera: Eulophidae), a Parasitoid of the Asian Citrus Psyllid (Hemiptera: Liviidae), Journal of Economic Entomology, 10.1093/jee/toz067, (2019).
Crossref
undefined Stejskal, undefined Vendl, undefined Li, undefined Aulicky, Minimal Thermal Requirements for Development and Activity of Stored Product and Food Industry Pests (Acari, Coleoptera, Lepidoptera, Psocoptera, Diptera and Blattodea): A Review, Insects, 10.3390/insects10050149, 10, 5, (149), (2019).
Crossref
Takaya Ikemoto, Keizi Kiritani, Novel Method of Specifying Low and High Threshold Temperatures Using Thermodynamic SSI Model of Insect Development, Environmental Entomology, 10.1093/ee/nvz031, (2019).
Crossref
Brady K. Quinn, Occurrence and predictive utility of isochronal, equiproportional, and other types of development among arthropods, Arthropod Structure & Development, 10.1016/j.asd.2018.11.007, (2018).
Crossref
Miguel Angel Borda, Pablo Daniel Sambucetti, Federico Hernan Gomez, Fabian Marcelo Norry, Genetic variation for egg‐to‐adult survival in rosophila melanogaster in a set of recombinant inbred lines reared under heat stress in a natural thermal environment, Entomologia Experimentalis et Applicata, 10.1111/eea.12728, 166, 10, (863-872), (2018).
Wiley Online Library
Julliana Barretto, Carlos Cultid-Medina, Federico Escobar, Annual Abundance and Population Structure of Two Dung Beetle Species in a Human-Modified Landscape, Insects, 10.3390/insects10010002, 10, 1, (2), (2018).
Crossref
Andrew J. Bladon, Matthew Lewis, Eleanor K. Bladon, Sam J. Buckton, Stuart Corbett, Steven R. Ewing, Matthew P. Hayes, Gwen E. Hitchcock, Richard Knock, Colin Lucas, Adam McVeigh, Rosa Menéndez, Jonah M. Walker, Tom M. Fayle, Edgar C. Turner, How butterflies keep their cool: Physical and ecological traits influence thermoregulatory ability and population trends, Journal of Animal Ecology, 10.1111/1365-2656.13319, 0, 0, (undefined).
Wiley Online Library

Volume166, Issue8

August 2018

Pages 607-617

Modeling temperature‐dependent development rate and phenology in insects: review of major developments, challenges, and future directions

Abstract

Introduction