A critical review of the use and performance of different function types for modeling temperature-dependent development of arthropod larvae

Abstract

1-506-343-7676 7 8 Highlights: 9  Temperature-dependent development functions of arthropod larvae were reviewed 10  Data from published studies were re-tested and fit with eight different function types 11  86.5 % of published studies did not fit their data with the best function of those tested 12  Performance differed among functions and was related to taxon and temperature range tested 13  Function type impacted predicted development times, so using the best function matters 14 15 16 17 18 19 20 21 22 23 2 ABSTRACT 24 Temperature-dependent development influences production rates of economically-and 25 ecologically-important arthropod species, including crustaceans important to fisheries and 26 agricultural pests. Numerous candidate equation types (development functions) exist to describe 27 the effect of temperature on development time, yet most studies use only a single type of 28 equation and there is no consensus as to which, if any model predicts development rates better 29 than the others, nor what the consequences of selecting a potentially incorrect model equation are 30 on predicted development times. In this study, a literature search was performed of studies fitting 31 development functions to development of arthropod larvae (87 species). The published data of 32 some (52) of these species were then fit with eight commonly-used development functions. 33 Overall performance of each function type and consequences of using a function other than the 34 best one to model data were assessed. Performance was also related to taxonomy and the range 35 of temperatures examined. The majority (86.5 %) of studies were found to not use the best 36 function out of those tested. Using the incorrect model lead to significantly less accurate (e.g., 37 mean difference ± SE 7.9 ± 1.7 %, range: 1-18 %) predictions of development times than the best 38 function. Overall, Heip Power, Quadratic, Bĕlehrádek, and Modified Arrhenius functions 39 performed well, Linear Rate and Tauti Exponential were intermediate, and the Linear Sum and 40 Brière-2 functions performed poorly. More complex functions only performed well when wide 41 temperature ranges were tested, which tended to be confined to studies of insects or arachnids 42 compared with those of crustaceans. Results indicate the biological significance of choosing the 43 best-fitting model to describe temperature-dependent development time data.44 45

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

“…Thus, efforts were made to develop models reducing the number of parameters (e.g., Briere model; Figure C), 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., ; Shi et al., ). 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, ; Rebaudo et al., ), even if it is biased at extreme temperatures.…”

“…() from 1900 to 2006, those by Jarošík et al. () for the developmental database on phenology models, those of the review of functions for modeling temperature development of arthropods by Quinn () 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.…”

“…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., ), which makes model choice constrained by uncertainty. In the review of the various performance functions modeling temperature‐dependent development of arthropods, Quinn () revealed that model choice is of critical importance because of the significant differences between model predictions (see also Shi et al., ; and Figure B‐D). In Quinn's () 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.…”

“…In the review of the various performance functions modeling temperature‐dependent development of arthropods, Quinn () revealed that model choice is of critical importance because of the significant differences between model predictions (see also Shi et al., ; and Figure B‐D). In Quinn's () 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., ).…”

“…(), Mirhosseini et al. (), and Quinn () 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.…”