| Type: | Package |
| Title: | Quantify the Relationship Between Development Rate and Temperature in Ectotherms |
| Version: | 0.2.4 |
| Author: | Francois Rebaudo [aut, cre] (2016-2022), Baptiste Regnier [aut] (PhD; 2019-2020), Camila Benavides [ctb] (M2 student; 2018), Tanusson Selvarajah [ctb] (L2 student; 2018), Nicolas Bonnal [ctb] (M1 student; 2018), Badre Rabhi [ctb] (L2 student; 2017), Quentin Struelens [ctb] (VIA; 2016) |
| Maintainer: | Francois Rebaudo <francois.rebaudo@ird.fr> |
| Description: | A set of functions to quantify the relationship between development rate and temperature and to build phenological models. The package comprises a set of models and estimated parameters borrowed from a literature review in ectotherms. The methods and literature review are described in Rebaudo et al. (2018) <doi:10.1111/2041-210X.12935>, Rebaudo and Rabhi (2018) <doi:10.1111/eea.12693>, and Regnier et al. (2021) <doi:10.1093/ee/nvab115>. An example can be found in Rebaudo et al. (2017) <doi:10.1007/s13355-017-0480-5>. |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| LazyData: | TRUE |
| Depends: | R (≥ 3.5.0) |
| RoxygenNote: | 7.2.3 |
| Suggests: | knitr, rmarkdown, testthat, minpack.lm (≥ 1.2-1) |
| VignetteBuilder: | knitr |
| URL: | https://github.com/frareb/devRate/ |
| BugReports: | https://github.com/frareb/devRate/issues |
| NeedsCompilation: | no |
| Packaged: | 2023-08-24 06:50:20 UTC; frareb |
| Repository: | CRAN |
| Date/Publication: | 2023-08-24 07:10:02 UTC |
devRate: A package to quantify the relationship between development rate and temperature in ectotherms.
Description
The devRate package allows quantifying the relationship between development rate and temperature in ectotherm organisms.
Citation
Please use citation("devRate") to cite the devRate package and/or
Rebaudo F, Struelens Q, Dangles O. Modelling temperature-dependent development
rate and phenology in arthropods: The devRate package for r. Methods Ecol Evol.
2017;00:1-7. https://doi.org/10.1111/2041-210X.12935.
Author's affiliation: UMR EGCE, Univ. ParisSud, CNRS, IRD, Univ. ParisSaclay, Gif-sur-Yvette, France
Overview
The devRate package provides three categories of functions:
- to find development rate information about a specific organism (Order, Family, Genus, species): which equations were used and what are the associated parameters (e.g., helpful to estimate starting values for your empirical data sets);
- to relate development rate and temperature; and
- to plot your empirical datasets and the associated fitted model, and/or to plot development curves from the literature.
Usage
You can use the package:
- to get development rate curves as a function of temperature for a specific organism (hundred of examples from the literature are included in the package);
- to know which equations exists and which are most used in the literature; and
- to relate development rate with temperature from your empirical data, using the equations from the package database.
Installation instructions
install.packages("devRate")
Documentation
The package includes two vignettes (long-form documentation):
- quickUserGuide: Using devRate package to fit development rate models to an empirical dataset
- modelEvaluation: Model evaluation using Shi et al. 2016 study
Analytis equation of development rate as a function of temperature.
Description
Analytis, S. (1977) Uber die Relation zwischen biologischer Entwicklung und Temperatur bei phytopathogenen Pilzen. Journal of Phytopathology 90(1): 64-76.
Usage
analytis_77
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa * (T - Tmin)^{bb} * (Tmax - T)^{cc}
where rT is the development rate, T the temperature, Tmin the minimum temperature, Tmax the maximum temperature, and aa, bb, and cc constants.
References
doi:10.1111/j.1439-0434.1977.tb02886.x
Bayoh and Lindsay equation of development rate as a function of temperature.
Description
Bayoh, M.N., Lindsay, S.W. (2003) Effect of temperature on the development of the aquatic stages of Anopheles gambiae sensu stricto (Diptera: Culicidae). Bulletin of entomological research 93(5): 375-81.
Usage
bayoh_03
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa + bb * T + cc * e^{T} + dd * e^{-T}
where rT is the development rate, T the temperature, and aa, bb, cc, and dd empirical constant parameters.
References
Beta2 equation of development rate as a function of temperature.
Description
Yin, X., Kropff, M.J., McLaren, G., and Visperas, R.M. (1995) A nonlinear model for crop development as a function of temperature. Agricultural and Forest Meteorology 77(1): 1-16.
Shi, P. J., Chen, L., Hui, C., & Grissino-Mayer, H. D. (2016). Capture the time when plants reach their maximum body size by using the beta sigmoid growth equation. Ecological Modelling, 320, 177-181.
Shi, P. J., Reddy, G. V., Chen, L., and 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(2), 211-215.
Usage
beta_16
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = rm * (\frac{T2 - T}/{T2 - Tm}) * (\frac{T - T1}/{Tm - T1})^{\frac{Tm - T1}/{T2 - Tm}}
where rT is the development rate, T the temperature, T1, T2, and Tm the model parameters.
References
doi:10.1016/j.ecolmodel.2015.09.012
Beta equation of development rate as a function of temperature.
Description
Yin, X., Kropff, M.J., McLaren, G., and Visperas, R.M. (1995) A nonlinear model for crop development as a function of temperature. Agricultural and Forest Meteorology 77(1): 1-16.
Usage
beta_95
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = e^{mu} * (T - Tb)^{aa} * (Tc - T)^{bb}
where rT is the development rate, T the temperature, mu, aa, and bb the model parameters, Tb the base temperature, and Tc the ceiling temperature.
References
doi:10.1016/0168-1923(95)02236-Q
Bieri equation 1 of development rate as a function of temperature.
Description
Bieri, M., Baumgartner, J., Bianchi, G., Delucchi, V., Arx, R. von. (1983) Development and fecundity of pea aphid (Acyrthosiphon pisum Harris) as affected by constant temperatures and by pea varieties. Mitteilungen der Schweizerischen Entomologischen Gesellschaft, 56, 163-171.
Kumar, S., and Kontodimas, D.C. (2012). Temperature-dependent development of Phenacoccus solenopsis under laboratory conditions. Entomologia Hellenica, 21, 25-38.
Usage
bieri1_83
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa * (T - Tmin) - (bb * e^{T - Tm})
where rT is the development rate, T the temperature, Tmin the minimum temperature, and aa, bb, and Tm fitted coefficients.
References
Briere et al equation 1 of development rate as a function of temperature.
Description
Briere, J.F., Pracros, P., le Roux, A.Y. and Pierre, S. (1999) A novel rate model of temperature-dependent development for arthropods. Environmental Entomology, 28, 22-29.
Usage
briere1_99
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa * T * (T - Tmin) * (Tmax - T)^{\frac{1}{2}}
where rT is the development rate, T the temperature, Tmin the low temperature developmental threshold, Tmax the lethal temperature, and aa an empirical constant.
References
Briere et al equation 2 of development rate as a function of temperature.
Description
Briere, J.F., Pracros, P., le Roux, A.Y. and Pierre, S. (1999) A novel rate model of temperature-dependent development for arthropods. Environmental Entomology, 28, 22-29.
Usage
briere2_99
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa * T * (T - Tmin) * (Tmax - T)^{\frac{1}{bb}}
where rT is the development rate, T the temperature, Tmin the low temperature developmental threshold, Tmax the lethal temperature, and aa and bb empirical constants.
References
Campbell et al. equation of development rate as a function of temperature.
Description
Campbell, A., Frazer, B. D., Gilbert, N. G. A. P., Gutierrez, A. P., & Mackauer, M. (1974). Temperature requirements of some aphids and their parasites. Journal of applied ecology, 431-438. <doi:10.2307/2402197>
Usage
campbell_74
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa + bb * T
where rT is the development rate, T the temperature, bb the slope, and aa the point at which the line crosses the rT axis when T = 0.
Life traits from Thermal Performance Curve
Description
Compute life traits from a Thermal Performance Curve
Usage
dRGetMetrics(
nlsDR,
prec = 0.1,
lowTempLim = 0,
highTempLimit = 60,
devLimit = 0.01,
printOut = FALSE
)
Arguments
nlsDR |
The object obtained from the |
prec |
The precision for the temperature (default = 0.1 degree celsius). |
lowTempLim |
The minimum temperature for the metrics (default = 0 degree celsius). |
highTempLimit |
The maximum temperature for the metrics (default = +60 degree celsius). |
devLimit |
The development rate considered as null (default = 0.01). |
printOut |
A logical to print the result (default = FALSE). |
Value
A matrix with one column and one row for each metric. The metrics names are the row names.
Examples
rawDevEggs <- matrix(
c(10, 0.031, 10, 0.039, 15, 0.047, 15, 0.059, 15.5,
0.066, 13, 0.072, 16, 0.083, 16, 0.100, 17, 0.100, 20, 0.100, 20,
0.143, 25, 0.171, 25, 0.200, 30, 0.200, 30, 0.180, 35, 0.001
), ncol = 2, byrow = TRUE)
mEggs <- devRateModel(
eq = taylor_81,
temp = rawDevEggs[,1],
devRate = rawDevEggs[,2],
startValues = list(Rm = 0.05, Tm = 30, To = 5)
)
myMetrics <- dRGetMetrics(nlsDR = mEggs, printOut = TRUE)
Life traits from the ectotherm database
Description
Life traits from the ectotherm database
Usage
dRGetMetricsInfo(
eq,
prec = 0.1,
lowTempLim = 0,
highTempLimit = 60,
devLimit = 0.01,
devThresh = 0.1,
lifeStage = "all",
colId = "genSp",
printOut = FALSE
)
Arguments
eq |
The name of the equation. |
prec |
The precision for the temperature (default = 0.1 degree celsius). |
lowTempLim |
The minimum temperature for the metrics (default = 0 degree celsius). |
highTempLimit |
The maximum temperature for the metrics (default = +60 degree celsius). |
devLimit |
The development rate considered as null (default = 0.01). |
devThresh |
The threshold in development rate to compute min and max temperature (default = 0.1). |
lifeStage |
The life stage on which the life traits should be computed (default = "all"; specify "" to take into account all life stages). |
colId |
The organism information for each column (default = genSp; choices = "ordersp" for Order, "familysp" for Family, "genussp" for Genus, "species" for species, and "gensp" for Genus and species). |
printOut |
A logical to print the result (default = FALSE). |
Value
A matrix with one column per organism and one row for each metric. The metrics names are the names of each row.
Examples
dRGetMetricsInfo(eq = taylor_81)
dRGetMetricsInfo(eq = taylor_81, devThresh = 0.1)
Simplified beta type equation of development rate as a function of temperature.
Description
Damos, P.T., and Savopoulou-Soultani, M. (2008). Temperature-dependent bionomics and modeling of Anarsia lineatella (Lepidoptera: Gelechiidae) in the laboratory. Journal of economic entomology, 101(5), 1557-1567.
Usage
damos_08
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa * (bb - \frac{T}{10}) * (\frac{T}{10})^{cc}
where rT is the development rate, T the temperature, and aa, bb, and cc empirical constant parameters.
References
Inverse second-order polynomial equation of development rate as a function of temperature.
Description
Damos, P., and Savopoulou-Soultani, M. (2011) Temperature-driven models for insect development and vital thermal requirements. Psyche: A Journal of Entomology, 2012.
Usage
damos_11
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{aa}{1 + bb * T + cc * T^{2}}
where rT is the development rate, T the temperature, and aa, bb, and cc empirical constant parameters.
References
Davidson equation of development rate as a function of temperature.
Description
Davidson, J. (1944). On the relationship between temperature and rate of development of insects at constant temperatures. The Journal of Animal Ecology:26-38. <doi:10.2307/1326>
Usage
davidson_44
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{K}{1 + e^{aa + bb * T}}
where rT is the development rate, T the temperature, K the distance between the upper and lower asymptote of the curve, aa the relative position of the origin of the curve on the abscissa, bb the degree of acceleration of development of the life stage in relation to temperature.
The list of all available equations of development rate as a function of temperature.
Description
The list of all available equations of development rate as a function of temperature.
Usage
devRateEqList
Format
An object of class list of length 37.
Default starting values for each equation listed in the devRateEqList object.
Description
Default starting values for each equation listed in the devRateEqList object.
Usage
devRateEqStartVal
Format
An object of class list of length 37.
Find models for species
Description
Find models for species
Usage
devRateFind(orderSP = "", familySP = "", species = "")
Arguments
orderSP |
Find models by Order. |
familySP |
Find models by Family. |
species |
Find models by species (Genus species). |
Details
The function looks for the species in the database and returns the number of occurrences for each model.
Value
A data.frame with the name of the equations, the number of occurrences in the database, and the number of parameters for each equation.
Examples
devRateFind(orderSP = "Lepidoptera")
devRateFind(familySP = "Gelechiidae")
## detailed example:
devRateFind(species = "Tuta absoluta")
## campbell_74 model has been used for T. absoluta
## Parameters from the campbell equation can be accessed by:
## campbell_74$startVal[campbell_74$startVal["genSp"] == "Tuta absoluta",]
Forecast ectotherm phenology as a function of temperature and development rate models
Description
Forecast ectotherm phenology as a function of temperature and development rate models
Usage
devRateIBM(tempTS, timeStepTS, models, numInd = 100, stocha, timeLayEggs = 1)
Arguments
tempTS |
The temperature time series (a vector). |
timeStepTS |
The time step of the temperature time series (a numeric in days). |
models |
The models for development rate (a list with objects of class nls). |
numInd |
The number of individuals for the simulation (an integer). |
stocha |
The standard deviation of a Normal distribution centered on development rate to create stochasticity among individuals (a numeric). Either a single number (same stochasticity for all stages) or a vector of length corresponding to the number of models used (different stochasticity for the phenological stages). |
timeLayEggs |
The delay between emergence of adults and the time where females lay eggs in time steps (a numeric). |
Value
A list with three elements: the table of phenology for each individual, the models used (nls objects), and the time series for temperature.
Examples
data(exTropicalMoth)
forecastTsolanivora <- devRateIBM(
tempTS = rnorm(n = 100, mean = 15, sd = 1),
timeStepTS = 1,
models = exTropicalMoth[[2]],
numInd = 100,
stocha = c(0.015, 0.005, 0.01),
timeLayEggs = 1)
Plot phenology table
Description
Plot phenology table
Usage
devRateIBMPlot(ibm, typeG = "density", threshold = 0.1)
Arguments
ibm |
The phenology model returned by devRateIBM function. |
typeG |
The type of plot ("density" or "hist"). |
threshold |
The threshold rate of individuals for being represented in a density plot (a numeric between 0 and 1). |
Value
Nothing.
Examples
data(exTropicalMoth)
forecastTsolanivora <- devRateIBM(
tempTS = rnorm(n = 100, mean = 15, sd = 1),
timeStepTS = 1,
models = exTropicalMoth[[2]],
numInd = 10,
stocha = 0.015,
timeLayEggs = 1)
devRateIBMPlot(ibm = forecastTsolanivora, typeG = "density", threshold = 0.1)
devRateIBMPlot(ibm = forecastTsolanivora, typeG = "hist")
Forecast ectotherm phenology as a function of temperature and development rate models available in the package database
Description
Forecast ectotherm phenology as a function of temperature and development rate models available in the package database
Usage
devRateIBMdataBase(
tempTS,
timeStepTS,
eq,
species,
lifeStages,
numInd = 10,
stocha,
timeLayEggs = 1
)
Arguments
tempTS |
The temperature time series (a vector). |
timeStepTS |
The time step of the temperature time series (a numeric with 1 = one day). |
eq |
The name of the equation (e.g., lactin2_95). |
species |
The species for the model (e.g., "Sesamia nonagrioides"). |
lifeStages |
The life stages available for the species and the model. |
numInd |
The number of individuals for the simulation (an integer). |
stocha |
The standard deviation of a Normal distribution centered on development rate to create stochasticity among individuals (a numeric). |
timeLayEggs |
The delay between emergence of adults and the time where females lay eggs in time steps (a numeric). |
Value
A list with three elements: the table of phenology for each individual, the models used (nls objects), and the time series for temperature.
Examples
forecastLactin2_95 <- devRateIBMdataBase(
tempTS = rnorm(n = 20, mean = 20, sd = 1),
timeStepTS = 10,
eq = lactin2_95,
species = "Sesamia nonagrioides",
lifeStages = c("eggs", "larva", "pupa"),
numInd = 10,
stocha = 0.015,
timeLayEggs = 1
)
Number of generations
Description
Computes the number of generations from the individual-based model fit.
Usage
devRateIBMgen(ibm)
Arguments
ibm |
The phenology model returned by devRateIBM function. |
Value
The simulated number of generations.
Examples
data(exTropicalMoth)
forecastTsolanivora <- devRateIBM(
tempTS = rnorm(n = 100, mean = 15, sd = 1),
timeStepTS = 1,
models = exTropicalMoth[[2]],
numInd = 10,
stocha = 0.015,
timeLayEggs = 1)
devRateIBMgen(ibm = forecastTsolanivora)
Forecast ectotherm phenology as a function of temperature and development rate models using known parameters
Description
Forecast ectotherm phenology as a function of temperature and development rate models using known parameters
Usage
devRateIBMparam(
tempTS,
timeStepTS,
eq,
myParam,
numInd = 10,
stocha,
timeLayEggs = 1
)
Arguments
tempTS |
The temperature time series (a vector). |
timeStepTS |
The time step of the temperature time series (a numeric with 1 = one day). |
eq |
The name of the equation (e.g., lactin2_95). |
myParam |
The known parameters for the equation (a list of list for each life stage). |
numInd |
The number of individuals for the simulation (an integer). |
stocha |
The standard deviation of a Normal distribution centered on development rate to create stochasticity among individuals (a numeric). |
timeLayEggs |
The delay between emergence of adults and the time where females lay eggs in time steps (a numeric). |
Details
Please note that this function is experimental and only works for the briere2_99 equation.
Value
A list with three elements: the table of phenology for each individual, the models used (nls objects), and the time series for temperature.
Examples
# with only one life stage
forecastX <- devRateIBMparam(
tempTS = rnorm(n = 20, mean = 20, sd = 1),
timeStepTS = 10,
eq = briere2_99,
myParam = list(
list(
aa = 0.0002,
Tmin = 10,
Tmax = 36.1,
bb = 2.84)
),
numInd = 10,
stocha = 0.015,
timeLayEggs = 1
)
# with two life stages
forecastXX <- devRateIBMparam(
tempTS = rnorm(n = 20, mean = 20, sd = 1),
timeStepTS = 10,
eq = briere2_99,
myParam = list(
lifeStage01 = list(
aa = 0.0002,
Tmin = 10,
Tmax = 36.1,
bb = 2.84),
lifeStage02 = list(
aa = 0.0004,
Tmin = 8,
Tmax = 35,
bb = 2.8)
),
numInd = 10,
stocha = 0.015,
timeLayEggs = 1
)
Display information about an equation
Description
Display information about an equation
Usage
devRateInfo(eq)
Arguments
eq |
The name of the equation. |
Value
Nothing.
Examples
devRateInfo(eq = davidson_44)
devRateInfo(eq = campbell_74)
devRateInfo(eq = taylor_81)
devRateInfo(eq = wang_82)
Predict development rate from a matrix of temperatures
Description
Create a map from a temperature matrix and a development rate curve
Usage
devRateMap(nlsDR, tempMap)
Arguments
nlsDR |
The result returned by the |
tempMap |
A matrix containing temperatures in degrees. |
Details
The devRateMap function is designed for a single ectotherm
life stage, but the resulted matrix of development rate can be performed
for each life stage in order to obtain the whole organism development.
Input temperatures should preferably cover the organism development period
rather than the whole year.
Value
A matrix with development rates predicted from the model.
Examples
myT <- 5:15
myDev <- -0.05 + rnorm(n = length(myT), mean = myT, sd = 1) * 0.01
myNLS <- devRateModel(eq = campbell_74, temp = myT, devRate = myDev,
startValues = list(aa = 0, bb = 0))
myMap <- devRateMap(nlsDR = myNLS, tempMap = matrix(rnorm(100, mean = 12, sd = 2), ncol=10))
Compute non-linear regression
Description
Determine the nonlinear least-squares estimates of the parameters of a
nonlinear model, on the basis of the nls function from package
stats.
Usage
devRateModel(eq, temp, devRate, startValues, dfData = NULL, algo = "GN", ...)
Arguments
eq |
The name of the equation. See |
temp |
The temperature (vector). |
devRate |
The development rate |
startValues |
Starting values for the regression (list). |
dfData |
A data.frame with the temperature in the first column and the development rate in the second column (alternative to the use of temp and devRate). |
algo |
The abbreviated name of the algorithm used for model fitting ( "GN" for Gauss-Newton algorithm, "LM" for Levenberg-Marquardt algorithm; "GN" is the default value). |
... |
Additional arguments for the |
Details
startValues for equations by Stinner et al. 1974 and Lamb
1992 are composed of two equations: one for the temperatures below the
optimal temperature and another for the temperatures above the optimal
temperature. For these equations, startValues should be a list
of two lists, where the second element only contain starting estimates not
specified in the first element, e.g., for Stinner et al.:
startValues <- list(list(C = 0.05, k1 = 5, k2 = -0.3), list(Topt = 30)),
and for Lamb 1992:
startValues <- list(list(Rm = 0.05, Tmax = 35, To = 15), list(T1 = 4))
The temperature should be provided as a vector in argument temp and
development rate in another vector in argument devRate. However, it is
possible to use the function with a data.frame containing the temperature in the
first column and the development rate in the sceond column, using the argument
dfData
NULL is returned when an unknown algorithm is entered.
Value
An object of class nls (except for Stinner et al. 1974 and
Lamb 1992 where the function returns a list of two objects of class
nls).
Examples
## Example with a linear model (no starting estimates)
myT <- 5:15
myDev <- -0.05 + rnorm(n = length(myT), mean = myT, sd = 1) * 0.01
myNLS <- devRateModel(
eq = campbell_74,
temp = myT,
devRate = myDev)
## Example with a non-linear model (starting estimates)
myT <- seq(from = 0, to = 50, by = 10)
myDev <- c(0.001, 0.008, 0.02, 0.03, 0.018, 0.004)
myNLS <- devRateModel(
eq = stinner_74,
temp = myT,
devRate = myDev,
startValues = list(
list(C = 0.05, k1 = 5, k2 = -0.3),
list(Topt = 30)))
## Example with a data.frame instead of two vectors for temperature and
## development rate
myDF <- data.frame(myT, myDev)
myNLS <- devRateModel(
eq = campbell_74,
dfData = myDF)
Fitting all models listed in devRateEqList to a development rate dataset
Description
This function fits all models listed in devRateEqList to a development rate dataset and then calculates a series of indices of goodness-of-fit for each fitted model.
Usage
devRateModelAll(
dfData,
eqList = devRate::devRateEqList,
eqStartVal = devRate::devRateEqStartVal,
propThresh = 0.01,
interval = c(0, 50),
...
)
Arguments
dfData |
A data.frame with the temperature in the first column and the development rate in the second column. |
eqList |
A list of models that can be retrieved from the object devRateEqList. The default value is the object devRateEqList. |
eqStartVal |
A list of sarting values for each model. The default value is the object devRateEqStartVal. |
propThresh |
The proportion of maximal development rate used as a threshold for estimating XTmin and XTmax for asymptotic equations (default value is 0.01) |
interval |
A vector containing the lower and upper boundaries of the interval of temperatures in which metrics are searched. |
... |
Additional arguments for the |
Details
Equations stinner_74 and lamb_92 are fitted and the resulting nls objects are showed in the first element of the returned list, however indices of goodness-of-fit are not provided. Equation campbell_74 is not fitted ( simple linear model).
Value
An object of class list with two elements. The first
element is a list with all the nls objects. The second element
is a data.frame.
In the data.frame, the first column corresponds to model
names and the second column to the number of parameters. The columns 3
to 6 correspond to the results of the function devRateQlStat, i.e.
RSS, RMSE, AIC, and BIC. The columns 7 to 11 correspond to the results
of the function devRateQlBio, i.e. CTmin, CTmax, Topt, XTmin, and
XTmax.
Examples
myDf <- exTropicalMoth$raw$egg
devRateModelAll(dfData = myDf)
Plot the empirical points and the regression
Description
Plot the empirical points and the regression
Usage
devRatePlot(eq, nlsDR, rangeT = 10, optText = TRUE, spe = TRUE, ...)
Arguments
eq |
The name of the equation. |
nlsDR |
The result returned by the |
rangeT |
The range of temperatures over which the regression is plotted. This argument may be overwritten depending on the equation. |
optText |
A logical indicating whether the name of the equation should be written in the topright corner of the plot. |
spe |
A logical indicating if special plotting rules from literature should apply. |
... |
Additional arguments for the plot. |
Value
Nothing.
Examples
myT <- 5:15
myDev <- -0.05 + rnorm(n = length(myT), mean = myT, sd = 1) * 0.01
myNLS <- devRateModel(eq = campbell_74, temp = myT, devRate = myDev,
startValues = list(aa = 0, bb = 0))
devRatePlot(eq = campbell_74, nlsDR = myNLS,
spe = TRUE, pch = 16, lwd = 2, ylim = c(0, 0.10))
Plot thermal performance curves from the literature
Description
Plot thermal performance curves from the literature
Usage
devRatePlotInfo(eq, sortBy = "genSp", stage = "all", ...)
Arguments
eq |
The name of the equation. |
sortBy |
The filter to separate species ("ordersp", "familysp", "genussp", "species", "genSp"). |
stage |
The life stage of the organism ("all", "eggs", "L1", "L2", "L3", "L4", "L5", "larva", "pupa", "prepupa", "female", "male", ...) |
... |
Aditional arguments for the plot. |
Value
Nothing.
Examples
devRatePlotInfo(eq = davidson_44, sortBy = "genSp", xlim = c(0, 40), ylim = c(0, 0.05))
devRatePlotInfo(eq = campbell_74, sortBy = "familysp", xlim = c(-10, 30), ylim = c(0, 0.05))
devRatePlotInfo(eq = taylor_81, sortBy = "ordersp", xlim = c(-20, 60), ylim = c(0, 0.2))
devRatePlotInfo(eq = wang_82, sortBy = "ordersp", xlim = c(0, 50), ylim = c(0, 0.06))
devRatePlotInfo(eq = stinner_74, sortBy = "ordersp", xlim = c(0, 50), ylim = c(0, 0.06))
Report model output from the NLS fit
Description
Provide a custom output of the NLS fit.
Usage
devRatePrint(myNLS, doPlots = FALSE)
Arguments
myNLS |
An object of class NLS |
doPlots |
A boolean to get the residual plot (default = FALSE) |
Value
A list of six objects (summary of the NLS fit; confidence intervals for the model parameters; test of normality; test of independence; AIC, BIC)
Examples
myT <- 5:15
myDev <- -0.05 + rnorm(n = length(myT), mean = myT, sd = 1) * 0.01
myNLS <- devRateModel(
eq = campbell_74,
temp = myT,
devRate = myDev,
startValues = list(aa = 0, bb = 0))
devRatePrint(myNLS)
rawDevEggs <- matrix(c(10, 0.031, 10, 0.039, 15, 0.047, 15, 0.059, 15.5, 0.066,
13, 0.072, 16, 0.083, 16, 0.100, 17, 0.100, 20, 0.100, 20, 0.143, 25, 0.171,
25, 0.200, 30, 0.200, 30, 0.180, 35, 0.001), ncol = 2, byrow = TRUE)
mEggs <- devRateModel(
eq = taylor_81,
temp = rawDevEggs[,1],
devRate = rawDevEggs[,2],
startValues = list(Rm = 0.05, Tm = 30, To = 5))
devRatePrint(myNLS = mEggs)
Biological likelihood of nls fits
Description
Return a table of 5 metrics of development (CTmin, CTmax, Topt, XTmin, XTmax)
Usage
devRateQlBio(nlsDR, propThresh = 0.01, eq, interval = c(0, 50))
Arguments
nlsDR |
A list of nls objects. |
propThresh |
The proportion of maximal development rate used as a threshold for estimating XTmin and XTmax for asymptotic equations (default value is 0.01) |
eq |
A list of equations used for nls fitting. |
interval |
A vector containing the lower and upper boundaries of the interval of temperatures in which metrics are searched. |
Details
NULL is returned when nlsDR or eq are not a list.
Value
An object of class data.frame with development metrics (CTmin,
Ctmax, Topt, XTmin, XTmax) in columns and nls objects in rows.
Examples
myDf <- data.frame(temp = seq(from = 0, to = 50, by = 10),
rT = c(0.001, 0.008, 0.02, 0.03, 0.018, 0.004))
myNLS <- list(
devRateModel(
eq = janisch_32,
df = myDf,
startValues = list(aa = 0.2, bb = 0.1, Dmin = 10, Topt = 30),
algo = "LM"),
devRateModel(
eq = kontodimas_04,
df = myDf,
startValues = list(aa = 1, Tmin = 7, Tmax = 40),
algo = "LM"),
devRateModel(
eq = poly2,
df = myDf,
startValues = list(a0 = 1, a1 = 1, a2 = 1),
algo = "LM"))
devRateQlBio(
nlsDR = myNLS,
eq = list(janisch_32, kontodimas_04, poly2),
propThresh = 0.1)
Statistical indices of the nls goodness-of-fit
Description
Return a table of multiple statistical indices of goodness-of-fit
Usage
devRateQlStat(nlsDR)
Arguments
nlsDR |
A list of |
Details
NULL is returned when nlsDR is not of type list. AIC and BIC are calculated using the RSS (Burnham and Anderson, 2002).
Value
A data.frame with statistical indices
in columns (RSS, RMSE, AIC, BIC) and nls objects in rows.
Examples
myDf <- data.frame(
temp = seq(from = 0, to = 50, by = 10),
rT = c(0.001, 0.008, 0.02, 0.03, 0.018, 0.004))
damos_08Fit <- devRateModel(
eq = damos_08,
dfData = myDf,
startValues = list(aa = 1, bb = 1, cc = 1),
algo = "LM")
kontodimas_04Fit <- devRateModel(
eq = kontodimas_04,
dfData = myDf,
startValues = list(aa = 1, Tmin = 7, Tmax = 40),
algo = "LM")
poly2Fit <- devRateModel(
eq = poly2,
dfData = myDf,
startValues = list(a0 = 1, a1 = 1, a2 = 1),
algo = "LM")
devRateQlStat(
nlsDR = list(damos_08Fit, kontodimas_04Fit, poly2Fit)
)
Tropical moth development rate at constant temperatures.
Description
This is a sample dataset to be used in the package examples. In this example, we used data from Crespo-Perez et al. (2011) on the potato tuber moth Tecia solanivora (Lepidoptera: Gelechiidae), a major crop pest in the central Andes of Ecuador. We used Web Plot Digitizer (Rohatgi 2015) to extract the data on development rate as a function of temperature.
Crespo-Perez, V., Rebaudo, F., Silvain, J.-F. & Dangles, O. (2011). Modeling invasive species spread in complex landscapes: the case of potato moth in Ecuador. Landscape ecology, 26, 1447-1461.
Rohatgi, A. (2015). WebPlotDigitalizer: HTML5 based online tool to extract numerical data from plot images.
Usage
exTropicalMoth
Format
A list of two elements with a list of three elements.
- raw
The raw data extracted from Crespo-Perez et al. 2011.
- eggs
raw temperatures and development rates
- larva
raw temperatures and development rates
- pupa
raw temperatures and development rates
- model
The nls object returned by the devRateModel function.
- eggs
nls object
- larva
nls object
- pupa
nls object
Harcourt and Yee equation of development rate as a function of temperature.
Description
Harcourt, D. and Yee, J. (1982) Polynomial algorithm for predicting the duration of insect life stages. Environmental Entomology, 11, 581-584.
Usage
harcourtYee_82
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = a0 + a1 * T + a2 * T^{2} + a3 * T^{3}
where rT is the development rate, T the temperature, and a0, a1, a2, and a3 are constants.
References
Holling type III equation of development rate as a function of temperature.
Description
Hilbert, DW, y JA Logan (1983) Empirical model of nymphal development for the migratory grasshopper, Melanoplus sanguinipes (Orthoptera: Acrididae). Environmental Entomology 12(1): 1-5.
Usage
hilbertLogan_83
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = phi * ((\frac{(T-Tb)^{2}}{(T-Tb)^{2} + aa^{2}}) - e^{-\frac{Tmax - (T-Tb)}{deltaT}})
where rT is the development rate, T the temperature, Tb the minimum temperature for development, deltaT the width of high temperature boundary area, Tmax the maximum temperature, and aa a constant.
References
Janisch equation of development rate as a function of temperature (Analytis modification).
Description
Janisch, E. (1932) The influence of temperature on the life-history of insects. Transactions of the Royal Entomological Society of London 80(2): 137-68.
Analytis, S. (1977) Uber die Relation zwischen biologischer Entwicklung und Temperatur bei phytopathogenen Pilzen. Journal of Phytopathology 90(1): 64-76.
Analytis, S. (1981). Relationship between temperature and development times in phytopathogenic fungus and in plant pests: a mathematical model. Agric. Res.(Athens), 5, 133-159.
Kontodimas, D.C., Eliopoulos, P.A., Stathas, G.J. and Economou, L.P. (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): 1-11.
Usage
janisch_32
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = (\frac{Dmin}{2} * (e^{aa*(T - Topt)} + e^{-bb*(T - Topt)}))^{-1}
where rT is the development rate, T the temperature, Topt the optimum temperature, Dmin, aa, and bb constants.
References
doi:10.1111/j.1365-2311.1932.tb03305.x
Kontodimas et al. equation of development rate as a function of temperature.
Description
Kontodimas, D.C., Eliopoulos, P.A., Stathas, G.J. and Economou, L.P. (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): 1-11.
Usage
kontodimas_04
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = aa * (T - Tmin)^{2} * (Tmax - T)
where rT is the development rate, T the temperature, Tmin the minimum temperature, Tmax the maximum temperature, and aa a constant.
References
https://academic.oup.com/ee/article/33/1/1/477793/
Lactin et al. equation 1 of development rate as a function of temperature.
Description
Lactin, Derek J, NJ Holliday, DL Johnson, y R Craigen (995) Improved rate model of temperature-dependent development by arthropods. Environmental Entomology 24(1): 68-75.
Usage
lactin1_95
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = e^{aa * T} - e^{aa * Tmax - \frac{Tmax - T}{deltaT}}
where rT is the development rate, T the temperature, and aa, Tmax, and deltaT fitted parameters.
References
Lactin et al. equation 2 of development rate as a function of temperature.
Description
Lactin, Derek J, NJ Holliday, DL Johnson, y R Craigen (995) Improved rate model of temperature-dependent development by arthropods. Environmental Entomology 24(1): 68-75.
Usage
lactin2_95
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = e^{aa * T} - e^{aa * Tmax - \frac{Tmax - T}{deltaT}} + bb
where rT is the development rate, T the temperature, and aa, bb, Tmax, and deltaT fitted parameters.
References
Lamb equation of development rate as a function of temperature.
Description
Lamb, R. J., Gerber, G. H., & Atkinson, G. F. (1984). Comparison of developmental rate curves applied to egg hatching data of Entomoscelis americana Brown (Coleoptera: Chrysomelidae). Environmental entomology, 13(3), 868-872.
Lamb, RJ. (1992) Developmental rate of Acyrthosiphon pisum (Homoptera: Aphididae) at low temperatures: implications for estimating rate parameters for insects. Environmental Entomology 21(1): 10-19.
Usage
lamb_92
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = Rm * e^{-\frac{1}{2} * (\frac{T - Tmax}{To})^{2}}
and
rT = Rm * e^{-\frac{1}{2} * (\frac{T - Tmax}{T1})^{2}}
where rT is the development rate, T the temperature, Rm the maximum development rate, Tmax the optimum temperature, and To and T1 the shape parameter giving the spread of the curve.
References
Logan et al. equation 10 of development rate as a function of temperature.
Description
Logan, J. A., Wollkind, D. J., Hoyt, S. C., and Tanigoshi, L. K. (1976). An analytic model for description of temperature dependent rate phenomena in arthropods. Environmental Entomology, 5(6), 1133-1140.
Usage
logan10_76
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = alpha * (\frac{1}{1 + cc * e^{- bb * T}} - e^{-\frac{Tmax - T}{deltaT}})
where rT is the development rate, T the temperature, Tmax the maximum temperature, deltaT the width of the high temperature boundary layer, and alpha and bb constants.
References
Logan et al. equation 6 of development rate as a function of temperature.
Description
Logan, J. A., Wollkind, D. J., Hoyt, S. C., and Tanigoshi, L. K. (1976). An analytic model for description of temperature dependent rate phenomena in arthropods. Environmental Entomology, 5(6), 1133-1140.
Usage
logan6_76
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = phi * (e^{bb * T} - e^{bb * Tmax - \frac{Tmax - T}{deltaT}})
where rT is the development rate, T the temperature, Tmax the maximum temperature, deltaT the width of the high temperature boundary layer, phi the developmental rate at some base temperature above developmental threshold, and bb a constant.
References
Performance-2 equation of development rate as a function of temperature.
Description
Shi, P., Ge, F., Sun, Y., and Chen, C. (2011) A simple model for describing the effect of temperature on insect developmental rate. Journal of Asia-Pacific Entomology 14(1): 15-20.
Wang, L., P. Shi, C. Chen, and F. Xue. 2013. Effect of temperature on the development of Laodelphax striatellus (Homoptera: Delphacidae). J. Econ. Entomol. 106: 107-114.
Shi, P. J., Reddy, G. V., Chen, L., and Ge, F. (2016). Comparison of Thermal Performance Equations in Describing Temperature-Dependent Developmental Rates of Insects:(I) Empirical Models. Annals of the Entomological Society of America, 109(2), 211-215.
Usage
perf2_11
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = cc * (T - T1) * (1 - e^{k * (T - T2)})
where rT is the development rate, T the temperature, T1 and T2 the conceptual lower and upper developmental thresholds at which development rates equal zero, and cc and k constants.
References
doi:10.1016/j.aspen.2010.11.008
Second-order polynomial equation of development rate as a function of temperature.
Description
A simple second-order polynomial equation.
Usage
poly2
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = a0 + a1 * T + a2 * T^{2}
where rT is the development rate, T the temperature, and a0, a1, and a2 are constants.
Fourth-order polynomial equation of development rate as a function of temperature.
Description
A simple fourth-order polynomial equation.
Usage
poly4
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = a0 + a1 * T + a2 * T^{2} + a3 * T^{3} + a4 * T^{4}
where rT is the development rate, T the temperature, and a0, a1, a2, a3, and a4 are constants.
Ratkowsky equation of development rate as a function of temperature (Shi modification).
Description
Ratkowsky, D.A., Olley, J., McMeekin, T.A., and Ball, A. (1982) Relationship between temperature and growth rate of bacterial cultures. Journal of Bacteriology 149(1): 1-5.
Ratkowsky, D.A., R.K. Lowry, T.A. McMeekin, A.N. Stokes, and R.E. Chandler. 1983. Model for bacterial culture growth rate throughout the entire biokinetic temperature range. Journal of Bacteriology 154: 1222-1226.
Shi, P., Ge, F., Sun, Y., and Chen, C. (2011) A simple model for describing the effect of temperature on insect developmental rate. Journal of Asia-Pacific Entomology 14(1): 15-20.
Usage
ratkowsky_82
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = (\sqrt{cc} * k1 * (T - T1) * (1 - e^{k2 * (T - T2)}))^{2}
where rT is the development rate, T the temperature, T1 and T2 the minimum and maximum temperatures at which rate of growth is zero, sqrt(cc) * k1 the slope of the regression as in the rootsq_82 equation, and k2 a constant. The Ratkowsky model designed for microorganisms has been modified by Shi et al. 2011 to describe the temperature-dependent development rates of insects.
References
doi:10.1128/jb.154.3.1222-1226.1983
Ratkowsky equation of development rate as a function of temperature (Shi 2016 modification).
Description
Ratkowsky, D.A., Olley, J., McMeekin, T.A., and Ball, A. (1982) Relationship between temperature and growth rate of bacterial cultures. Journal of Bacteriology 149(1): 1-5.
Ratkowsky, D.A., R.K. Lowry, T.A. McMeekin, A.N. Stokes, and R.E. Chandler. 1983. Model for bacterial culture growth rate throughout the entire biokinetic temperature range. Journal of Bacteriology 154: 1222-1226.
Shi, P. J., Reddy, G. V., Chen, L., and 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(2), 211-215.
Usage
ratkowsky_83
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = (cc * (T - T1) * (1 - e^{k * (T - T2)}))^2
where rT is the development rate, T the temperature, T1 and T2 the minimum and maximum temperatures at which rate of growth is zero, cc the slope of the regression as in the rootsq_82 equation, and k a constant. The Ratkowsky model designed for microorganisms has been modified by Shi et al. 2016 to describe the temperature-dependent development rates of insects.
References
Regniere equation of development rate as a function of temperature.
Description
Regniere, J., Powell, J., Bentz, B., and Nealis, V. (2012) Effects of temperature on development, survival and reproduction of insects: experimental design, data analysis and modeling. Journal of Insect Physiology 58(5): 634-47.
Usage
regniere_12
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = phi * (e^{bb * (T - Tb)} - \frac{Tm - T}{Tm - Tb} * e^{-bb * \frac{T - Tb}{deltab}} - \frac{T - Tb}{Tm - Tb} * e^{\frac{bb * (Tm - Tb) - (Tm - T)}{deltam}})
where rT is the development rate, T the temperature, Tb the minimum temperature, Tm the maximum temperature and phi, bb, deltab, and deltam constants (see source for more details).
References
doi:10.1016/j.jinsphys.2012.01.010
Root square equation of development rate as a function of temperature.
Description
Ratkowsky, D.A., Olley, J., McMeekin, T.A., and Ball, A. (1982) Relationship between temperature and growth rate of bacterial cultures. Journal of Bacteriology 149(1): 1-5.
Usage
rootsq_82
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = (bb * (T - Tb))^{2}
where rT is the development rate, T the temperature, bb the slope of the regression line, and Tb a conceptual temperature of no metabolic significance.
References
Schoolfield et al. equation of development rate as a function of temperature for intermediate to high temperatures only.
Description
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. Wagner, T.L., Wu, H.I., Sharpe, P.S.H., Schoolfield, R.M., Coulson, R.N. (1984) Modeling insect development rates: a literature review and application of a biophysical model. Annals of the Entomological Society of America 77(2): 208-20.
Usage
schoolfieldHigh_81
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{p25 * \frac{T + 273.16}{298} * e^{\frac{aa}{1.987} * (\frac{1}{298} - \frac{1}{T + 273.16})}}{1 + e^{\frac{dd}{1.987} * (\frac{1}{ee} - \frac{1}{T + 273.16})}}
where rT is the development rate, T the temperature, p25 the development rate at 25 degrees Celsius assuming no enzyme inactivation, aa the enthalpy of activation of the reaction that is catalyzed by the enzyme, bb the change in enthalpy associated with low temperature inactivation of the enzyme, cc the the temperature at which the enzyme is 1/2 active and 1/2 low temperature inactive, dd the cange in enthalpy associated with high temperature inactivation of the enzyme, and ee the temperature at which the enzyme is 1/2 active and 1/2 high temperature inactive.
References
doi:10.1016/0022-5193(81)90246-0
Schoolfield et al. equation of development rate as a function of temperature for intermediate to low temperatures only.
Description
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. Wagner, T.L., Wu, H.I., Sharpe, P.S.H., Schoolfield, R.M., Coulson, R.N. (1984) Modeling insect development rates: a literature review and application of a biophysical model. Annals of the Entomological Society of America 77(2): 208-20.
Usage
schoolfieldLow_81
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{p25 * \frac{T + 273.16}{298} * e^{\frac{aa}{1.987} * (\frac{1}{298} - \frac{1}{T + 273.16})}}{1 + e^{\frac{bb}{1.987} * (\frac{1}{cc} - \frac{1}{T + 273.16})}}
where rT is the development rate, T the temperature, p25 the development rate at 25 degrees Celsius assuming no enzyme inactivation, aa the enthalpy of activation of the reaction that is catalyzed by the enzyme, bb the change in enthalpy associated with low temperature inactivation of the enzyme, cc the the temperature at which the enzyme is 1/2 active and 1/2 low temperature inactive, dd the cange in enthalpy associated with high temperature inactivation of the enzyme, and ee the temperature at which the enzyme is 1/2 active and 1/2 high temperature inactive.
References
doi:10.1016/0022-5193(81)90246-0
Schoolfield et al. equation of development rate as a function of temperature.
Description
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.
Usage
schoolfield_81
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{p25 * \frac{T + 273.16}{298} * e^{\frac{aa}{1.987} * (\frac{1}{298} - \frac{1}{T + 273.16})}}{1 + e^{\frac{bb}{1.987} * (\frac{1}{cc} - \frac{1}{T + 273.16})} + e^{\frac{dd}{1.987} * (\frac{1}{ee} - \frac{1}{T + 273.16})}}
where rT is the development rate, T the temperature, p25 the development rate at 25 degree Celsius assuming no enzyme inactivation, aa the enthalpy of activation of the reaction that is catalyzed by the enzyme, bb the change in enthalpy associated with low temperature inactivation of the enzyme, cc the temperature at which the enzyme is 1/2 active and 1/2 low temperature inactive, dd the change in enthalpy associated with high temperature inactivation of the enzyme, and ee the temperature at which the enzyme is 1/2 active and 1/2 high temperature inactive.
References
doi:10.1016/0022-5193(81)90246-0
Sharpe and DeMichele equation of development rate as a function of temperature.
Description
Sharpe, P.J. & DeMichele, D.W. (1977) Reaction kinetics of poikilotherm development. Journal of Theoretical Biology, 64, 649-670.
Usage
sharpeDeMichele_77
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{(T + 273.16) * e^{\frac{aa - \frac{bb}{T + 273.16}}{1.987}}}{1 + e^{\frac{cc - \frac{dd}{T + 273.16}}{1.987}} + e^{\frac{ff - \frac{gg}{T + 273.16}}{1.987}}}
where rT is the development rate, T the temperature, and aa, bb, cc, dd, ff, and gg thermodynamic parameters.
References
doi:10.1016/0022-5193(77)90265-X
Shi equation of development rate as a function of temperature.
Description
Shi, P., Ge, F., Sun, Y., and Chen, C. (2011) A simple model for describing the effect of temperature on insect developmental rate. Journal of Asia-Pacific Entomology 14(1): 15-20.
Usage
shi_11
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = cc * (1 - e^{-k1 * (T - T1)}) * (1 - e^{k2 * (T - T2)})
where rT is the development rate, T the temperature, T1 and T2 the conceptual lower and upper developmental thresholds at which development rates equal zero, and cc k1, and k2 constants.
References
doi:10.1016/j.aspen.2010.11.008
Stinner et al equation of development rate as a function of temperature.
Description
Stinner, R., Gutierrez, A. & Butler, G. (1974) An algorithm for temperature-dependent growth rate simulation. The Canadian Entomologist, 106, 519-524.
Usage
stinner_74
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{C}{1 + e^{k1 + k2 * T}}
and
rT = \frac{C}{1 + e^{k1 + k2 * (2 * Topt - T)}}
where rT is the development rate, T the temperature, Topt the optimum temperature, k1 and k2 constants. "[...] the relationship [is] inverted when the temperature is above an optimum [...] T = 2 * Topt - T for T >= Topt." Stinner et al. 1974.
References
Taylor equation of development rate as a function of temperature.
Description
Taylor, F. (1981) Ecology and evolution of physiological time in insects. American Naturalist, 1-23.
Lamb, RJ. (1992) Developmental rate of Acyrthosiphon pisum (Homoptera: Aphididae) at low temperatures: implications for estimating rate parameters for insects. Environmental Entomology 21(1): 10-19.
Usage
taylor_81
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = Rm * e^{-\frac{1}{2} * (\frac{T - Tm}{To})^{2}}
where rT is the development rate, T the temperature, Rm the maximum development rate, Tm the optimum temperature, and To the rate at which development rate falls away from Tm.
Hagstrum et Milliken equation of development rate as a function of temperature retrieved from Wagner 1984.
Description
Hagstrum, D.W., Milliken, G.A. (1988) Quantitative analysis of temperature, moisture, and diet factors affecting insect development. Annals of the Entomological Society of America 81(4): 539-46.
Wagner, T.L., Wu, H.I., Sharpe, P.S.H., Schoolfield, R.M., Coulson, R.N. (1984) Modeling insect development rates: a literature review and application of a biophysical model. Annals of the Entomological Society of America 77(2): 208-20.
Usage
wagner_88
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{1}{\frac{1 + e^{\frac{cc}{1.987} * (\frac{1}{dd} - \frac{1}{T + 273.16})}}{aa*\frac{T + 273.16}{298.15}*e^{\frac{bb}{1.987}*(\frac{1}{298.15} - \frac{1}{T + 273.16})}}}
where rT is the development rate, T the temperature, and aa, bb, cc, and dd are thermodynamic parameters.
References
Wang et al. equation of development rate as a function of temperature.
Description
Wang, R., Lan, Z. and Ding, Y. (1982) Studies on mathematical models of the relationship between insect development and temperature. Acta Ecol. Sin, 2, 47-57.
Usage
wang_82
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{K}{1 + e^{-r*(T - T0)}} * (1 - e^{-\frac{T - TL}{aa}}) * (1 - e^{-\frac{TH - T}{aa}})
where rT is the development rate, T the temperature, and K, r, T0, TH, and TL constants.
References
Wang and Engel equation of development rate as a function of temperature.
Description
Wang, E., and Engel, T. (1998) Simulation of phenological development of wheat crops. Agricultural systems 58(1): 1-24.
Usage
wangengel_98
Format
A list of eight elements describing the equation.
- eq
The equation (formula object).
- eqAlt
The equation (string).
- name
The name of the equation.
- ref
The equation reference.
- refShort
The equation reference shortened.
- startVal
The parameters found in the literature with their references.
- com
An optional comment about the equation use.
- id
An id to identify the equation.
Details
Equation:
rT = \frac{2 * (T - Tmin)^{aa} * (Topt - Tmin)^{aa} - (T - Tmin)^{2 * aa}}{(Topt - Tmin)^{2 * aa}}
where rT is the development rate, T the temperature, Tmin the minimum temperature, Topt the optimum temperature, and aa a constant.