Package 'devRate'

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

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

doi:10.1079/BER2003259

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

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

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

http://www.e-periodica.ch

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

doi:10.1093/ee/28.1.22

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

doi:10.1093/ee/28.1.22

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.

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

doi:10.1093/jee/101.5.1557

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

doi:10.1155/2012/123405

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.

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

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.

Description

Default starting values for each equation listed in the devRateEqList object.

Usage

devRateEqStartVal

Format

An object of class list of length 37.

Description

Find models for species

Usage

devRateFind(orderSP = "", familySP = "", species = "")

Arguments

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",]

Description

Forecast ectotherm phenology as a function of temperature and development rate models

Usage

devRateIBM(tempTS, timeStepTS, models, numInd = 100, stocha, timeLayEggs = 1)

Arguments

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)

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

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
)

Description

Computes the number of generations from the individual-based model fit.

Usage

devRateIBMgen(ibm)

Arguments

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)

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

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
)

Description

Plot phenology table

Usage

devRateIBMPlot(ibm, typeG = "density", threshold = 0.1)

Arguments

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")

Description

Display information about an equation

Usage

devRateInfo(eq)

Arguments

Value

Nothing.

Examples

devRateInfo(eq = davidson_44)
devRateInfo(eq = campbell_74)
devRateInfo(eq = taylor_81)
devRateInfo(eq = wang_82)

Description

Create a map from a temperature matrix and a development rate curve

Usage

devRateMap(nlsDR, tempMap)

Arguments

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))

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

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)

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

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)

Description

Plot the empirical points and the regression

Usage

devRatePlot(eq, nlsDR, rangeT = 10, optText = TRUE, spe = TRUE, ...)

Arguments

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))

Description

Plot thermal performance curves from the literature

Usage

devRatePlotInfo(eq, sortBy = "genSp", stage = "all", ...)

Arguments

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))

Description

Provide a custom output of the NLS fit.

Usage

devRatePrint(myNLS, doPlots = FALSE)

Arguments

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)

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

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)

Description

Return a table of multiple statistical indices of goodness-of-fit

Usage

devRateQlStat(nlsDR)

Arguments

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)
)

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

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)

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

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)

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

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

doi:10.1093/ee/11.3.581

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

doi:10.1093/ee/12.1.1

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

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/

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

doi:10.1093/ee/24.1.68

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

doi:10.1093/ee/24.1.68

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

doi:10.1093/ee/21.1.10

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

doi:10.1093/ee/5.6.1133

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

doi:10.1093/ee/5.6.1133

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

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.

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.

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.149.1.1-5.1982

doi:10.1128/jb.154.3.1222-1226.1983

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

doi:10.1093/aesa/sav121

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

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

doi:10.1128/jb.149.1.1-5.1982

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

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

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

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

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

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

doi:10.4039/Ent106519-5

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.

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

doi:10.1093/aesa/77.2.208

doi:10.1093/aesa/81.4.539

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

http://en.cnki.com.cn

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.

References

doi:10.1016/S0308-521X(98)00028-6