Example thermal performance curves of bacterial growth

Description

A dataset containing example data of growth rates of the bacteria Pseudomonas fluorescens in the presence and absence of its phage, phi2. Growth rates were measured across a range of assay temperatures to incorporate the entire thermal performance of the bacteria The dataset is the cleaned version so some data points have been omitted. There are multiple independent measurements per temperature for each treatment.

Usage

data("bacteria_tpc")

Format

A data frame with 649 rows and 7 variables:

phage

whether the bacteria was grown with or without phage

temp

the assay temperature at which the growth rate was measured (degrees centigrade)

rate

estimated growth rate per hour

Source

Daniel Padfield

References

Padfield, D., Castledine, M., & Buckling, A. (2020). Temperature-dependent changes to host–parasite interactions alter the thermal performance of a bacterial host. The ISME Journal, 14(2), 389-398.

Examples

data("bacteria_tpc")
library(ggplot2)
ggplot(bacteria_tpc) +
 geom_point(aes(temp, rate, col = phage))

Beta model for fitting thermal performance curves

Description

Beta model for fitting thermal performance curves

Usage

beta_2012(temp, a, b, c, d, e)

Arguments

Details

Equation:

rate=\frac{a\left(\frac{temp-b+\frac{c(d-1)}{d+e-2}}{c}\right)^{d-1} \cdot \left(1-\frac{temp-b+\frac{c(d-1)}{d+e-2}}{c}\right)^{e-1}}{{\left(\frac{d-1}{d+e-2}\right)}^{d-1}\cdot \left(\frac{e-1}{d+e-2}\right)^{e-1}}

Start values in get_start_vals are derived from the data or sensible values from the literature.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model difficult to fit.

Author(s)

Daniel Padfield

References

Niehaus, Amanda C., et al. Predicting the physiological performance of ectotherms in fluctuating thermal environments. Journal of Experimental Biology 215.4: 694-701 (2012)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'beta_2012')
# fit model
mod <- nls.multstart::nls_multstart(rate~beta_2012(temp = temp, a, b, c, d, e),
data = d,
iter = c(7,7,7,7,7),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'beta_2012'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'beta_2012'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Boatman model for fitting thermal performance curves

Description

Boatman model for fitting thermal performance curves

Usage

boatman_2017(temp, rmax, tmin, tmax, a, b)

Arguments

Details

Equation:

rate= r_{max} \cdot \left(sin\bigg(\pi\left(\frac{temp-t_{min}}{t_{max} - t_{min}}\right)^{a}\bigg)\right)^{b}

Start values in get_start_vals are derived from the data or sensible values from the literature.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Boatman, T. G., Lawson, T., & Geider, R. J. A key marine diazotroph in a changing ocean: The interacting effects of temperature, CO2 and light on the growth of Trichodesmium erythraeum IMS101. PLoS ONE, 12, e0168796 (2017)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'boatman_2017')
# fit model
mod <- nls.multstart::nls_multstart(rate~boatman_2017(temp = temp, rmax, tmin, tmax, a, b),
data = d,
iter = c(4,4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'boatman_2017'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'boatman_2017'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Briere2 model for fitting thermal performance curves

Description

Briere2 model for fitting thermal performance curves

Usage

briere2_1999(temp, tmin, tmax, a, b)

Arguments

Details

Equation:

rate=a\cdot temp \cdot(temp - t_{min}) \cdot (t_{max} - temp)^{\frac{1}{b}}

Start values in get_start_vals are derived from the data or sensible values from the literature.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Brière, J.F., Pracros, P., Le Roux, A.Y., Pierre, J.S., A novel rate model of temperature-dependent development for arthropods. Environmental Entomololgy, 28, 22–29 (1999)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'briere2_1999')
# fit model
mod <- nls.multstart::nls_multstart(rate~briere2_1999(temp = temp, tmin, tmax, a, b),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'briere2_1999'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'briere2_1999'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Calculate extra parameters of a thermal performance curve

Description

Calculate extra parameters of a thermal performance curve

Usage

calc_params(model)

Arguments

Details

Currently estimates:

• maximum rate (rmax) using get_rmax()

• optimum temperature (topt) using get_topt()

• critical thermal maximum (ctmax) using get_ctmax()

• critical thermal minimum (ctmin) using get_ctmin()

• activation energy (e) using get_e()

• deactivation energy (eh) using get_eh()

• q10 value using get_q10()

• thermal safety margin using get_thermalsafetymargin()

• thermal tolerance using get_thermaltolerance()

• thermal performance breadth using get_breadth()

• skewness using get_skewness()

Value

a dataframe containing the estimates of key TPC traits for a given model object. If any parameters cannot be calculated for a thermal performance curve, they will return NA.

Example metabolic thermal performance curves

Description

A dataset containing example data of rates of photosynthesis and respiration of the phytoplankton Chlorella vulgaris. Instantaneous rates of metabolism were made across a range of assay temperatures to incorporate the entire thermal performance of the populations. The dataset is the cleaned version so some datapoints have been omitted.

Usage

data("chlorella_tpc")

Format

A data frame with 649 rows and 7 variables:

curve_id

a unique value for each separate curve

growth_temp

the growth temperature that the culture was maintained at before measurements were taken (degrees centigrade)

process

whether the cultures had been kept for a long time at their growth temperature (adaptation/~100 generations) or a short time (a measure of acclimation/~10 generations)

flux

whether the curve depicts respiration or gross photosynthesis

temp

the assay temperature at which the metabolic rate was measured (degrees centigrade)

rate

the metabolic rate measured (micro mol O2 micro gram C-1 hr-1)

Source

Daniel Padfield

References

Padfield, D., Yvon-durocher, G., Buckling, A., Jennings, S. & Yvon-durocher, G. (2015). Rapid evolution of metabolic traits explains thermal adaptation in phytoplankton, Ecology Letters, 19, 133-142.

Examples

data("chlorella_tpc")
library(ggplot2)
ggplot(chlorella_tpc) +
 geom_point(aes(temp, rate, col = process)) +
 facet_wrap(~ growth_temp + flux)

DeLong enzyme-assisted Arrhenius model for fitting thermal performance curves

Description

DeLong enzyme-assisted Arrhenius model for fitting thermal performance curves

Usage

delong_2017(temp, c, eb, ef, tm, ehc)

Arguments

Details

Equation:

rate = c \cdot exp\frac{-(e_b-(e_f(1-\frac{temp + 273.15}{t_m})+e_{hc} \cdot ((temp + 273.15) - t_m - (temp + 273.15) \cdot ln(\frac{temp + 273.15}{t_m}))))}{k \cdot (temp + 273.15)}

where k is Boltzmann's constant with a value of 8.62e-05 and tm is actually tm - 273.15

Start values in get_start_vals are derived from the data or sensible values from the literature.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

DeLong, John P., et al. The combined effects of reactant kinetics and enzyme stability explain the temperature dependence of metabolic rates. Ecology and evolution 7.11 (2017): 3940-3950.

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'delong_2017')
# fit model
mod <- nls.multstart::nls_multstart(rate~delong_2017(temp = temp, c, eb, ef, tm,ehc),
data = d,
iter = c(4,4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'delong_2017'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'delong_2017'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Modified deutsch model for fitting thermal performance curves

Description

Modified deutsch model for fitting thermal performance curves

Usage

deutsch_2008(temp, rmax, topt, ctmax, a)

Arguments

Details

Equation:

\textrm{if} \quad temp < t_{opt}: rate = r_{max} \cdot exp^{-\bigg(\frac{temp-t_{opt}}{2a}\bigg)^2}

\textrm{if} \quad temp > t_{opt}: rate = r_{max} \cdot \left(1 - \bigg(\frac{temp - t_{opt}}{t_{opt} - ct_{max}}\bigg)^2\right)

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Deutsch, C. A., Tewksbury, J. J., Huey, R. B., Sheldon, K. S., Ghalambor, C. K., Haak, D. C., & Martin, P. R. Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences, 105(18), 6668-6672. (2008)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'deutsch_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~deutsch_2008(temp = temp, rmax, topt, ctmax, a),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'deutsch_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'deutsch_2008'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Flinn model for fitting thermal performance curves

Description

Flinn model for fitting thermal performance curves

Usage

flinn_1991(temp, a, b, c)

Arguments

Details

Equation:

rate= \frac{1}{1+a+b \cdot temp+c \cdot temp^2}

Start values in get_start_vals are derived from previous methods from the literature.

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Flinn PW Temperature-dependent functional response of the parasitoid Cephalonomia waterstoni (Gahan) (Hymenoptera, Bethylidae) attacking rusty grain beetle larvae (Coleoptera, Cucujidae). Environmental Entomology, 20, 872–876, (1991)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'flinn_1991')
# fit model
mod <- nls.multstart::nls_multstart(rate~flinn_1991(temp = temp, a, b, c),
data = d,
iter = c(4,4,4),
start_lower = start_vals - 1,
start_upper = start_vals + 1,
lower = get_lower_lims(d$temp, d$rate, model_name = 'flinn_1991'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'flinn_1991'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Gaussian model for fitting thermal performance curves

Description

Gaussian model for fitting thermal performance curves

Usage

gaussian_1987(temp, rmax, topt, a)

Arguments

Details

Equation:

rate = r_{max} \cdot exp^{\bigg(-0.5 \left(\frac{|temp-t_{opt}|}{a}\right)^2\bigg)}

Start values in get_start_vals are derived from the data

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Lynch, M., Gabriel, W., Environmental tolerance. The American Naturalist. 129, 283–303. (1987)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'gaussian_1987')
# fit model
mod <- nls.multstart::nls_multstart(rate~gaussian_1987(temp = temp,rmax, topt,a),
data = d,
iter = c(4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'gaussian_1987'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'gaussian_1987'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Estimate thermal performance breadth of a thermal performance curve

Description

Estimate thermal performance breadth of a thermal performance curve

Usage

get_breadth(model, level = 0.8)

Arguments

Details

Thermal performance breadth is calculated as the range of temperatures over which a curve's rate is at least 0.8 of peak. This defaults to a proportion of 0.8 but can be changed using the level argument.

Value

Numeric estimate of thermal performance breadth (in ºC)

Estimate the critical thermal maximum of a thermal performance curve

Description

Estimate the critical thermal maximum of a thermal performance curve

Usage

get_ctmax(model)

Arguments

Details

Critical thermal maximum is calculated by predicting over a temperature range 50 ºC beyond the maximum value in the dataset. The predicted rate value closest to 0 is then extracted. When this is impossible due to the curve formula (i.e the Sharpe-Schoolfield model), the temperature where the rate is 5 percent of the maximum rate is estimated. Predictions are done every 0.001 ºC so the estimate of the critical thermal maximum should be accurate up to 0.001 ºC.

Value

Numeric estimate of critical thermal maximum (ºC)

Estimate the critical thermal minimum of a thermal performance curve

Description

Estimate the critical thermal minimum of a thermal performance curve

Usage

get_ctmin(model)

Arguments

Details

Optimum temperature is calculated by predicting over a temperature range 50 degrees lower than the minimum value in the dataset. The predicted rate value closest to 0 is then extracted. When this is impossible due to the curve formula (i.e the Sharpe-Schoolfield model), the temperature where the rate is 5 percent of the maximum rate is estimated. Predictions are done every 0.001 ºC value so the estimate of the critical thermal minimum should be accurate up to 0.001 ºC.

Value

Numeric estimate of critical thermal minimum (ºC)

Estimate the activation energy of a thermal performance curve

Description

Estimate the activation energy of a thermal performance curve

Usage

get_e(model)

Arguments

Details

Fits a modified-Boltzmann equation to all raw data below the optimum temperature (ºC; as estimated by get_topt).

Value

Numeric estimate of activation energy (eV)

Estimate the deactivation energy of a thermal performance curve

Description

Estimate the deactivation energy of a thermal performance curve

Usage

get_eh(model)

Arguments

Details

Fits a modified-Boltzmann equation to all raw data beyond the optimum temperature (ºC; as estimated by get_topt).

Value

Numeric estimate of activation energy (eV)

Set broad lower limits on parameter values

Description

Sets wide lower limits on parameter values for each TPC model

Usage

get_lower_lims(x, y, model_name)

Arguments

Value

Named list of lower limits given the data and model being fitted

Author(s)

Daniel Padfield

Lists the models available in rTPC

Description

Lists the models available in rTPC

Usage

get_model_names()

Value

character vector of thermal performance curves available in rTPC

Examples

get_model_names()

Estimate the q10 value of a thermal performance curve

Description

Estimate the q10 value of a thermal performance curve

Usage

get_q10(model)

Arguments

Details

Fits the q10 portion of rezende_2019 to all raw data below the optimum temperature (ºC; as estimated by get_topt).

Value

Numeric estimate of q10 value

Estimate maximum rate of a thermal performance curve

Description

Estimate maximum rate of a thermal performance curve

Usage

get_rmax(model)

Arguments

Details

Maximum rate is calculated by predicting over the temperature range using the previously estimated parameters and picking the maximum rate value. Predictions are done every 0.001 ºC.

Value

Numeric estimate of maximum rate

Estimates skewness of a thermal performance curve

Description

Estimates skewness of a thermal performance curve

Usage

get_skewness(model)

Arguments

Details

Skewness is calculated from the values of activation energy (e) and deactivation energy (eh) as: skewness = e - eh. A negative skewness indicates the TPC is left skewed, the drop after the optimum is steeper than the rise up to the optimum. A positive skewness means that the TPC is right skewed and a value of 0 would mean the curve is symmetrical around the optimum.

Value

Numeric estimate of skewness

Estimate start values for TPC fitting

Description

Estimates sensible start values for fitting thermal performance curves

Usage

get_start_vals(x, y, model_name)

Arguments

Value

Named list of start parameters given the data and model being fitted

Author(s)

Daniel Padfield

Estimate thermal safety margin of a thermal performance curve

Description

Estimate thermal safety margin of a thermal performance curve

Usage

get_thermalsafetymargin(model)

Arguments

Details

Thermal safety margin is calculated as: CTmax - Topt. This is calculated using the functions get_ctmax and get_topt.

Value

Numeric estimate of thermal safety margin (in ºC)

Estimate thermal tolerance of a thermal performance curve

Description

Estimate thermal tolerance of a thermal performance curve

Usage

get_thermaltolerance(model)

Arguments

Details

Thermal tolerance is calculated as: CTmax - CTmin. This is calculated using the functions get_ctmax and get_ctmin.

Value

Thermal tolerance (in ºC)

Estimate optimum temperature of a thermal performance curve

Description

Estimate optimum temperature of a thermal performance curve

Usage

get_topt(model)

Arguments

Details

Optimum temperature (ºC) is calculated by predicting over the temperature range using the previously estimated parameters and keeping the temperature where the largest rate value occurs. Predictions are done every 0.001 ºC so the estimate of optimum temperature should be accurate up to 0.001 ºC.

Value

Numeric estimate of optimum temperature (in ºC)

Set broad upper limits on parameter values

Description

Sets wide upper limits on parameter values for each TPC model

Usage

get_upper_lims(x, y, model_name)

Arguments

Value

Named list of upper limits given the data and model being fitted

Author(s)

Daniel Padfield

Hinshelwood model for fitting thermal performance curves

Description

Hinshelwood model for fitting thermal performance curves

Usage

hinshelwood_1947(temp, a, e, b, eh)

Arguments

Details

Equation:

rate=a \cdot exp^{\frac{-e}{k \cdot (temp + 273.15)}} - b \cdot exp^\frac{-e_h}{k \cdot (temp + 273.15)}

where k is Boltzmann's constant with a value of 8.62e-05

Start values in get_start_vals are taken from the literature.

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model difficult to fit.

References

Hinshelwood C.N. The Chemical Kinetics of the Bacterial Cell. Oxford University Press. (1947)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'hinshelwood_1947')
# fit model
mod <- nls.multstart::nls_multstart(rate~hinshelwood_1947(temp = temp,a, e, b, eh),
data = d,
iter = c(5,5,5,5),
start_lower = start_vals - 1,
start_upper = start_vals + 1,
lower = get_lower_lims(d$temp, d$rate, model_name = 'hinshelwood_1947'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'hinshelwood_1947'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Jöhnk model for fitting thermal performance curves

Description

Jöhnk model for fitting thermal performance curves

Usage

joehnk_2008(temp, rmax, topt, a, b, c)

Arguments

Details

Equation:

rate=r_{max} \bigg(1 + a \bigg(\bigg(b^{temp-t_{opt}} -1\bigg) - \frac{ln(b)}{ln(c)}(c^{temp-t_{opt}} -1)\bigg)\bigg)

Start values in get_start_vals are derived from the data or sensible values from the literature.

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Joehnk, Klaus D., et al. Summer heatwaves promote blooms of harmful cyanobacteria. Global change biology 14.3: 495-512 (2008)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'joehnk_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~joehnk_2008(temp = temp, rmax, topt, a, b, c),
data = d,
iter = c(3,3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'joehnk_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'joehnk_2008'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Johnson-Lewin model for fitting thermal performance curves

Description

Johnson-Lewin model for fitting thermal performance curves

Usage

johnsonlewin_1946(temp, r0, e, eh, topt)

Arguments

Details

Equation:

rate= \frac{r_0 \cdot exp^{\frac{-e}{k\cdot (temp + 273.15)}}}{1 + exp^{-\frac{e_h -\big(\frac{e_h}{(t_{opt} + 273.15)} + k \cdot ln\big(\frac{e}{e_h - e}\big) \big) \cdot (temp + 273.15)}{k \cdot (temp + 273.15)}}}

where k is Boltzmann's constant with a value of 8.62e-05.

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model difficult to fit.

References

Johnson, Frank H., and Isaac Lewin. The growth rate of E. coli in relation to temperature, quinine and coenzyme. Journal of Cellular and Comparative Physiology 28.1 (1946): 47-75.

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'johnsonlewin_1946')
# fit model
mod <- suppressWarnings(
nls.multstart::nls_multstart(rate~johnsonlewin_1946(temp = temp, r0, e, eh, topt),
data = d,
iter = c(5,5,5,5),
start_lower = start_vals - 1,
start_upper = start_vals + 1,
lower = get_lower_lims(d$temp, d$rate, model_name = 'johnsonlewin_1946'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'johnsonlewin_1946'),
supp_errors = 'Y',
convergence_count = FALSE)
)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Kamykowski model for fitting thermal performance curves

Description

Kamykowski model for fitting thermal performance curves

Usage

kamykowski_1985(temp, tmin, tmax, a, b, c)

Arguments

Details

Equation:

rate= a \cdot \big( 1 - exp^{-b\cdot \big(temp-t_{min}\big)}\big) \cdot \big( 1-exp^{-c \cdot \big(t_{max}-temp\big)}\big)

Start values in get_start_vals are derived from the data or sensible values from the literature.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Kamykowski, Daniel. A survey of protozoan laboratory temperature studies applied to marine dinoflagellate behaviour from a field perspective. Contributions in Marine Science. (1985).

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'kamykowski_1985')
# fit model
mod <- nls.multstart::nls_multstart(rate~kamykowski_1985(temp = temp, tmin, tmax, a, b, c),
data = d,
iter = c(3,3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'kamykowski_1985'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'kamykowski_1985'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Lactin2 model for fitting thermal performance curves

Description

Lactin2 model for fitting thermal performance curves

Usage

lactin2_1995(temp, a, b, tmax, delta_t)

Arguments

Details

Equation:

rate= = exp^{a \cdot temp} - exp^{a \cdot t_{max} - \bigg(\frac{t_{max} - temp}{\delta _{t}}\bigg)} + b

Start values in get_start_vals are derived from the data or sensible values from the literature.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Lactin, D.J., Holliday, N.J., Johnson, D.L. & Craigen, R. Improved rate models of temperature-dependent development by arthropods. Environmental Entomology 24, 69-75 (1995)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'lactin2_1995')
# fit model
mod <- nls.multstart::nls_multstart(rate~lactin2_1995(temp = temp, a, b, tmax, delta_t),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'lactin2_1995'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'lactin2_1995'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Lobry-Rosso-Flandros (LRF) model for fitting thermal performance curves

Description

Lobry-Rosso-Flandros (LRF) model for fitting thermal performance curves

Usage

lrf_1991(temp, rmax, topt, tmin, tmax)

Arguments

Details

Equation:

rate= rmax \cdot \frac{(temp - t_{max}) \cdot (temp - t_{min})^2}{(t_{opt} - t_{min}) \cdot ((t_{opt} - t_{min}) \cdot (temp - t_{opt}) - (t_{opt} - t_{max}) \cdot (t_{opt} + t_{min} - 2 \cdot temp))}

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

Author(s)

Daniel Padfield

References

Rosso, L., Lobry, J. R., & Flandrois, J. P. An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. Journal of Theoretical Biology, 162(4), 447-463. (1993)

Examples

# load in ggplot
library(ggplot2)
library(nls.multstart)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'sharpeschoolhigh_1981')
# fit model
mod <- nls_multstart(rate~lrf_1991(temp = temp, rmax, topt, tmin, tmax),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'lrf_1991'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'lrf_1991'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Modified gaussian model for fitting thermal performance curves

Description

Modified gaussian model for fitting thermal performance curves

Usage

modifiedgaussian_2006(temp, rmax, topt, a, b)

Arguments

Details

Equation:

rate = r_{max} \cdot exp^{\bigg[-0.5 \left(\frac{|temp-t_{opt}|}{a}\right)^b\bigg]}

Start values in get_start_vals are derived from the data and gaussian_1987

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model difficult to fit.

References

Angilletta Jr, M. J. (2006). Estimating and comparing thermal performance curves. Journal of Thermal Biology, 31(7), 541-545.

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'modifiedgaussian_2006')
# fit model
mod <- nls.multstart::nls_multstart(rate~modifiedgaussian_2006(temp = temp, rmax, topt, a, b),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'modifiedgaussian_2006'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'modifiedgaussian_2006'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

O'Neill model for fitting thermal performance curves

Description

O'Neill model for fitting thermal performance curves

Usage

oneill_1972(temp, rmax, ctmax, topt, q10)

Arguments

Details

Equation:

rate = r_{max} \cdot \bigg(\frac{ct_{max} - temp}{ct_{max} - t_{opt}}\bigg)^{x} \cdot exp^{x \cdot \frac{temp - t_{opt}}{ct_{max} - t_{opt}}}

where: x = \frac{w^{2}}{400}\cdot\bigg(1 + \sqrt{1 + \frac{40}{w}}\bigg)^{2}

and:\ w = (q_{10} - 1)\cdot (ct_{max} - t_{opt})

Start values in get_start_vals are derived from the data and previous values in the literature

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

O’Neill, R.V., Goldstein, R.A., Shugart, H.H., Mankin, J.B. Terrestrial Ecosystem Energy Model. Eastern Deciduous Forest Biome Memo Report Oak Ridge. The Environmental Sciences Division of the Oak Ridge National Laboratory. (1972)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'oneill_1972')
# fit model
mod <- nls.multstart::nls_multstart(rate~oneill_1972(temp = temp, rmax, ctmax, topt, q10),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'oneill_1972'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'oneill_1972'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Pawar model for fitting thermal performance curves

Description

Pawar model for fitting thermal performance curves

Usage

pawar_2018(temp, r_tref, e, eh, topt, tref)

Arguments

Details

This model is a modified version of sharpeschoolhigh_1981 that explicitly models the optimum temperature. Equation:

rate= \frac{r_{tref} \cdot exp^{\frac{-e}{k} (\frac{1}{temp + 273.15}-\frac{1}{t_{ref} + 273.15})}}{1 + (\frac{e}{eh - e}) \cdot exp^{\frac{e_h}{k}(\frac{1}{t_opt + 273.15}-\frac{1}{temp + 273.15})}}

where k is Boltzmann's constant with a value of 8.62e-05.

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

Author(s)

Daniel Padfield

References

Kontopoulos, Dimitrios - Georgios, Bernardo García-Carreras, Sofía Sal, Thomas P. Smith, and Samraat Pawar. Use and Misuse of Temperature Normalisation in Meta-Analyses of Thermal Responses of Biological Traits. PeerJ. 6 (2018),

Examples

# load in ggplot
library(ggplot2)
library(nls.multstart)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'pawar_2018')
# fit model
mod <- nls_multstart(rate~pawar_2018(temp = temp, r_tref, e, eh, topt, tref = 20),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'pawar_2018'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'pawar_2018'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Quadratic model for fitting thermal performance curves

Description

Quadratic model for fitting thermal performance curves

Usage

quadratic_2008(temp, a, b, c)

Arguments

Details

Equation:

rate = a + b \cdot temp + c \cdot temp^2

Start values in get_start_vals are derived from the data using previous methods in the literature

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Montagnes, David JS, et al. Short‐term temperature change may impact freshwater carbon flux: a microbial perspective. Global Change Biology 14.12: 2823-2838. (2008)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'quadratic_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~quadratic_2008(temp = temp, a, b, c),
data = d,
iter = c(4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'quadratic_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'quadratic_2008'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Ratkowsky model for fitting thermal performance curves

Description

Ratkowsky model for fitting thermal performance curves

Usage

ratkowsky_1983(temp, tmin, tmax, a, b)

Arguments

Details

Equation:

rate = (a \cdot (temp-t_{min}))^2 \cdot (1-exp(b \cdot (temp-t_{max})))^2

Start values in get_start_vals are derived from the data and previous values in the literature.

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Ratkowsky, D.A., Lowry, R.K., McMeekin, T.A., Stokes, A.N., Chandler, R.E., Model for bacterial growth rate throughout the entire biokinetic temperature range. J. Bacteriol. 154: 1222–1226 (1983)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'ratkowsky_1983')
# fit model
mod <- nls.multstart::nls_multstart(rate~ratkowsky_1983(temp = temp, tmin, tmax, a, b),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'ratkowsky_1983'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'ratkowsky_1983'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Rezende model for fitting thermal performance curves

Description

Rezende model for fitting thermal performance curves

Usage

rezende_2019(temp, q10, a, b, c)

Arguments

Details

Equation:

\textrm{if} \quad temp < b: rate = a \cdot 10 ^{\frac{\log_{10} (q_{10})}{(\frac{10}{temp})}}

\textrm{if} \quad temp > b: rate = a \cdot 10 ^{\frac{\log_{10} (q_{10})}{(\frac{10}{temp})}} \cdot \bigg(1-c \cdot (b-temp)^2 \bigg)

Start values in get_start_vals are derived from the data and previous values in the literature.

Limits in get_lower_lims and get_upper_lims are based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Rezende, Enrico L., and Francisco Bozinovic. Thermal performance across levels of biological organization. Philosophical Transactions of the Royal Society B 374.1778 (2019): 20180549.

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'rezende_2019')
# fit model
mod <- nls.multstart::nls_multstart(rate~rezende_2019(temp = temp, q10, a, b, c),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'rezende_2019'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'rezende_2019'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Full Sharpe-Schoolfield model for fitting thermal performance curves

Description

Full Sharpe-Schoolfield model for fitting thermal performance curves

Usage

sharpeschoolfull_1981(temp, r_tref, e, el, tl, eh, th, tref)

Arguments

Details

Equation:

rate= \frac{r_{tref} \cdot exp^{\frac{-e}{k} (\frac{1}{temp + 273.15}-\frac{1}{t_{ref} + 273.15})}}{1+ exp^{\frac{e_l}{k}(\frac{1}{t_l} - \frac{1}{temp + 273.15})} + exp^{\frac{e_h}{k}(\frac{1}{t_h}-\frac{1}{temp + 273.15})}}

where k is Boltzmann's constant with a value of 8.62e-05.

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

Author(s)

Daniel Padfield

References

Schoolfield, R. M., Sharpe, P. J. & Magnuson, C. E. Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. Journal of Theoretical Biology 88, 719-731 (1981)

Examples

# load in ggplot
library(ggplot2)
library(nls.multstart)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'sharpeschoolfull_1981')
# fit model
mod <- nls_multstart(rate~sharpeschoolfull_1981(temp = temp, r_tref, e, el, tl, eh, th, tref = 20),
data = d,
iter = c(3,3,3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'sharpeschoolfull_1981'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'sharpeschoolfull_1981'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Sharpe-Schoolfield model (high temperature inactivation only) for fitting thermal performance curves

Description

Sharpe-Schoolfield model (high temperature inactivation only) for fitting thermal performance curves

Usage

sharpeschoolhigh_1981(temp, r_tref, e, eh, th, tref)

Arguments

Details

Equation:

rate= \frac{r_{tref} \cdot exp^{\frac{-e}{k} (\frac{1}{temp + 273.15}-\frac{1}{t_{ref} + 273.15})}}{1 + exp^{\frac{e_h}{k}(\frac{1}{t_h}-\frac{1}{temp + 273.15})}}

where k is Boltzmann's constant with a value of 8.62e-05.

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

Author(s)

Daniel Padfield

References

Schoolfield, R. M., Sharpe, P. J. & Magnuson, C. E. Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. J. Theor. Biol. 88, 719-731 (1981)

Examples

# load in ggplot
library(ggplot2)
library(nls.multstart)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'sharpeschoolhigh_1981')
# fit model
mod <- nls_multstart(rate~sharpeschoolhigh_1981(temp = temp, r_tref, e, eh, th, tref = 20),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'sharpeschoolhigh_1981'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'sharpeschoolhigh_1981'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Sharpe-Schoolfield model (low temperature inactivation only) for fitting thermal performance curves

Description

Sharpe-Schoolfield model (low temperature inactivation only) for fitting thermal performance curves

Usage

sharpeschoollow_1981(temp, r_tref, e, el, tl, tref)

Arguments

Details

Equation:

rate= \frac{r_{tref} \cdot exp^{\frac{-e}{k} (\frac{1}{temp + 273.15}-\frac{1}{t_{ref} + 273.15})}}{1 + exp^{\frac{e_l}{k}(\frac{1}{t_l} - \frac{1}{temp + 273.15})}}

where k is Boltzmann's constant with a value of 8.62e-05.

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

Author(s)

Daniel Padfield

References

Schoolfield, R. M., Sharpe, P. J. & Magnuson, C. E. Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. J. Theor. Biol. 88, 719-731 (1981)

Examples

# load in ggplot
library(ggplot2)
library(nls.multstart)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'sharpeschoollow_1981')
# fit model
mod <- nls_multstart(rate~sharpeschoollow_1981(temp = temp, r_tref, e, el, tl, tref = 20),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'sharpeschoollow_1981'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'sharpeschoollow_1981'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Spain model for fitting thermal performance curves

Description

Spain model for fitting thermal performance curves

Usage

spain_1982(temp, a, b, c, r0)

Arguments

Details

Equation:

rate = r_0 \cdot exp^{a \cdot temp} \cdot (1-b \cdot exp^{c \cdot temp})

Start values in get_start_vals are derived from the data or plucked from thin air.

Limits in get_lower_lims and get_upper_lims are derived from the data or plucked from thin air.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

BASIC Microcomputer Models in Biology. Addison-Wesley, Reading, MA. 1982

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'spain_1982')
# fit model
mod <- nls.multstart::nls_multstart(rate~spain_1982(temp = temp, a, b, c, r0),
data = d,
iter = c(3,3,3,3),
start_lower = start_vals - 1,
start_upper = start_vals + 1,
lower = get_lower_lims(d$temp, d$rate, model_name = 'spain_1982'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'spain_1982'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Thomas model (2012) for fitting thermal performance curves

Description

Thomas model (2012) for fitting thermal performance curves

Usage

thomas_2012(temp, a, b, c, topt)

Arguments

Details

Equation:

rate = a \cdot exp^{b \cdot temp} \bigg(1-\bigg(\frac{temp - t_{opt}}{c}\bigg)^2\bigg)

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Thomas, Mridul K., et al. A global pattern of thermal adaptation in marine phytoplankton. Science 338.6110, 1085-1088 (2012)

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'thomas_2012')
# fit model
mod <- nls.multstart::nls_multstart(rate~thomas_2012(temp = temp, a, b, c, topt),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 1,
start_upper = start_vals + 2,
lower = get_lower_lims(d$temp, d$rate, model_name = 'thomas_2012'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'thomas_2012'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Thomas model (2017) for fitting thermal performance curves

Description

Thomas model (2017) for fitting thermal performance curves

Usage

thomas_2017(temp, a, b, c, d, e)

Arguments

Details

Equation:

rate = a \cdot exp^{b \cdot temp} - (c + d \cdot exp^{e \cdot temp})

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based on extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Thomas, Mridul K., et al. Temperature–nutrient interactions exacerbate sensitivity to warming in phytoplankton. Global change biology 23.8 (2017): 3269-3280.

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'thomas_2017')
# fit model
mod <- nls.multstart::nls_multstart(rate~thomas_2017(temp = temp, a, b, c, d, e),
data = d,
iter = c(3,3,3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'thomas_2017'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'thomas_2017'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()

Weibull model for fitting thermal performance curves

Description

Weibull model for fitting thermal performance curves

Usage

weibull_1995(temp, a, topt, b, c)

Arguments

Details

Equation:

rate = a \cdot \bigg( \frac{c-1}{c}\bigg)^{\frac{1-c}{c}}\bigg(\frac{temp-t_{opt}}{b}+\bigg(\frac{c-1}{c}\bigg)^{\frac{1}{c}}\bigg)^{c-1}exp^{-\big(\frac{temp-t_{opt}}{b}+\big( \frac{c-1}{c}\big)^{\frac{1}{c}}\big)^c} + \frac{c-1}{c}

Start values in get_start_vals are derived from the data.

Limits in get_lower_lims and get_upper_lims are derived from the data or based extreme values that are unlikely to occur in ecological settings.

Value

a numeric vector of rate values based on the temperatures and parameter values provided to the function

Note

Generally we found this model easy to fit.

References

Angilletta Jr, Michael J. Estimating and comparing thermal performance curves. Journal of Thermal Biology 31.7 (2006): 541-545.

Examples

# load in ggplot
library(ggplot2)

# subset for the first TPC curve
data('chlorella_tpc')
d <- subset(chlorella_tpc, curve_id == 1)

# get start values and fit model
start_vals <- get_start_vals(d$temp, d$rate, model_name = 'weibull_1995')
# fit model
mod <- nls.multstart::nls_multstart(rate~weibull_1995(temp = temp, a, topt, b, c),
data = d,
iter = c(4,4,4,4),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'weibull_1995'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'weibull_1995'),
supp_errors = 'Y',
convergence_count = FALSE)

# look at model fit
summary(mod)

# get predictions
preds <- data.frame(temp = seq(min(d$temp), max(d$temp), length.out = 100))
preds <- broom::augment(mod, newdata = preds)

# plot
ggplot(preds) +
geom_point(aes(temp, rate), d) +
geom_line(aes(temp, .fitted), col = 'blue') +
theme_bw()