Analytis-Kontodimas model for fitting thermal performance curves

Description

Analytis-Kontodimas model for fitting thermal performance curves

Usage

analytiskontodimas_2004(temp, a, tmin, tmax)

Arguments

Details

Equation:

rate = a \cdot \left(T - T_{\text{min}}\right)^2 \cdot \left(T_{\text{max}} - T\right)

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.

Author(s)

Francis Windram

References

Kontodimas, D. C., Eliopoulos, P. A., Stathas, G. J. & Economou, L. P. 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. Environ. Entomol. 33, 1–11 (2004).

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 = 'analytiskontodimas_2004')
# fit model
mod <- nls.multstart::nls_multstart(rate~analytiskontodimas_2004(temp = temp, a, tmin, tmax),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'analytiskontodimas_2004'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'analytiskontodimas_2004'),
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()

Ashrafi I model for fitting thermal performance curves

Description

Ashrafi I model for fitting thermal performance curves

Usage

ashrafi1_2018(temp, a, b, c)

Arguments

Details

Equation:

rate=a + b \cdot temp^{2} + log(temp) + c \cdot temp^{3}

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.

Author(s)

Daniel Padfield

References

Ashrafi, R. et al. Broad thermal tolerance is negatively correlated with virulence in an opportunistic bacterial pathogen. Evolutionary Applications 11, 1700–1714 (2018).

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 = 'ashrafi1_2018')
# fit model
mod <- nls.multstart::nls_multstart(rate~ashrafi1_2018(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 = 'ashrafi1_2018'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'ashrafi2_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()

Ashrafi II model for fitting thermal performance curves

Description

Ashrafi II model for fitting thermal performance curves

Usage

ashrafi2_2018(temp, a, b, c)

Arguments

Details

Equation:

rate=a + b \cdot temp^{\frac{3}{2}} + c \cdot temp^{2}

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.

Author(s)

Francis Windram

References

Ashrafi, R. et al. Broad thermal tolerance is negatively correlated with virulence in an opportunistic bacterial pathogen. Evolutionary Applications 11, 1700–1714 (2018).

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 = 'ashrafi2_2018')
# fit model
mod <- nls.multstart::nls_multstart(rate~ashrafi2_2018(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 = 'ashrafi2_2018'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'ashrafi2_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()

Ashrafi III model for fitting thermal performance curves

Description

Ashrafi III model for fitting thermal performance curves

Usage

ashrafi3_2018(temp, a, b, c)

Arguments

Details

Equation:

rate = \frac{1}{(a + b \cdot exp^{temp} + d \cdot exp^{-temp})}

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.

Author(s)

Daniel Padfield

References

Ashrafi, R. et al. Broad thermal tolerance is negatively correlated with virulence in an opportunistic bacterial pathogen. Evolutionary Applications 11, 1700–1714 (2018).

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 = 'ashrafi3_2018')
# fit model
mod <- nls.multstart::nls_multstart(rate~ashrafi3_2018(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 = 'ashrafi3_2018'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'ashrafi3_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()

Ashrafi IV model for fitting thermal performance curves

Description

Ashrafi IV model for fitting thermal performance curves

Usage

ashrafi4_2018(temp, a, b, c, d)

Arguments

Details

Equation:

rate = a + b \cdot (temp + 273.15) + c \cdot log((temp + 273.15)^2) + \cdot \sqrt{temp + 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.

Author(s)

Daniel Padfield

References

Ashrafi, R. et al. Broad thermal tolerance is negatively correlated with virulence in an opportunistic bacterial pathogen. Evolutionary Applications 11, 1700–1714 (2018).

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 = 'ashrafi4_2018')
# fit model
mod <- nls.multstart::nls_multstart(rate~ashrafi4_2018(temp = temp, a, b, c, d),
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 = 'ashrafi4_2018'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'ashrafi4_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()

Ashrafi V model for fitting thermal performance curves

Description

Ashrafi V model for fitting thermal performance curves

Usage

ashrafi5_2018(temp, a, b, c, d)

Arguments

Details

Equation:

rate = a + b \cdot log(temp + 273.15)^2 + c \cdot log(temp + 273.15) + \frac{d \cdot log(temp + 273.15)}{temp + 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.

Author(s)

Daniel Padfield

References

Ashrafi, R. et al. Broad thermal tolerance is negatively correlated with virulence in an opportunistic bacterial pathogen. Evolutionary Applications 11, 1700–1714 (2018).

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 = 'ashrafi5_2018')
# fit model
mod <- nls.multstart::nls_multstart(rate~ashrafi5_2018(temp = temp, a, b, c, d),
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 = 'ashrafi5_2018'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'ashrafi5_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()

Atkin model for fitting thermal performance curves

Description

Atkin model for fitting thermal performance curves

Usage

atkin_2005(temp, r0, a, b)

Arguments

Details

Equation:

rate = B_0 \cdot (a - b \cdot T)^{\frac{T}{10}}

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.

Author(s)

Francis Windram

References

Atkin, OK, Bruhn D, Tjoelker MG. Response of Plant Respiration to Changes in Temperature: Mechanisms and Consequences of Variations in Q10 Values and Acclimation. In Plant Respiration. 2005.

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 = 'atkin_2005')
# fit model
mod <- nls.multstart::nls_multstart(rate~atkin_2005(temp = temp, r0, a, b),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'atkin_2005'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'atkin_2005'),
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()

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()

Simplified Beta-type model for fitting thermal performance curves

Description

Simplified Beta-type model for fitting thermal performance curves

Usage

betatypesimplified_2008(temp, rho, alpha, beta)

Arguments

Details

Equation:

rate = \rho \cdot \left(a - \frac{T}{10}\right) \cdot \left(\frac{T}{10}\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.

Author(s)

Francis Windram

References

Damos, P. & Savopoulou-Soultani, M. Temperature-dependent bionomics and modeling of Anarsia lineatella (Lepidoptera: Gelechiidae) in the laboratory. J. Econ. Entomol. 101, 1557–1567 (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 = 'betatypesimplified_2008')
# fit model
mod <- nls.multstart::nls_multstart(rate~betatypesimplified_2008(temp = temp, rho, alpha, beta),
data = d,
iter = c(7,7,7),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'betatypesimplified_2008'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'betatypesimplified_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()

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()

Brière I model for fitting thermal performance curves

Description

Brière I model for fitting thermal performance curves

Usage

briere1_1999(temp, tmin, tmax, a)

Arguments

Details

Equation:

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

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.

Author(s)

Francis Windram

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 = 'briere1_1999')
# fit model
mod <- nls.multstart::nls_multstart(rate~briere1_1999(temp = temp, tmin, tmax, a),
data = d,
iter = c(3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'briere1_1999'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'briere1_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()

Simplified Brière I model for fitting thermal performance curves

Description

Simplified Brière I model for fitting thermal performance curves

Usage

briere1simplified_1999(temp, tmin, tmax, a)

Arguments

Details

Equation:

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

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.

Author(s)

Francis Windram

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 = 'briere1simplified_1999')
# fit model
mod <- nls.multstart::nls_multstart(rate~briere1simplified_1999(temp = temp, tmin, tmax, a),
data = d,
iter = c(3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'briere1simplified_1999'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'briere1simplified_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()

Brière II model for fitting thermal performance curves

Description

Brière II 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()

Simplified Brière II model for fitting thermal performance curves

Description

Simplified Brière II model for fitting thermal performance curves

Usage

briere2simplified_1999(temp, tmin, tmax, a, b)

Arguments

Details

Equation:

rate=a \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 = 'briere2simplified_1999')
# fit model
mod <- nls.multstart::nls_multstart(rate~briere2simplified_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 = 'briere2simplified_1999'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'briere2simplified_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()

Extended Brière model for fitting thermal performance curves

Description

Extended Brière model for fitting thermal performance curves

Usage

briereextended_2021(temp, tmin, tmax, a, b, d)

Arguments

Details

Equation:

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

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

Cruz-Loya, M. et al. Antibiotics shift the temperature response curve of Escherichia coli growth. mSystems 6, e00228–21 (2021).

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 = 'briereextended_2021')
# fit model
mod <- nls.multstart::nls_multstart(rate~briereextended_2021(temp = temp, tmin, tmax, a, b, d),
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 = 'briereextended_2021'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'briereextended_2021'),
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()

Simplified Extended Brière model for fitting thermal performance curves

Description

Simplified Extended Brière model for fitting thermal performance curves

Usage

briereextendedsimplified_2021(temp, tmin, tmax, a, b, d)

Arguments

Details

Equation:

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

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

Cruz-Loya, M. et al. Antibiotics shift the temperature response curve of Escherichia coli growth. mSystems 6, e00228–21 (2021).

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 = 'briereextendedsimplified_2021')
# fit model
mod <- nls.multstart::nls_multstart(
  rate~briereextendedsimplified_2021(temp = temp, tmin, tmax, a, b, d),
  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 = 'briereextendedsimplified_2021'),
  upper = get_upper_lims(d$temp, d$rate, model_name = 'briereextendedsimplified_2021'),
  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()

Eubank model for fitting thermal performance curves

Description

Eubank model for fitting thermal performance curves

Usage

eubank_1973(temp, topt, a, b)

Arguments

Details

Equation:

rate = \frac{a}{(T-T_{\text{opt}})^2+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 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.

Author(s)

Francis Windram

References

Eubank, W. P., Atmar, J. W. & Ellington, J. J. The significance and thermodynamics of fluctuating versus static thermal environments on Heliothis zea egg development rates. Environ. Entomol. 2, 491–496 (1973).

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 = 'eubank_1973')
# fit model
mod <- nls.multstart::nls_multstart(rate~eubank_1973(temp = temp, topt, a, b),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'eubank_1973'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'eubank_1973'),
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()

flexTPC model for fitting thermal performance curves

Description

flexTPC model for fitting thermal performance curves

Usage

flextpc_2024(temp, tmin, tmax, rmax, alpha, beta)

Arguments

Details

Equation:

rate=r_{\text{max}}\left[\left(\frac{T - T_{\text{min}}}{\alpha}\right)^\alpha\left(\frac{T_{\text{max}}-T}{1-\alpha}\right)^{1-\alpha}\left(\frac{1}{T_{\text{max}}-T_{\text{min}}}\right)\right]^{\frac{\alpha(1-\alpha)}{\beta^2}}

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 this model requires larger iter values in nls_multstart to fit reliably.

Author(s)

Francis Windram

References

Cruz-Loya M, Mordecai EA, Savage VM. A flexible model for thermal performance curves. bioRxiv [Preprint]. 2024

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 = 'flextpc_2024')
# fit model
mod <- nls.multstart::nls_multstart(rate~flextpc_2024(temp = temp, tmin, tmax, rmax, alpha, beta),
data = d,
iter = c(5,5,5,5,5),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'flextpc_2024'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'flextpc_2024'),
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()

Modified gaussian model for fitting thermal performance curves

Description

Modified gaussian model for fitting thermal performance curves

Usage

gaussianmodified_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.

This function was previously called modifiedgaussian_2006() however this is now deprecated and will be removed in the future.

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 = 'gaussianmodified_2006')
# fit model
mod <- nls.multstart::nls_multstart(rate~gaussianmodified_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 = 'gaussianmodified_2006'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'gaussianmodified_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()

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

Francis Windram

Lists or searches the models available in rTPC

Description

Lists or searches the models available in rTPC

Usage

get_model_names(model, returnall = FALSE)

Arguments

Value

character vector of thermal performance curves available in rTPC

Author(s)

Daniel Padfield

Francis Windram

Examples

get_model_names()
get_model_names("briere")

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

Francis Windram

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)

Get a formula object for calling a TPC

Description

Get a formula object for calling a TPC

Usage

get_tpc_as_formula(model_name, temp, trait, explicit = FALSE)

Arguments

Value

A formula calling the expected TPC

Author(s)

Francis Windram

Examples

get_tpc_as_formula("briere1_1999", "temperature", "rate")
# > rate ~ briere1_1999(temp = temperature, tmin, tmax, a)

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

Francis Windram

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()

Janisch I model for fitting thermal performance curves

Description

Janisch I model for fitting thermal performance curves

Usage

janisch1_1925(temp, m, a, topt)

Arguments

Details

Equation:

rate = \frac{1}{\frac{m}{2} \cdot \left[a^{T-T_{\text{opt}}}+a^{-(T-T_{\text{opt}})}\right]}

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.

Author(s)

Francis Windram

References

Janisch, E. Über die Temperaturabhängigkeit biologischer Vorgänge und ihre kurvenmäßige Analyse. Pflüger's Arch. Physiol. 209, 414–436 (1925).

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 = 'janisch1_1925')
# fit model
mod <- nls.multstart::nls_multstart(rate~janisch1_1925(temp = temp, m, a, topt),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'janisch1_1925'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'janisch1_1925'),
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()

Janisch II model for fitting thermal performance curves

Description

Janisch II model for fitting thermal performance curves

Usage

janisch2_1925(temp, m, a, b, topt)

Arguments

Details

Equation:

rate = \frac{1}{\frac{m}{2} \cdot \left[a^{T-T_{\text{opt}}}+b^{-(T-T_{\text{opt}})}\right]}

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.

Author(s)

Francis Windram

References

Janisch, E. Über die Temperaturabhängigkeit biologischer Vorgänge und ihre kurvenmäßige Analyse. Pflüger's Arch. Physiol. 209, 414–436 (1925).

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 = 'janisch2_1925')
# fit model
mod <- nls.multstart::nls_multstart(rate~janisch2_1925(temp = temp, m, a, b, topt),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'janisch2_1925'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'janisch2_1925'),
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 model for fitting thermal performance curves

Description

Lobry model for fitting thermal performance curves

Usage

lobry_1991(temp, rmax, topt, tmin, tmax)

Arguments

Details

Equation:

rate = rmax \cdot (1 - \frac{(temp - topt)^2)}{(temp - topt)^2 + temp \cdot (tmax + tmin - temp) - tmax \cdot tmin}

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.

Author(s)

Daniel Padfield

References

Lobry, J. R., Rosso, L., & Flandrois, J. P. (1991). A FORTRAN subroutine for the determination of parameter confidence limits in non-linear models. Binary, 3(86-93), 25.

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 = 'lobry_1991')
# fit model
mod <- nls.multstart::nls_multstart(rate~lobry_1991(temp = temp, rmax, topt, tmin, tmax),
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 = 'lobry_1991'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'lobry_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()

Mitchell Angilletta model for fitting thermal performance curves

Description

Mitchell Angilletta model for fitting thermal performance curves

Usage

mitchell_2009(temp, topt, a, b)

Arguments

Details

Equation:

rate=\frac{1}{2 \cdot b} \cdot (1 + cos(\frac{temp - t_{opt}}{b} \cdot \pi)) \cdot a

When temperatures fall below topt - b or above topt + b, rates are set to 0 to prevent multimodality.

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.

Author(s)

Daniel Padfield

References

Mitchell, W. A., & Angilletta Jr, M. J. (2009). Thermal games: frequency-dependent models of thermal adaptation. Functional Ecology, 510-520.

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 = 'mitchell_2009')
# fit model
mod <- nls.multstart::nls_multstart(rate~mitchell_2009(temp = temp, topt, a, b),
data = d,
iter = c(3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'mitchell_2009'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'mitchell_2009'),
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()

Perform a quick, automated, TPC fit

Description

Performs a simple TPC fit using nls_multstart. This function tries to use a sensible default configuration, however if you want to use the more custom elements of nls_multstart then you will need to construct your own.

Usage

quickfit_tpc(data, model_name, temp, trait, start_adjusts = 0, iter, ...)

Arguments

Value

The nls model object of the fit model

Author(s)

Francis Windram

Examples

## Not run: 
data("chlorella_tpc")

d <- subset(chlorella_tpc, curve_id == 1)

quickfit_tpc(
  d,
  "briere1_1999",
  "temp",
  "rate",
  start_adjusts = 10,
  iter = 150
)

quickfit_tpc(
  d,
  "briere1_1999",
  "temp",
  "rate",
  start_adjusts = 0.8,
  iter = c(5,5,5)
)

## End(Not run)

Perform an automated quick tpc fit across models and curves

Description

Performs a TPC fit using nls_multstart and map. This function tries to use a sensible default configuration, however if you need to to use the more custom elements of nls_multstart then you will need to construct your own.

Usage

quickfit_tpc_multi(
  data,
  model_names,
  temp,
  trait,
  start_adjusts = 0,
  iter,
  ...
)

Arguments

Value

A tibble of model fits

Note

The parameters temp, trait, start_adjusts, iter, lhstype, gridstart, or force can be specified per-model by providing a vector of values of a length equal to the number of models to be fit.

Author(s)

Francis Windram

Daniel Padfield

Examples

## Not run: 
# load example data
data("chlorella_tpc")

# subset for just the first 5 curves
d <- subset(chlorella_tpc, curve_id <= 5)


quickfit_tpc_multi(d, c("briere1_1999", "briere2_1999"), "temp", "rate")

quickfit_tpc_multi(d, c("briere1_1999", "briere2_1999"), "temp", "rate", start_adjusts = 10)

quickfit_tpc_multi(d, c("briere1_1999", "briere2_1999"), "temp", "rate", iter = c(100, 150))

## End(Not run)

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()

Rosso model for fitting thermal performance curves

Description

Rosso model for fitting thermal performance curves

Usage

rosso_1993(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 = 'rosso_1993')
# 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 = 'rosso_1993'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'rosso_1993'),
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()

Stinner model for fitting thermal performance curves

Description

Stinner model for fitting thermal performance curves

Usage

stinner_1974(temp, rmax, topt, a, b)

Arguments

Details

Equation:

\textrm{if} \quad temp <= t_{opt}: rate = rmax \cdot \frac{1 + exp^{a + b \cdot t_{opt}}}{(1 + exp^{a + b \cdot temp}}

\textrm{if} \quad temp <= t_{opt}: rate = rmax \cdot \frac{1 + exp^{a + b \cdot t_{opt}}}{(1 + exp^{a + b \cdot (2 \cdot t_{opt} - temp)}}

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.

Author(s)

Daniel Padfield

References

Stinner, R. E., Gutierrez, A. P., & Butler Jr, G. D. (1974). An algorithm for temperature-dependent growth rate simulation12. The Canadian Entomologist, 106(5), 519-524.

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 = 'stinner_1974')
# fit model
mod <- nls.multstart::nls_multstart(rate~stinner_1974(temp = temp, rmax, topt, a, b),
data = d,
iter = c(5,5,5,5),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'stinner_1974'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'stinner_1974'),
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()

Taylor-Sexton model for fitting thermal performance curves

Description

Taylor-Sexton model for fitting thermal performance curves

Usage

taylorsexton_1972(temp, rmax, tmin, topt)

Arguments

Details

Equation:

rate = R_{\text{max}} \cdot \frac{-(T-T_{\text{min}})^4 + 2 \cdot (T - T_{\text{min}})^2 \cdot (T_{\text{opt}}-T_{\text{min}})^2}{(T_{\text{opt}}-T_{\text{min}})^4}

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.

Author(s)

Francis Windram

References

Taylor, S. E. & Sexton, O. J. Some implications of leaf tearing in Musaceae. Ecology 53, 143–149 (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 = 'taylorsexton_1972')
# fit model
mod <- nls.multstart::nls_multstart(rate~taylorsexton_1972(temp = temp, rmax, tmin, topt),
data = d,
iter = 200,
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'taylorsexton_1972'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'taylorsexton_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()

Thomas model (2012) for fitting thermal performance curves

Description

Thomas model (2012) for fitting thermal performance curves

Usage

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

Arguments

Details

Equation:

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

Tomlinson-Phillips model for fitting thermal performance curves

Description

Tomlinson-Phillips model for fitting thermal performance curves

Usage

tomlinsonphillips_2015(temp, a, b, c)

Arguments

Details

Equation:

rate = a \cdot [\exp{(b \cdot T) - \exp{(T-c)}}]

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 somewhat difficult to fit.

Author(s)

Francis Windram

References

Tomlinson, S. & Phillips, R. D. Differences in metabolic rate and evaporative water loss associated with sexual dimorphism in thynnine wasps. J. Insect Physiol. 78, 62–68 (2015).

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 = 'tomlinsonphillips_2015')
# fit model
mod <- nls.multstart::nls_multstart(rate~tomlinsonphillips_2015(temp = temp, a, b, c),
data = d,
iter = c(3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'tomlinsonphillips_2015'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'tomlinsonphillips_2015'),
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()

Warren-Dreyer model for fitting thermal performance curves

Description

Warren-Dreyer model for fitting thermal performance curves

Usage

warrendreyer_2006(temp, rmax, topt, a)

Arguments

Details

Equation:

rate = R_{\text{max}} \cdot \exp{\left[-0.5 \cdot \left(\frac{\ln{\frac{T}{T_{\text{opt}}}}}{a}\right)^2\right]}

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.

Author(s)

Francis Windram

References

Warren, C. R. & Dreyer, E. Temperature response of photosynthesis and internal conductance to CO2: results from two independent approaches. J. Exp. Bot. 57, 3057–3067 (2006).

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 = 'warrendreyer_2006')
# fit model
mod <- nls.multstart::nls_multstart(rate~warrendreyer_2006(temp = temp, rmax, topt, a),
data = d,
iter = c(3,3,3),
start_lower = start_vals - 10,
start_upper = start_vals + 10,
lower = get_lower_lims(d$temp, d$rate, model_name = 'warrendreyer_2006'),
upper = get_upper_lims(d$temp, d$rate, model_name = 'warrendreyer_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()

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()