Models
Arrhenius family
These models return a dimensionless correction factor (= 1 at T_ref). Parameters are stored in Kelvin. Use temperature_correction(m, T) or call m(T).
ArrheniusModel
\[f(T) = \exp\!\left(\frac{T_A}{T_{\text{ref}}} - \frac{T_A}{T}\right)\]
Single-parameter model (Kooijman 2010). T_A is the Arrhenius temperature (K); T_ref is the reference temperature where f = 1.
Constructor: arrhenius(; activation_energy=0.65u"eV", reference_temperature=293.15u"K")
SharpSchoolHighModel
Arrhenius with high-temperature enzyme deactivation:
\[r(T) = \rho_{\text{ref}} \cdot \frac{e^{T_A/T_{\text{ref}} - T_A/T}} {1 + e^{T_{AH}/T_H - T_{AH}/T}}\]
Constructor: sharpe_schoolfield_high(; activation_energy, reference_temperature, high_temperature, high_deactivation_energy, rate_at_reference)
SharpSchoolLowModel
Arrhenius with low-temperature enzyme suppression:
\[r(T) = \rho_{\text{ref}} \cdot \frac{e^{T_A/T_{\text{ref}} - T_A/T}} {1 + e^{T_{AL}/T - T_{AL}/T_L}}\]
Constructor: sharpe_schoolfield_low(; ..., low_temperature, low_deactivation_energy, ...)
SharpSchoolFullModel
Full Schoolfield (1981) model — both low and high inactivation, with the $T/T_{\text{ref}}$ pre-factor from the original paper (Eq. 4):
\[r(T) = \rho_{\text{ref}} \cdot \frac{T}{T_{\text{ref}}} \cdot \frac{e^{T_A/T_{\text{ref}} - T_A/T}} {1 + e^{T_{AL}/T - T_{AL}/T_L} + e^{T_{AH}/T_H - T_{AH}/T}}\]
rate_at_reference is the rate in the absence of inactivation at T_ref (T_ref assumed to be in the central Arrhenius zone).
Constructor: sharpe_schoolfield(; activation_energy, reference_temperature, low_temperature, low_deactivation_energy, high_temperature, high_deactivation_energy, rate_at_reference)
SharpSchoolDEBModel
DEBtool normalised Schoolfield model (tempcorr convention). No $T/T_{\text{ref}}$ factor; instead the numerator is corrected so that temperature_correction(m, T_ref) == rate_at_reference exactly for any parameter values:
\[r(T) = \rho_{\text{ref}} \cdot e^{T_A/T_{\text{ref}} - T_A/T} \cdot \frac{1 + e^{T_{AL}/T_{\text{ref}} - T_{AL}/T_L} + e^{T_{AH}/T_H - T_{AH}/T_{\text{ref}}}} {1 + e^{T_{AL}/T - T_{AL}/T_L} + e^{T_{AH}/T_H - T_{AH}/T}}\]
Use this variant when computing CTE for DEB parameter estimation (NicheMapR).
Constructor: sharpe_schoolfield_deb(; ...)
JohnsonLewinModel
Original 1946 enzyme kinetics model — structurally identical to SharpSchoolHighModel:
\[r(T) = \rho_{\text{ref}} \cdot \frac{e^{T_A/T_{\text{ref}} - T_A/T}} {1 + e^{T_{AH}/T_H - T_{AH}/T}}\]
Constructor: johnson_lewin(; ...)
Phenomenological TPC family
These models use thermal_performance(m, T) (or m(T)) with temperatures in °C (bare floats or Unitful).
UniversalTPCModel
Scale-invariant two-parameter TPC (Arnoldi et al. 2025):
\[y(x) = e^x(1 - x), \quad x = \frac{T - T_{\text{opt}}}{E}\]
Peak at T_opt (where x = 0, y = 1); zero at T_opt + E (CTmax); asymptotic approach to zero at cold temperatures (CTmin = −∞).
Constructor: utpc(; optimal_temperature, thermal_breadth, maximum_performance=1.0)
Stored internally: T_opt in Kelvin (bare Float64), E in Kelvin.
DeutschModel
Gaussian rise below optimum, quadratic decline above:
\[r(T) = \begin{cases} r_{\max} \exp\!\left(-\left(\frac{T - T_{\text{opt}}}{2\sigma}\right)^2\right) & T < T_{\text{opt}} \\[4pt] r_{\max} \left(1 - \left(\frac{T - T_{\text{opt}}}{T_{\text{opt}} - T_{\max}}\right)^2\right) & T \geq T_{\text{opt}} \end{cases}\]
Constructor: deutsch(; maximum_rate, optimal_temperature, critical_thermal_maximum, width_parameter)
Briere1Model / Briere2Model
Brière (1999) models for insect development rates:
\[r(T) = c \cdot T \cdot (T - T_{\min}) \cdot \sqrt{T_{\max} - T} \quad \text{(Brière 1)}\]
\[r(T) = c \cdot T \cdot (T - T_{\min}) \cdot (T_{\max} - T)^{1/d} \quad \text{(Brière 2)}\]
Constructors: briere(; rate_constant, minimum_temperature, maximum_temperature [, shape_parameter])
GaussianModel
Symmetric Gaussian:
\[r(T) = r_{\max} \exp\!\left(-\frac{1}{2}\left(\frac{T - T_{\text{opt}}}{\sigma}\right)^2\right)\]
Constructor: gaussian(; maximum_rate, optimal_temperature, width_parameter)
Thomas2012Model
Quadratic TPC (Thomas et al. 2012):
\[r(T) = c \cdot (T - T_{\text{opt}} + b) \cdot (b - (T - T_{\text{opt}}))\]
Constructor: thomas(; rate_constant, shape_parameter, optimal_temperature) (2012 variant)
Thomas2017Model
Asymmetric skewed-Gaussian (Thomas et al. 2017):
\[r(T) = r_{\max} \exp\!\left(-\frac{(T-T_{\text{opt}})^2}{2\sigma(T)^2}\right)\]
with $\sigma(T) = \sigma_L$ below T_opt, $\sigma_R$ above (controlled by skewness).
Constructor: thomas(; maximum_rate, optimal_temperature, width_parameter, skewness) (2017 variant)
PawarModel
Metabolic TPC with biologically-interpretable parameters (Pawar et al. 2018): Arrhenius rise characterised by activation_energy (eV), with high-temperature deactivation controlled by deactivation_energy and peak_temperature.
Constructor: pawar(; rate_at_reference, activation_energy, deactivation_energy, peak_temperature, reference_temperature)
Lactin2Model
Modified Lactin (1995) model for insect development:
\[r(T) = \exp(\rho T) - \exp\!\left(\rho T_{\max} - \frac{T_{\max} - T}{\delta}\right) + \lambda\]
Constructor: lactin2(; rate_constant, maximum_temperature, delta_temperature, intercept)
TDT family
Use survival_time(m, T) (minutes to knockdown at constant temperature T °C).
LogLinearTDTModel
Log-linear (Jørgensen et al. 2021):
\[t(T) = t_{\text{ref}} \cdot 10^{(T_{\text{CTmax}} - T) / z}\]
Parameters:
z_value: °C for a 10-fold change in knockdown timereference_ctmax: sCTmax atreference_durationreference_duration: exposure duration definingreference_ctmax(min)incipient_temperature: temperature below which injury is negligible
Constructor: log_linear_tdt(; z_value, reference_ctmax, reference_duration=60.0, incipient_temperature=30.0)
Derived quantities:
temperature_maximum(m)— temperature where mean knockdown = 1 min (Rezende parameterisation)ctmax_at_duration(m, t)— sCTmax for any exposure durationdynamic_ctmax(m, ramp_rate)— predicted ramp CTmax (Jørgensen Eq. 7a)static_ctmax_from_dynamic(m, dctmax, ramp_rate)— recover sCTmax from dCTmax (Eq. 7b)
Fluctuating exposures:
accumulated_injury(m, T_series, dt)— cumulative injury vector (Eq. 3)time_to_failure(m, T_series, dt)— minutes until injury = 1
ToleranceLandscape
Semi-parametric distributional model (Rezende et al. 2014, 2020). Stores the full empirical survival curve S(τ) z-shifted to a reference temperature.
Fields: z_value, temperature_maximum, mean_assay_temperature, survival_curve (n×2 matrix)
Constructor: tolerance_landscape(; z_value, temperature_maximum, mean_assay_temperature, survival_curve) Usually created by fit_tolerance_landscape(data::IndividualKnockdownData).
Functions:
dynamic_survival(tl, T_series; dt_minutes, recovery_model)— iterative curve-shiftingdaily_mortality(tl, T_series_24h)— 1 − survival over one daycumulative_survival(tl, days)— product of daily survival fractions