Curve Fitting

All fitting functions use LsqFit.jl (nonlinear least squares) or ordinary least squares where appropriate.

TPC fitting

Generic models

fit_thermal_performance_curve(ModelType, temperatures, rates;
                              initial_parameters=nothing, weights=nothing)

Supported generic models: UniversalTPCModel, GaussianModel, DeutschModel. Returns a fitted instance of ModelType. Initial parameters are estimated from data heuristics if initial_parameters is nothing.

temps = [5, 10, 15, 20, 25, 30, 35, 40, 45]
rates = [0.1, 0.3, 0.6, 0.9, 1.0, 0.9, 0.5, 0.1, 0.0]

m_fit = fit_thermal_performance_curve(UniversalTPCModel, temps, rates)

Sharpe-Schoolfield models

SharpSchoolFullModel and SharpSchoolDEBModel have a specialised overload with initial parameter estimates from the Schoolfield et al. (1981) graphical method (piecewise OLS on the Arrhenius plot):

fit_thermal_performance_curve(SharpSchoolFullModel, temperatures, rates;
                              T_ref=298.15u"K",
                              log_transform=true,
                              initial_parameters=nothing,
                              weights=nothing)

log_transform=true (default): minimises sum of squared log-residuals $\sum(\log \hat{r}_i - \log r_i)^2$. Appropriate when rates span orders of magnitude; matches the Schoolfield et al. (1981) Marquardt fit.

log_transform=false: minimises absolute residuals; use with weights for weighted least squares (e.g. weights = 1 ./ rates for equal relative weighting of each point).

Graphical initial estimates (Schoolfield 1981, Figure 2):

The data are split into cold / middle / hot fractions. OLS is fitted to $\ln r \sim 1/T$ in each region. From the slopes:

T_A  ≈ −slope_middle
T_AL ≈ −slope_cold − T_A
T_AH ≈  slope_hot  + T_A

TL and TH are found from the intersections of the cold / hot OLS lines with the half-Arrhenius line (middle line shifted down by ln 2).

TDT fitting

Static knockdown data

Provide group-summary mean knockdown times at each assay temperature:

data = StaticKnockdownData(temperatures=[36, 38, 40, 42, 44],
                           knockdown_times=[289, 72, 18, 4.5, 1.1])
m_tdt = fit_thermal_death_time_curve(data; reference_duration=60.0)

Fits $\log_{10}(t) \sim T$ by OLS. Returns a LogLinearTDTModel.

Dynamic CTmax data

Provide knockdown temperatures observed at multiple ramp rates:

data = DynamicKnockdownData(ramp_rates=[0.1, 0.25, 0.5],
                             dynamic_ctmax_values=[40.2, 41.8, 43.1],
                             start_temperature=20.0)
m_tdt = fit_thermal_death_time_curve(data; reference_duration=60.0)

Uses Jørgensen (2021) Eq. 7a in NLS (≥ 3 ramp rates) or a root-finding scan (2 rates).

Tolerance landscape

Requires individual-level knockdown data (one row per organism):

data = IndividualKnockdownData(temperatures=assay_temps,
                               knockdown_times=times_to_knockdown)
tl = fit_tolerance_landscape(data; n_bins=1000)

Algorithm (Rezende et al. 2014, tolerance.landscape()):

OLS on $\log_{10}(t) \sim T$ → z-value, T_max
Z-shift all knockdown times to the mean assay temperature: $t_{\text{shifted}} = t \cdot 10^{(T - \bar{T}) / z}$
Compute empirical survival function S(τ) on shifted times
Store as n_bins-row matrix (interpolated to regular grid)

The resulting ToleranceLandscape can then be used for dynamic_survival predictions.

Data container types

IndividualKnockdownData(; temperatures, knockdown_times)
StaticKnockdownData(; temperatures, knockdown_times)
DynamicKnockdownData(; ramp_rates, dynamic_ctmax_values, start_temperature)

All temperature arguments accept Unitful quantities or bare floats (°C assumed).