The packages I use

#| label: setup
library(tidyverse)   # dplyr, tidyr, ggplot2
library(brms)        # bayesian regression
library(tidybayes)   # tidy posteriors
library(ggdist)      # nice uncertainty geoms
theme_set(theme_minimal(base_size = 13))

A small simulated dataset

The TDT model assumes survival time scales log-linearly with temperature:

where (the thermal sensitivity) is the slope and is the intercept. To make the post self-contained, let’s simulate ten flies measured at five temperatures.

#| label: simulate
set.seed(2026)

tdt_sim <- expand_grid(
  temperature = c(36, 37, 38, 39, 40),
  replicate   = 1:10
) |>
  mutate(
    log10_time = 4.6 - 0.18 * temperature + rnorm(n(), 0, 0.08),
    time_min   = 10^log10_time
  )

head(tdt_sim)

Fit a Bayesian linear model

brms is a thin, expressive wrapper around Stan. For a TDT curve I almost always start with a simple Gaussian model on log10_time, with weakly informative priors on the intercept and slope.

#| label: fit
fit <- brm(
  log10_time ~ temperature,
  data    = tdt_sim,
  family  = gaussian(),
  prior   = c(
    prior(normal(4, 1),    class = "Intercept"),
    prior(normal(-0.2, 0.1), class = "b"),
    prior(exponential(5), class = "sigma")
  ),
  chains  = 4,
  iter    = 2000,
  cores   = 4,
  refresh = 0
)

summary(fit)

Pull out the posterior and plot

tidybayes::add_epred_draws() gives you posterior predictions for any new grid of temperatures, in long format ready for ggplot2.

#| label: plot
#| fig-cap: "TDT curve fitted with brms. The thick line is the posterior median; the band is the 95% credible interval."
new_temp <- tibble(temperature = seq(35.5, 40.5, length.out = 100))

post_pred <- new_temp |>
  add_epred_draws(fit, ndraws = 500)

ggplot(post_pred, aes(x = temperature, y = .epred)) +
  stat_lineribbon(.width = c(0.5, 0.8, 0.95),
                  alpha = 0.5, fill = "#5f7d63") +
  geom_point(
    data = tdt_sim,
    aes(y = log10_time),
    inherit.aes = FALSE,
    alpha = 0.6, colour = "#3e5642", size = 2
  ) +
  scale_fill_brewer(palette = "Greens", guide = "none") +
  labs(
    x = "Temperature (°C)",
    y = expression(log[10]~lethal~time~(min)),
    title = "Thermal death time (TDT) curve",
    subtitle = "Simulated *Drosophila* heat-tolerance data"
  )

Why a Bayesian model?

For TDT curves specifically I find Bayesian fits useful for three reasons:

1. Honest uncertainty in derived quantities. The thermal sensitivity , the Critical Thermal Maximum at one minute (CTmax₁), or the projected survival at 41 °C are all functions of the model parameters. With posterior draws, propagating that uncertainty to any derived quantity is just mutate().
2. Natural multilevel extensions. Once you have replicates from different lines, populations, or species, you can extend the model to log10_time ~ temperature + (temperature | line) and the syntax barely changes.
3. Priors as documentation. The priors above are weak but not flat — they encode what we already know from decades of TDT data. That alone makes the model easier to defend in review.

If you are new to brms, Solomon Kurz’s Statistical Rethinking with brms translation is an excellent companion. For a more macrophysiology-flavoured walkthrough, check the supplementary materials of Rezende et al. (2014) — the paper that introduced TDT to the ectotherm thermal-tolerance literature.

Reproducibility

The code in this post is the entire post — there is no hidden setup. To rerun it:

git clone https://github.com/felixpleiva/felixpleiva.github.io
cd felixpleiva.github.io/posts/2026-04-tdt-curves-brms
quarto render

If the version of brms you have installed differs, the posterior summaries will move slightly but the visual story will be the same.