Fitting thermal death time (TDT) curves with `brms`

brms

ggplot2

thermal-tolerance

bayesian

A worked example of how I fit and visualise TDT curves in R using brms — from raw survival times to a clean ggplot2 figure with credible intervals.

Author

Félix P. Leiva

Published

April 12, 2026

Thermal death time (TDT) curves describe how survival time at a stressful temperature decreases as temperature rises. They underpin a lot of recent work on heat tolerance — including our 2024 Functional Ecology paper on intraspecific variation of heat tolerance in Drosophila. In this post I show the minimal R workflow I keep coming back to: simulate some data, fit a Bayesian linear model on the log-time, and plot the curve with credible intervals.

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:

\[ \log_{10}(t_{\text{lethal}}) = \alpha - z \cdot T \]

where $z$ (the thermal sensitivity) is the slope and $\alpha$ 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:

Honest uncertainty in derived quantities. The thermal sensitivity $z$, 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().
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.
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.

--- title: "Fitting thermal death time (TDT) curves with `brms`" description: "A worked example of how I fit and visualise TDT curves in R using brms — from raw survival times to a clean ggplot2 figure with credible intervals." author: "Félix P. Leiva" date: "2026-04-12" categories: [R, brms, ggplot2, thermal-tolerance, bayesian] image: thumbnail.png image-alt: "Thermal death time curve fitted with brms" format: html: code-fold: false code-tools: true code-link: true code-block-bg: true code-block-border-left: "#5f7d63" fig-width: 7 fig-height: 4.5 fig-align: center engine: markdown execute: eval: false # the R code is shown verbatim; rendering does not require knitr warning: false message: false --- Thermal death time (TDT) curves describe how survival time at a stressful temperature decreases as temperature rises. They underpin a lot of recent work on heat tolerance — including [our 2024 *Functional Ecology* paper](https://doi.org/10.1111/1365-2435.14485) on intraspecific variation of heat tolerance in *Drosophila*. In this post I show the minimal R workflow I keep coming back to: simulate some data, fit a Bayesian linear model on the log-time, and plot the curve with credible intervals. ## The packages I use ```{r} #| 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: $$ \log_{10}(t_{\text{lethal}}) = \alpha - z \cdot T $$ where $z$ (the *thermal sensitivity*) is the slope and $\alpha$ is the intercept. To make the post self-contained, let's simulate ten flies measured at five temperatures. ```{r} #| 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. ```{r} #| 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`. ```{r} #| 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 $z$, 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](https://bookdown.org/content/4857/) is an excellent companion. For a more macrophysiology-flavoured walkthrough, check the supplementary materials of [Rezende et al. (2014)](https://doi.org/10.1111/1365-2435.12268) — 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: ```bash 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.