Author: Daniel Padfield
Date: 2026-04-10

# Fitting many curves using rTPC

#### Daniel Padfield

#### 2026-04-10

#### A brief example of how to fit many models to multiple TPCs using rTPC, nls.multstart and the tidyverse.

## Things to consider

- Go through all the other Things to consider sections in the other vignettes.
- Think carefully about how to do model selection on the whole dataset.
- If you care about specific parameters (e.g. optimum temperature or activation energy) then you might want to pick a single “best” model for the whole dataset.
- If you care about the overall fit and its shape, then you might want to do pick a “best” model on each individual curve.
- You should read resources about model selection to inform your decisions.

    # load packages
    library(rTPC)
    library(nls.multstart)
    library(broom)
    library(tidyverse)

In the final part of the general pipeline, we demonstrate how multiple models can be fitted to multiple TPCs. Instead of picking all 49 model formulations to demonstrate this approach, we will use only 2 models in this example: gaussian_1987() and sharpeschoolhigh_1981().

We can demonstrate the fitting of multiple curves by modelling all 60 TPCs from the example dataset of rTPC curve from the example dataset rTPC. These TPCs are of respiration and photosynthesis of the aquatic algae, Chlorella vulgaris. These algae differed in their growth temperature, `growth_temp`, and how long they had been grown at that temperature, `process`, either for ~100 or ~10 generations.

Using a similar approach to `vignette('fit_many_models')`, models can be fitted to each curve using list columns and purrr::map() to fit and store multiple models in a data frame.

When fitting lots of models at once, it is useful to know the progress the code as it may take a long time to run.The R package purrr now has progress bars built in; you can add a progress bar to the map() function using the argument .progress. To make this work, we need to only do a single map() call, so we will write a function that fits both models that we will then pass to purrr. This is how we strongly recommend fitting multiple models using map().

    # load in data
    data("chlorella_tpc")
    d <- chlorella_tpc

    # write function to fit both models
    fit_TPCs <- function(d, ...) {
      # get start values and fit gaussian
      start_vals <- rTPC::get_start_vals(
        d$temp,
        d$rate,
        model_name = 'gaussian_1987'
      )

      mod_gaussian <- nls.multstart::nls_multstart(
        rate ~ rTPC::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 = rTPC::get_lower_lims(d$temp, d$rate, model_name = 'gaussian_1987'),
        upper = rTPC::get_upper_lims(d$temp, d$rate, model_name = 'gaussian_1987'),
        supp_errors = 'Y',
        convergence_count = FALSE,
        ...
      )

      # get start values and fit sharpe schoolfield
      start_vals <- rTPC::get_start_vals(
        d$temp,
        d$rate,
        model_name = 'sharpeschoolhigh_1981'
      )

      # fit model
      mod_ss <- nls.multstart::nls_multstart(
        rate ~
          rTPC::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 = rTPC::get_lower_lims(
          d$temp,
          d$rate,
          model_name = 'sharpeschoolhigh_1981'
        ),
        upper = rTPC::get_upper_lims(
          d$temp,
          d$rate,
          model_name = 'sharpeschoolhigh_1981'
        ),
        supp_errors = 'Y',
        convergence_count = FALSE,
        ...
      )

      return(tibble::tibble(
        gaussian = list(mod_gaussian),
        sharpeschoolhigh = list(mod_ss)
      ))
    }

    # fit two chosen model formulation in rTPC
    d_fits <- nest(d, data = c(temp, rate)) %>%
      mutate(
        mods = map(
          data,
          ~ fit_TPCs(d = .x),
          .progress = TRUE
        )
      ) %>%
      unnest(mods)

    #> ██████████████████████████████ 100% | ETA: 0s

Like previous vignettes, the predictions of each model can be estimated using broom::augment(). To do this, we first create a new list column containing high resolution temperature values by taking the `min` and `max` of each curve. Next we stack the models and finally we get the new predictions using the map2(), which allows us to use both `fit` and `new_data` list columns. After unnesting the `preds` column, we are then left with high resolution predictions for each curve. As this code covers a lot of steps, each line of the code is commented.

    # create new list column of for high resolution data
    d_preds <- mutate(d_fits, new_data = map(data, ~tibble(temp = seq(min(.x$temp), max(.x$temp), length.out = 100)))) %>%
      # get rid of original data column
      select(., -data) %>%
      # stack models into a single column, with an id column for model_name
      pivot_longer(., names_to = 'model_name', values_to = 'fit', c(gaussian,sharpeschoolhigh)) %>%
      # create new list column containing the predictions
      # this uses both fit and new_data list columns
      mutate(preds = map2(fit, new_data, ~augment(.x, newdata = .y))) %>%
      # select only the columns we want to keep
      select(curve_id, growth_temp, process, flux, model_name, preds) %>%
      # unlist the preds list column
      unnest(preds)

    glimpse(d_preds)
    #> Rows: 12,000
    #> Columns: 7
    #> $ curve_id    <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
    #> $ growth_temp <dbl> 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20…
    #> $ process     <chr> "acclimation", "acclimation", "acclimation", "acclimation"…
    #> $ flux        <chr> "respiration", "respiration", "respiration", "respiration"…
    #> $ model_name  <chr> "gaussian", "gaussian", "gaussian", "gaussian", "gaussian"…
    #> $ temp        <dbl> 16.00000, 16.33333, 16.66667, 17.00000, 17.33333, 17.66667…
    #> $ .fitted     <dbl> 0.02790076, 0.03175769, 0.03607053, 0.04088150, 0.04623512…

We can then plot the predictions of each curve using ggplot2.

    # plot
    ggplot(d_preds) +
      geom_line(aes(temp, .fitted, col = model_name)) +
      geom_point(aes(temp, rate), d) +
      facet_wrap(~curve_id, scales = 'free_y', ncol = 6) +
      theme_bw() +
      theme(legend.position = 'none') +
      scale_color_brewer(type = 'qual', palette = 2) +
      labs(x = 'Temperature (ºC)',
           y = 'Metabolic rate',
           title = 'All fitted thermal performance curves',
           subtitle = 'gaussian in green; sharpeschoolhigh in orange')

The traits of each thermal performance curve can also easily be calculated.

    # stack models and calculate extra params
    d_params <- pivot_longer(d_fits, names_to = 'model_name', values_to = 'fit', c(gaussian,sharpeschoolhigh)) %>%
      mutate(params = map(fit, calc_params, .progress = TRUE)) %>%
      select(curve_id, growth_temp, process, flux, model_name, params) %>%
      unnest(params)
    #>  ■■■■■■■■■■■■■■■                   48% |  ETA:  4s
    #>  ■■■■■■■■■■■■■■■■■■■■■■■■■■        83% |  ETA:  1s

    glimpse(d_params)
    #> Rows: 120
    #> Columns: 16
    #> $ curve_id              <dbl> 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, …
    #> $ growth_temp           <dbl> 20, 20, 20, 20, 23, 23, 27, 27, 27, 27, 30, 30, …
    #> $ process               <chr> "acclimation", "acclimation", "acclimation", "ac…
    #> $ flux                  <chr> "respiration", "respiration", "respiration", "re…
    #> $ model_name            <chr> "gaussian", "sharpeschoolhigh", "gaussian", "sha…
    #> $ rmax                  <dbl> 1.4972473, 1.8127063, 1.7935416, 1.9798352, 0.94…
    #> $ topt                  <dbl> 36.338, 41.646, 35.554, 39.007, 34.615, 35.170, …
    #> $ ctmin                 <dbl> 18.695, 2.539, 18.835, 6.086, 17.368, 11.970, 15…
    #> $ ctmax                 <dbl> 53.981, 45.558, 52.272, 47.680, 51.861, 53.064, …
    #> $ e                     <dbl> 0.6758954, 0.5802496, 0.8427748, 0.6621701, 1.02…
    #> $ eh                    <dbl> 1.0767824, 11.4840311, 1.0954099, 2.4774826, 1.1…
    #> $ q10                   <dbl> 2.373766, 2.063147, 2.927011, 2.305129, 3.722119…
    #> $ thermal_safety_margin <dbl> 17.643, 3.912, 16.718, 8.673, 17.246, 17.894, 18…
    #> $ thermal_tolerance     <dbl> 35.286, 43.019, 33.437, 41.594, 34.493, 41.094, …
    #> $ breadth               <dbl> 9.651, 5.371, 9.165, 6.495, 9.442, 7.714, 10.354…
    #> $ skewness              <dbl> -0.400887075, -10.903781453, -0.252635109, -1.81…

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