A simulated ramping assay of thermal tolerance, with two levels of oxygen

Times to loss of equilibrium of 320 juvenile salmonids warmed from 14 degrees C at a constant rate until they failed or the water reached 29.5 degrees C, simulated from a known model. The fish were run in 32 trials of ten. Four ramp rates (0.025, 0.1, 0.2 and 0.3 degrees C per minute) are crossed with two levels of dissolved oxygen (10 and 5 mg/L), four trials of each combination. The fish were watched throughout, so each failure was observed at a known time.

Usage

ramp_assay

Format

A tibble with 320 rows, one per fish, and 8 columns:

id: Integer, the fish.
trial: Character, the trial the fish was in ("R01" to "R32").
path_id: Character, the ramp ("r0.025", "r0.1", "r0.2", "r0.3"), the key to its temperature trajectory.
rate: Numeric, the ramp rate, degrees C per minute.
do: Numeric, dissolved oxygen in the trial, mg/L (10 or 5).
mass: Numeric, body mass, g.
event: Integer, 1 if the fish lost equilibrium, 0 if it survived to the end of the ramp.
t_event: Numeric, the time of failure, or of the end of the ramp for a survivor, minutes from its start.

Source

Simulated by data-raw/make-example-data.R in the package's repository.

Details

The slow rate allows the same data to show what the choice of ramp rates lets a model estimate: the three faster rates span 3-fold, and the rates of 0.025, 0.1 and 0.3 span 12-fold (see the vignette Ramping assays).

The data are simulated, not measured. The values are plausible for a juvenile rainbow trout acclimated to 14 degrees C, and stand for no particular study.

The model the data were simulated from

The hazard of losing equilibrium is h0(tau) M(T), with an exponential failure rate M(T) = a exp(b (T - 26)) and a Weibull baseline h0(tau) = (k / s) (tau / s)^(k - 1), with times in minutes. The values, stored as attr(ramp_assay, "truth"), are b = 1.7 per degree C, k = 1.5, s = 60 minutes, and log a = -2.13 at 26 degrees C for a 15 g fish in normoxia. log a varies among trials with a standard deviation of 0.3 and rises by 0.03 per gram of body mass. At a constant temperature half the fish then fail in about 1 hour at 27 degrees C, 10 hours at 25 and 4 days at 23. static_assay was simulated from the same model.

Low dissolved oxygen raises the failure rate, and the more so the warmer the water: each mg/L of oxygen below 10 adds 0.3 + 0.04 (T - 26) to log M(T). The effect is 0.3 per mg/L at 26 degrees C and changes by 0.04 for each degree (0.38 at 28 degrees C, 0.22 at 24), which is the form that the interaction of a co-stressor with temperature fits (see costressor()). The two values are stored as b_do and d_do.

Examples

head(ramp_assay)
#> # A tibble: 6 × 8
#>      id trial path_id  rate    do  mass event t_event
#>   <int> <chr> <chr>   <dbl> <dbl> <dbl> <int>   <dbl>
#> 1     1 R01   r0.1      0.1    10  10.2     1    136.
#> 2     2 R01   r0.1      0.1    10  18.3     1    133.
#> 3     3 R01   r0.1      0.1    10  15.2     1    132 
#> 4     4 R01   r0.1      0.1    10  26.3     1    130.
#> 5     5 R01   r0.1      0.1    10  23.8     1    125.
#> 6     6 R01   r0.1      0.1    10  18.6     1    132.

# The four ramps, from 14 to 29.5 degrees C.
rates <- c(0.025, 0.1, 0.2, 0.3)
path  <- ramp_path(c("r0.025", "r0.1", "r0.2", "r0.3"), T_start = 14, rate = rates,
                   t_max = 15.5 / rates)
# No grid is given: the intervals follow the ramp in steps of 0.1 degrees C.
long  <- build_hazard_data(ramp_assay, path, "continuous",
                           covariates = c("mass", "do", "trial"))
#> ℹ The intervals at risk were divided further, into 43406 rows from 325, so that
#>   temperature changes by at most 0.1 degrees within each.
#> ℹ The hazard is taken as constant within an interval, which biases the fit when
#>   temperature changes much within it. Failures at a known time are also given a
#>   short closing interval, so their hazard is that of the moment of failure.
#> ℹ Set `grid_dT` to change the step, or to `Inf` to keep the intervals as given.
head(long)
#> # A tibble: 6 × 13
#>      id  mass    do trial path_id   tau exposure    Ta failed    Tr log_tau
#>   <int> <dbl> <dbl> <chr> <chr>   <dbl>    <dbl> <dbl>  <int> <dbl>   <dbl>
#> 1     1  10.2    10 R01   r0.1    0.500    0.999  14.0      0  27.5  -0.694
#> 2     1  10.2    10 R01   r0.1    1.50     0.999  14.1      0  27.5   0.405
#> 3     1  10.2    10 R01   r0.1    2.50     0.999  14.2      0  27.5   0.916
#> 4     1  10.2    10 R01   r0.1    3.50     0.999  14.3      0  27.5   1.25 
#> 5     1  10.2    10 R01   r0.1    4.50     0.999  14.4      0  27.5   1.50 
#> 6     1  10.2    10 R01   r0.1    5.50     0.999  14.5      0  27.5   1.70 
#> # ℹ 2 more variables: tau_ref <dbl>, log_exposure <dbl>