Functional stability properties

Overview of the data

We illustrate the use of estar functions on a dataset from an ecotoxicological study about the effects of the chlorpyrifos insecticide on a community of aquatic macroinvertebrates (Brink et al. 1996; Wijngaarden et al. 1996). The insecticide negatively affects freshwater macroinvertebrates, and, to a lesser degree, zooplankton species. This insecticide was applied at four different concentrations (0.1, 0.9, 6, and 44 microg/ L), with two replicates per concentration level. Additionally, four replicates were used as control, undisturbed systems (‘baseline’ in estar terminology). In response to a pulse disturbance, Brink et al. (1996) reports decreased and destabilized community diversity, but no effects on gross primary production nor respiration. The community is composed of 128 species, classified into 5 functional groups: herbivores, detriti-herbivores, carnivores, omnivores, and detritivores.

Organism mean count (log axis) of the five functional groups over the course of ecotoxicological experiment. The vertical dashed line identifies the time when the insecticide was applied (at week 0), and facets represent the different concentrations (micro g/L).
Organism mean count (log axis) of the five functional groups over the course of ecotoxicological experiment. The vertical dashed line identifies the time when the insecticide was applied (at week 0), and facets represent the different concentrations (micro g/L).
Organism count (mean +- sd in grey) of the five functional groups over the course of ecotoxicological experiment. The vertical line identifies the time when the insecticide was applied (at week 0), and facets represent the different concentrations (micro g/L).
Organism count (mean +- sd in grey) of the five functional groups over the course of ecotoxicological experiment. The vertical line identifies the time when the insecticide was applied (at week 0), and facets represent the different concentrations (micro g/L).

Main functions

Examples of each function applied to the example dataset. For the functions that require a user-defined time step when were the system has recovered, we use week 28, when all groups seem to have stabilized their growth curve (Fig.1).

Functional stability

Invariability

Invariability calculated as the inverse of standard deviation of residuals of the linear model that predicts the log response ratio of the state variable in the disturbed and baseline systems by time. The baseline system in our example dataset is reflected by control ditches, to which no pesticide was applied. The time frame is defined by tb_i and specified in the data frame d_data (aquacomm_resps, Fig. 2-a).

invariability(
  type = "functional",
  mode = "lm_res",
  response = "lrr",
  metric_tf = c(1, max(aquacomm_resps$time)),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 1.862129

Invariability calculated as the inverse of standard deviation of residuals of the linear model fitted to predict the state variable in the disturbed system by time (Fig. 2-b).

invariability(
  type = "functional",
  mode = "lm_res",
  metric_tf = c(1, max(aquacomm_resps$time)),
  response = "v",
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 0.003769501

Invariability calculated as the inverse of the coefficient of variation of the log response ratio of the state variable in the disturbed and baseline systems (Fig. 2-c).

invariability(
  type = "functional",
  response = "lrr",
  mode = "cv",
  metric_tf = c(1, max(aquacomm_resps$time)),
  vd_i = "statvar_db",
  td_i = "time",
  b_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  d_data = aquacomm_resps
)
#> [1] 0.03962186

Invariability calculated as the inverse of the coefficient of variation of a state variable in the disturbed system (Fig. 2-d).

invariability(
  type = "functional",
  response = "v",
  mode = "cv",
  metric_tf = c(1, max(aquacomm_resps$time)),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 1.083218
Figure 2: Schematic representation of how functional invariability is calculated by `estar`: $lrr$ and $diff$ refer to the log response ratio and the difference between the state variable in the disturbed system compared to the baseline time-series, $t_d$ is the time of disturbance. a) and b) illustrate the calculation of invariability as the coefficient of variation of the log response ratio and the difference, respectively; c and d) illustrate invariability calculated as the standard deviation of the residuals of the fitted linear model (blue solid line) of the log response ration and difference, respectively, as functions of time.

Figure 2: Schematic representation of how functional invariability is calculated by estar: \(lrr\) and \(diff\) refer to the log response ratio and the difference between the state variable in the disturbed system compared to the baseline time-series, \(t_d\) is the time of disturbance. a) and b) illustrate the calculation of invariability as the coefficient of variation of the log response ratio and the difference, respectively; c and d) illustrate invariability calculated as the standard deviation of the residuals of the fitted linear model (blue solid line) of the log response ration and difference, respectively, as functions of time.

Resistance

Resistance calculated in relation to an independent baseline time series (b = "input"), as the log response ratio (res_mode = "lrr") of the state variable in the disturbed and baseline systems at the first time step following disturbance (res_time = "defined", res_t = 1, Fig. 3-a).

resistance(
  type = "functional",
  b = "input",
  res_mode = "lrr",
  res_time = "defined",
  res_t = 1,
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] -0.3432519

Resistance calculated in relation to a baseline time series (b = "input"), as the highest (res_time = "max") log response ratio (res_mode = "lrr") of the state variable in the disturbed and baseline (independent) systems during a given time frame (res_tf = c(0.14, 28), Fig. 3-b).

resistance(
  type = "functional",
  b = "input",
  res_mode = "lrr",
  res_time = "max",
  res_tf = c(0.14, 28),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 1.166994

Resistance calculated in relation to a baseline time series (b = "input"), as the difference (res_mode = "diff") at the first time step following disturbance (res_time = "defined", res_t = 1, Fig. 3-c).

resistance(
  type = "functional",
  b = "input",
  res_mode = "diff",
  res_time = "defined",
  res_t = 1,
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] -43

Resistance calculated in relation to a baseline time series (b = "input"), as the highest (res_time = "max") absolute difference (res_mode = "diff") during a given time fram, from the first day after to disturbance until week 28, when recovery is assumed to have happened (res_tf = c(0.14, 28), Fig. 3-d).

resistance(
  type = "functional",
  b = "input",
  res_mode = "diff",
  res_time = "max",
  res_tf = c(0.14, 28),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 664.25

Resistance calculated in relation to a pre-disturbance baseline (b = "d"), composed of the state variable values in the three time steps before disturbance (b_tf = c(-4, -0.14)), as the highest (res_time = "max") absolute difference (res_mode = "diff") during a given time frame (res_tf = c(0.14, 28), Fig. 3-d).

resistance(
  type = "functional",
  b = "d",
  b_tf = c(-4, 0.14),
  res_time = "max",
  res_mode = "diff",
  res_tf =c(0.14, 28),
  vd_i = "statvar_bl",
  td_i = "time",
  d_data = aquacomm_resps
)
#> [1] 423.8333

Resistance calculated in relation to a pre-disturbance baseline (b = "d"), composed of the state variable values in the three time steps before disturbance (b_tf = c(-4, -0.14)), as the highest (res_time = "defined") absolute log-ratio (res_mode = "lrr") at a precise time step (res_t = 1), Fig. 3-d).

resistance(
  type = "functional",
  b = "d",
  b_tf = c(-4, 0.14),
  res_mode = "lrr",
  res_time = "defined",
  res_t = 1,
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps
)
#> [1] -0.5681957
Figure 3: Schematic representation of how functional rate of recovery is calculated by `estar`: $lrr$ and $diff$ refer, respectively, to the log response ratio and to the difference between the state variable in the disturbed system in relation to the baseline value(s), $v$ to 'state variable', $t_{res}$, is the user-defined time step when resistance is calculated, and $t_{high}$, to the time step of the highest response in relation to the baseline. The four possibilities of calculating resistance (a-d) resistance result from calculating resistance from $lrr$ and $diff$ at time steps $t_{res}$ and $t_{high}$.

Figure 3: Schematic representation of how functional rate of recovery is calculated by estar: \(lrr\) and \(diff\) refer, respectively, to the log response ratio and to the difference between the state variable in the disturbed system in relation to the baseline value(s), \(v\) to ‘state variable’, \(t_{res}\), is the user-defined time step when resistance is calculated, and \(t_{high}\), to the time step of the highest response in relation to the baseline. The four possibilities of calculating resistance (a-d) resistance result from calculating resistance from \(lrr\) and \(diff\) at time steps \(t_{res}\) and \(t_{high}\).

Extent of recovery

Extent of recovery calculated as the log response ratio (response = "lrr") of the state variable in the disturbed and baseline independent systems (b = "input"), at a user-defined time step whenrecovery is assumed to have happened (t_rec = 28, Fig. 4-a).

recovery_extent(
  type = "functional",
  response = "lrr",
  b = "input",
  t_rec = 28,
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
) 
#> [1] 1.166994

Extent of recovery calculated as the log response ratio (response = "lrr") of the state variable in the disturbed time-series in relation to the state variable pre-disturbance (b = "d"), summarized by the mean value (summ_mode = "mean" - default, over a period b_tf = c(-4, 0)). The extent of recovery is calculated at the point we understand all groups have stabilized (t_rec = 28, Fig. 4-a).

recovery_extent(
  type = "functional",
  response = "lrr",
  b = "d",
  summ_mode = "mean",
  b_tf = c(-4, 0),
  t_rec = 28,
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps
)
#> [1] 1.65396

Extent of recovery calculated as the difference (response = "diff") between the state variables in a disturbed time-series and the baseline (b = "input"), at the predefined time step (t_rec = 28, Fig. 4-b).

recovery_extent(
  type = "functional",
  response = "diff",
  b = "input",
  t_rec = 28,
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 664.25
Figure 4: Schematic representation of how functional extent of recovery is calculated by `estar`. $t_{post}$ is the user-defined timestep when recovery is supposed to have happened. a) $lrr$ is the log response ratio of the state variable in the disturbed system compared to the baseline time-series and b) $diff$ to the difference between them.

Figure 4: Schematic representation of how functional extent of recovery is calculated by estar. \(t_{post}\) is the user-defined timestep when recovery is supposed to have happened. a) \(lrr\) is the log response ratio of the state variable in the disturbed system compared to the baseline time-series and b) \(diff\) to the difference between them.

Rate of recovery

Rate of recovery calculated as the slope of the linear model which predicts the log response ratio of the state variable in the disturbed system compared to the baseline (b = "input) by time (since one day after disturbance until recovery, metric_tf = c(0.14, 28), Fig. 5-a).

recovery_rate(
  type = "functional",
  response = "lrr",
  b = "input",
  metric_tf = c(0.14, 28),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 0.01850625

Rate of recovery calculated as the slope of the linear model which predicts the values of the state variable in the disturbed system(response = "v") by time (over a time frame (metric_tf = c(0.14, 28), Fig. 5-b).

recovery_rate(
  type = "functional",
  response = "v",
  b = "input",
  metric_tf = c(0.14, 28),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 21.06659
Figure 5: Schematic representation of how functional rate of recovery is calculated by `estar`: a) $lrr$ is the log response ratio of the state variable in the disturbed system compared to the baseline time-series, b) $v$ is the state variable. The blue solid line identifies the linear model fitted to predict the response from time (along with its equation) and the double-headed arrow identifies the slope, which is the measure of rate of recovery

Figure 5: Schematic representation of how functional rate of recovery is calculated by estar: a) \(lrr\) is the log response ratio of the state variable in the disturbed system compared to the baseline time-series, b) \(v\) is the state variable. The blue solid line identifies the linear model fitted to predict the response from time (along with its equation) and the double-headed arrow identifies the slope, which is the measure of rate of recovery

Persistence

Proportion of time over which the state variable stays within 1 standard deviation from the mean of the state variable values from an independent baseline (b = "input") since recovery until the end of the experiment (metric_tf = c(28, 56), Fig. 6).

persistence(
  type = "functional",
  b = "input",
  metric_tf = c(28, 56),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 0.4

Proportion of time over which the state variable stays within 1 standard deviation from the mean of the state variable values during a pre-disturbance (b = "d") time period (b_tf = c(-4, 0.14)). Persistence is measured after recovery until the end of the experiment (metric_tf = c(28, 56), Fig. 6).

persistence(
  type = "functional",
  b = "d",
  b_tf = c(-4, 0.14),
  metric_tf = c(28, 56),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps
)
#> [1] 0.2
Figure 6: Schematic representation of how functional persistence is calculated by `estar`: $v_b \pm sd_b$ is the standard deviation limit around the mean ($v_b$) of the baseline state variable. $t_a$ is the period for which persistence is calculated for, and $t_P$, the period during which the state variable remained inside the limits.

Figure 6: Schematic representation of how functional persistence is calculated by estar: \(v_b \pm sd_b\) is the standard deviation limit around the mean (\(v_b\)) of the baseline state variable. \(t_a\) is the period for which persistence is calculated for, and \(t_P\), the period during which the state variable remained inside the limits.

Overall Ecological Vulnerability

Area under the curve of the log response ratio (response = "lrr") between the state variable in the disturbed and baseline scenarios, since shortly after the disturbance (we don’t have data from t = 0, the moment of application of the insecticide) until the the end of the observation period (metric_tf = c(0.14, 56)).

oev(
  type = "functional",
  response = "lrr",
  metric_tf = c(0.14, 56),
  vd_i = "statvar_db",
  td_i = "time",
  d_data = aquacomm_resps,
  vb_i = "statvar_bl",
  tb_i = "time",
  b_data = aquacomm_resps
)
#> [1] 12.06002
Figure 7: Schematic representation of the calculation of overall ecological etability in `estar`: $lrr$ is the log response ratio of the state variable in the disturbed system compared to the baseline time-series, $t_d$ is the time step when disturbance happened. The purple shaded area is the area under the curve calculated by the metric.

Figure 7: Schematic representation of the calculation of overall ecological etability in estar: \(lrr\) is the log response ratio of the state variable in the disturbed system compared to the baseline time-series, \(t_d\) is the time step when disturbance happened. The purple shaded area is the area under the curve calculated by the metric.

Compositional stability

The functions for functional stability can be used to calculate the stability of community composition from community compositional data. To do so, the functions call the vegdist function (from the vegan package), which can be parameterized with the method and binary arguments. Here, we use the default arguments method and binary, which means the Bray-Curtis dissimilarity is used.

# Reformatting the macroinvertebrate community long-format data into 
# community composition data
comm_data <- aquacomm_fgps |>
    dplyr::group_by(time, treat) |>
    dplyr::filter(treat %in% c(0, 44)) |>
    dplyr::summarize_at(vars(herb, detr_herb, carn, omni, detr),
                        mean) |>
    dplyr::ungroup()

control_comm <- comm_data |>
        dplyr::filter(treat == 0) |>
        dplyr::select(-treat)
dist_comm <- comm_data |>
        dplyr::filter(treat == 44) |>
        dplyr::select(-treat)

It is worth noting that, if the user wants to calculate compositional stability from other metrics (possibly not available through vegdist), they can input it as a single variable time-series, as demonstrated in the section “Functional stability”.

Invariability

Invariability calculated for the the whole time-series (since disturbance, metric_tf = c(0.14, 56)).

invariability(
  type = "compositional",
  metric_tf = c(0.14, 56),
  comm_d = dist_comm,
  comm_b = control_comm,
  comm_t = "time")

Resistance

Resistance can be calculated in two ways:

  • As the maximal resistance (res_time = "max") over a time period defined by the user. In this case, from the first day to the 28th week after disturbance, when recovery is assumed to have happened (res_tf = c(0.14, 28)).
resistance(type = "compositional",
          res_tf = c(0.14, 28),
          res_time = "max",
          comm_d = dist_comm,
          comm_b = control_comm,
          comm_t = "time")
#> [1] 0.8255708
  • At a time step chosen by the user (res_time = "defined"). In this case, when recovery is assumed to have happened (week 28, res_t = 28), but often at the first time step after disturbance.
resistance(type = "compositional",
          res_time = "defined",
          res_t = 28,
          comm_d = dist_comm,
          comm_b = control_comm,
          comm_t = "time")

Rate of recovery

Rate of recovery of the community between the first day after disturbance and recovery at week 28 (metric_tf = c(0.14, 28)).

recovery_rate(type = "compositional",
              metric_tf = c(0.14, 28),
              comm_d = dist_comm,
              comm_b = control_comm,
              comm_t = "time")
#> [1] -0.01956683

Extent of recovery

Since we assume recovery happened by week 28, we calculate its extent by that time (t_rec = 28).

recovery_extent(type = "compositional",
          t_rec = 28,
          comm_d = dist_comm,
          comm_b = control_comm,
          comm_t = "time")
#> [1] 0.1808847

Persistence

Here, the community is considered to be persistent if it’s dissimilarity stays between 0.5 and 0.9 (low_lim = 0.5, high_lim = 0.9). We check if the community stayed in this persistence zone after recovery (week 28) until the end of the experiment (week 56, metric_tf = c(28, 56)).

persistence(type = "compositional",
            b = "input",
            metric_tf = c(28, 56),
            comm_d = dist_comm,
            comm_b = control_comm,
            comm_t = "time",
            low_lim = 0.5,
            high_lim = 0.9)
#> [1] 0

Overall Ecological Vulnerability

oev(type = "compositional",
    metric_tf = c(0.14, 56),
    comm_d = dist_comm,
    comm_b = control_comm,
    comm_t = "time")
#> [1] 21.48959

Performance

We conducted the benchmark analysis of the execution time of the different forms of calculating the temporal metrics. The number attached to the function name in “Function calls” identifies the order in which the function call appears in the vignette. The code used for the analysis is available in performance_analysis.R.

While the time to run the calls can differ significantly from each other, the execution time did not exceed 0.01 seconds for our example.

Invariability

df_list$inv_benchmark %>%
  dplyr::select(-neval) %>% 
  kableExtra::kbl() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))
Function call Min. Lower quart. Mean Median Upper quart. Max. Signif.
inv_1 0.0014164 0.0014735 0.0016353 0.0015438 0.0017443 0.0023509 a
inv_2 0.0006531 0.0006831 0.0008838 0.0007071 0.0007976 0.0139417 b
inv_3 0.0009451 0.0009935 0.0011644 0.0010308 0.0011675 0.0083914 b
inv_4 0.0002154 0.0002320 0.0002611 0.0002464 0.0002753 0.0004148 c
inv_5 0.0028998 0.0030259 0.0034541 0.0031485 0.0037542 0.0113028 d
Density distribution of execution times of 100 runs of each of the different options of the invariability() function demonstrated in the vignette.
Density distribution of execution times of 100 runs of each of the different options of the invariability() function demonstrated in the vignette.

Resistance

df_list$resis_benchmark %>%
  dplyr::select(-neval) %>% 
  kableExtra::kbl() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))
Function call Min. Lower quart. Mean Median Upper quart. Max. Signif.
res_1 0.0009469 0.0009977 0.0010777 0.0010387 0.0011214 0.0020407 ab
res_2 0.0009569 0.0010313 0.0011357 0.0010765 0.0011542 0.0020992 b
res_3 0.0009378 0.0010048 0.0012091 0.0010494 0.0011710 0.0097086 b
res_4 0.0009659 0.0010300 0.0011139 0.0010689 0.0011442 0.0020303 ab
res_5 0.0004311 0.0004867 0.0009812 0.0005134 0.0005570 0.0361469 ab
res_6 0.0004284 0.0004756 0.0005224 0.0004999 0.0005432 0.0009084 a
res_7 0.0005006 0.0005966 0.0007023 0.0006893 0.0007642 0.0013301 ab
Density distribution of execution times of 100 runs of each of the different options of the resistance() function demonstrated in the vignette.
Density distribution of execution times of 100 runs of each of the different options of the resistance() function demonstrated in the vignette.

Recovery rate

df_list$rate_benchmark %>%
  dplyr::select(-neval) %>% 
  kableExtra::kbl() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))
Function call Min. Lower quart. Mean Median Upper quart. Max. Signif.
rate_1 0.0013755 0.0015069 0.0019669 0.0016006 0.0017432 0.0169870 a
rate_2 0.0013663 0.0015557 0.0022521 0.0016213 0.0017893 0.0435986 a
rate_3 0.0011144 0.0012737 0.0014516 0.0013936 0.0015002 0.0029469 a
rate_5 0.0026548 0.0028239 0.0032189 0.0030085 0.0032579 0.0102492 b
Density distribution of execution times of 100 runs of each of the different options of the recovery_rate() function demonstrated in the vignette.
Density distribution of execution times of 100 runs of each of the different options of the recovery_rate() function demonstrated in the vignette.

Recovery extent

df_list$extent %>%
  dplyr::select(-neval) %>% 
  kableExtra::kbl() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))
Function call Min. Lower quart. Mean Median Upper quart. Max. Signif.
extent_1 0.0009035 0.0009214 0.0011066 0.0009417 0.0009661 0.0086971 a
extent_2 0.0008951 0.0009300 0.0009608 0.0009422 0.0009650 0.0012373 a
extent_3 0.0002346 0.0002493 0.0004213 0.0002545 0.0002637 0.0163742 b
extent_4 0.0004379 0.0004662 0.0004930 0.0004767 0.0004934 0.0008234 b
Density distribution of execution times of 100 runs of each of the different options of the recovery_extent() function demonstrated in the vignette.
Density distribution of execution times of 100 runs of each of the different options of the recovery_extent() function demonstrated in the vignette.

Persistence

df_list$persist_benchmark %>%
  dplyr::select(-neval) %>% 
  kableExtra::kbl() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))
Function call Min. Lower quart. Mean Median Upper quart. Max. Signif.
persist_1 0.0008512 0.0008862 0.0009366 0.0009018 0.0009348 0.0014930 a
persist_2 0.0007750 0.0007975 0.0011494 0.0008130 0.0008492 0.0314413 a
persist_3 0.0016617 0.0016924 0.0018602 0.0017233 0.0018600 0.0089108 b
Density distribution of execution times of 100 runs of each of the different options of the persistence() function demonstrated in the vignette.
Density distribution of execution times of 100 runs of each of the different options of the persistence() function demonstrated in the vignette.

Overall Ecological Vulnerability

df_list$oev_benchmark %>%
  dplyr::select(-neval) %>% 
  kableExtra::kbl() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))
Function call Min. Lower quart. Mean Median Upper quart. Max. Signif.
oev_1 0.0012155 0.0012589 0.0014019 0.0012888 0.0013369 0.0086462 a
oev_2 0.0027354 0.0028414 0.0030923 0.0029112 0.0030109 0.0101471 b
Density distribution of execution times of 100 runs of each of the different options of the oev() function demonstrated in the vignette.
Density distribution of execution times of 100 runs of each of the different options of the oev() function demonstrated in the vignette.

References

Brink, Paul J. van den, René P. A. Van Wijngaarden, Wil G. H. Lucassen, Theo C. M. Brock, and Peter Leeuwangh. 1996. “Effects of the Insecticide Dursban® 4E (Active Ingredient Chlorpyrifos) in Outdoor Experimental Ditches: II. Invertebrate Community Responses and Recovery.” Environmental Toxicology and Chemistry 15 (7): 1143–53. https://doi.org/http://doi.wiley.com/10.1002/etc.5620150719.
Wijngaarden, René P. A. van, Paul J. van den Brink, Steven J. H. Crum, Theo C. M. Brock, Peter Leeuwangh, and Oude Jan H. Voshaar. 1996. “Effects of the Insecticide Dursban® 4E (Active Ingredient Chlorpyrifos) in Outdoor Experimental Ditches: I. Comparison of Short-Term Toxicity Between the Laboratory and the Field.” Environmental Toxicology and Chemistry 15 (7): 1133–42. https://doi.org/https://doi.org/10.1002/etc.5620150718.