LIME tutorial

3.1 Build biological parameters required by LIME

Please visit LIME documentation for further details.

The biological parameters here provided contains the union of those required by LB-SPR and LIME. Let’s strip off LBSPR’s specific parameters. In addition, it is important to pay attention to two special parameters: i) rec_variability_mean and rec_variability_sd are the mean and standard deviation of control distribution applied to the estimates of recruitment, to avoid this parameter to shoot out unrealistically (Rudd and Thorson, 2017). The values of such variables were obtained from Thorson et al., 2014.

bio_params <- spp_sampling_details$bio_params
bio_params$fecb <- NULL
bio_params
#> $linf
#> [1] 42.41
#> 
#> $k
#> [1] 0.21
#> 
#> $t0
#> [1] -1.202
#> 
#> $lwa
#> [1] 0.012
#> 
#> $lwb
#> [1] 3.011
#> 
#> $l50
#> [1] 19.45
#> 
#> $M
#> [1] 0.354
#> 
#> $max_age
#> [1] 9
#> 
#> $rec_variability_mean
#> [1] 0.748
#> 
#> $rec_variability_sd
#> [1] 0.293
#> 
#> $max_age
#> [1] 9
#> 
#> $l95
#> [1] 22.37

3.2 Build exploitation parameters required by LIME

Unlike LB-SPR, LIME needs selectivity priors and a penalty to constraint the potential estimated values of the fishing mortality from year to year (Rudd and Thorson, 2017). Rudd and Thorson, 2017 therefore suggests to calculate the SL50 as the halfway length between the first one observed in the length composition and that of the mode. Then SL95 is calculated as SL50 * 1.15, in the same fashion as defined by Prince et al., 2022 for the maturation ogive. As for the fishing mortality prior, the default 0.2 value was taken (Rudd and Thorson, 2017).

summary_catch <- catch_data$long %>%
  dplyr::select(MeanLength, catch) %>%
  dplyr::group_by(MeanLength) %>%
  dplyr::summarise(total_catch = sum(catch))
catch_mode <- summary_catch$MeanLength[which.max(summary_catch$total_catch)]
sl50 <- median(min(summary_catch$MeanLength):catch_mode)
sel_params <- list(
  sl50 = sl50,
  sl95 = sl50 * 1.15
)

exploitation_params <- list(
  s50 = sel_params$sl50,
  s95 = sel_params$sl95,
  sigmaF = 0.2
)
exploitation_params
#> $s50
#> [1] 12.5
#> 
#> $s95
#> [1] 14.375
#> 
#> $sigmaF
#> [1] 0.2

3.3 Build extra-detail context

Lime, being an age-structured model, needs to be told whether the provided selectivity and maturity is at length or at age. Additionally, we use this data structure to let LIME know that the steepness should be set to h = 0.7

extra_lht_details <- list(
  binwidth = 1,
  selex_input = "length",
  maturity_input = "length",
  nseasons = 1,
  nfleets = 1,
  h = 0.7
)

3.4 Instantiate and run LIME

Similar to LB-SPR, if LIME is run with the flag simul set to TRUE, a population-dynamic simulation function is triggered, providing the following extra details for each time step:

• Observed catch-at-length
• Relative observed catch-at-length (each catch is divided by the maximum)
• Standardised age structure of the underlying fished population
• Standardised age structure of the underlying unfished population
• Standardised estimated catch-at-length as a result of applying the estimated selectivity to the estimated fished population

# Find SL50 and SL95 prior
iim_lime_logistic <- lbmstoolbox::LimeLbms$new(
  bio_params,
  exploitation_params,
  catch_data
)
lht_context <- iim_lime_logistic$build_lht_context(extra_lht_details)
result_lime <- iim_lime_logistic$run(lht_context, simul = TRUE)

3.5 Breaking down results

Results are provided in two flavors: i) evaluation where estimates of the model are held and ii) simulation where the aforementioned extra details can be found. Within this section, also the raw output yielded by the simulation function are provided, should you be interested in doing more with it.

In addition, the estimate dataframe provides the confidence intervals of F, SPR and R(Recruitment) . These columns are prefixed by lower and upper, respectively.

result_lime$evaluation$estimates %>%
  head(3)

result_lime$simulation$model_info$catch %>%
  head(3)

result_lime$simulation$model_info$population %>%
  head(3)

4.1 Estimates plot

A quick example on how to plot SPR and its confidence interval is shown below.

estimates <- result_lime$evaluation$estimates
g <- estimates %>%
  ggplot2::ggplot(ggplot2::aes(x = years, y = SPR)) +
  ggplot2::geom_point() +
  ggplot2::geom_line() +
  ggplot2::geom_ribbon(ggplot2::aes(x = years, ymin = lower_spr, ymax = upper_spr, fill = "maroon2", alpha = 0.1)) +
  ggplot2::theme_bw() +
  ggplot2::theme(legend.position = "none")

g

4.2 Simulation plot

Below two different plots are displayed. The first one shows the estimated catch for the estimated fished length structured for year 2015. The second one plots the estimated aged-based fished and unfished populations for the same year.

catch_2015 <- result_lime$simulation$model_info$catch %>%
  dplyr::filter(year == 2015) %>%
  dplyr::select(lengths, exp_catch)

g <- catch_2015 %>%
  ggplot2::ggplot(ggplot2::aes(x = lengths, y = exp_catch)) +
  ggplot2::geom_point() +
  ggplot2::geom_line() +
  ggplot2::xlab("Lengths") +
  ggplot2::ylab("Standardised relative catch")

g

population_2015 <- result_lime$simulation$model_info$population %>%
  dplyr::filter(year == 2015) %>%
  dplyr::select(age, unfished_pop, fished_pop) %>%
  tidyr::pivot_longer(!age, names_to = "variables", values_to = "values")

g <- population_2015 %>%
  ggplot2::ggplot(ggplot2::aes(x = age, y = values, color = variables)) +
  ggplot2::geom_point() +
  ggplot2::geom_line() +
  ggplot2::xlab("Ages") +
  ggplot2::ylab("Standardised relative populations") +
  ggplot2::scale_color_manual(
    name = "Catch Type",
    values = c(
      unfished_pop = "seagreen",
      fished_pop = "tomato"
    )
  )

g