conditional_lambda.qmd

# Conditional effect of covariates {#sec-cond-lambda}

In this chapter, we assessed the conditional effects of each covariate on the population growth rate ($\lambda$) for each species.
Specifically, we quantified how $\lambda$ varies with changes in competition intensity for both conspecific and heterospecific individuals.
Furthermore, we examined how $\lambda$ changes in response to variations in mean annual temperature and mean annual precipitation, spanning the range from the minimum to maximum observed values in the dataset.
This analysis is similar to the sensitivity analysis discussed in @sec-sensAnalysis.
However, due to the larger number of conditions for each covariate, we performed this analysis using only 50 replicates from the posterior distribution of the parameters.

For the competition effect analysis, we maintained temperature and precipitation at the optimal conditions defined by the average of the optimal climate conditions among the growth, survival, and recruitment models.
When assessing the effect of conspecific competition, heterospecific competition was set to null.
Conversely, when evaluating the effect of heterospecific competition, the conspecific competition was defined as a small population size of $N = 0.1$.

We evaluated the climate effect under two competition conditions: low competition, where conspecific population size was set to $N = 0.1$, and high conspecific competition, where population size was established at the 99th percentile distribution of plot basal area experienced by the species in the dataset.
When analyzing temperature, precipitation was held at its optimal condition, and vice versa.

```{r,include=FALSE,echo=FALSE}
Echo=FALSE
Eval=TRUE
Cache=FALSE
Warng=FALSE
Msg=FALSE
library(tidyverse)
library(ggdist)
library(ggpubr)
library(ggrepel)
library(ggiraph)
```

```{r loadPars,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
data_path <- readLines('_data.path')
pars_path <- file.path(data_path, 'output_sim_processed')

## Species if info
spIds <- read_csv(
  file.path(
    data_path, 'species_id.csv'
  )
) |>
mutate(
  shade = factor(shade, levels = c('tolerant', 'intermediate', 'intolerant')),
  shade_sylvics = factor(shade_sylvics, levels = c('very-tolerant',
                                            'tolerant',
                                            'intermediate',
                                            'intolerant',
                                            'very-intolerant'
                                            )),
  succession = factor(succession, levels = c('pioneer',
                                              'intermediate',
                                              'climax'))
) |>
filter(sp_to_analyze)

file_url <- 'https://github.com/willvieira/forest-IPM/raw/master/simulations/marginal_lambda/output_processed/lambdas.RDS'

lambdas <- readRDS(gzcon(url(file_url))) |>
  filter(species_id %in% spIds$species_id_old)

# load data to unscale climate variables and function to scale climate back to original range
clim_scaleRange <- readRDS(file.path(data_path, 'climate_scaleRange.RDS')) |>
  bind_cols()

unscaleClim <- function(
  value,
  # if value is temp or prec
  clim,
  # temp and prec range are vectors of format [min, max]
  temp_rg = clim_scaleRange$bio_01_mean,
  prec_rg = clim_scaleRange$bio_12_mean
) {
  if(clim == 'temp') {
    return( value * (temp_rg[2] - temp_rg[1]) + temp_rg[1] )
  }else if(clim == 'prec') {
    return( value * (prec_rg[2] - prec_rg[1]) + prec_rg[1] )
  } else{
    stop('Clim must be either `temp` or `prec` character.')
  }
}
```

## Competition effect

```{r lambdaComp,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
#| label: fig-lambdaComp
#| fig-width: 8
#| fig-height: 4.5
#| fig-cap: "The Average and 90% confidence interval values for the population growth rate ($\\lambda$) as a function of conspecific (left panel) and heterospecific (right panel) competition intensity."

lambdas |>
  filter(sim == 'competition') |>
  # return comp value back to numeric as climate sim got out
  mutate(comp = as.numeric(comp)) |>
  mutate(
    lambda = log(lambda),
    var = case_match(
      var,
      'cons' ~ 'Conspecific',
      'het' ~ 'Heterospecific'
    )
  ) |>
  filter(species_id != '18032ABIBAL') |>
  left_join(
    spIds,
    by = c('species_id' = 'species_id_old')
  ) |>
  group_by(species_name, var, comp) |>
  reframe(
    mean_lambda = mean(lambda),
    sd_lambda = sd(lambda),
    ci_9 = mean_lambda + qt( c(0.9), n() - 1) * sd_lambda,
    ci_1 = mean_lambda + qt( c(0.1), n() - 1) * sd_lambda
  ) |>
  ggplot() +
  aes(comp, mean_lambda) +
  geom_ribbon_interactive(aes(ymin = ci_1, ymax = ci_9), alpha = 0.3,color=NA) +
  geom_line_interactive() +
  aes(tooltip = species_name, data_id = species_name) +
  facet_wrap(~var) +
  geom_hline(yintercept = 0, linetype = 2, alpha = 0.5) +
  theme_classic() +
  labs(
    x = 'Plot basal area (m2/ha)',
    y = expression('ln('~lambda~')')
  ) +
  theme(legend.position = 'none') ->
p1

tooltip_css <- "background-color:#fc8d59;padding:5px;border-radius:3px;font-style:italic;"

girafe(
  ggobj = p1,
  options = list(
    opts_tooltip(css = tooltip_css, opacity = 1),
    opts_hover_inv(css = "opacity:0.1;"),
    opts_hover(css = "stroke-width:2.5px;"),
    opts_sizing(width = 1),
    opts_toolbar(position = 'top', saveaspng = FALSE),
    opts_zoom(max = 5)
  )
)
```


## Climate effect

```{r lambdaClimData,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
lambdas |>
  filter(species_id %in% spIds$species_id_old) |>
  filter(sim == 'climate') |>
  mutate(
    var = case_match(
      var,
      'temp' ~ 'Temperature',
      'prec' ~ 'Precipitation'
    ),
    comp = case_match(
      comp,
      'high' ~ 'High competition',
      'low' ~ 'Low competition'
    ),
    comp = factor(comp, levels = c('Low competition', 'High competition'))
  ) |>
  filter(species_id != '18032ABIBAL') |>
  left_join(
    spIds,
    by = c('species_id' = 'species_id_old')
  ) |>
  group_by(species_name, var, comp, clim) |>
  reframe(
    mean_lambda = mean(log(lambda)),
    sd_lambda = sd(lambda),
    ci_9 = mean_lambda + qt( c(0.9), n() - 1) * sd_lambda,
    ci_1 = mean_lambda + qt( c(0.1), n() - 1) * sd_lambda
  ) ->
clim_dt
```


### Mean annual temperature

```{r lambdaTempplot,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
#| label: fig-lambdaTempplot
#| fig-width: 8
#| fig-height: 4.5
#| fig-cap: "The Average and 90% confidence interval values for the population growth rate ($\\lambda$) as a function of mean annual temperature for low (left panel) and high (right panel) competition intensity."

clim_dt |>
  filter(var == 'Temperature') |>
  mutate(
    clim = unscaleClim(clim, 'temp')
  ) |>
  ggplot() +
  aes(clim, mean_lambda) +
  geom_ribbon_interactive(aes(ymin = ci_1, ymax = ci_9), alpha = 0.3,color=NA) +
  geom_line_interactive() +
  aes(tooltip = species_name, data_id = species_name) +
  facet_grid(~comp) +
  geom_hline(yintercept = 0, linetype = 2, alpha = 0.5) +
  theme_classic() +
  labs(
    x = 'Mean annual temperature',
    y = expression('ln('~lambda~')')
  ) +
  theme(legend.position = 'none') +
  ylim(-0.05, 0.11) ->
p_temp

girafe(
  ggobj = p_temp,
  options = list(
    opts_tooltip(css = tooltip_css, opacity = 1),
    opts_hover_inv(css = "opacity:0.1;"),
    opts_hover(css = "stroke-width:2.5px;"),
    opts_sizing(width = 1),
    opts_toolbar(position = 'top', saveaspng = FALSE),
    opts_zoom(max = 5)
  )
)
```

### Mean annual precipitation

```{r lambdaPrec,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
#| label: fig-lambdaPrec
#| fig-width: 8
#| fig-height: 4.5
#| fig-cap: "The Average and 90% confidence interval values for the population growth rate ($\\lambda$) as a function of mean annual precipitation for low (left panel) and high (right panel) competition intensity."

clim_dt |>
  filter(var == 'Precipitation') |>
  mutate(
    clim = unscaleClim(clim, 'prec')
  ) |>
  ggplot() +
  aes(clim, mean_lambda) +
  geom_ribbon_interactive(aes(ymin = ci_1, ymax = ci_9), alpha = 0.3,color=NA) +
  geom_line_interactive() +
  aes(tooltip = species_name, data_id = species_name) +
  facet_grid(~comp) +
  geom_hline(yintercept = 0, linetype = 2, alpha = 0.5) +
  theme_classic() +
  labs(
    x = 'Mean annual precipitation',
    y = expression('ln('~lambda~')')
  ) +
  theme(legend.position = 'none')  +
  ylim(-0.05, 0.11)->
p_prec

girafe(
  ggobj = p_prec,
  options = list(
    opts_tooltip(css = tooltip_css, opacity = 1),
    opts_hover_inv(css = "opacity:0.1;"),
    opts_hover(css = "stroke-width:2.5px;"),
    opts_sizing(width = 1),
    opts_toolbar(position = 'top', saveaspng = FALSE),
    opts_zoom(max = 5)
  )
)
```