6 Pre-Calculate Growth

Purpose: Precalculate growth to look-up growth rates based on weight, temperature, and p-value (proportion of temperature-adjusted maximum consumption).

Source dependencies

6.1 Set-up

Set parameters for O. mykiss

Code

Constants <- fncReadConstants()
pred.en.dens <- 5900 #predator energy density
oxy <- 13560 #oxygen consumed
pff <- 0.1 #percent indigestible prey
prey.en.dens <- 3500 # see Railsback and Rose 1999, Beauchamp et al. 2007

Set up arrays. Sequences must match the lookup sequences defined in fncGrowthFish(), fncGrowthPossible(), and the IBM simulation loop.

Code

waterTemps <- cbind("pid" = seq(1, length(seq(0.1, 25, 0.1))), "WT" = seq(0.1, 25, 0.1))
pvals   <- seq(0.01, 1.0, 0.01)    # p-value (100 values)
weights <- seq(0.25, 6000, 0.25)   # fish mass (24,000 values)
wt.growth <- array(NA, dim = c(nrow(waterTemps), length(pvals), length(weights))) # dim = c(250 WTs, 100 pvals, 24000 weights)
respiration <- consumption <- wastes <- cmax <- wt.growth

6.2 Calculate growth

Loop through arrays to record growth for each case

Code

for(w in 1:dim(wt.growth)[3]){
  ww <- weights[w]
  for(r in 1:dim(wt.growth)[2]){
    pp <- pvals[r]
    Input <- fncGetBioEParms("cutthroat", pred.en.dens, prey.en.dens, oxy, pff,
                             waterTemps,
                             startweights = rep(ww, nrow(waterTemps)),
                             pvals = rep(pp, nrow(waterTemps)))

    Results <- BioE(Input, Constants) #run BioE code given input and constants
    wt.growth[,r,w]   <- c(Results$Gg_WinBioE)  # growth in g/g/d, standardized by fish weight
    consumption[,r,w] <- c(Results$Consumption)
    wastes[,r,w]      <- c(Results$Egestion + Results$Excretion + Results$S.resp)
    respiration[,r,w] <- c(Results$Respiration)
    cmax[,r,w]        <- c(Results$Consumption_max)

    ## In Joules instead of grams:
    # wt.growth[,r,w]   <- c(Results$Growth_j)
    # consumption[,r,w] <- c(Results$Consumption_j)
    # wastes[,r,w]      <- c(Results$Egestion_j + Results$Excretion_j + Results$Sj.resp)
    # respiration[,r,w] <- c(Results$Respiration_j)
  }
  if (w %% 500 == 0) print(w)
}

Save outputs. Only ‘wt.growth’ is needed for simulations. The others are merely for plotting below.

Code

save("wt.growth",    file = "data/wt.growth.array_pval_cuttCACB.RData")
save("respiration",  file = "data/respiration.array_pval_cuttCACB.RData")
save("wastes",       file = "data/wastes.array_pval_cuttCACB.RData")
save("consumption",  file = "data/consumption_pval_cuttCACB.array.RData")
save("cmax",         file = "data/cmax.array_pval_cuttCACB.RData")

Load back in to plot

Code

load("data/wt.growth.array_pval_sthdCACB.RData")
load("data/consumption_pval_sthdCACB.array.RData")
load("data/wastes.array_pval_sthdCACB.RData")
load("data/respiration.array_pval_sthdCACB.RData")
load("data/cmax.array_pval_sthdCACB.RData")

6.3 Plot output

6.3.1 Growth rate

Plot growth rate by temperature for fish of varying sizes, across the full range of p-values. Line color runs blue (low p) → red (high p).

Code

# Representative mass indices for the new array (step = 0.25 g): 1g→4, 10g→40, 100g→400, 250g→1000, 500g→2000, 1500g→6000
mass_idx <- c(4, 40, 400, 1000, 2000, 6000)
mass_lbl <- c(1, 10, 100, 250, 500, 1500)

map_dfr(seq_along(mass_idx), \(k) {
  map_dfr(seq(1, 100, by = 5), \(pi) {
    tibble(
      weight_g = factor(paste0(mass_lbl[k], " g"), levels = paste0(mass_lbl, " g")),
      pval     = pvals[pi],
      temp     = waterTemps[, "WT"],
      growth   = wt.growth[, pi, mass_idx[k]]
    )
  })
}) |>
  ggplot(aes(x = temp, y = growth, color = pval, group = pval)) +
  geom_line(linewidth = 0.4) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "black") +
  facet_wrap(~ weight_g, ncol = 3) +
  scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") +
  coord_cartesian(ylim = c(-0.06, 0.16)) +
  labs(x = "Water temperature (°C)", y = "Growth rate (g/g/d)") +
  theme_bw() + theme(panel.grid = element_blank())

Plot growth potential by weight under different temperatures (panels) and p-values (line color: blue = low, red = high).

Code

tempseq <- seq(1, length(waterTemps[,"WT"]), by = 45)
w_show  <- which(weights <= 50)  # focus on 0–50 g range

map_dfr(seq_along(tempseq), \(ti) {
  temp_val <- waterTemps[tempseq[ti], "WT"]
  map_dfr(seq(1, 100, by = 5), \(pi) {
    tibble(
      temp_label = factor(paste0(temp_val, " °C"),
                          levels = paste0(waterTemps[tempseq, "WT"], " °C")),
      pval   = pvals[pi],
      weight = weights[w_show],
      growth = wt.growth[tempseq[ti], pi, w_show]
    )
  })
}) |>
  ggplot(aes(x = weight, y = growth, color = pval, group = pval)) +
  geom_line(linewidth = 0.4) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "black") +
  facet_wrap(~ temp_label, ncol = 3) +
  scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") +
  coord_cartesian(ylim = c(-0.05, 0.1)) +
  labs(x = "Weight (g)", y = "Growth rate (g/g/d)") +
  theme_bw() + theme(panel.grid = element_blank())

6.3.2 Maintenance p-value

The maintenance p-value is the minimum proportion of maximum consumption a fish must achieve to maintain positive growth at a given temperature and body size. It increases with body size (as allometric C_max declines) and deviates from its optimum at extreme temperatures (where respiration costs rise relative to consumption capacity). Lines in the optimal-temperature plots above are truncated at each p-value’s maintenance boundary; below we visualise the full surface.

Code

# For every [temperature, weight] cell, find the minimum p-value at which growth > 0.
# Note: as.vector() is column-major (ti varies fast); t() transposes so wi varies fast,
# matching the row order produced by expand_grid(ti, wi).
maint <- apply(wt.growth, c(1, 3), function(gvec) {
  pos <- which(gvec > 0)
  if (length(pos) > 0) pvals[min(pos)] else NA_real_
})

breaks_pv <- seq(0.1, 0.9, by = 0.1)

maint_df_full <- expand_grid(ti = seq_len(nrow(maint)), wi = seq_len(ncol(maint))) |>
  mutate(
    temp       = waterTemps[ti, "WT"],
    weight     = weights[wi],
    maint_pval = as.vector(t(maint))
  )

# Extract contour midpoints in a legible weight range for labelling
contour_data <- ggplot_build(
  ggplot(maint_df_full, aes(x = weight, y = temp, z = maint_pval)) +
    geom_contour(breaks = breaks_pv, na.rm = TRUE)
)$data[[1]]

label_pts <- contour_data |>
  filter(x > 500, x < 2500) |>
  group_by(level) |>
  slice(n() %/% 2) |>
  ungroup() |>
  mutate(label = as.character(round(as.numeric(level), 1)))

maint_df_full |>
  ggplot(aes(x = weight, y = temp, fill = maint_pval)) +
  geom_raster() +
  geom_contour(aes(z = maint_pval), breaks = breaks_pv,
               color = "white", linewidth = 0.4, na.rm = TRUE) +
  geom_label(data = label_pts, aes(x = x, y = y, label = label),
             size = 2.8, linewidth = 0, fill = alpha("white", 0.5),
             color = "grey20", inherit.aes = FALSE) +
  scale_fill_gradientn(
    colors   = hcl.colors(100, "Temps"),
    name     = "Maintenance\np-value",
    limits   = c(0, 1),
    na.value = "grey70"
  ) +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(
    x       = "Fish weight (g)",
    y       = "Water temperature (°C)",
    title   = "Minimum p-value required for positive growth",
    caption = "Grey: growth impossible even at p = 1.0."
  ) +
  theme_bw()

Plot optimal growth temperature and maximum growth rate by fish weight across a range of p-values (blue = low, red = high). Each line is set to NA for weights at which that p-value cannot sustain positive growth at any temperature — i.e., where consumption falls below the maintenance ration. Consequently, line endpoints trace the maintenance p-value boundary: the minimum p-value required for zero net growth at a given body size. Lines are shorter at lower p-values because smaller fish are already below the maintenance threshold, and the boundary shifts to larger sizes as p-value increases.

Code

optgrowth_df <- map_dfr(seq(1, 100, by = 5), \(pi) {
  mat    <- wt.growth[, pi, ]                          # 250 temp × 24000 weight matrix
  best_t <- apply(mat, 2, which.max)                   # temperature index of max growth, per weight
  max_g  <- mat[cbind(best_t, seq_along(best_t))]
  tibble(
    pval      = pvals[pi],
    weight    = weights,
    # NA where max growth is negative: optimal temp is undefined when no positive growth is possible
    opttemp   = if_else(max_g > 0, waterTemps[best_t, "WT"], NA_real_),
    maxgrowth = if_else(max_g > 0, max_g,                    NA_real_)
  )
})

ggplot(optgrowth_df, aes(x = weight, y = opttemp, color = pval, group = pval)) +
  geom_line(linewidth = 0.4, na.rm = TRUE) +
  scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") +
  labs(x = "Fish weight (g)", y = "Optimal temperature for growth (°C)") +
  theme_bw() + theme(panel.grid = element_blank()) + 
  coord_cartesian(xlim = c(0, 2000))

Code

ggplot(optgrowth_df, aes(x = weight, y = maxgrowth, color = pval, group = pval)) +
  geom_line(linewidth = 0.4, na.rm = TRUE) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "black") +
  scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") +
  labs(x = "Fish weight (g)", y = "Maximum growth rate (g/g/d)") +
  theme_bw() + theme(panel.grid = element_blank()) + 
  coord_cartesian(xlim = c(0, 2000))

6.3.3 Consumption

Consumption by temperature for representative fish sizes, across the full range of p-values (blue = low, red = high):

Code

map_dfr(seq_along(mass_idx), \(k) {
  map_dfr(seq(1, 100, by = 5), \(pi) {
    tibble(
      weight_g = factor(paste0(mass_lbl[k], " g"), levels = paste0(mass_lbl, " g")),
      pval     = pvals[pi],
      temp     = waterTemps[, "WT"],
      cons     = consumption[, pi, mass_idx[k]]
    )
  })
}) |>
  ggplot(aes(x = temp, y = cons, color = pval, group = pval)) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "black") +
  geom_line(linewidth = 0.4) +
  facet_wrap(~ weight_g, ncol = 3) +
  scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") +
  coord_cartesian(ylim = c(0, 0.6)) +
  labs(x = "Water temperature (°C)", y = "Consumption (g/g/d)") +
  theme_bw() + theme(panel.grid = element_blank())

6.3.4 Energy budget

Create multi-panel energy budget plots for different sized fish: Consumption = metabolism + wastes + growth

Scope for growth is thus the difference between Consumption and (metabolism + wastes), i.e., the space between the Consumption and Wastes lines. Shown at p = 0.5 (index 50):

Code

budget_cols <- c("Consumption" = "#2166ac", "Wastes" = "#1a9641", "Respiration" = "#d73027")

map_dfr(seq_along(mass_idx), \(k) {
  mi   <- mass_idx[k]
  temp <- waterTemps[, "WT"]
  bind_rows(
    tibble(weight_g = paste0(mass_lbl[k], " g"), component = "Consumption", temp = temp, rate = consumption[, 50, mi]),
    tibble(weight_g = paste0(mass_lbl[k], " g"), component = "Wastes",      temp = temp, rate = wastes[,      50, mi]),
    tibble(weight_g = paste0(mass_lbl[k], " g"), component = "Respiration", temp = temp, rate = respiration[, 50, mi])
  )
}) |>
  mutate(
    weight_g  = factor(weight_g,  levels = paste0(mass_lbl, " g")),
    component = factor(component, levels = names(budget_cols))
  ) |>
  ggplot(aes(x = temp, y = rate, color = component)) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "black") +
  geom_line(linewidth = 0.6) +
  facet_wrap(~ weight_g, ncol = 3) +
  scale_color_manual(values = budget_cols, name = NULL) +
  coord_cartesian(ylim = c(0, 0.3)) +
  labs(x = "Water temperature (°C)", y = "Rate (g/g/d)") +
  theme_bw() +
  theme(legend.position = "bottom", panel.grid = element_blank())

Create single panel ‘growth banana’ as in FB4 documentation: shaded region is the scope for growth (p = 0.5, 500g fish):

Code

mi <- 2000  # index for 500g fish

tibble(
  temp        = waterTemps[, "WT"],
  consumption = consumption[, 50, mi],
  wastes      = wastes[,      50, mi],
  respiration = respiration[, 50, mi]
) |>
  ggplot(aes(x = temp)) +
  geom_ribbon(aes(ymin = respiration, ymax = wastes), fill = "grey80") +
  geom_line(aes(y = consumption, color = "Consumption"), linewidth = 0.8) +
  geom_line(aes(y = wastes,      color = "Wastes"),      linewidth = 0.8) +
  geom_line(aes(y = respiration, color = "Respiration"), linewidth = 0.8) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "grey60") +
  scale_color_manual(values = budget_cols, name = NULL) +
  coord_cartesian(ylim = c(0, 0.05)) +
  labs(x = "Water temperature (°C)", y = "Rate (g/g/d)",
       title = "500 g fish, p = 0.5",
       subtitle = "Shaded = scope for growth") +
  theme_bw() +
  theme(legend.position = "bottom", panel.grid = element_blank())

--- title: "Pre-Calculate Growth" --- ```{r include=FALSE} library(tidyverse) library(ggpubr) library(egg) ``` **Purpose:** Precalculate growth to look-up growth rates based on weight, temperature, and p-value (proportion of temperature-adjusted maximum consumption). Source dependencies ```{r include=FALSE} #| cache: false source("Habitat.R") source("Functions.R") ``` ## Set-up Set parameters for *O. mykiss* ```{r} Constants <- fncReadConstants() pred.en.dens <- 5900 #predator energy density oxy <- 13560 #oxygen consumed pff <- 0.1 #percent indigestible prey prey.en.dens <- 3500 # see Railsback and Rose 1999, Beauchamp et al. 2007 ``` Set up arrays. Sequences must match the lookup sequences defined in `fncGrowthFish()`, `fncGrowthPossible()`, and the IBM simulation loop. ```{r} #| cache: false waterTemps <- cbind("pid" = seq(1, length(seq(0.1, 25, 0.1))), "WT" = seq(0.1, 25, 0.1)) pvals <- seq(0.01, 1.0, 0.01) # p-value (100 values) weights <- seq(0.25, 6000, 0.25) # fish mass (24,000 values) wt.growth <- array(NA, dim = c(nrow(waterTemps), length(pvals), length(weights))) # dim = c(250 WTs, 100 pvals, 24000 weights) respiration <- consumption <- wastes <- cmax <- wt.growth ``` ## Calculate growth Loop through arrays to record growth for each case ```{r eval=FALSE} for(w in 1:dim(wt.growth)[3]){ ww <- weights[w] for(r in 1:dim(wt.growth)[2]){ pp <- pvals[r] Input <- fncGetBioEParms("cutthroat", pred.en.dens, prey.en.dens, oxy, pff, waterTemps, startweights = rep(ww, nrow(waterTemps)), pvals = rep(pp, nrow(waterTemps))) Results <- BioE(Input, Constants) #run BioE code given input and constants wt.growth[,r,w] <- c(Results$Gg_WinBioE) # growth in g/g/d, standardized by fish weight consumption[,r,w] <- c(Results$Consumption) wastes[,r,w] <- c(Results$Egestion + Results$Excretion + Results$S.resp) respiration[,r,w] <- c(Results$Respiration) cmax[,r,w] <- c(Results$Consumption_max) ## In Joules instead of grams: # wt.growth[,r,w] <- c(Results$Growth_j) # consumption[,r,w] <- c(Results$Consumption_j) # wastes[,r,w] <- c(Results$Egestion_j + Results$Excretion_j + Results$Sj.resp) # respiration[,r,w] <- c(Results$Respiration_j) } if (w %% 500 == 0) print(w) } ``` Save outputs. Only 'wt.growth' is needed for simulations. The others are merely for plotting below. ```{r eval=FALSE} save("wt.growth", file = "data/wt.growth.array_pval_cuttCACB.RData") save("respiration", file = "data/respiration.array_pval_cuttCACB.RData") save("wastes", file = "data/wastes.array_pval_cuttCACB.RData") save("consumption", file = "data/consumption_pval_cuttCACB.array.RData") save("cmax", file = "data/cmax.array_pval_cuttCACB.RData") ``` Load back in to plot ```{r} #| cache: false load("data/wt.growth.array_pval_sthdCACB.RData") load("data/consumption_pval_sthdCACB.array.RData") load("data/wastes.array_pval_sthdCACB.RData") load("data/respiration.array_pval_sthdCACB.RData") load("data/cmax.array_pval_sthdCACB.RData") ``` ## Plot output ### Growth rate Plot growth rate by temperature for fish of varying sizes, across the full range of p-values. Line color runs blue (low p) → red (high p). ```{r fig.width=7, fig.height=6} # Representative mass indices for the new array (step = 0.25 g): 1g→4, 10g→40, 100g→400, 250g→1000, 500g→2000, 1500g→6000 mass_idx <- c(4, 40, 400, 1000, 2000, 6000) mass_lbl <- c(1, 10, 100, 250, 500, 1500) map_dfr(seq_along(mass_idx), \(k) { map_dfr(seq(1, 100, by = 5), \(pi) { tibble( weight_g = factor(paste0(mass_lbl[k], " g"), levels = paste0(mass_lbl, " g")), pval = pvals[pi], temp = waterTemps[, "WT"], growth = wt.growth[, pi, mass_idx[k]] ) }) }) |> ggplot(aes(x = temp, y = growth, color = pval, group = pval)) + geom_line(linewidth = 0.4) + geom_hline(yintercept = 0, linetype = "dashed", color = "black") + facet_wrap(~ weight_g, ncol = 3) + scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") + coord_cartesian(ylim = c(-0.06, 0.16)) + labs(x = "Water temperature (°C)", y = "Growth rate (g/g/d)") + theme_bw() + theme(panel.grid = element_blank()) ``` Plot growth potential by weight under different temperatures (panels) and p-values (line color: blue = low, red = high). ```{r fig.width=7, fig.height=6} tempseq <- seq(1, length(waterTemps[,"WT"]), by = 45) w_show <- which(weights <= 50) # focus on 0–50 g range map_dfr(seq_along(tempseq), \(ti) { temp_val <- waterTemps[tempseq[ti], "WT"] map_dfr(seq(1, 100, by = 5), \(pi) { tibble( temp_label = factor(paste0(temp_val, " °C"), levels = paste0(waterTemps[tempseq, "WT"], " °C")), pval = pvals[pi], weight = weights[w_show], growth = wt.growth[tempseq[ti], pi, w_show] ) }) }) |> ggplot(aes(x = weight, y = growth, color = pval, group = pval)) + geom_line(linewidth = 0.4) + geom_hline(yintercept = 0, linetype = "dashed", color = "black") + facet_wrap(~ temp_label, ncol = 3) + scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") + coord_cartesian(ylim = c(-0.05, 0.1)) + labs(x = "Weight (g)", y = "Growth rate (g/g/d)") + theme_bw() + theme(panel.grid = element_blank()) ``` ### Maintenance p-value The **maintenance p-value** is the minimum proportion of maximum consumption a fish must achieve to maintain positive growth at a given temperature and body size. It increases with body size (as allometric C~max~ declines) and deviates from its optimum at extreme temperatures (where respiration costs rise relative to consumption capacity). Lines in the optimal-temperature plots above are truncated at each p-value's maintenance boundary; below we visualise the full surface. ```{r fig.width=7, fig.height=5} # For every [temperature, weight] cell, find the minimum p-value at which growth > 0. # Note: as.vector() is column-major (ti varies fast); t() transposes so wi varies fast, # matching the row order produced by expand_grid(ti, wi). maint <- apply(wt.growth, c(1, 3), function(gvec) { pos <- which(gvec > 0) if (length(pos) > 0) pvals[min(pos)] else NA_real_ }) breaks_pv <- seq(0.1, 0.9, by = 0.1) maint_df_full <- expand_grid(ti = seq_len(nrow(maint)), wi = seq_len(ncol(maint))) |> mutate( temp = waterTemps[ti, "WT"], weight = weights[wi], maint_pval = as.vector(t(maint)) ) # Extract contour midpoints in a legible weight range for labelling contour_data <- ggplot_build( ggplot(maint_df_full, aes(x = weight, y = temp, z = maint_pval)) + geom_contour(breaks = breaks_pv, na.rm = TRUE) )$data[[1]] label_pts <- contour_data |> filter(x > 500, x < 2500) |> group_by(level) |> slice(n() %/% 2) |> ungroup() |> mutate(label = as.character(round(as.numeric(level), 1))) maint_df_full |> ggplot(aes(x = weight, y = temp, fill = maint_pval)) + geom_raster() + geom_contour(aes(z = maint_pval), breaks = breaks_pv, color = "white", linewidth = 0.4, na.rm = TRUE) + geom_label(data = label_pts, aes(x = x, y = y, label = label), size = 2.8, linewidth = 0, fill = alpha("white", 0.5), color = "grey20", inherit.aes = FALSE) + scale_fill_gradientn( colors = hcl.colors(100, "Temps"), name = "Maintenance\np-value", limits = c(0, 1), na.value = "grey70" ) + scale_x_continuous(expand = c(0, 0)) + scale_y_continuous(expand = c(0, 0)) + labs( x = "Fish weight (g)", y = "Water temperature (°C)", title = "Minimum p-value required for positive growth", caption = "Grey: growth impossible even at p = 1.0." ) + theme_bw() ``` Plot optimal growth temperature and maximum growth rate by fish weight across a range of p-values (blue = low, red = high). Each line is set to `NA` for weights at which that p-value cannot sustain positive growth at any temperature — i.e., where consumption falls below the maintenance ration. Consequently, line endpoints trace the **maintenance p-value boundary**: the minimum p-value required for zero net growth at a given body size. Lines are shorter at lower p-values because smaller fish are already below the maintenance threshold, and the boundary shifts to larger sizes as p-value increases. ```{r fig.width=7, fig.height=5} optgrowth_df <- map_dfr(seq(1, 100, by = 5), \(pi) { mat <- wt.growth[, pi, ] # 250 temp × 24000 weight matrix best_t <- apply(mat, 2, which.max) # temperature index of max growth, per weight max_g <- mat[cbind(best_t, seq_along(best_t))] tibble( pval = pvals[pi], weight = weights, # NA where max growth is negative: optimal temp is undefined when no positive growth is possible opttemp = if_else(max_g > 0, waterTemps[best_t, "WT"], NA_real_), maxgrowth = if_else(max_g > 0, max_g, NA_real_) ) }) ggplot(optgrowth_df, aes(x = weight, y = opttemp, color = pval, group = pval)) + geom_line(linewidth = 0.4, na.rm = TRUE) + scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") + labs(x = "Fish weight (g)", y = "Optimal temperature for growth (°C)") + theme_bw() + theme(panel.grid = element_blank()) + coord_cartesian(xlim = c(0, 2000)) ggplot(optgrowth_df, aes(x = weight, y = maxgrowth, color = pval, group = pval)) + geom_line(linewidth = 0.4, na.rm = TRUE) + geom_hline(yintercept = 0, linetype = "dashed", color = "black") + scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") + labs(x = "Fish weight (g)", y = "Maximum growth rate (g/g/d)") + theme_bw() + theme(panel.grid = element_blank()) + coord_cartesian(xlim = c(0, 2000)) ``` ### Consumption Consumption by temperature for representative fish sizes, across the full range of p-values (blue = low, red = high): ```{r fig.width=7, fig.height=6} map_dfr(seq_along(mass_idx), \(k) { map_dfr(seq(1, 100, by = 5), \(pi) { tibble( weight_g = factor(paste0(mass_lbl[k], " g"), levels = paste0(mass_lbl, " g")), pval = pvals[pi], temp = waterTemps[, "WT"], cons = consumption[, pi, mass_idx[k]] ) }) }) |> ggplot(aes(x = temp, y = cons, color = pval, group = pval)) + geom_hline(yintercept = 0, linetype = "dashed", color = "black") + geom_line(linewidth = 0.4) + facet_wrap(~ weight_g, ncol = 3) + scale_color_gradientn(colors = hcl.colors(100, "Temps"), name = "P-value") + coord_cartesian(ylim = c(0, 0.6)) + labs(x = "Water temperature (°C)", y = "Consumption (g/g/d)") + theme_bw() + theme(panel.grid = element_blank()) ``` ### Energy budget Create multi-panel energy budget plots for different sized fish: *Consumption* = *metabolism* + *wastes* + *growth* Scope for growth is thus the difference between *Consumption* and (*metabolism* + *wastes*), i.e., the space between the Consumption and Wastes lines. Shown at p = 0.5 (index 50): ```{r fig.width=7, fig.height=6} budget_cols <- c("Consumption" = "#2166ac", "Wastes" = "#1a9641", "Respiration" = "#d73027") map_dfr(seq_along(mass_idx), \(k) { mi <- mass_idx[k] temp <- waterTemps[, "WT"] bind_rows( tibble(weight_g = paste0(mass_lbl[k], " g"), component = "Consumption", temp = temp, rate = consumption[, 50, mi]), tibble(weight_g = paste0(mass_lbl[k], " g"), component = "Wastes", temp = temp, rate = wastes[, 50, mi]), tibble(weight_g = paste0(mass_lbl[k], " g"), component = "Respiration", temp = temp, rate = respiration[, 50, mi]) ) }) |> mutate( weight_g = factor(weight_g, levels = paste0(mass_lbl, " g")), component = factor(component, levels = names(budget_cols)) ) |> ggplot(aes(x = temp, y = rate, color = component)) + geom_hline(yintercept = 0, linetype = "dashed", color = "black") + geom_line(linewidth = 0.6) + facet_wrap(~ weight_g, ncol = 3) + scale_color_manual(values = budget_cols, name = NULL) + coord_cartesian(ylim = c(0, 0.3)) + labs(x = "Water temperature (°C)", y = "Rate (g/g/d)") + theme_bw() + theme(legend.position = "bottom", panel.grid = element_blank()) ``` Create single panel 'growth banana' as in FB4 documentation: shaded region is the scope for growth (p = 0.5, 500g fish): ```{r fig.width=5, fig.height=4} mi <- 2000 # index for 500g fish tibble( temp = waterTemps[, "WT"], consumption = consumption[, 50, mi], wastes = wastes[, 50, mi], respiration = respiration[, 50, mi] ) |> ggplot(aes(x = temp)) + geom_ribbon(aes(ymin = respiration, ymax = wastes), fill = "grey80") + geom_line(aes(y = consumption, color = "Consumption"), linewidth = 0.8) + geom_line(aes(y = wastes, color = "Wastes"), linewidth = 0.8) + geom_line(aes(y = respiration, color = "Respiration"), linewidth = 0.8) + geom_hline(yintercept = 0, linetype = "dashed", color = "grey60") + scale_color_manual(values = budget_cols, name = NULL) + coord_cartesian(ylim = c(0, 0.05)) + labs(x = "Water temperature (°C)", y = "Rate (g/g/d)", title = "500 g fish, p = 0.5", subtitle = "Shaded = scope for growth") + theme_bw() + theme(legend.position = "bottom", panel.grid = element_blank()) ```