1. Load libraries

library(tidyverse)
library(readxl)
library(dplyr)
library(plyr)
library(openxlsx)
library(pbkrtest)
library(psycho)
library(pander)
library(ggpubr)
library(knitr)
library(kableExtra) # For Markdown tables
library(report) # textual summaries of analysis

library(lme4) # to fit the linear mixed effect model
library(lmerTest)
library(fitdistrplus) # to fit probability distributions
library(emmeans) # to compare contrasts
library(bbmle) # for AICtab
library(sjPlot) # for plot_model function
library(DHARMa) # for GLMM model diagnostics

knitr::opts_chunk$set(echo = TRUE)

2. Load data

  # Select trait
    trait <- "AerobicScope"

  # Set working directory of executing R. script
    setwd(paste("C:/Users/oelle/Documents/Meine Dokumente/Research/Projects/Project_RockLobster/Temperature acclimation/Aerobic scope/Statistics/LinearMixedEffectModelling/", trait, "/", sep = ""))
  
  # Load tidy raw data in long format
    mo2_data_long <- read.csv("C:/Users/oelle/Documents/Meine Dokumente/Research/Projects/Project_RockLobster/Temperature acclimation/Aerobic scope/Statistics/MO2_data_Tidy_RawData_long.csv")

3. Process data

  # Shorten column names
    names(mo2_data_long)[c(5,6)] <- c("AccTemp", "ExpTemp")
  
  # Define fixed effects as factors
    mo2_data_long$AntTag <- as.factor(mo2_data_long$AntTag)
    mo2_data_long$Species <- as.factor(mo2_data_long$Species)
    mo2_data_long$AccTemp <- as.factor(mo2_data_long$AccTemp)
    mo2_data_long$ExpTemp <- as.factor(mo2_data_long$ExpTemp)
    mo2_data_long$Sex <- as.factor(mo2_data_long$Sex)

  # Subset data by trait
    sub_trait <- subset(mo2_data_long, Trait == trait)

4. Find best probability distribution of data to check assumptions for linear model

Find best distribution fit using fitdistrplus package

  # Plot data versus a range of distrubutions
    descdist(sub_trait$value, boot = 1000)

## summary statistics
## ------
## min:  16.18   max:  121.76 
## median:  84.69 
## mean:  82.43444 
## estimated sd:  20.76008 
## estimated skewness:  -0.7854203 
## estimated kurtosis:  3.608739
  # Fit various distributions
    nd <- fitdist(sub_trait$value, "norm")
## $start.arg
## $start.arg$mean
## [1] 82.43444
## 
## $start.arg$sd
## [1] 20.66374
## 
## 
## $fix.arg
## NULL
    gd <- fitdist(sub_trait$value, "gamma")
## $start.arg
## $start.arg$shape
## [1] 15.91474
## 
## $start.arg$rate
## [1] 0.1930593
## 
## 
## $fix.arg
## NULL
    wd <- fitdist(sub_trait$value, "weibull")
## $start.arg
## $start.arg$shape
## [1] 3.702822
## 
## $start.arg$scale
## [1] 92.17977
## 
## 
## $fix.arg
## NULL
    lnd <- fitdist(sub_trait$value, "lnorm")
## $start.arg
## $start.arg$meanlog
## [1] 4.369264
## 
## $start.arg$sdlog
## [1] 0.3225733
## 
## 
## $fix.arg
## NULL
  # Plot distributions for the data
    plot.legend <- c("Normal", "gamma", "Weibull", "LogNormal")
    denscomp(list(nd, gd, wd, lnd), legendtext = plot.legend)

  # QQ plot
    qqcomp(list(nd, gd, wd, lnd), legendtext = plot.legend)

  # Perform goodness of fit test to select best distribution
    gofstat(list(nd, gd, wd, lnd), fitnames = c("Normal", "gamma", "Weibull", "LogNormal"))
## Goodness-of-fit statistics
##                                  Normal     gamma    Weibull LogNormal
## Kolmogorov-Smirnov statistic 0.08510534 0.1354993 0.06386793 0.1597644
## Cramer-von Mises statistic   0.17227356 0.5082014 0.08967312 0.7525458
## Anderson-Darling statistic   1.11153080 3.0383902 0.66887090 4.4307737
## 
## Goodness-of-fit criteria
##                                  Normal    gamma  Weibull LogNormal
## Akaike's Information Criterion 964.6209 990.1547 959.4582  1009.864
## Bayesian Information Criterion 969.9852 995.5190 964.8224  1015.228

–> Anderson-Darling statistics gives good measure for fit for both middle and tail of distribution

–> Data fit best to a normal or weibull distribution

5. Plot data

# Gplot
   ggplot(sub_trait, aes(x = ExpTemp, y = value, fill = as.factor(AccTemp), alpha = .5)) +
        geom_boxplot(outlier.size = 0) +
        ylab(trait) +
        facet_wrap(~ Species, scales = "free")+
        geom_point(pch = 21, position = position_jitterdodge(seed = 100))+
        geom_text(aes(label=AntTag, color = as.factor(AccTemp)), alpha = .8, position = position_jitterdodge(seed = 100))

# Line Plot comparing both species
  ggline(sub_trait, x = "ExpTemp", y = "value", 
      add = c("mean_ci", "jitter"),              # Add mean_se and jitter points
      # add.params = list(size = 0.7),             # Add point size
      # label = "AntTag",             # Add point labels
      # #label.select = list(top.up = 2),           # show only labels for the top 2 points
      # font.label = list(color = "Species"),          # Color labels by .y., here gene names
      # repel = TRUE,                              # Use repel to avoid labels overplotting
      color = "Species", 
      palette = "jco")

6. Summary statistics

By species

# Summary statistics
  substrait_stats <- ddply(sub_trait, c("Species"), summarise,
                  mean = mean(value, na.rm = TRUE),
                  n = length(value),
                  sd = sd(value, na.rm = TRUE),
                  ci = qt(0.975, n) * sd / sqrt(n),
                  lower_ci = mean-ci, 
                  upper_ci = mean+ci,
                  min = min(value),
                  max = max(value))
   
# Round values
  substrait_stats <- substrait_stats %>% mutate_if(is.numeric, round, digit = 3)
   
# Display results
  substrait_stats %>% kbl(digits = 1, caption = trait) %>%  kable_classic()
AerobicScope
Species mean n sd ci lower_ci upper_ci min max
Jasus edwardsii 75.6 54 19.5 5.3 70.3 81.0 23.7 120.5
Sagmariasus verreauxi 89.2 54 19.9 5.4 83.8 94.6 16.2 121.8

By species and experimental temperature

# Summary statistics
  substrait_stats <- ddply(sub_trait, c("Species", "ExpTemp"), summarise,
                  mean = mean(value, na.rm = TRUE),
                  n = length(value),
                  sd = sd(value, na.rm = TRUE),
                  ci = qt(0.975, n) * sd / sqrt(n),
                  lower_ci = mean-ci, 
                  upper_ci = mean+ci,
                  min = min(value),
                  max = max(value))
   
# Round values
  substrait_stats <- substrait_stats %>% mutate_if(is.numeric, round, digit = 3)
   
# Display results
  substrait_stats %>% kbl(digits = 1, caption = trait) %>%  kable_classic()
AerobicScope
Species ExpTemp mean n sd ci lower_ci upper_ci min max
Jasus edwardsii 14 74.7 18 16.0 7.9 66.8 82.7 44.3 101.3
Jasus edwardsii 17.5 75.4 18 24.5 12.1 63.2 87.5 23.7 120.5
Jasus edwardsii 21.5 76.8 18 18.2 9.0 67.8 85.8 32.7 102.2
Sagmariasus verreauxi 14 81.3 18 14.9 7.4 73.9 88.7 51.2 105.6
Sagmariasus verreauxi 17.5 92.3 18 18.8 9.3 83.0 101.6 34.6 113.0
Sagmariasus verreauxi 21.5 94.0 18 23.5 11.6 82.4 105.7 16.2 121.8

7. Linear mixed effect modelling

7.A Find best model

Fit the most complex model with all meaningful fixed factors

Animal ID (AntTag) as random factor

# REML has to be put to FALSE as models can only be compared using ML
  
  # Start with the most complex model
    complex_model <- lmer(value ~ ExpTemp * 
                            AccTemp * 
                            Species + 
                            Sex +
                            Weight_g +
                            (1|AntTag), data = sub_trait, REML = FALSE)

  # Model summary
    anova(complex_model)
## Type III Analysis of Variance Table with Satterthwaite's method
##                          Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## ExpTemp                  613.03  306.51     2 71.161  2.3141 0.106251   
## AccTemp                  230.44  115.22     2 38.252  0.8699 0.427127   
## Species                 1311.38 1311.38     1 38.414  9.9006 0.003187 **
## Sex                      127.91  127.91     1 39.627  0.9657 0.331718   
## Weight_g                 545.48  545.48     1 43.566  4.1183 0.048560 * 
## ExpTemp:AccTemp         2222.29  555.57     4 71.210  4.1944 0.004169 **
## ExpTemp:Species          517.32  258.66     2 71.583  1.9528 0.149360   
## AccTemp:Species          381.61  190.80     2 38.541  1.4405 0.249270   
## ExpTemp:AccTemp:Species  213.04   53.26     4 71.614  0.4021 0.806518   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

7.B Find the best model by backward elimination of non-significant effects of linear mixed effects model using the step function of the LmerTest package

(the model with the lowest AIC and significant p value is the best)

  # Backward elimination
    step_result <- step(complex_model)
    step_result
## Backward reduced random-effect table:
## 
##              Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)    
## <none>                    22 -446.22 936.44                         
## (1 | AntTag)          0   21 -461.38 964.76 30.327  1   3.65e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Backward reduced fixed-effect table:
## Degrees of freedom method: Satterthwaite 
## 
##                         Eliminated  Sum Sq Mean Sq NumDF  DenDF F value
## ExpTemp:AccTemp:Species          1  213.04   53.26     4 71.614  0.4021
## Sex                              2  139.21  139.21     1 39.864  1.0277
## AccTemp:Species                  3  364.98  182.49     2 38.701  1.3489
## ExpTemp:Species                  4  520.12  260.06     2 71.446  1.9211
## Weight_g                         5  409.26  409.26     1 44.395  2.8763
## Species                          0  933.09  933.09     1 38.348  6.5437
## ExpTemp:AccTemp                  0 2250.83  562.71     4 70.629  3.9462
##                           Pr(>F)   
## ExpTemp:AccTemp:Species 0.806518   
## Sex                     0.316814   
## AccTemp:Species         0.271448   
## ExpTemp:Species         0.153938   
## Weight_g                0.096893 . 
## Species                 0.014596 * 
## ExpTemp:AccTemp         0.006007 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Model found:
## value ~ ExpTemp + AccTemp + Species + (1 | AntTag) + ExpTemp:AccTemp
  # Extract the model that step found:
    final_model <- get_model(step_result)
    
  # Model summary
    anova(final_model)
## Type III Analysis of Variance Table with Satterthwaite's method
##                  Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## ExpTemp          589.05  294.53     2 70.664  2.0655 0.134342   
## AccTemp          186.95   93.48     2 38.297  0.6555 0.524886   
## Species          933.09  933.09     1 38.348  6.5437 0.014596 * 
## ExpTemp:AccTemp 2250.83  562.71     4 70.629  3.9462 0.006007 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

7.C Re-run model fit using REML estimation

Best model: ExpTemp * AccTemp + Species + (1 | AntTag)

    # Remodel using Maximum likelyhood estimation
      final_model <- lmer(value ~ ExpTemp *
                            AccTemp +
                            Species +
                            (1|AntTag), data = sub_trait, REML = TRUE)

    # Model summary  
      summary(final_model)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: value ~ ExpTemp * AccTemp + Species + (1 | AntTag)
##    Data: sub_trait
## 
## REML criterion at convergence: 854.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9881 -0.5056  0.1133  0.5103  1.7286 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  AntTag   (Intercept) 231.7    15.22   
##  Residual             155.9    12.49   
## Number of obs: 108, groups:  AntTag, 39
## 
## Fixed effects:
##                              Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)                    74.879      6.176  57.525  12.125  < 2e-16 ***
## ExpTemp17.5                     3.012      5.206  65.451   0.579  0.56490    
## ExpTemp21.5                    -5.868      5.318  67.967  -1.103  0.27374    
## AccTemp17.5                     4.792      7.852  63.268   0.610  0.54383    
## AccTemp21.5                   -12.350      7.921  61.391  -1.559  0.12413    
## SpeciesSagmariasus verreauxi   13.231      5.471  34.398   2.418  0.02104 *  
## ExpTemp17.5:AccTemp17.5        -4.976      7.362  65.448  -0.676  0.50154    
## ExpTemp21.5:AccTemp17.5         8.471      7.442  66.726   1.138  0.25907    
## ExpTemp17.5:AccTemp21.5         9.941      7.286  64.266   1.364  0.17724    
## ExpTemp21.5:AccTemp21.5        25.207      7.367  65.586   3.422  0.00108 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ExT17.5 ExT21.5 AT17.5 AT21.5 SpcsSv ET17.5:AT1 ET21.5:AT1
## ExpTemp17.5 -0.422                                                           
## ExpTemp21.5 -0.437  0.511                                                    
## AccTemp17.5 -0.621  0.329   0.338                                            
## AccTemp21.5 -0.625  0.327   0.336   0.489                                    
## SpcsSgmrssv -0.449  0.007   0.014  -0.016  0.005                             
## ET17.5:AT17  0.296 -0.707  -0.361  -0.466 -0.231  0.000                      
## ET21.5:AT17  0.310 -0.365  -0.715  -0.472 -0.240 -0.005  0.516               
## ET17.5:AT21  0.302 -0.715  -0.365  -0.235 -0.459 -0.005  0.505      0.261    
## ET21.5:AT21  0.315 -0.369  -0.722  -0.244 -0.465 -0.010  0.261      0.516    
##             ET17.5:AT2
## ExpTemp17.5           
## ExpTemp21.5           
## AccTemp17.5           
## AccTemp21.5           
## SpcsSgmrssv           
## ET17.5:AT17           
## ET21.5:AT17           
## ET17.5:AT21           
## ET21.5:AT21  0.506
    # Anova to test main effects of final model representing the combined significance for all coefficients
      anova(final_model)
## Type III Analysis of Variance Table with Satterthwaite's method
##                  Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## ExpTemp          585.13  292.57     2 64.671  1.8764 0.16138  
## AccTemp          182.79   91.40     2 34.352  0.5862 0.56192  
## Species          911.77  911.77     1 34.398  5.8477 0.02104 *
## ExpTemp:AccTemp 2256.78  564.20     4 64.639  3.6185 0.01008 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
      report(anova(final_model))
## Type 3 ANOVAs only give sensible and informative results when covariates are
##   mean-centered and factors are coded with orthogonal contrasts (such as those
##   produced by 'contr.sum', 'contr.poly', or 'contr.helmert', but *not* by the
##   default 'contr.treatment').
## The ANOVA suggests that:
## 
##   - The main effect of ExpTemp is statistically not significant and small (F(2) = 1.88, p = 0.161; Eta2 (partial) = 0.05, 90% CI [0.00, 0.15])
##   - The main effect of AccTemp is statistically not significant and small (F(2) = 0.59, p = 0.562; Eta2 (partial) = 0.03, 90% CI [0.00, 0.14])
##   - The main effect of Species is statistically significant and large (F(1) = 5.85, p = 0.021; Eta2 (partial) = 0.15, 90% CI [0.01, 0.33])
##   - The interaction between ExpTemp and AccTemp is statistically significant and large (F(4) = 3.62, p = 0.010; Eta2 (partial) = 0.18, 90% CI [0.03, 0.29])
## 
## Effect sizes were labelled following Field's (2013) recommendations.
    # Table output from sjPlot
      tab_model(final_model)
  value
Predictors Estimates CI p
(Intercept) 74.88 62.78 – 86.98 <0.001
ExpTemp [17.5] 3.01 -7.19 – 13.22 0.563
ExpTemp [21.5] -5.87 -16.29 – 4.56 0.270
AccTemp [17.5] 4.79 -10.60 – 20.18 0.542
AccTemp [21.5] -12.35 -27.88 – 3.18 0.119
Species [Sagmariasus
verreauxi]
13.23 2.51 – 23.95 0.016
ExpTemp [17.5] * AccTemp
[17.5]
-4.98 -19.41 – 9.45 0.499
ExpTemp [21.5] * AccTemp
[17.5]
8.47 -6.11 – 23.06 0.255
ExpTemp [17.5] * AccTemp
[21.5]
9.94 -4.34 – 24.22 0.172
ExpTemp [21.5] * AccTemp
[21.5]
25.21 10.77 – 39.65 0.001
Random Effects
σ2 155.92
τ00 AntTag 231.67
ICC 0.60
N AntTag 39
Observations 108
Marginal R2 / Conditional R2 0.172 / 0.667
    # Textual report of the model
      report(final_model)
## We fitted a linear mixed model (estimated using REML and nloptwrap optimizer) to predict value with ExpTemp, AccTemp and Species (formula: value ~ ExpTemp * AccTemp + Species). The model included AntTag as random effect (formula: ~1 | AntTag). The model's total explanatory power is substantial (conditional R2 = 0.67) and the part related to the fixed effects alone (marginal R2) is of 0.17. The model's intercept, corresponding to ExpTemp = 14, AccTemp = 14 and Species = Jasus edwardsii, is at 74.88 (95% CI [62.78, 86.98], t(96) = 12.13, p < .001). Within this model:
## 
##   - The effect of ExpTemp [17.5] is statistically non-significant and positive (beta = 3.01, 95% CI [-7.19, 13.22], t(96) = 0.58, p = 0.563; Std. beta = 0.15, 95% CI [-0.35, 0.64])
##   - The effect of ExpTemp [21.5] is statistically non-significant and negative (beta = -5.87, 95% CI [-16.29, 4.56], t(96) = -1.10, p = 0.270; Std. beta = -0.28, 95% CI [-0.78, 0.22])
##   - The effect of AccTemp [17.5] is statistically non-significant and positive (beta = 4.79, 95% CI [-10.60, 20.18], t(96) = 0.61, p = 0.542; Std. beta = 0.23, 95% CI [-0.51, 0.97])
##   - The effect of AccTemp [21.5] is statistically non-significant and negative (beta = -12.35, 95% CI [-27.88, 3.18], t(96) = -1.56, p = 0.119; Std. beta = -0.59, 95% CI [-1.34, 0.15])
##   - The effect of Species [Sagmariasus verreauxi] is statistically significant and positive (beta = 13.23, 95% CI [2.51, 23.95], t(96) = 2.42, p = 0.016; Std. beta = 0.64, 95% CI [0.12, 1.15])
##   - The interaction effect of AccTemp [17.5] on ExpTemp [17.5] is statistically non-significant and negative (beta = -4.98, 95% CI [-19.41, 9.45], t(96) = -0.68, p = 0.499; Std. beta = -0.24, 95% CI [-0.93, 0.46])
##   - The interaction effect of AccTemp [17.5] on ExpTemp [21.5] is statistically non-significant and positive (beta = 8.47, 95% CI [-6.11, 23.06], t(96) = 1.14, p = 0.255; Std. beta = 0.41, 95% CI [-0.29, 1.11])
##   - The interaction effect of AccTemp [21.5] on ExpTemp [17.5] is statistically non-significant and positive (beta = 9.94, 95% CI [-4.34, 24.22], t(96) = 1.36, p = 0.172; Std. beta = 0.48, 95% CI [-0.21, 1.17])
##   - The interaction effect of AccTemp [21.5] on ExpTemp [21.5] is statistically significant and positive (beta = 25.21, 95% CI [10.77, 39.65], t(96) = 3.42, p < .001; Std. beta = 1.21, 95% CI [0.52, 1.91])
## 
## Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using the Wald approximation.

–> Effect of species

–> Interaction between experimental and acclimation temperature

Summary table of main effects

library(effectsize)

# Calculate anova test stats for model
aov_lme <-anova(final_model)

# Caculate partial effects size
eta = eta_squared(aov_lme)

# Create output stats table
lme_table <- round(aov_lme[, c(1,2,4)], 1)

# Attach F statistics
lme_table$F_value <- paste(round(aov_lme[,5],2), " (", aov_lme[,3], ")", sep = "")

# Attach p value
lme_table$p_value <- format(aov_lme[, 6], digits = 4)

# Create string with eta and 90% eta range and join with table
lme_table$Partial_Eta <- paste(round(eta$Eta2_partial, 2), " [", round(eta$CI_low, 2), "-", round(eta$CI_high, 2), "]", sep = "")

# Save table as csv
write.csv(lme_table, "Model_summary.csv")

# Print table
kable(lme_table, 
      format = "html", 
      row.names = TRUE,
      caption = "Model summary for main effects",
      col.names =  c("Sum of sqares", "Mean squares", "Den df", "F(df)", "p value", "Partical squared eta (CI 90%)")) %>%
  kable_classic(full_width = F, html_font = "Cambria")
Model summary for main effects
Sum of sqares Mean squares Den df F(df) p value Partical squared eta (CI 90%)
ExpTemp 585.1 292.6 64.7 1.88 (2) 0.16138 0.05 [0-0.15]
AccTemp 182.8 91.4 34.4 0.59 (2) 0.56192 0.03 [0-0.14]
Species 911.8 911.8 34.4 5.85 (1) 0.02104 0.15 [0.01-0.33]
ExpTemp:AccTemp 2256.8 564.2 64.6 3.62 (4) 0.01008 0.18 [0.03-0.29]

8. Model diagnostics

# Use of DHARMa package see https://cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html

# Set see for reproducibility of residual simulation
  set.seed(1000)

  # Simulate residuals
  # (scaled residual value of 0.5 means that half of the simulated data are higher than the observed value)
    simulationOutput <- simulateResiduals(fittedModel = final_model, plot = F)
    
  # Plot scaled residuals 
  # Plot 1 = QQ plot with test for KS, overdispersion and outliers
  # Plot 2 = Residuals plot
    plot(simulationOutput)

  # Plot against predictors to check for further deviations
    plotResiduals(simulationOutput, sub_trait$AccTemp)

    plotResiduals(simulationOutput, sub_trait$ExpTemp)

    plotResiduals(simulationOutput, sub_trait$Species)

## –> QQ plot not perfect but acceptable ## –> Model diagnostics do not show apparent violations of model assumptions

9. Multiple comparisons across treatment levels

9.A Multiple comparisons between acclimation temperatures for each experimental temperature

# Perform multiple comparisions using the emmeans package
# Instructions here https://cran.r-project.org/web/packages/emmeans/vignettes/interactions.html

contrasts <- emmeans(final_model, pairwise ~   AccTemp | ExpTemp | Species, type = "response", adjust = "bonferroni")

# Display interaction plots
  emmip(final_model, AccTemp ~ ExpTemp | Species)

# Convert results to dataframe (https://aosmith.rbind.io/2019/03/25/getting-started-with-emmeans/)
  contrasts_df <- contrasts$contrasts %>% 
                summary(infer = TRUE) %>% 
                as.data.frame()   

# Plot comparisons
### blue bars are confidence intervals for the EMMs, and the red arrows are for the comparisons among them. If an arrow from one mean overlaps an arrow from another group, the difference is not “significant,” based on the adjust setting (which defaults to "tukey") and the value of alpha (which defaults to 0.05)
### https://cran.r-project.org/web/packages/emmeans/vignettes/comparisons.html
  
plot(contrasts, comparisons = TRUE)

# Save contrasts in table
      contrasts_expTemp <- contrasts_df[, c(1:4,9,10)] %>% mutate(p.value = round(p.value, 3))
    # Rename column headers
      names(contrasts_expTemp)[1:6] <- c("AccTemp", "ExpTemp", "Species", "Difference", "t-ratio", "p")
      
    # Add significance descriptor
      contrasts_expTemp$contrasts_sign <- ifelse(contrasts_expTemp$p < 0.05, "Yes", "No")
      
    # Add trait columns
      contrasts_expTemp$Trait <- trait
      
    # Save contrasts results
      write.csv(contrasts_expTemp,paste("Contrasts_AcclimationTemperature_", trait, ".csv", sep = ""))
      
# Display as HTML table colouring significant p values red
  contrasts_expTemp   %>%   mutate(p = cell_spec(p, "html", color = ifelse(p < 0.05, "red", "grey"))) %>%
                kable(escape = FALSE)  %>%
                kable_styling(bootstrap_options = c('hover'))
AccTemp ExpTemp Species Difference t-ratio p contrasts_sign Trait
14 - 17.5 14 Jasus edwardsii -4.7923955 -0.6099558 1 No AerobicScope
14 - 21.5 14 Jasus edwardsii 12.3498986 1.5583451 0.373 No AerobicScope
17.5 - 21.5 14 Jasus edwardsii 17.1422940 2.1505725 0.107 No AerobicScope
14 - 17.5 17.5 Jasus edwardsii 0.1832713 0.0232475 1 No AerobicScope
14 - 21.5 17.5 Jasus edwardsii 2.4092909 0.3035954 1 No AerobicScope
17.5 - 21.5 17.5 Jasus edwardsii 2.2260196 0.2787547 1 No AerobicScope
14 - 17.5 21.5 Jasus edwardsii -13.2633251 -1.6846128 0.291 No AerobicScope
14 - 21.5 21.5 Jasus edwardsii -12.8573054 -1.6223711 0.33 No AerobicScope
17.5 - 21.5 21.5 Jasus edwardsii 0.4060196 0.0508441 1 No AerobicScope
14 - 17.5 14 Sagmariasus verreauxi -4.7923955 -0.6099558 1 No AerobicScope
14 - 21.5 14 Sagmariasus verreauxi 12.3498986 1.5583451 0.373 No AerobicScope
17.5 - 21.5 14 Sagmariasus verreauxi 17.1422940 2.1505725 0.107 No AerobicScope
14 - 17.5 17.5 Sagmariasus verreauxi 0.1832713 0.0232475 1 No AerobicScope
14 - 21.5 17.5 Sagmariasus verreauxi 2.4092909 0.3035954 1 No AerobicScope
17.5 - 21.5 17.5 Sagmariasus verreauxi 2.2260196 0.2787547 1 No AerobicScope
14 - 17.5 21.5 Sagmariasus verreauxi -13.2633251 -1.6846128 0.291 No AerobicScope
14 - 21.5 21.5 Sagmariasus verreauxi -12.8573054 -1.6223711 0.33 No AerobicScope
17.5 - 21.5 21.5 Sagmariasus verreauxi 0.4060196 0.0508441 1 No AerobicScope

9.B Multiple comparisons between experimental temperatures for each acclimation temperature

# Perform multiple comparisions using the emmeans package
# Instructions here https://cran.r-project.org/web/packages/emmeans/vignettes/interactions.html

contrasts <- emmeans(final_model, pairwise ~  ExpTemp | AccTemp | Species, type = "response", adjust = "bonferroni")

# Display interaction plots
  emmip(final_model, AccTemp ~ ExpTemp | Species)

# Convert results to dataframe (https://aosmith.rbind.io/2019/03/25/getting-started-with-emmeans/)
  contrasts_df <- contrasts$contrasts %>% 
                summary(infer = TRUE) %>% 
                as.data.frame()   

# Plot comparisons
### blue bars are confidence intervals for the EMMs, and the red arrows are for the comparisons among them. If an arrow from one mean overlaps an arrow from another group, the difference is not “significant,” based on the adjust setting (which defaults to "tukey") and the value of alpha (which defaults to 0.05)
### https://cran.r-project.org/web/packages/emmeans/vignettes/comparisons.html
  
plot(contrasts, comparisons = TRUE)

# Save contrasts in table
      contrasts_expTemp <- contrasts_df[, c(1:4,9,10)] %>% mutate(p.value = round(p.value, 3))
    # Rename column headers
      names(contrasts_expTemp)[1:6] <- c("ExpTemp", "AccTemp", "Species", "Difference", "t-ratio", "p")
      
    # Add significance descriptor
      contrasts_expTemp$contrasts_sign <- ifelse(contrasts_expTemp$p < 0.05, "Yes", "No")
      
    # Add trait columns
      contrasts_expTemp$Trait <- trait
      
    # Save contrasts results
      write.csv(contrasts_expTemp,paste("Contrasts_ExperimentalTemperature_", trait, ".csv", sep = ""))
      
# Display as HTML table colouring significant p values red
contrasts_expTemp   %>%   mutate(p = cell_spec(p, "html", color = ifelse(p < 0.05, "red", "grey"))) %>%
                kable(escape = FALSE)  %>%
                kable_styling(bootstrap_options = c('hover'))
ExpTemp AccTemp Species Difference t-ratio p contrasts_sign Trait
14 - 17.5 14 Jasus edwardsii -3.011892 -0.5777632 1 No AerobicScope
14 - 21.5 14 Jasus edwardsii 5.868037 1.1005499 0.825 No AerobicScope
17.5 - 21.5 14 Jasus edwardsii 8.879930 1.7034130 0.28 No AerobicScope
14 - 17.5 17.5 Jasus edwardsii 1.963774 0.3767108 1 No AerobicScope
14 - 21.5 17.5 Jasus edwardsii -2.602892 -0.4993128 1 No AerobicScope
17.5 - 21.5 17.5 Jasus edwardsii -4.566667 -0.8958322 1 No AerobicScope
14 - 17.5 21.5 Jasus edwardsii -12.952500 -2.5408612 0.041 Yes AerobicScope
14 - 21.5 21.5 Jasus edwardsii -19.339167 -3.7937184 0.001 Yes AerobicScope
17.5 - 21.5 21.5 Jasus edwardsii -6.386667 -1.2528572 0.645 No AerobicScope
14 - 17.5 14 Sagmariasus verreauxi -3.011892 -0.5777632 1 No AerobicScope
14 - 21.5 14 Sagmariasus verreauxi 5.868037 1.1005499 0.825 No AerobicScope
17.5 - 21.5 14 Sagmariasus verreauxi 8.879930 1.7034130 0.28 No AerobicScope
14 - 17.5 17.5 Sagmariasus verreauxi 1.963774 0.3767108 1 No AerobicScope
14 - 21.5 17.5 Sagmariasus verreauxi -2.602892 -0.4993128 1 No AerobicScope
17.5 - 21.5 17.5 Sagmariasus verreauxi -4.566667 -0.8958322 1 No AerobicScope
14 - 17.5 21.5 Sagmariasus verreauxi -12.952500 -2.5408612 0.041 Yes AerobicScope
14 - 21.5 21.5 Sagmariasus verreauxi -19.339167 -3.7937184 0.001 Yes AerobicScope
17.5 - 21.5 21.5 Sagmariasus verreauxi -6.386667 -1.2528572 0.645 No AerobicScope

9.C Multiple comparisons between species for each experimental temperature

# Perform multiple comparisions using the emmeans package
# Instructions here https://cran.r-project.org/web/packages/emmeans/vignettes/interactions.html

contrasts <- emmeans(final_model, pairwise ~  Species | ExpTemp, type = "response", adjust = "bonferroni")

# Display interaction plots
  emmip(final_model, ExpTemp ~ Species)

# Convert results to dataframe (https://aosmith.rbind.io/2019/03/25/getting-started-with-emmeans/)
  contrasts_df <- contrasts$contrasts %>% 
                summary(infer = TRUE) %>% 
                as.data.frame()   

# Plot comparisons
### blue bars are confidence intervals for the EMMs, and the red arrows are for the comparisons among them. If an arrow ### from one mean overlaps an arrow from another group, the difference is not “significant,” based on the adjust setting ### (which defaults to "tukey") and the value of alpha (which defaults to 0.05)
### https://cran.r-project.org/web/packages/emmeans/vignettes/comparisons.html
plot(contrasts, comparisons = TRUE)

# Save contrasts in table
      contrasts_expTemp <- contrasts_df[, c(1:3,8,9)] %>% mutate(p.value = round(p.value, 3))
    # Rename column headers
      names(contrasts_expTemp)[1:5] <- c("Contrast", "ExpTemp", "Difference", "t-ratio", "p")
      
    # Add significance descriptor
      contrasts_expTemp$contrasts_sign <- ifelse(contrasts_expTemp$p < 0.05, "Yes", "No")
      
    # Add trait columns
      contrasts_expTemp$Trait <- trait
      
    # Save contrasts results
      write.csv(contrasts_expTemp,paste("Contrasts_Species_", trait, ".csv", sep = ""))
      
# Display as HTML table colouring significant p values red
contrasts_expTemp   %>%   mutate(p = cell_spec(p, "html", color = ifelse(p < 0.05, "red", "grey"))) %>%
                kable(escape = FALSE)  %>%
                kable_styling(bootstrap_options = c('hover'))
Contrast ExpTemp Difference t-ratio p contrasts_sign Trait
Jasus edwardsii - Sagmariasus verreauxi 14 -13.23081 -2.417294 0.021 Yes AerobicScope
Jasus edwardsii - Sagmariasus verreauxi 17.5 -13.23081 -2.417294 0.021 Yes AerobicScope
Jasus edwardsii - Sagmariasus verreauxi 21.5 -13.23081 -2.417294 0.021 Yes AerobicScope

10. R Session Information

report_system()
## Analyses were conducted using the R Statistical language (version 4.1.2; R Core Team, 2021) on Windows 10 x64 (build 19043)
report_packages()
##   - ggpubr (version 0.4.0; Alboukadel Kassambara, 2020)
##   - effectsize (version 0.4.5; Ben-Shachar M et al., 2020)
##   - bbmle (version 1.0.24; Ben Bolker and R Development Core Team, 2021)
##   - Matrix (version 1.3.4; Douglas Bates and Martin Maechler, 2021)
##   - lme4 (version 1.1.27.1; Douglas Bates et al., 2015)
##   - DHARMa (version 0.4.4; Florian Hartig, 2021)
##   - pander (version 0.6.4; Gergely Daróczi and Roman Tsegelskyi, 2021)
##   - ggplot2 (version 3.3.5; Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2016.)
##   - plyr (version 1.8.6; Hadley Wickham, 2011)
##   - stringr (version 1.4.0; Hadley Wickham, 2019)
##   - forcats (version 0.5.1; Hadley Wickham, 2021)
##   - tidyr (version 1.1.3; Hadley Wickham, 2021)
##   - readxl (version 1.3.1; Hadley Wickham and Jennifer Bryan, 2019)
##   - readr (version 1.4.0; Hadley Wickham and Jim Hester, 2020)
##   - dplyr (version 1.0.7; Hadley Wickham et al., 2021)
##   - kableExtra (version 1.3.4; Hao Zhu, 2021)
##   - tibble (version 3.1.2; Kirill Müller and Hadley Wickham, 2021)
##   - lmerTest (version 3.1.3; Kuznetsova A et al., 2017)
##   - purrr (version 0.3.4; Lionel Henry and Hadley Wickham, 2020)
##   - sjPlot (version 2.8.10; Lüdecke D, 2021)
##   - psycho (version 0.6.1; Makowski, 2018)
##   - report (version 0.4.0; Makowski et al., 2020)
##   - fitdistrplus (version 1.1.5; Marie Laure Delignette-Muller, Christophe Dutang, 2015)
##   - openxlsx (version 4.2.4; Philipp Schauberger and Alexander Walker, 2021)
##   - R (version 4.1.2; R Core Team, 2021)
##   - emmeans (version 1.6.2.1; Russell Lenth, 2021)
##   - survival (version 3.2.13; Therneau T, 2021)
##   - pbkrtest (version 0.5.1; Ulrich Halekoh, Søren Højsgaard, 2014)
##   - MASS (version 7.3.54; Venables et al., 2002)
##   - tidyverse (version 1.3.1; Wickham et al., 2019)
##   - knitr (version 1.33; Yihui Xie, 2021)