For testing which would be the best approach I’m going to use the last sampling (week 16)

Eukaryotes

Explore alpha diversity

Difference in treatment groups and metacommunities

The variances in the groups are not homogen. This could be a problem.

Distribution of alpha diversity

Here are the distributions with different transformations

The original is not too bad, but the natural logarithmic and Box-Cox transformation looks good. For the Box-Cox transformation see: https://ourcodingclub.github.io/tutorials/data-scaling/ I just learnt about this, if we want to be safe we can use log, but I will test both.

Mixed-effect modles

Log models

Summaries

Model where metacommunity is the random effect

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(alpha_div) ~ Treatment + (1 | Metacom_ID)
##    Data: XI_mixmodel_df_euk
## 
## REML criterion at convergence: 9.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8890 -0.7380  0.2057  0.4700  2.0467 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  Metacom_ID (Intercept) 0.01483  0.1218  
##  Residual               0.06026  0.2455  
## Number of obs: 30, groups:  Metacom_ID, 6
## 
## Fixed effects:
##                     Estimate Std. Error t value
## (Intercept)          5.23209    0.09465  55.276
## Treatmentfragmented -0.32556    0.13386  -2.432
## 
## Correlation of Fixed Effects:
##             (Intr)
## Trtmntfrgmn -0.707

Model where the created “random” variable is the random effect

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(alpha_div) ~ Treatment + (1 | random)
##    Data: XI_mixmodel_df_euk
## 
## REML criterion at convergence: 9.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9567 -0.5866  0.1425  0.5163  2.2267 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  random   (Intercept) 0.009289 0.09638 
##  Residual             0.064215 0.25341 
## Number of obs: 30, groups:  random, 3
## 
## Fixed effects:
##                     Estimate Std. Error t value
## (Intercept)          5.23209    0.08589  60.915
## Treatmentfragmented -0.32556    0.09253  -3.518
## 
## Correlation of Fixed Effects:
##             (Intr)
## Trtmntfrgmn -0.539

These look very similar.

Check models

I think that the created random variable makes the model fit better, so I will use that in the future.

Box-Cox models

Summaries

## Linear mixed model fit by REML ['lmerMod']
## Formula: bc_alpha_div ~ Treatment + (1 | random)
##    Data: XI_mixmodel_df_euk
## 
## REML criterion at convergence: -285.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1360 -0.6778  0.2648  0.5912  1.6128 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  random   (Intercept) 1.872e-07 0.0004326
##  Residual             1.683e-06 0.0012973
## Number of obs: 30, groups:  random, 3
## 
## Fixed effects:
##                       Estimate Std. Error  t value
## (Intercept)          0.9658885  0.0004178 2311.639
## Treatmentfragmented -0.0015457  0.0004737   -3.263
## 
## Correlation of Fixed Effects:
##             (Intr)
## Trtmntfrgmn -0.567

Check model

I honestly can’t tell which model fits better. Both transformations look good, maybe the regular log transformation is a bit better.

Original models

Just to have a comparison I will plot out the model with the original data

Summary

## Linear mixed model fit by REML ['lmerMod']
## Formula: alpha_div ~ Treatment + (1 | random)
##    Data: XI_mixmodel_df_euk
## 
## REML criterion at convergence: 304.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.65602 -0.43214  0.02219  0.42060  2.88716 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  random   (Intercept)  395.8   19.89   
##  Residual             2383.0   48.82   
## Number of obs: 30, groups:  random, 3
## 
## Fixed effects:
##                     Estimate Std. Error t value
## (Intercept)           198.33      17.05  11.631
## Treatmentfragmented   -62.07      17.83  -3.482
## 
## Correlation of Fixed Effects:
##             (Intr)
## Trtmntfrgmn -0.523

Check model

GLMM

The model was created with the gamma distribution and log link function.

Summary

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: alpha_div ~ Treatment + (1 | random)
##    Data: XI_mixmodel_df_euk
## 
##      AIC      BIC   logLik deviance df.resid 
##    316.1    321.7   -154.1    308.1       26 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.69715 -0.66305  0.03493  0.47611  2.83363 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  random   (Intercept) 0.005813 0.07624 
##  Residual             0.060734 0.24644 
## Number of obs: 30, groups:  random, 3
## 
## Fixed effects:
##                     Estimate Std. Error t value Pr(>|z|)    
## (Intercept)          5.27681    0.09420  56.016  < 2e-16 ***
## Treatmentfragmented -0.36219    0.08772  -4.129 3.65e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## Trtmntfrgmn -0.468

Check modell

This also fits just as good as the others.