Statistical analysis
We addressed the study questions with several analyses, focusing on
different dataset levels dependent on data availability. Thebiodiversity dataset contains all macrophyte recordings (274
mapped transects in 100 field campaigns, mapping of lake in one year is
called field campaign ) of the selected 28 lakes. As no complete
information is available for all mapped lakes and years, we compiled two
subsets of the biodiversity dataset : The environmental &
biodiversity dataset is a subset dataset with all macrophyte recordings
for which all abiotic data (see Table 1) were available. This dataset
includes data from 12 lakes, 27 field campaigns and 147 transects. For
the biodiversity time series dataset we selected all lakes for
which repeated mappings for at least 3 years were available. This
condition was fulfilled for 17 lakes mapped in 73 field campaigns along
194 transects. Analyses for each research question are described below.
For the first question, concerning the general depth distribution
pattern, we used the richness components including the different DDG
measures and determined pattern types. We plotted as general DDG curves
the mean and standard deviation of alpha, beta and gamma richness for
each depth (Question 1.1). We performed simultaneous tests for linear
models with multiple comparisons of means using Tukey contrasts that are
robust under non-normality, heteroscedasticity and variable sample size
(Herberich et al. 2010) to compare the richness across depth for
significant difference. Furthermore, we plotted the different DDG peaks
(DDG measures) for alpha, beta and gamma richness and determined the
corresponding regression line by fitting a linear model. We classified
the DDG curves for all three richness measures in four pattern types
depending on the depth of the richness curve maximum: Decreasing
(Dmax > -1m), shallow hump-shaped
(Dmax between -1 and -2 m), deep hump-shaped
(Dmax between -2 and -4 m) and increasing
(Dmax < -4 m) (Fig. 1d). To determine
the correlations between the different diversity components (Question
1.2) we performed a Pearson correlation test between depth dependent
richness components. Furthermore, we tested for correlations between DDG
measures across the different richness components. A Chi-square test
helped to look at associations between pattern types and biodiversity
components.
For the second question, concerning the drivers of the diversity depth
gradient, we analysed the influence of abiotic data on the DDG using theenvironmental & biodiversity dataset . We log-transformed the
abiotic and biotic data. To show that the diversity metrics of theenvironmental & biodiversity dataset are representative for the
diversity metrics of biodiversity dataset we applied the
PERMANOVA test adonis2 , using the R package ‘vegan’ which
compares centroids and the variance (Oksanen et al. 2019). A
non-significant result (p >0.05) confirms that
centroids and variance of two groups are not different (Supporting
information). To identify the driving factors on the richness peaks we
used Generalized Additive Mixed-Effect Models (GAMMs), computed with the
R package ’gamm4’ (Wood 2011). The D(α,β,γ,max)and R(α,β,γ,max) were used as response variables,
the lake as random effect. To reduce the high correlations between
abiotic factors (Pearson correlation test) we performed a Principle
Component Analysis (PCA) analysis and named the main axis
(>80% variance) after the corresponding abiotic factor,
whenever an axis encompassed more than 40% of the variation of a
variable. We used the loadings of the main PCA axes (>80%
variance) as explanatory variables for the GAMM. We constructed a full
model with all PCA axes, then we stepwise excluded the least significant
terms until obtaining a minimal model (Wood 2008).
To answer the third questions about the temporal change of the depth
diversity gradient, we used the biodiversity time series dataset .
First, we calculate the Invariability Coefficient (IC) as inverse of the
Coefficient of Variation (CV):
\begin{equation}
IC=\frac{1}{\text{CV}}=\frac{1}{\frac{\text{sd}}{\text{mean}}}\ =\frac{\text{mean}}{\text{sd}}\nonumber \\
\end{equation}The IC is a statistical tool to evaluate the degree of invariability
also for datasets with different means (Question 3.1). To check for
temporal trends, we built simple linear regression models for depth
independent gamma richness and the DDG measures,D(α,β,γ,max) andR(α,β,γ,max), as response variables and time as
explanatory variable for (a) the complete dataset and (b) each
individual lake. We identified all models that showed significant linear
trends (p <0.1) and characterized the direction of their
slopes (Question 3.2).