Congruence, but no cascade—Pelagic biodiversity across three trophic levels in Nordic lakes

Abstract Covariation in species richness and community structure across taxonomical groups (cross‐taxon congruence) has practical consequences for the identification of biodiversity surrogates and proxies, as well as theoretical ramifications for understanding the mechanisms maintaining and sustaining biodiversity. We found there to exist a high cross‐taxon congruence between phytoplankton, zooplankton, and fish in 73 large Scandinavian lakes across a 750 km longitudinal transect. The fraction of the total diversity variation explained by local environment alone was small for all trophic levels while a substantial fraction could be explained by spatial gradient variables. Almost half of the explained variation could not be resolved between local and spatial factors, possibly due to confounding issues between longitude and landscape productivity. There is strong consensus that the longitudinal gradient found in the regional fish community results from postglacial dispersal limitations, while there is much less evidence for the species richness and community structure gradients at lower trophic levels being directly affected by dispersal limitation over the same time scale. We found strong support for bidirectional interactions between fish and zooplankton species richness, while corresponding interactions between phytoplankton and zooplankton richness were much weaker. Both the weakening of the linkage at lower trophic levels and the bidirectional nature of the interaction indicates that the underlying mechanism must be qualitatively different from a trophic cascade.

The subset of 73 lakes included in the env table has 4268 records of 18 variables. The first 3 columns define the sample by lake name, lake ID, and sample date ( Lake , ID , Date ). The next 2 columns define the taxon as unique 4 + 4 letter genus/species abbreviation codes ( Rubin.code ) and numerical identifiers ( RebeccaID ). The following 7 columns define the taxonomy ( Kingdom , Phylum , Class , Order , Family , Genus , Species ), while the last 5 columns represents the microscopy counts and cell volume measurements: Number is the actual number of units counted in the analysed area of the counting chamber. The actual count multiplied by Factor gives the number of units per liter of sample. The measure cell volume of the counting unit (µm ) is given by Spec.vol . Biovolume per unit sample volume ( Bio.vol as mm / m = µg ww / L) is given by the product of Number , Factor , and Spec.vol Adjusting singletons for different subsample sizes Standard phytoplankton counting procedures have been focused on estimation of biomass rather than biodiversity. This means that different taxa are counted over different subsamples (areas of the counting chamber) and/or at different magnifications. In other words, a count of 1 does not does not mean that there was only 1 unit in the sample, just in that particular subsample. Since single and double occurrences play a special role in some richnness estimators, we have a potential problem since all singletons in a sample may not be from the same subsample size.

Converting biovolume units to detection units
The Factor field is inversely proportional to counted area, such that the smallest value of Factor will correspond to the largest counted area in a given sample. In other words, if we find the smallest value of Factor for each sample ( fmin ), then we can use this to adjust all counts in the same sample to the same subsample volume. By rounding upward ( ceiling() ), we ensure that the adjusted counts ( Nadj ) remain positive. fmin <-aggregate(pp$Factor, by = list(Lake = pp$Lake), min) names(fmin) <-c("Lake", "fmin") This adjustment hopefully has less bias in the number of singletons (11.6%) and doubletons (4.9%) than the original uncorrected counts.

Crosstabulating adjusted counts
We are now ready to use tapply() to crosstabulate the adjusted counts by sample ( ID ) and taxon ( Rubin.code ). Since missing values in the crosstabulation are true absences, we need to change them to zeros. Many of the 395 taxa are rare, and less than half the species are present in 5 lakes or more. The estimateR() function from the vegan package estimates Chao and ACE richness from the subsampling-adjusted count data s <-estimateR(nt) # Chao & ACE richness estimators S$S.chao1 <-s["S.chao1", ] S$S.ACE <-s["S. ACE", ] Biovolume-rarefied richness Rarefaction allows us to adjust richness estimates according to counting effort, by rarefying all counts to the sample with the least counting effort. Different taxa being counted at different resolutions and subsample sizes makes it difficult to use rarefaction directly on the adjusted counts, since rescaling for true singletons will inflate the counts of common taxa. Instead of a count-based resampling we therefore use a biovolume fraction-based rarefaction, as used by Özkan et al (2016).
For that, we first need to crosstabulate biovolumes by lake and taxon, and normalize to taxon contributions to relative biovolume contributions.

Genus richness
We can make a less operator-dependent and more robust richness measure by counting the number of genera instead of number of species. For this, we first need to crosstabulate the count data by Genus instead of taxon ( Rubin.code ), and then calculate genus richness as the sum of genus occurrences within sites ng <-tapply(pp$Nadj, list(as.factor(pp$ID), pp$Genus), sum) ng[is.na(ng)] <-0 # change NAs to true absences S$G.obs <-rowSums(ng > 0) # Genus richness

Information theory-based diversity indices
We also use the relative biovolume fractions to calculate information theoretical diversity indices (Shannon (H) and Simpson (D)) and from them, the first and second Renyi numbers (H1 = exp(H) and H2 = 1 / D)  All the richness indices are strongly correlated with observed richness, while the correlations with information theoretical diversity indices (H1 and H2) are weaker. Taxon richness estimated from the taxa observed in at least 5 lakes is 85% \(\pm\) 3% of observed richness, while genus richness is 58% \(\pm\) 2% of taxon richness (1.7 taxa / genus). Extrapolated richness estimators (Chao1 and ACE) are both about 5% \(\pm\) 5% higher than observed richness, while rarefied richness is on the average 58% \(\pm\) 4% of observed richness. The "effective number of species" as indicated by the Renyi numbers (H1 and H2) are around 26% \(\pm\) 4% and 12% \(\pm\) 4% of observed richness, respectively. Since all richness and diversity indicators correlate reasonably well with observed richness ( S.obs ) it makes sense to focus on this particular indicator in the rest of this work.