Can size distributions of European lake fish communities be predicted by trophic positions of their fish species?

Abstract An organism's body size plays an important role in ecological interactions such as predator–prey relationships. As predators are typically larger than their prey, this often leads to a strong positive relationship between body size and trophic position in aquatic ecosystems. The distribution of body sizes in a community can thus be an indicator of the strengths of predator–prey interactions. The aim of this study was to gain more insight into the relationship between fish body size distribution and trophic position in a wide range of European lakes. We used quantile regression to examine the relationship between fish species' trophic position and their log‐transformed maximum body mass for 48 fish species found in 235 European lakes. Subsequently, we examined whether the slopes of the continuous community size distributions, estimated by maximum likelihood, were predicted by trophic position, predator–prey mass ratio (PPMR), or abundance (number per unit effort) of fish communities in these lakes. We found a positive linear relationship between species' maximum body mass and average trophic position in fishes only for the 75% quantile, contrasting our expectation that species' trophic position systematically increases with maximum body mass for fish species in European lakes. Consequently, the size spectrum slope was not related to the average community trophic position, but there were negative effects of community PPMR and total fish abundance on the size spectrum slope. We conclude that predator–prey interactions likely do not contribute strongly to shaping community size distributions in these lakes.


Table S1
Overview of all fish species found in our lake dataset. For each species we note trophic position (according to FishBase (Froese & Pauly, 2021)), mean length (cm, from our dataset), mean weight (g, calculated from mean length with species-specific conversions), maximum length of species in our dataset (cm, largest individual caught), the maximum weight of the individual with the maximum length (g, calculated from their length with species-specific conversions), the maximum length of the species (cm, according to FishBase), and their maximum weight (g, calculated from their length with species-specific conversions), the number of lakes a species was caught in (N lakes) and the total number of individuals of this species in our dataset (N ind.), and the species-specific length-weight conversion coefficients (from FishBase (Froese & Pauly, 2021)).

Species
Common

Figure S1
Comparison between the slopes based on maximum likelihood (MLE, as used in the study) and the ordinary least squares (OLS) approach. OLS slopes were based on binning of size classes and calculated with linear regressions. Both for good fit lakes (r(233) = 0.81, p < 0.001) and ill fit lakes (r(127) = 0.84, p < 0.001) there was a positive correlation between the slopes based on the two different methods.

Figure S2
Here we show examples of two lakes with a relatively good MLE fit (a and b), and two lakes with a relatively ill MLE fit (c and d). In these plots we show the individual size distribution and MLE (bins) fit (red solid line), with 95% CI intervals (red dashed line). The horizontal green line shows the range of body sizes for each bin, with its value on the y-axis corresponding to the total number of individuals in bins whose minima are ≥ the bin's minimum. The vertical span of each grey bar shows the possible range of the number of individuals with body mass ≥ the body mass of individuals in that bin (its horizontal span is the same as for the green lines) (according to Edwards et al. (2020)). In the "ill-fitting" graphs one can see that there is an underestimation of individuals in the "small fish" (before the intersect of the red MLE curve with the data), and an overestimation of "large fish" (after the intersect of the red MLE curve with the data). Note that both y and x axes are displayed on a log scale, which is a similar depiction of how traditional SS slopes are displayed.

Figure S3
Map showing the distribution of lakes in our study, including lakes with a "good fit" (black circles) as well as lakes with a "bad fit" which were excluded from analyses (red triangles).

Figure S5
Marginal effect plots between the exponent b of the size spectrum and a) the species richness, b) the maximum temperature, c) total Phosphorus (log10), d) maximum depth (log10) and e) area (log10). The lines are significant regression lines with 95% CI intervals. Model outputs are shown in Table 3. N=235 lakes

Figure S6
Comparison of exponent b calculated with fish with weight 8-2000 g (main analyses) and with weight 8-1000 g.

Table S3
Fish size 8-1000 g. Output of the model (linear mixed model with a structure to account for potential spatial autocorrelation) relating the exponent b of the size spectrum to the mean trophic position of the community, PPMR, CPUE, the species richness and four environmental covariates (maximum temperature, total phosphorus, maximum depth and lake area). In the last two columns standardized values and errors are noted. R 2 of the model is 0.40. N = 235 lakes. Significance codes: *** p < 0.001; ** p < 0.01; * p < 0.05; + p<0.1.