Fig. 3.

Frequency of negative, positive, and non-associated pair-wise interactions between among-lake richness versus within-lake abundance. a Frequency of significantly positive, nonsignificant, and negative associations among 231 species pairs of freshwater fish in 721 lakes, for two classes of data: lake presence/absence (differences in among-lake richness) and lake abundance based on catch per unit effort for each species in each lake (differences in within-lake abundance). We hypothesized an increase in the frequency of negative interactions within-lakes but this was generally not the case, for both species pairs in the ‘same’ temperature class (e.g., two species of ‘warm-water’ fish, Supplementary Table 1) versus ‘different’ classes (warm vs cold-water species). b Relative change in the importance of four major explanatory factors (climate, morphometry, water quality, and negative species interactions) between BRT analyses of among-lake richness to BRT analyses of within-lake abundance (see Supplementary Table 3). Significant thresholds were based on an α < 0.05