Causal networks of phytoplankton diversity and biomass are modulated by environmental context
Quantification of causal networksWe first compared the relative strengths of causal links across systems (Supplementary Fig. S3). Phytoplankton species richness was the major controlling factor for phytoplankton biomass (significant in 16 of 19 sites, Fig. 2a) in these diverse aquatic systems, consistent with experimental studies17. However, the averaged linkage strength for this effect was not significantly different from that of NO3 (i.e., BD → EF vs. NO3 → EF; permutation test P = 0.501), highlighting that nitrogen availability was equally important in affecting phytoplankton biomass in natural systems.Fig. 2: Relative strengths of various modules.Standardized linkage strengths of causal variables affecting (a) phytoplankton biomass and (b) species richness (here, BD) and loop weights for various types of (c) pairwise feedbacks and (d) triangular feedbacks. All statistics were calculated from the 19 independent sites (n = 19) and depicted as joint violins and box plots to present the empirical distribution that labels the maxima and minima at the top and bottom of the violins, respectively, and shows 25, 50, and 75% quantiles in the boxes with whiskers presenting at most 1.5 * interquartile range. The two numbers within the parentheses (S; R1) above each violin plot report the number of significant results in CCM (S; labeled blue) and the number of systems in which a particular module had the greatest strength (i.e., rank 1; R1; labeled red). Source data are provided as a Source Data file.Full size imageIn the opposite direction, phytoplankton biomass was a significant driver of phytoplankton species richness in most ecosystems (15 of 19 sites, Fig. 2b). However, NO3 more often had a stronger effect, appearing as the most important driver in 11 of 19 sites compared to phytoplankton biomass (4 of 19 sites) (Fig. 2b). Although the difference in effect strength was not significant (permutation test, P = 0.162), these results implicated nitrogen availability as an essential determinant affecting both phytoplankton diversity and biomass. As a sensitivity test, we also examined the effects of Shannon diversity. The results suggest that the importance of nutrients is robust to the use of other diversity indexes (e.g., Shannon diversity in Supplementary Fig. S4), although the causal effects from phytoplankton biomass became relatively more important compared to biomass effects on species richness (Fig. 2b). Based on these findings, we inferred that processes influencing nutrients (e.g., external loadings and internal cycling38) need to be considered when investigating aquatic biodiversity. Changes in those processes (e.g., climatic39 or anthropogenic40 driven nutrient changes) may indeed substantially impact phytoplankton biodiversity, and subsequent ecosystem functioning.The importance of NO3 uncovered in our analyses might not be a counter-intuitive result, as many systems analyzed in this study were P-rich. For instance, the average phosphate concentration was 57.5 and 41.7 μgP/L for Lake Mendota (Me) and Lake Monona (Mo) (Supplementary Table S1), respectively. In addition, there were also high total phosphorus (TP) concentrations in shallow lake systems, e.g., average TP was 106.1, 112.5, and 126.4 μgP/L in Lake Inba (Ib), Lake Kasumigaura (Ks), and Müggelsee (Mu), respectively. Phosphorus was not always a limiting factor in eutrophic and mesotrophic systems, e.g., Lake Kasumigaura41 and Lake Geneva (Gv)42. In addition, nitrogen was deficient and limited cyanobacteria bloom in Müggelsee (Mu)43. Nonetheless, we cannot exclude the possibility of colimitation44 in N and P and the possibility that P availability also depends on N45, which warrants further investigation.Apart from nutrients and temperature, the causal effects of other important drivers on phytoplankton biomass and diversity were also examined, though not in all 19 systems due to data limitation. The causal effects of physical environmental factors, such as irradiance and water column stability, were presented in Supplementary Fig. S5; the results indicated that the quantified causal strengths on average were not as strong as the effects of diversity and nutrients. Moreover, the effects of consumers (e.g., zooplankton), which have been suggested as important drivers affecting species diversity of phytoplankton communities46, were also examined. Based on our analysis of zooplankton, the causal effects of herbivorous crustaceans on phytoplankton biomass and diversity were significant in most of the analyzed systems. However, these effects were on average not as strong as the effects of phytoplankton diversity and nutrients, respectively (Supplementary Fig. S6). Nonetheless, these findings were not generalized to all 19 systems due to a lack of complete datasets as shown in Supplementary Table S3, and thus warrant more detailed investigation in future studies.In addition to individual causal effects, we investigated feedbacks across systems. Pairwise feedbacks (e.g., BD ↔ EF and NO3 ↔ EF) were common (Fig. 2c). However, the averaged linkage strength was often stronger in one direction when involving BD (Fig. 3). Specifically, the average strength of BD → EF was stronger than for the opposite direction of EF → BD (permutation test P = 0.015); BD → EF was stronger than EF → BD in 14 of the 19 systems (Fig. 3). In addition, biodiversity effects on nutrients (BD → NO3 and BD → PO4) were also stronger than their reversed effects (NO3 → BD and PO4 → BD) in 12 and 13 systems, respectively. In comparison, the interactions between nutrients and productivity were more symmetrical: nutrient effects on biomass (NO3 → EF and PO4 → EF) were stronger than biomass effects on nutrients (EF → NO3 and EF → PO4) in only 9 and 8 of 19 systems, respectively. These results supported the previous findings8 that biodiversity effects more often operate at short-term scales, which makes effects more observable in our monthly-scale analyses than feedback effects on diversity, which are expected to occur on a more prolonged timescale, e.g., through slowly changing nutrient cycling31 or decomposition47. Nevertheless, the timescale dependence of causal interactions in ecosystem networks is a topic that needs further study.Fig. 3: Directional bias in pairwise feedbacks.The difference in standardized linkage strengths between the two directions was computed for each pairwise feedback and depicted as joint violin and box plots. All statistics were calculated from the 19 independent sites (n = 19) and depicted as joint violins and box plots to present the empirical distribution that labels the maxima and minima at the top and bottom of the violins, respectively, and shows 25, 50, and 75% quantiles in the boxes with whiskers presenting at most 1.5 * interquartile range. The number above the plot indicates the number of systems with a positive difference in linkage strength. For example, BD → EF was stronger than its feedback, EF → BD, in 14 of the systems. In general, the strength of diversity effects (BD → EF, BD → NO3, BD → PO4) was usually stronger than feedback effects (EF → BD, NO3 → BD, PO4 → BD). Source data are provided as a Source Data file.Full size imageSubsequently, we quantified the strengths of pairwise feedbacks as the geometric mean of the linkage strengths in each direction, following a previous study9 (see more details in Methods). Among these feedbacks (Fig. 2c and Supplementary Fig. S7), BD ↔ NO3 had the highest median and average strength (0.78 and 0.68, respectively) across systems. However, strengths of BD ↔ NO3 were highly variable among systems (large interquartile range in Fig. 2c), and thus were only significant in 11 of 19 systems, compared to BD ↔ EF (15 of 19 systems). These findings reinforced the importance of nutrients as key determinants for aquatic biodiversity and implied that nutrient effects are context-dependent. In other words, BD ↔ NO3 was less common than BD ↔ EF across systems, despite its stronger average strength. The prevalence of BD ↔ EF indicated a need for more long-term experiments and process-based/theoretical modeling accounting for bidirectional interactions between diversity and biomass16, because bidirectional interactions and feedbacks may challenge our simple predictions for ecosystem dynamics, based on knowledge of unidirectional interactions30.Quantification of the causal network also allowed us to analyze triangular feedbacks. Within the conceptual framework of Fig. 1b, there are four kinds of triangular feedbacks involving biodiversity, ecosystem functioning, and either nitrate or phosphate (Type I: BD → EF → NO3 and BD → EF → PO4; Type II: EF → BD → NO3 and EF → BD → PO4). There was at least one significant triangular feedback in 14 of 19 sites (Fig. 2d). More specifically, NO3-associated feedbacks (Type I-N and Type II-N) were usually stronger than PO4-associated feedbacks (Type I-P and Type II-P) (Fig. 2d), although the difference in strength among the four types of feedbacks was not significant (Fig. 2d; Kruskal–Wallis test, P = 0.59). The dominance of NO3-associated feedbacks in our study was attributed to many of the sites being marine and eutrophic lakes, which are likely to be N-limited due to an imbalance in external loadings48 or strong denitrification49. Among both NO3- and PO4-associated feedbacks, there were no significant differences in strength between Type I and Type II feedbacks (Supplementary Fig. S7), suggesting that biodiversity can directly influence biomass (Type I), as well as through a pathway that involves endogenous nutrient variables (Type II) and eventually feeds back on itself.Causal networks under environmental contextsOur empirical analyses revealed state dependency of the causal links and feedbacks among biodiversity, biomass, and environmental factors in natural systems; that is, their strengths were highly dependent on the state of other variables. Based on a cross-system comparison (Methods), strengths of individual links (e.g., BD → EF), pairwise feedbacks (e.g., BD ↔ EF), and triangular feedbacks (e.g., BD → EF → NO3 → BD) varied systematically, depending on environmental characteristics (Fig. 4 and Supplementary Fig. S8). Ecosystems with higher species diversity (long-term average species richness) and lower average PO4 concentrations had stronger BD → EF links (Fig. 4a; correlation coefficient r = 0.600 and −0.513; P = 0.007 and 0.025 for species diversity and PO4, respectively). These results were further confirmed by stepwise regression, indicating that the ecosystems characterized by higher diversity, lower average temperature, and oligotrophic conditions had stronger BD → EF (best-fit regression model: BD → EF strength = 0.663 + 0.171*BD − 0.139*T − 0.096*PO4; F3, 15 = 9.958 and P More
