Relationships of temperature and biodiversity with stability of natural aquatic food webs

The study addresses whether and how climate warming and biodiversity change jointly affect the ecological stability of natural food webs, a fundamental yet unresolved question. Ecological stability is multidimensional; here the authors integrate two key components: structural stability, quantified as the volume contraction rate (trace of the Jacobian), indicating robustness of population dynamics to parameter changes, and temporal stability, quantified by temporal variation in species abundances (lower variation indicates higher stability). Prior work has shown temperature alters ecological parameters such as interaction strengths and growth rates, with unclear implications for multitrophic food webs where trophic levels differ in temperature sensitivity. Experimental and simulation studies report negative, neutral, or positive warming effects on temporal stability, potentially mediated by species synchrony and trophic-group-specific responses. Biodiversity is another key driver, with mixed evidence for effects on temporal stability, and a lack of direct evidence on structural stability in food webs. Most prior conclusions rely on short-term experiments or models with limited temperature ranges, which may not capture time-varying interactions and adaptation in natural ecosystems. The authors therefore take an integrative, data-driven approach using long-term time series from 19 planktonic food webs to quantify both structural and temporal stability over time and assess their relationships with temperature and biodiversity.

The paper situates its work within several strands of literature: (1) Stability dimensions: ecological stability comprises multiple facets, and combining structural (volume contraction rate, related to Jacobian trace) and temporal (variation in abundance) stability offers a more complete picture. (2) Temperature effects: Warming can modify interaction strengths, attack rates, handling times, and growth rates, with prior evidence of temperature-driven changes in structural stability in competitive communities and diverse outcomes for temporal stability in food webs (negative, neutral, positive). Mechanisms include altered species synchrony and trophic-level-specific variability. (3) Biodiversity effects: Studies report positive or neutral effects of biodiversity on temporal stability, but effects on structural stability within food webs remain largely untested. (4) Methodological gaps: Previous research often relies on short-term experiments or simulations that may not capture long-term, time-varying interaction networks typical of natural ecosystems. New empirical dynamic modeling approaches enable reconstructing dynamic interaction networks and structural stability from field data. This study fills gaps by jointly evaluating warming and biodiversity associations with both stability dimensions across many natural food webs over decadal scales.

Data: The authors compiled 19 long-term (10–30 years) seasonal time series from Europe and North America: 7 lakes, 3 marine systems (Western English Channel, Wadden Sea, Narragansett Bay), and 9 river estuaries. Species were mainly plankton; fish were excluded due to data limitations (sampling frequency, changing units). Time series were standardized to seasonal averages (trimonthly), with two missing seasonal points linearly interpolated. Species were classified into trophic groups (producers, herbivores, omnivores, predators). Species occurring at least once per 1.5 years were retained for analyses; a sensitivity analysis included rarer species (occurring once per 2 years). Abundance and temperature time series were normalized (zero mean, unit variance) for EDM analyses; raw data were used for temporal stability computations. Interaction inference (EDM): For each dataset, causal interactions among species were inferred using convergent cross mapping (CCM). Embedding dimensions E (2–9) were selected via univariate simplex projection minimizing mean absolute error. Causality required: (1) cross-mapping skill exceeding 95% of seasonality-preserving null surrogates (seasonal anomalies shuffled), and (2) significant convergence with increasing library length (Kendall’s tau trend and Fisher’s Z comparing largest vs smallest library lengths). Time-lagged CCM (0–6 months) accommodated delayed effects and was used to identify and remove likely indirect links (longer lag and lower predictive skill than direct links). Time-varying interaction strengths: Given established causal links, the multiview distance regularised S-map (MDR S-map) estimated time-varying Jacobian matrices. MDR S-map combines multiview state-space reconstruction to derive multiview distances and weights with a regularized, locally weighted S-map to estimate high-dimensional interaction coefficients (regression coefficients approximating discrete-time Jacobian entries). Parameters (state-dependence θ, penalization λ, and adjustment α) were tuned via cross-validation to minimize one-step forecast error. The trace of each Jacobian (Tr(J)) at each time point was computed. Stability metrics: Structural stability was quantified as the volume contraction rate, equivalent to Tr(J); smaller Tr(J) indicates higher structural stability (lower sensitivity to parameter perturbations). Temporal stability was quantified as the coefficient of variation (CV) of total community abundance using a 1.5-year moving window (6 time points); a wider 3-year window was used for robustness checks. Temporal stability of each trophic group (producers, consumers, predators) was computed analogously. Species synchrony: Species synchrony (φ) for the whole food web and for each trophic group was calculated as φ = Σ_i (σ_i/σ)^2, where σ^2 is variance of total abundance and σ_i is the standard deviation of species i. φ ranges from 0 (complete asynchrony) to 1 (perfect synchrony). Biodiversity metrics: Time-varying species richness (number of species with positive abundance per time point) and Simpson diversity (1 − Σ p_i^2) were computed. Statistical analyses: Linear mixed models (two-sided) related temperature, species richness, and Simpson diversity to (a) structural stability (Tr(J)), (b) temporal stability (CV), (c) contributions to Tr(J) from trophic groups (sums of diagonal Jacobian entries for producers, consumers, predators), and (d) species synchrony (φ). Random effects accounted for year, season, and sampling location as appropriate. Additional analyses examined latitudinal patterns and whether temperature influenced biodiversity (richness, Simpson). Network structural attributes (link density L/S, connectance L/S^2, food chain length) and their relationships with stability were also assessed. All analyses were conducted in R (rEDM, lme4, zoo).

- Across 19 planktonic food webs, higher temperatures were associated with lower structural stability (higher Tr(J)) and lower temporal stability (higher CV). These trends were consistent across systems overall but varied within systems. - Biodiversity effects were not consistent across stability dimensions: species richness was associated with lower structural stability but higher temporal stability; Simpson diversity was associated with higher temporal stability and showed no consistent association with structural stability. - System-level counts: Temperature had negative effects on structural stability in 13/19 food webs and on temporal stability in 11/19. Species richness negatively affected structural stability in 14/19 and positively affected temporal stability in 17/19. Simpson diversity positively affected temporal stability in 13/19. - Latitude: Structural stability showed no latitudinal trend; temporal stability was higher at higher latitudes. - Temperature did not significantly affect either biodiversity index (species richness or Simpson diversity), suggesting predominantly direct temperature effects on stability rather than indirect effects via biodiversity. - Mechanisms for structural stability: Temperature effects on structural stability were largely mediated by increased contributions from predators (sum of predator diagonal Jacobian entries), which increased Tr(J), reducing structural stability. Species richness increased contributions from consumers; effects on contributions from producers were not detected. - Mechanisms for temporal stability: Temporal stability of food webs was linked to species synchrony. Warmer temperatures increased overall species synchrony (raising CV, reducing temporal stability), whereas higher species richness and Simpson diversity decreased synchrony (lowering CV, increasing temporal stability). Producers’ temporal stability and synchrony strongly influenced whole-food-web stability and synchrony; Simpson diversity increased temporal stability across all trophic groups, while temperature and richness most strongly affected producers. - Network structure: Higher mean temperature was associated with lower link density (L/S), which in turn reduced temporal stability. Higher mean species richness increased link density, which increased temporal stability. Connectance (L/S^2) and food chain length showed no detectable effects on structural or temporal stability. - Results were robust to varying the moving window length for CV and to inclusion of rarer species.

The findings demonstrate that warmer temperatures erode both structural and temporal stability in natural planktonic food webs. Structural stability reductions appear to arise from temperature-driven changes in predator dynamics, reflected in increased diagonal contributions in the Jacobian for predators, indicating reduced robustness to parameter perturbations. Temporal stability reductions under warming are linked to increased species synchrony at the community level, which amplifies aggregate variability. In contrast, biodiversity effects are nuanced: greater species richness may destabilize structure (lower structural stability) while stabilizing dynamics over time (higher temporal stability), and higher Simpson diversity generally stabilizes temporal dynamics. These stabilizing biodiversity effects on temporal dynamics are mediated partly through reduced synchrony and enhanced link density, with producers playing a central role in determining community-level synchrony and stability. The absence of a temperature effect on biodiversity indices suggests that warming impacts stability primarily via direct physiological and interaction-mediated pathways rather than through biodiversity changes over the timescales studied. Together, the results underscore the importance of considering multiple stability dimensions and trophic-group-specific mechanisms when evaluating the effects of global change on ecosystem functioning.

This study integrates long-term data from 19 natural planktonic food webs with empirical dynamic modeling to jointly assess how temperature and biodiversity relate to structural and temporal stability. Warmer temperatures consistently reduce both forms of stability, driven by predator-dominated contributions to structural instability and by increased community synchrony for temporal instability. Biodiversity changes do not have uniform effects across stability dimensions: species richness tends to reduce structural stability yet enhance temporal stability, while Simpson diversity promotes temporal stability. Network structure (link density) and producers’ dynamics are key mediators of whole-community outcomes. These results provide field-based evidence that warming can erode ecosystem stability in natural food webs and highlight that biodiversity’s role is context-dependent across stability facets. Future work could experimentally test the causal mechanisms inferred here, extend analyses to additional ecosystem types and higher trophic levels (e.g., fish), incorporate trait and body-size information, and develop predictive frameworks that jointly model temperature, biodiversity, interaction networks, and multiple stability dimensions over longer timescales.

- Observational design: The analyses are correlational; while termed effects, relationships are associations and may be influenced by unmeasured covariates. - Taxonomic scope: Fish were excluded due to data limitations; results pertain mainly to planktonic components and may not generalize to entire food webs including higher vertebrate consumers. - Data harmonization: Seasonal averaging to a common trimonthly resolution and interpolation of two missing seasonal points may smooth short-term dynamics. - Species inclusion: Species rarest than once per 1.5 years were initially excluded to avoid zero-inflation in time series; although sensitivity analyses with rarer species yielded similar conclusions, exclusion may affect network reconstruction. - System dependence: Within-system responses varied, indicating context dependency across ecosystems. - Methodological assumptions: EDM/CCM and MDR S-map rely on adequate time series length and stationarity of embedding; inferred Jacobians approximate local linearizations and may be sensitive to noise and parameter tuning.