Fig. 3: Analysis of rate of change (RoC) in algal production and diversity relative to climate change.

a GAM-based time series representations of ecosystem (TOC, pigments and algal diversity from sedaDNA) and climate dynamics (regional temperature from instrument measurement, modeling and ice δ¹⁸O reconstruction), respectively, alongside their corresponding RoC, with 95% simultaneous confidence intervals (CI) depicted by color ribbons, with red lines marking significant acceleration (the 95% CI do not encompass zero) of phytoplankton abundance and temperature warming within the past two centuries. The horizontal dashed line is located to distinguish between acceleration and deceleration (RoC = 0). Ecosystem and climatic RoC for statistical analysis in (b) and (c) were generated based on multivariate rate calculations in (a). b Comparative statistics highlighting all RoC values summarized within climate and ecosystem across distinct timeframes. Black lines mark the mean values, while illustrate the disparity in RoC between climate and ecosystem, emphasizing periods of significant divergence. Parentheses with significance markers indicate differences between any two groups, based on ANOVA analysis. The significance levels are *p < 0.05, **p < 0.01, ***p < 0.001. c The ratio of RoC between ecosystem and climate on a 1:1 scale, illustrating the relative pace of change in each domain. Gradient color scatters denote the dynamic of RoC over time at different periods. The black dashed line represents the 1:1 line, while the black solid line shows the GAM-fitted result for the scatter points. The RoC of climate change as the independent variable (predictors) and the rate of ecological change as the dependent variable (responses). The gray shading indicates the 95% CI. The red horizontal error bars represent the uncertainty of the climate rate (95% CI), and the light blue vertical error bars represent the uncertainty of the ecological rate (95% CI).