In lakes, the production and emission of methane (CH₄) have been linked to lake trophic status. However, few studies have quantified the temporal response of lake CH₄ dynamics to primary productivity at the ecosystem scale or considered how the response may vary across lakes. Here, we investigate relationships between lake CH₄ dynamics and ecosystem primary productivity across both space and time using data from five lakes in northern Wisconsin, USA. From 2014 to 2019, we estimated hypolimnetic CH₄ storage rates for each lake using timeseries of hypolimnetic CH₄ concentration through the summer season. Across all lakes and years, hypolimnetic CH₄ storage ranged from <0.001 to 7.6 mmol CH₄ m⁻² d⁻¹ and was positively related to the mean summer rate of gross primary productivity (GPP). However, within‐lake temporal responses to GPP diverged from the spatial relationship, and GPP was not a significant predictor of interannual variability in CH₄ storage at the lake scale. Using these data, we consider how and why temporal responses may differ from spatial patterns and demonstrate how extrapolating cross‐lake relationships for prediction at the lake scale may substantially overestimate the rate of change of CH₄ dynamics in response to lake primary productivity. We conclude that future predictions of lake‐mediated climate feedbacks in response to a shifting distribution of trophic status should incorporate both varying lake responses and the temporal scale of change.

中文翻译：

---

湖泊中的甲烷与初级生产力：时空关系的差异

在湖泊中，甲烷（CH ₄）的产生和排放与湖泊的营养状态有关。但是，很少有研究在生态系统规模上量化湖泊CH ₄动力学对初级生产力的时间响应，或考虑响应在整个湖泊之间如何变化。在这里，我们使用来自美国威斯康星州北部五个湖泊的数据研究了CH ₄动力学与空间和时间上生态系统初级生产力之间的关系。从2014年到2019年，我们使用整个夏季的低通量CH ₄浓度的时间序列，估算了每个湖泊的低通量CH ₄储存速率。在所有湖泊和年份中，低通量CH ₄储量范围从<0.001至7.6 mmol CH ₄  m ^-2  d ^-1，与夏季平均总初级生产率（GPP）呈正相关。但是，湖内对GPP的时间响应与空间关系不同，并且GPP并不是湖泊规模CH ₄储存年际变化的重要预测因子。利用这些数据，我们考虑时间响应如何以及为什么可能与空间模式不同，并证明在湖尺度上外推跨湖关系进行预测可能会大大高估CH ₄的变化率湖泊初级生产力的动态变化。我们得出的结论是，随着营养状况的不断变化，对湖泊介导的气候反馈的未来预测应该既包含变化的湖泊响应，也包含变化的时间尺度。