Statistical power and the detection of global change responses: The case of leaf production in old-growth forests

Forests sequester a substantial portion of anthropogenic carbon emissions. Many open questions concern how. We address two of these questions. Has leaf and fine litter production changed? And what is the contribution of old-growth forests? We address these questions with long-term records (≥10 years) of total, reproductive, and especially foliar fine litter production from 32 old-growth forests. We expect increases in forest productivity associated with rising atmospheric carbon dioxide concentrations and, in cold climates, with rising temperatures. We evaluate the statistical power of our analysis using simulations of known temporal trends parameterized with sample sizes (number of years) and levels of interannual variation observed for each record. Statistical power is inadequate to detect biologically plausible trends for records lasting less than 20 years. Modest interannual variation characterizes fine litter production, and more variable phenomena will require even longer records to evaluate global change responses with sufficient statistical power. Just four old-growth forests have records of fine litter production lasting longer than 20 years, and these four provide no evidence for increases. Three of the four forests are in central Panama, also have long-term records of wood production, and both components of aboveground production are unchanged over 21 to 38 years. The possibility that recent increases in forest productivity are limited for old-growth forests deserves more attention. The data files and R scripts found here enable the user to recreate these analyses.

森林可固存相当份额的人为碳排放。关于其固碳的具体机制，仍存在诸多悬而未决的问题。本研究聚焦其中两个核心问题：叶片与细枯落物（fine litter）的生产是否发生改变？以及原始森林（old-growth forests）的固碳贡献究竟如何？

我们依托32处原始森林的长期观测记录（观测时长≥10年），涵盖总枯落物、繁殖器官枯落物，尤其是叶片细枯落物的生产数据，以解答上述疑问。我们预期，森林生产力将随大气二氧化碳浓度升高而提升；在寒冷气候区域，森林生产力还会伴随气温上升而进一步增加。

我们通过模拟已知时间趋势的方式评估本分析的统计功效（statistical power），该模拟以各观测记录的样本量（即观测年数）及实测年际变异（interannual variation）水平作为参数进行构建。结果显示，对于观测时长不足20年的记录，其统计功效不足以检测出具备生物学合理性的可信趋势。细枯落物生产的年际变异幅度相对较小，而对于变异性更强的现象，则需要更长的观测记录，才能以足够的统计功效评估其对全球变化的响应。

目前仅有4处原始森林拥有时长超过20年的细枯落物生产观测记录，而这4处记录均未提供生产力提升的相关证据。其中3处原始森林位于巴拿马中部，同时具备木材生产的长期观测数据；在21至38年的观测周期内，这两项地上生产力指标均未出现显著变化。

原始森林的生产力提升幅度可能存在局限，这一可能性值得学界给予更多关注。本数据集附带的数据文件与R脚本可支持用户完整复现本研究的所有分析流程。