Biomass distribution among size classes follows a power law where the Log-abundance of taxa scales to Log-size with a slope that responds to environmental abiotic and biotic conditions. The interactions between ecological mechanisms controlling the slope of locally realized size-abundance relationships (SAR) are however not well understood. Here we tested how warming, nutrient levels, and grazing affect the slope of phytoplankton community SARs in decadal time-series from eight Swiss lakes of the peri-alpine region, which underwent environmental forcing due to climate change and oligotrophication. We expected rising temperature to have a negative effect on slope (favoring small phytoplankton), and increasing nutrient levels and grazing pressure to have a positive effect (benefiting large phytoplankton). Using a random forest approach to extract robust patterns from the noisy data, we found that the effects of temperature (direct and indirect through water column stability), nutrient availability (phosphorus and total biomass), and large herbivore (copepods and daphnids) grazing and selectivity on slope were non-linear and interactive. Increasing water temperature or total grazing pressure, and decreasing phosphorus levels, had a positive effect on slope (favoring large phytoplankton, which are predominantly mixotrophic in the lake dataset). Our results therefore showed patterns that were opposite to the expected long-term effects of temperature and nutrient levels, and support a paradigm in which (i) small phototrophic phytoplankton appear to be favored under high nutrients levels, low temperature and low grazing, and (ii) large mixotrophic algae are favored under oligotrophic conditions when temperature and grazing pressure are high. The effects of temperature were stronger under nutrient limitation, and the effects of nutrients and grazing were stronger at high temperature. Our study shows that the phytoplankton local SARs in lakes respond to both the independent and the interactive effects of resources, grazing and water temperature in a complex, unexpected way, and observations from long-term studies can deviate significantly from general theoretical expectations.

中文翻译：

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八个瑞士湖泊中的相互作用温度，养分和浮游动物放牧控制浮游植物的大小-丰度关系。

大小类别之间的生物量分布遵循幂律，其中分类单元的对数丰度以对环境非生物和生物条件有响应的斜率缩放为对数大小。但是，人们对控制局部实现的大小－丰度关系（SAR）的斜率的生态机制之间的相互作用尚不甚了解。在这里，我们测试了变暖，养分含量和放牧如何以十年为时间序列，对来自高寒周缘地区的八个瑞士湖泊的浮游植物群落SAR的坡度产生影响，这些湖泊由于气候变化和富营养化而经历了环境强迫。我们预计温度升高对坡度会产生负面影响（有利于小型浮游植物），而提高养分水平和放牧压力会带来积极影响（有利于大型浮游植物）。使用随机森林方法从嘈杂的数据中提取鲁棒的模式，我们发现温度（直接和间接通过水柱稳定性），养分利用率（磷和总生物量）以及大型草食动物（足足纲和水蚤）的影响斜率的选择性是非线性的和相互作用的。升高水温或总放牧压力以及降低磷含量对坡度有积极影响（有利于大型浮游植物，这在湖泊数据集中主要是营养混合型）。因此，我们的结果显示出与预期的温度和养分水平长期影响相反的模式，并支持以下范例：（i）在高养分水平，低温和低放牧条件下，小型光养浮游植物似乎受到青睐，（ii）在温度和放牧压力高的贫营养条件下，首选大型营养营养藻类。在养分限制条件下，温度的影响较强，在高温下，养分和放牧的影响较强。我们的研究表明，湖泊中的浮游植物局部SAR以复杂，出乎意料的方式响应资源，放牧和水温的独立和交互作用，长期研究的观察结果可能与一般的理论预期有很大差异。