Abstract. The exchange rate of inorganic phosphorus (P) between the soil solution and solid phase, also known as soil solution P turnover, is essential for describing the kinetics of bioavailable P. While soil solution P turnover (K m ) can be determined by tracing radioisotopes in a soil-solution system, few studies have done so. We believe that this is due to a lack of understanding on how to derive K m from isotopic exchange kinetic (IEK) experiments, a common form of radioisotope dilution study. Here, we provide a derivation of calculating K m using parameters obtained from IEK experiments. We then calculated K m for 217 soils from published IEK experiments in terrestrial ecosystems, and also that of 18 long-term P fertilizer field experiments. Analysis of the global compilation data set revealed a negative relationship between concentrations of soil solution P and K m . Furthermore, K m buffered isotopically exchangeable P in soils with low concentrations of soil solution P. This finding was supported by an analysis of long-term P fertilizer field experiments, which revealed a negative relationship between K m and phosphate-buffering capacity. Our study highlights the importance of calculating K m for understanding the kinetics of P between the soil solid and solution phases where it is bioavailable. We argue that our derivation can also be used to calculate soil solution turnover of other environmentally relevant and strongly sorbing elements that can be traced with radioisotopes, such as zinc, cadmium, nickel, arsenic, and uranium.
Learning, especially rapid learning, is critical for survival. However, learning is hard: a large number of synaptic weights must be set based on noisy, often ambiguous, sensory information. In such a high-noise regime, keeping track of probability distributions over weights is the optimal strategy. Here we hypothesize that synapses take that strategy; in essence, when they estimate weights, they include error bars. They then use that uncertainty to adjust their learning rates, with more uncertain weights having higher learning rates. We also make a second, independent, hypothesis: synapses communicate their uncertainty by linking it to variability in PSP size, with more uncertainty leading to more variability. These two hypotheses cast synaptic plasticity as a problem of Bayesian inference, and thus provide a normative view of learning. They generalize known learning rules, offer an explanation for the large variability in the size of postsynaptic potentials, and make falsifiable experimental predictions.
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