Robert Redfield (1898–1958)

Geomancy is common in Southeast Asia. The imaginative association of disparate spatial and temporal coordinates allows discourses to emerge in which problems that cannot be resolved in the real world may be ‘thought’ through geomantic images and symbols. The Hindu‐Buddhist cosmographies of Southeast Asia form a framework within which the ‘geomancies’ of minority peoples take place. By modifying the relations of the real world, or depicting them in a timeless way, geomancy like poetry may allow changes to be experienced at a conceptual level before they are introduced into pragmatic affairs, or act against suck changes being brought about.     

Uncertainties in Data and Spurious Correlations Related to the Redfield Ratio

Spurious correlations is a fundamental problem in situations where the y‐variable is a function of x, such as ratios u/x versus x or u, or products, such as u × x versus x or u, or expressions such as (u–x) versus x. The theory of spurious correlations was developed more than 100 years ago and yet there are numerous papers in aquatic ecology presenting results as if they were mechanistically meaningful when they, in fact, are clearly spurious. This is specifically so in contexts related to some of the most important issues in aquatic ecology namely the question of “limiting” nutrient and the Redfield ratio, defined as either TN/TP or DIN/DIP (TN = total‐N, TP = total‐P, DIN = dissolved inorganic N, DIP dissolved inorganic P). We have demonstrated by systematic tests using randomly generated data that the patterns in spurious relationships can be identical to patterns in empirical data that have been interpretated in mechanistic terms. We have collected empirical data from the Baltic Sea, Kattegat and Skagerack and tested those data to see if spurious relationships exist. The r² ‐values vary from 0.90 (TN/TP versus TP), 0.67 (DIN/DIP versus DIN), 0.40 (DIN/DIP versus DIP) to 0.014 (TN/TP versus TN). Very little mechanistic understanding about “limiting nutrient” and/or the role of TN/TP or DIN/DIP‐ratios can be deduced from these – and similar results – because they are spurious. We have also shown that the ratios TN/TP and DIN/DIP have significantly higher coefficients of variations (CV) than TN, TP, DIN and DIP individually. This explains why these ratios generally are poor predictors in contexts of nutrient limitation and in modeling of primary production. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The origins of the Redfield nitrogen-to-phosphorus ratio are in a homoeostatic protein-to-rRNA ratio

One of the most intriguing patterns in the biosphere is the similarity of the atomic nitrogen-to-phosphorus ratio (N:P) = 16 found in waters throughout the deep ocean and in the plankton in the upper ocean. Although A.C. Redfield proposed in 1934 that the intracellular properties of plankton were central to this pattern, no theoretical significance for N:P = 16 in cells had been found. Here, we use theoretical modelling and a compilation of literature data for prokaryotic and eukaryotic microbes to show that the balance between two fundamental processes, protein and rRNA synthesis, results in a stable biochemical attractor that homoeostatically produces a given protein:rRNA ratio. Furthermore, when biochemical constants and reasonable kinetic parameters for protein synthesis and ribosome production under nutrient-replete conditions are applied in the model, it predicts a stable protein:rRNA ratio of 3 ± 0.7, which corresponds to N:P = 16 ± 3. The model also predicts that N-limitation, by constraining protein synthesis rates, will result in N:P ratios below the Redfield value while P-limitation, by constraining RNA production rates, will produce ratios above the Redfield value. Hence, one of most biogeochemically significant patterns on Earth is inherently rooted in the fundamental structure of life.     

Redfield revisited: variability of C:N:P in marine microalgae and its biochemical basis

Cytological events immediately following plasmogamy in Durvillaea potatorum are described. Eggs contain several types of cytoplasmic vesicle differing in size and appearance. Histochemical tests and measurements are used to characterise and distinguish different types of vesicle containing phenolic compounds, lipids and polysaccharides. Within 2 min of plasmogamy, small phenolic vesicles located just below the egg membrane undergo mass synchronised exocytosis. The contents of these vesicles are discharged as phenolic bodies on the outside of the membrane. Secretion of phenolic bodies precedes secretion of the primary zygote wall by several minutes. Limited secretion of phenolics also occurs in unfertilised eggs. Peripheral phenolic vesicles are distinguishable from physodes, which also contain phenolic compounds but which are significantly larger and tend to be localised around the egg nucleus. The possible functional significance of the phenolic bodies is discussed. Coated pits and vesicles are common in zygotes, and their presence is evidence for endocytosis.     

Excitation Dynamics in Phycoerythrin 545: Modeling of Steady-State Spectra and Transient Absorption with Modified Redfield Theory

We model the spectra and excitation dynamics in the phycobiliprotein antenna complex PE545 isolated from the unicellular photosynthetic cryptophyte algae Rhodomonas CS24. The excitonic couplings between the eight bilins are calculated using the CIS/6-31G method. The site energies are extracted from a simultaneous fit of the absorption, circular dichroism, fluorescence, and excitation anisotropy spectra together with the transient absorption kinetics using the modified Redfield approach. Quantitative fit of the data enables us to assign the eight exciton components of the spectra and build up the energy transfer picture including pathways and timescales of energy relaxation, thus allowing a visualization of excitation dynamics within the complex.     

Mixing of exciton and charge-transfer states in Photosystem II reaction centers: modeling of Stark spectra with modified Redfield theory

We propose an exciton model for the Photosystem II reaction center (RC) based on a quantitative simultaneous fit of the absorption, linear dichroism, circular dichroism, steady-state fluorescence, triplet-minus-singlet, and Stark spectra together with the spectra of pheophytin-modified RCs, and so-called RC5 complexes that lack one of the peripheral chlorophylls. In this model, the excited state manifold includes a primary charge-transfer (CT) state that is supposed to be strongly mixed with the pure exciton states. We generalize the exciton theory of Stark spectra by 1), taking into account the coupling to a CT state (whose static dipole cannot be treated as a small parameter in contrast to usual excited states); and 2), expressing the line shape functions in terms of the modified Redfield approach (the same as used for modeling of the linear responses). This allows a consistent modeling of the whole set of experimental data using a unified physical picture. We show that the fluorescence and Stark spectra are extremely sensitive to the assignment of the primary CT state, its energy, and coupling to the excited states. The best fit of the data is obtained supposing that the initial charge separation occurs within the special-pair PD1PD2. Additionally, the scheme with primary electron transfer from the accessory chlorophyll to pheophytin gave a reasonable quantitative fit. We show that the effectiveness of these two pathways is strongly dependent on the realization of the energetic disorder. Supposing a mixed scheme of primary charge separation with a disorder-controlled competition of the two channels, we can explain the coexistence of fast sub-ps and slow ps components of the Phe-anion formation as revealed by different ultrafast spectroscopic techniques.     

Performance of the Redfield Ratio and a Family of Nutrient Limitation Indicators as Thresholds for Phytoplankton N vs. P Limitation

We aim to define the best nutrient limitation indicator predicting phytoplankton biomass increase as a result of nutrient enrichment (N, P, or both). We compare the abilities of different indicators, based on chemical measurements of nitrogen (N) and phosphorus (P) fractions in the initial plankton community, to predict the limiting factor for phytoplankton growth as inferred independently from short-term laboratory experiments on the same natural communities in a data set from NE Baltic Sea (Tamminen and Andersen, Mar Ecol Prog Ser 340:121–138, 2007). The best indicators had a true positive rate of about 80% for predicting both N and P limitation, but with a higher false positive rate for N than for P limitation (25 vs. 5%). Estimated threshold ratios for total nutrients (TN:TP) were substantially higher than the Redfield ratio, reflecting the relatively high amounts of biologically less available dissolved organic N in the study area. The best overall performing indicator, DIN:TP, had chlorophyll-response based threshold ratios far below Redfield, with N limitation below 2:1 and P limitation above 5:1 (by atoms). On the contrary, particulate N:P ratio was the overall worst predictor for N or P limitation, with values clustering around the Redfield N:P ratio (16:1, by atoms) independent of the limiting factor. Estimated threshold ratios based on inorganic nutrients (DIN:DIP) and so-called biologically available nutrients (BAN:BAP = (PON + DIN):(POP + DIP)) were also generally clearly above 16:1, indicating that the Redfield ratio rather reflects the transition from N limitation to combined N + P limitation, than to single limitation by P. Coastal systems are complex systems with regard to nutrient dynamics, historically considered to represent the transition from P-limited freshwater to N-limited marine systems. Our analysis shows that rather simple ratios reflect phytoplankton requirement for nutrients. Based on the high prediction performance, analytical considerations, and general data availability, the DIN:TP ratio appears to be the best indicator for inferring in situ N vs. P limitation of phytoplankton from chemical monitoring data.