Seasonal variation in marine C:N:P stoichiometry: can the composition of seston explain stable Redfield ratios?

Seston is suspended particulate organic matter, comprising a mixture of autotrophic, heterotrophic and detrital material. Despite variable proportions of these components, marine seston often exhibits relatively small deviations from the Redfield ratio (C:N:P = 106:16:1). Two time-series from the Norwegian shelf in Skagerrak are used to identify drivers of the seasonal variation in seston elemental ratios. An ordination identified water mass characteristics and bloom dynamics as the most important drivers for determining C:N, while changes in nutrient concentrations and biomass were most important for the C:P and N:P relationships. There is no standardized method for determining the functional composition of seston and the fractions of POC, PON and PP associated with phytoplankton, therefore any such information has to be obtained by indirect means. In this study, a generalized linear model was used to differentiate between the live autotrophic and non-autotrophic sestonic fractions, and for both stations the non-autotrophic fractions dominated with respective annual means of 76 and 55%. This regression model approach builds on assumptions (e.g. constant POC:Chl-a ratio) and the robustness of the estimates were explored with a bootstrap analysis. In addition the autotrophic percentage calculated from the statistical model was compared with estimated phytoplankton carbon, and the two independent estimates of autotrophic percentage were comparable with similar seasonal cycles. The estimated C:nutrient ratios of live autotrophs were, in general, lower than Redfield, while the non-autotrophic C:nutrient ratios were higher than the live autotrophic ratios and above, or close to, the Redfield ratio. This is due to preferential remineralization of nutrients, and the P content mainly governed the difference between the sestonic fractions. Despite the seasonal variability in seston composition and the generally low contribution of autotrophic biomass, the variation observed in the total seston ratios was low compared to the variation found in dissolved and particulate pools. Sestonic C:N:P ratios close to the Redfield ratios should not be used as an indicator of phytoplankton physiological state, but could instead reflect varying contributions of sestonic fractions that sum up to an elemental ratio close to Redfield

Variation in the seston C:N ratio of the Arctic Ocean and pan-Arctic shelves

Studying more than 3600 observations of particulate organic carbon (POC) and particulate organic nitrogen (PON), we evaluate the applicability of the classic Redfield C:N ratio (6.6) and the recently proposed Sterner ratio (8.3) for the Arctic Ocean and pan-Arctic shelves. The confidence intervals for C:N ranged from 6.43 to 8.82, while the average C:N ratio for all observations was 7.4. In general, neither the Redfield or Sterner ratios were applicable, with the Redfield ratio being too low and the Sterner ratio too high. On a regional basis, all northern high latitude regions had a C:N ratio significantly higher than the Redfield ratio, except the Arctic Ocean (6.6), Chukchi (6.4) and East Siberian (6.5) Seas. The latter two regions were influenced by nutrient-rich Pacific waters, and had a high fraction of autotrophic (i.e. algal-derived) material. The C:N ratios of the Laptev (7.9) and Kara (7.5) Seas were high, and had larger contributions of terrigenous material. The highest C:N ratios were in the North Water (8.7) and Northeast Water (8.0) polynyas, and these regions were more similar to the Sterner ratio. The C:N ratio varied between regions, and was significantly different between the Atlantic (6.7) and Arctic (7.9) influenced regions of the Barents Sea, while the Atlantic dominated regions (Norwegian, Greenland and Atlantic Barents Seas) were similar (6.7–7). All observations combined, and most individual regions, showed a pattern of decreasing C:N ratios with increasing seston concentrations. This meta-analysis has important implications for ecosystem modelling, as it demonstrated the striking temporal and spatial variability in C:N ratios and challenges the common assumption of a constant C:N ratio. The non-constant stoichiometry was believed to be caused by variable contributions of autotrophs, heterotrophs and detritus to seston, and a significant decrease in C:N ratios with increasing Chlorophyll a concentrations supports this view. This study adds support to the use of a power function model, where the exponent is system-specific, but we suggest a general Arctic relationship, where POC = 7.4 PON0.89

Extracting risk neutral probability densities by fitting implied volatility smiles: some methodological points and an application to the 3M Euribor futures option prices

Following Shimko (1993), a large amount of research has evolved around the problem of extracting risk neutral densities from options prices by interpolating the Balck-Scholes implied volatility smile. Some of the methods recently proposed use variants of the cubic spline. Thesee methods have the property of producing non-differentiable probability densities. We argue that this is an undesirable feature and suggest circumventing the problem by fitting a smoothing spline of higher order polynomials with a relatively low number of knot points. In the estimations we opt for a measure of roughness penalty, which is more appropriate than the plain second partial derivative often used. We apply this technique to the LIFFE three-month Euribor future option proces. Constant horizon risk neutral densities are calculated and summary statistics from these densities are used to assess market uncertainty on a day-by-day basis. Finally, we analyse the impact of the 11 September attacks on the expectation of future Euribor interest rates. JEL Classification: C14, F33, G15

Extracting risk neutral probability densities by fitting implied volatility smiles: Some methodological points and an application to the 3M Euribor futures option prices

Following Shimko (1993), a large amount of research has evolved around the problem of extracting risk neutral densities from options prices by interpolating the Black-Scholes implied volatility smile. Some of the methods recently proposed use variants of the cubic spline. These methods have the property of producing non-differentiable probability densities. We argue that this is an undesirable feature and suggest circumventing the problem by fitting a smoothing spline of higher order polynomials with a relatively low number of knot points. In the estimations we opt for a measure of roughness penalty, which is more appropriate than the plain second partial derivative often used. We apply this technique to the LIFFE three-month Euribor futures option prices. Constant horizon risk neutral densities are calculated and summary statistics from these densities are used to assess market uncertainty on a day-by-day basis. Finally, we analyse the impact of the 11 September attacks on the expectation of future Euribor interest rates

Extracting risk neutral probability densities by fitting implied volatility smiles: some methodological points and an application to the 3M Euribor futures option prices

Following Shimko (1993), a large amount of research has evolved around the problem of extracting risk neutral densities from options prices by interpolating the Balck-Scholes implied volatility smile. Some of the methods recently proposed use variants of the cubic spline. Thesee methods have the property of producing non-differentiable probability densities. We argue that this is an undesirable feature and suggest circumventing the problem by fitting a smoothing spline of higher order polynomials with a relatively low number of knot points. In the estimations we opt for a measure of roughness penalty, which is more appropriate than the plain second partial derivative often used. We apply this technique to the LIFFE three-month Euribor future option proces. Constant horizon risk neutral densities are calculated and summary statistics from these densities are used to assess market uncertainty on a day-by-day basis. Finally, we analyse the impact of the 11 September attacks on the expectation of future Euribor interest rates