A statistical approach to evaluating distance metrics and analog assignments for pollen records

The modern analog technique typically uses a distance metric to determine the dissimilarity between fossil and modern biological assemblages. Despite this quantitative approach, interpretation of distance metrics is usually qualitative and rules for selection of analogs tend to be ad hoc. We present a statistical tool, the receiver operating characteristic (ROC) curve, which provides a framework for identifying analogs from distance metrics. If modern assemblages are placed into groups (e.g., biomes), this method can (1) evaluate the ability of different distance metrics to distinguish among groups, (2) objectively identify thresholds of the distance metric for determining analogs, and (3) compute a likelihood ratio and a Bayesian probability that a modern group is an analog for an unknown (fossil) assemblage. Applied to a set of 1689 modern pollen assemblages from eastern North America classified into eight biomes, ROC analysis confirmed that the squared-chord distance (SCD) outperforms most other distance metrics. The optimal threshold increased when more dissimilar biomes were compared. The probability of an analog vs no-analog result (a likelihood ratio) increased sharply when SCD decreased below the optimal threshold, indicating a nonlinear relationship between SCD and the probability of analog. Probabilities of analog computed for a postglacial pollen record at Tannersville Bog (Pennsylvania, USA) identified transitions between biomes and periods of no analog.     

Anthropogenic contributions to atmospheric Hg, Pb and As accumulation recorded by peat cores from southern Greenland and Denmark dated using the C “bomb pulse curve”

Mercury concentrations are clearly elevated in the surface and sub-surface layers of peat cores collected from a minerotrophic (“groundwater-fed”) fen in southern Greenland (GL) and an ombrotrophic (“rainwater-fed”) bog in Denmark (DK). Using ¹⁴C to precisely date samples since ca. AD 1950 using the “atmospheric bomb pulse,” the chronology of Hg accumulation in GL is remarkably similar to the bog in DK where Hg was supplied only by atmospheric deposition: this suggests not only that Hg has been supplied to the surface layers of the minerotrophic core (GL) primarily by atmospheric inputs, but also that the peat cores have preserved a consistent record of the changing rates of atmospheric Hg accumulation. The lowest Hg fluxes in the GL core (0.3 to 0.5 μg/m²/yr) were found in peats dating from AD 550 to AD 975, compared to the maximum of 164 μg/m²/yr in AD 1953. Atmospheric Hg accumulation rates have since declined, with the value for 1995 (14 μg/m²/yr) comparable to the value for 1995 obtained by published studies of atmospheric transport modelling (12 μg/m²/yr).The greatest rates of atmospheric Hg accumulation in the DK core are also found in the sample dating from AD 1953 and are comparable in magnitude (184 μg/m²/yr) to the GL core; again, the fluxes have since gone into strong decline. The accumulation rates recorded by the peat core for AD 1994 (14 μg/m²/yr) are also comparable to the value for 1995 obtained by atmospheric transport modelling (18 μg/m²/yr). Comparing the Pb/Ti and As/Ti ratios of the DK samples with the corresponding crustal ratios (or “natural background values” for preanthropogenic peat) shows that the samples dating from 1953 also contain the maximum concentration of “excess” Pb and As. The synchroneity of the enrichments of all three elements (Hg, Pb, and As) suggests a common source, with coal-burning the most likely candidate. Independent support for this interpretation was obtained from the Pb isotope data (²⁰⁶Pb/²⁰⁷Pb = 1.1481 ± 0.0002 in the leached fraction and 1.1505 ± 0.0002 in the residual fraction) which is too radiogenic to be explained in terms of gasoline lead alone, but compares well with values for U.K. coals. In contrast, the lowest values for ²⁰⁶Pb/²⁰⁷Pb in the DK profile (1.1370 ± 0.0003 in the leached fraction and 1.1408 ± 0.0003 in the residual fraction) are found in the sample dating from AD 1979: this shows that the maximum contribution of leaded gasoline occurred approximately 25 yr after the zenith in total anthropogenic Pb deposition.     

Determination of food web support and trophic position of the mummichog,Fundulus heteroclitus, in New Jersey smooth cordgrass (Spartina alterniflora), common reed (Phragmites australis), and restored salt marshes

The invasion ofPhragmites australis into tidal marshes formerly dominated bySpartina alterniflora has resulted in considerable interest in the consequences of this invasion for the ecological functions of marsh habitat. We examined the provision of trophic support for a resident marsh fish,Fundulus heteroclitus, in marshes dominated byP. australis, byS. alterniflora, and in restored marshes, using multiple stable isotope analysis. We first evaluated our ability to distinguish among potential primary producers using the multiple stable isotope approach. Within a tidal creek system we found significant marsh and elevation effects on microalgal isotope values, and sufficient variability and overlap in primary producer isotope values to create some difficulty in identifying unique end members. The food webs supportingF. heteroclitus production were examined using dual isotope plots. At both sites, the δ¹³C values ofF. heteroclitus were clustered over values for benthic microalgae (BMI) and approximately midway between δ¹³C values ofSpartina andPhragmites. Based on comparisons of fish and primary producer δ¹³C, δ¹⁵N, and δ³⁴S values, and consideration ofF. heteroclitus feeding habits, we conclude that BMI were a significant component of the food web supportingF. heteroclitus in these brackish marshes, especially recently-hatched fish occupying pools on the marsh surface. A 2‰ difference in δ¹³C betweenFundulus occupying nearly adjacentSpartina andPhragmites marshes may be indicative of relatively less reliance on BMI and greater reliance onPhragmites production inPhragmites-dominated marshes, a conclusion consistent with the reduced BMI biomass found inPhragmites marshes. The mean δ¹³C value ofF. heteroclitus from restored marshes was intermediate between values of fish from naturally occurringSpartina marshes and areas invaded byPhragmites. We also examined the isotopic evidence for ontogenetic changes in the trophic position of larval and juvenileF. heteroclitus. We found significant positive relationships betweenF. heteroclitus δ¹⁵N values and total length, reflective of an increase in trophic position as fish grow.F. heteroclitus δ¹⁵N values indicate that these fish are feeding approximately two trophic levels above primary producers.     

Computational study of tetrahedral Al–Si and octahedral Al–Mg ordering in phengite

 As part of a wider study of the nature and origins of cation order–disorder in micas, a variety of computational techniques have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K₂ ^[6](Al₃Mg)^[4](Si₇Al)O₂₀(OH)₄. Values of the atomic exchange interaction parameters J _n used to model the energies of order–disorder were calculated. Both tetrahedral Al–Si and octahedral Al–Mg ordering were studied and hence three types of interaction parameter were necessary: for T–T, O–O and T–O interactions (where T denotes tetrahedral sites and O denotes octahedral sites). Values for the T–T and O–O interactions were taken from results on other systems, whilst we calculated new values for the T–O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets alone and independently produces different results from modelling a whole T–O–T layer, hence justifying the inclusion of the T–O interactions. Simulations of a whole T–O–T layer of phengite indicated the presence of short-range order, but no long-range order was observed. Received: 8 August 2002 / Accepted: 14 February 2003 Acknowledgements The authors are grateful to EPSRC (EJP) and the Royal Society (CIS) for financial support. Monte Carlo simulations were performed on the Mineral Physics Group's Beowulf cluster and the University of Cambridge's High Performance Computing Facility.     

Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields

The basic concepts of spectral and multiscale selective reconstruction of (geophysically relevant) vector fields on the sphere from error-affected data is outlined in detail. The reconstruction mechanism is formulated under the assumption that spectral as well as multiscale approximation is well-representable in terms of only a certain number of expansion coefficients at the various resolution levels. It is shown that spectral denoising by means of orthogonal expansions in terms of vector spherical harmonics reflects global a priori information of the noise (e.g., in form of a covariance tensor field), whereas multiscale signal-to-noise thresholding can be performed under locally dependent noise information within a multiresolution analysis in terms of spherical vector wavelets. An application of the multiscale formalism to Earth's magnetic field determination is presented.     

Kinetics and Mechanism of Trithionate and Tetrathionate Oxidation at Low pH by Hydroxyl Radicals

The oxidation kinetics of trithionate (S₃O₆^2- ) and tetrathionate (S₄O ₆ ^2- ) with hydroxyl radicals (OH^*) have been investigated in systems analogous to acid mine drainage (AMD) environments. The discovery of hydroxyl radical (OH^*) formation on pyrite surfaces (Borda et al., 2003) suggests hydroxyl radicals may affect the oxidation kinetics of intermediate sulfur species such as tetrathionate. Cyclic voltammetry experiments in acidic solutions indicate that the reaction of S₄O ₆ ^2- with OH^* goes through an unknown intermediate, tentatively assigned as S₃O ₄ ^n- . An outer-sphere electron transfer mechanism for the reaction of S₄O ₆ ^2- with OH^* to form S₃O ₄ ^n- is proposed based on experimental results. Oxidation rates for trithionate and tetrathionate in the presence of Fenton's reagent (which forms hydroxyl radicals) are too fast to be directly measured using UV-Vis spectrophotometry, electrochemical, or stop-flow spectrophotometry methods. Competitive reaction kinetics within the context of the Haber—Weiss mechanism suggests that the rate constant for the oxidation of trithionate and tetrathionate with OH^* is in excess of 10⁸ M^-1 sec^-1.     

Strontium isotope evolution of Late Permian and Triassic seawater

The ⁸⁷Sr/⁸⁶Sr values based on brachiopods and conodonts define a nearly continuous record for the Late Permian and Triassic intervals. Minor gaps in measurements exist only for the uppermost Brahmanian, lower part of the Upper Olenekian, and Middle Norian, and only sparse data are available for the Late Permian. These 219 measurements include 67 brachiopods and 114 conodont samples from the Tethyan realm as well as 37 brachiopods and one conodont sample from the mid-European Middle Triassic Muschelkalk Sea. The Late Permian/Lower Triassic interval is characterized by a steep 1.3 × 10⁻³ rise, from 0.7070 at the base of the Dzhulfian to 0.7082 in the late Olenekian, a rate of change comparable to that in the Cenozoic. In the mid-Triassic (Anisian and Ladinian), the isotope values fall to 0.7075, followed again by a rise to 0.7081 in the Middle/Late Norian. The ⁸⁷Sr/⁸⁶Sr values decline again in the Late Norian (Sevatian) and Rhaetian to 0.7076.The sharp rise in the ⁸⁷Sr/⁸⁶Sr values during the Late Permian/Early Triassic was coincident with widespread clastic sedimentation. Because of the paucity of tectonic uplifts, the enhanced erosion may have been due to intermittent humid phases, during mainly an arid interval, coupled with the absence of a dense protective land plant cover following the mass extinction during the latest Permian. The apex of the ⁸⁷Sr/⁸⁶Sr curve at the Olenekian/Anisian boundary coincides with cessation of the large-scale clastic sedimentation and also marks the final recovery of land vegetation, as indicated by the renewed onset of coal formation in the Middle Triassic. The rising ⁸⁷Sr/⁸⁶Sr values from the Middle Carnian to the Late Norian coincide with the uplift and erosion of the Cimmeride-Indosinian orogens marking the closure of the Palaeotethys. The subsequent Rhaetian decline that continues into Jurassic (Pliensbachian/Toarcian boundary), on the other hand, coincides with the opening of the Vardar Ocean and its eastern continuation in the Izmir-Ankara Ophiolitic Belt.Samples from the Upper Muschelkalk are more radiogenic than the global trend. This may reflect separation of the basin from the open ocean. Due to strong meteoric influx from a large land mass in the north, the Germanic Basin became increasing brackish up section in the north and east, but because of the high evaporation rates, the salt content was not much reduced in the southern and central basin where a rich, but increasingly endemic, marine fauna survived.     

Heterogeneous electron-transfer kinetics with synchrotron Fe Mössbauer spectroscopy

In the first known kinetic application of the technique, synchrotron ⁵⁷Fe-Mössbauer spectroscopy was used to follow the rate of heterogeneous electron transfer between aqueous reagents and a solid phase containing Fe. The solid, a synthetic ⁵⁷Fe-enriched Fe(III)-bearing pyroaurite-like phase having terephthalate (TA) in the interlayer [Mg₃Fe(OH)₈(TA)_0.5 · 2H₂O], was reduced by Na₂S₂O₄ and then reoxidized by K₂Cr₂O₇ by means of a novel flow-through cell. Synchrotron Mössbauer spectra were collected in the time domain at 30-s intervals. Integration of the intensity obtained during a selected time interval in the spectra allowed sensitive determination of Fe(II) content as a function of reaction time. Analysis of reaction end member specimens by both the synchrotron technique and conventional Mössbauer spectroscopy yielded comparable values for Mössbauer parameters such as center shift and Fe(II)/Fe(III) area ratios. Slight differences in quadrupole splitting values were observed, however. A reactive diffusion model was developed that fit the experimental Fe(II) kinetic data well and allowed the extraction of second-order rate constants for each reaction. Thus, in addition to rapidly collecting high quality Mössbauer data, the synchrotron technique seems well suited for aqueous rate experiments as a result of the penetrating power of 14.4 keV X-rays and high sensitivity to Fe valence state.     

Geochemistry of eucrites: genesis of basaltic eucrites, and Hf and Ta as petrogenetic indicators for altered antarctic eucrites

We performed instrumental neutron activation analysis on a large suite of antarctic and nonantarctic eucrites, including unbrecciated, brecciated, and polymict eucrites and cumulate and noncumulate eucrites. We evaluate the use of Hf and Ta, two highly incompatible elements, as sensitive indicators of partial melting or fractional crystallization processes. Comparison with rare earth element (REE) data from nonantarctic and antarctic eucrites shows that Hf and Ta are unaffected by the terrestrial alteration that has modified the REE contents and patterns of some antarctic eucrites. The major host phases for Hf and Ta—zircon, baddeleyite, ilmenite, and titanite—are much less susceptible to terrestrial alteration than the phosphate hosts of REEs. The host phases for Hf and Ta are minor or trace phases, so sample heterogeneity is a serious concern for obtaining representative compositions. The trace lithophile and siderophile element contents of noncumulate eucrites do not allow for a single, simple model for the petrogenesis of the howardite-eucrite-diogenite suite. Fractional crystallization models cannot reproduce the compositional relationship between eucrites of the main group-Nuevo Laredo trend and those of the Stannern trend. Equilibrium crystallization models cannot explain the trace element diversity observed among diogenites. Partial melting models cannot explain the W variations among eucrites, unless source regions had different metal contents. We suggest that slight variations in oxygen fugacity of eucrite source regions during partial melting can explain the W variations without requiring different metal contents. This hypothesis may fail to account for eucrite Co contents, however.