Compound-specific radiocarbon analysis (CSRA) provides the possibility to date sample material at a molecular level. N-alkanes are considered as specific compounds with high potential to CSRA. As these compounds originate from plant waxes, their radiocarbon (14C) analysis can provide valuable information about the age and origin of organic materials. This helps to reconstruct and understand environmental conditions and changes in vegetation in the past. However, CSRA has two main challenges: The small sample size of CSRA samples, making them extremely sensitive to blank effects, and the input of unknown amounts of extraneous carbon during the analytical procedure. According to the previous study from Sun and co-workers, we used different-sized aliquots of leaves Fagus sylvatica (nC27, nC29) and Festuca rubra agg (nC31, nC33) as modern standards and two commercial standards (nC26, nC28) as fossil standards for blank determination. A third commercial standard (nC27) with predetermined radiocarbon content of F14C = 0.71 (14C age of 2700 BP) serves to evaluate the blank correction. We found that the blank assessment of Sun and co-workers is also applicable to n-alkanes, with a minimum sample size of 15 µg C for dependable CSRA dates. We determined that the blank introduced during the analytical procedure has a mass of (4.1 ± 0.7) µg carrying a radiocarbon content of F14C = 0.25 ± 0.05. Applying the blank correction to a sediment sample from Lake Holzmaar (Germany) shows that all four isolated n-alkanes have similar 14C ages. However, the bulk material of the sediment and branches found in the sediment core are younger than the CSRA dates. We conclude that the disparity between the actual age of analysed organic material and the age inferred from radiocarbon results, which can occur in sediment traps due to delayed deposition, is the reason for the CSRA age.

As the main global terrestrial ecosystem component, grasslands are extremely sensitive to global climate change. With increasing human activities over the last century, grassland ecosystems have been degraded to different degrees. However, the evolution of lake-grassland ecosystems in recent centuries remains unclear due to the dearth of high-resolution records. Here, we present high-resolution lacustrine sediment grain size, pollen (Artemisia, Myriophyllum), Pediastrum, and n-alkane records from Ganggeng Nur Lake to investigate vegetation, lake evolution, and human effects in semiarid northern China. Four stages were identified from the last ca. 150 years: (1) the natural evolution stage (AD 1870–1945), in which there was a wet climate around Ganggeng Nur and the lake level rose from increased runoff; (2) the human disturbance stage (AD 1945–1967), in which the regional climate got drier and human activities began having a detectable effect on the grassland ecosystem; (3) the human transformation stage (AD 1967–2005), in which a completely arid climate coupled with the implementation of a series of land reclamation policies resulted in a large reduction in grassland areas, extensive soil erosion, exacerbated climate change, and shrinking lake areas; and (4) the posttreatment stage (AD 2005–2018), in which soil erosion was alleviated by policy implementation and a favorable humid climate.

To elucidate the dynamics of terrestrial leaf waxes in a high-altitude lake system, we performed compound-specific radiocarbon analysis (CSRA) of long-chain n-alkanes in two sediment core sections from Lake Karakul (Pamirs, Tajikistan) and in surface soil samples from the catchment area. We aimed to answer the question whether the n-alkanes are delivered into the lake sediment with substantial delay due to storage in soils, which may cause a potential bias when used as paleoenvironmental proxies. In the surface soils, the CSRA results reveal an age range of n-alkanes from modern to 2278 ± 155 cal BP. In the two sediment core samples, three of the four n-alkane ages fell on the lower ends of the 1σ-uncertainty ranges of modeled ages of the sediments (based on AMS 14C-TOC and OSL dating results). We conclude that sedimentary leaf waxes represent compounds with intermediate turnover time in soils, for example originating from alluvial plains close to the shores. Overall, the results provide evidence that sedimentary leaf wax compounds in this cold and arid setting are potentially older than the conventional age model indicates, but these findings need to be interpreted in context of the generally large uncertainty ranges of such age models.

Measuring diet choice in grazing animals is challenging, complicating the assessment of feed efficiency in pasture-based systems. Furthermore, animals may modify their intake of a forage species depending on its nutritive value and on their own physiological status. Various fecal markers have been used to estimate feed intake in grazing animals. However, plant-wax markers such as n-alkanes (ALK) and long-chain alcohols may provide reliable estimates of both dietary choices and intakes. Still, their use in beef cattle has been relatively limited. The present study was designed to test the reliability of the ALK technique to estimate diet choices in beef heifers. Twenty-two Angus-cross heifers were evaluated at both post-weaning and yearling age. At each age, they were offered both red clover and fescue hay as cubes. Following 3-week acclimation periods, daily intake of each forage species was assessed daily for 10 days. During the final 5 days, fecal grab samples were collected twice daily. The ALK fecal concentrations were adjusted using recovery fractions compiled from literature. Diet composition was estimated using two statistical methods. Post-weaning, dietary choices were reliably estimated, with low residual error, regardless of the statistical approach adopted. The regression of observed on estimated red clover proportion ranged from 0.85±0.08 to 1.01±0.09 for fecal samples collected in the p.m. and for daily proportions once averaged, respectively. However, at yearling age, the estimates were less reliable. There was a tendency to overestimate the red clover proportion in diets of heifers preferring fescue, and vice versa. This was due to greater variability in ALK fecal concentrations in the yearling heifers. Overall, the ALK technique provided a reliable tool for estimating diet choice in animals fed a simple forage diet. Although further refinements in the application of this methodology are needed, plant-wax markers provide opportunities for evaluating diet composition in grazing systems in cattle.

Aliphatic and polycyclic aromatic hydrocarbons (AHs and PAHs) were investigated in soil and meltwater stream sediments near the Uruguayan Artigas Research Station (BCAA). Gas chromatography with flame ionization detection and gas chromatography mass spectrometry were used to determine the composition of AHs and PAHs, respectively. Total AH concentrations were in the range 0.57–2333 µg g-1, while total PAH concentrations were in the range 1.36–51 650 ng g-1. Based on AH and PAH concentrations, sites in the service area and next to the boat storeroom are highly contaminated, while the other sites sampled have moderate to low contamination levels or are not impacted. High unresolved complex mixture concentrations indicate the occurrence of previous petrogenic contamination, but the dominance of low molecular weight and alkyl PAHs indicate recent oil introductions. Anthropogenic hydrocarbons dominate and are related to diesel fuel and organic residue combustion, fuel storage and boat traffic. Petrogenic contamination is relatively high, as at other Antarctic stations, but is restricted to the boat storeroom and the service area where the incinerator, the generator room and fuel tanks are located. Improvements made in fuel management procedures and the dismantling of the old fuel tanks will reduce the risk of diesel leaks and their impact on the environment near the BCAA. This study provides reference information for future environmental monitoring.

In the hinterland of deserts, it is difficult to reconstruct paleovegetation using fossil pollen because of the low pollen concentration. Therefore, an efficient method is needed to reconstruct the paleovegetation of desert regions. In this study, 34 Holocene calcareous root tube (CRT) samples were collected from the Alashan Desert in northwest China, and lipid molecular proxies from CRTs were selected to address this deficiency. The results show that n-alkanes mainly maximized at C27, C29, and C16, and that the carbon preference index is close to 1. Thus, the sources of n-alkanes from CRTs were the roots of higher plants and microorganisms, and thus changes in n-alkanes from CRTs could reveal variations in vegetation cover. The n-alkane Cmax of long-chain n-alkanes (C>25) in CRTs, maximizing at C27, indicated that vegetation in the Alashan Desert was characterized by shrub vegetation during the Holocene. Changes in the ratio of (C27+C29)/(C31+C33) indicated that the biomass of shrub vegetation increased during the period 7–2 cal ka BP. Moreover, the relative concentration of short-chain to long-chain n-alkanes decreased from 7 to 2 cal ka BP, suggesting that the effective moisture decreased during that period.

There is an ongoing controversial discussion as to whether n-alkane lipid biomarkers—and organic matter of loess in general—reflect a synsedimentary paleoenvironmental/climate signal or whether they are significantly affected by postdepositional “contamination,” for example related to root and rhizomicrobial activity. In order to address this issue at our study site (the Middle to Late Weichselian loess-paleosol sequence Gleina in Saxony, Germany), we determined and compared radiocarbon ages of bulk n-alkanes and sedimentation ages, as assessed by optically stimulated luminescence (OSL) dating. The bulk n-alkanes of the four dated samples yielded calibrated 14C ages ranging from 24.1 to 49.7 cal ka BP (95.4% probability ranges). While the three uppermost n-alkane samples are well within the range or even slightly older than the OSL-inferred sedimentation ages, the lowermost n-alkane sample is slightly younger than the OSL ages. There is hence little or no evidence at our study site for n-alkanes in loess-paleosol sequences being significantly “contaminated” by deep subsoil rooting or microbial processes. We propose a 14C isotope mass balance calculation for estimating such contaminations quantitatively. Radiocarbon dating of bulk n-alkanes might have great potential for Quaternary research, and we encourage further comparative 14C and OSL studies.

Central China has experienced stronger summer monsoon during warm periods such as Marine Isotope Stages (MIS) 1 and 3, and weaker summer monsoon during cool periods such as MIS 2. The evolution history of Dajiuhu subalpine peatland in central China can help investigate how the expansion and shrinkage of peatland were associated with monsoonal strength over the last glacial–interglacial cycle. Here we apply bulk organic carbon and molecular biomarkers (hopane and n-alkane) to reconstruct the evolution history for the Dajiuhu peatland over the past 40,000 yr. The results indicate fluctuations between lacustrine and peat-like deposition during MIS 3, steady lacustrine deposition during MIS 2, and peatland initiation and expansion during MIS 1 in the Dajiuhu peatland. Therefore, at the glacial–interglacial scale, warmer summer and cooler winter conditions in interglacial periods are crucial to trigger peat deposition, whereas reduced evaporation in glacial period instead of decreased monsoonal-driven precipitation would have played a predominant role in the regional effective moisture balance. However, within the Holocene (MIS 1), monsoonal precipitation changes appear to be the main controller on millennial-scale variations of water-table level of the Dajiuhu peatland.

The Black Sea is connected to a large drainage area including the European Russian Plain, part of the Alps and southeastern Europe. To study the hydrological changes in this basin over the last 40,000 years, we measured specific terrigenous biomarkers for wetland vegetation in well-dated sediments from the northwestern Black Sea, spanning the last glacial period (lacustrine phase) and the Holocene (marine phase). Low abundances of these biomarkers are observed during the North Atlantic ice melting and cooling events known as Heinrich Events 4 to 2, the Last Glacial Maximum and the Younger Dryas Event. Increased biomarker inputs characterize the mild climate phases known as Dansgaard–Oeschger Interstadials, the Bølling/Allerød and Preboreal Warmings indicating increased erosion due to permafrost degradation, higher primary productivity and/or wetland extension in the drainage basin. The final retreat of the Fennoscandian Ice Sheet from the Russian Plain occurs during the early part of Heinrich Event 1 and is characterized by increased biomarker concentrations in a typical series of four deglacial clay layers. For the last glacial period, the correspondence in timing between the biomarker records and the atmospheric CH4 record from ice cores, suggests an important CH4 contribution due to boreal permafrost thawing and wetland emission.

One of the difficulties in reporting accurate radiocarbon results from compound-specific radiocarbon analysis (CSRA) is the lack of suitable process standard materials to correct for the amount and 14C content of carbon added during extensive sample processing. We evaluated the use of n-alkanes extracted from modern grass material (1.224±0.006 fraction modern) as process standards for CSRA. The n-alkanes were isolated using preparative capillary gas chromatography (PCGC) from two independent chemical extraction methods applied to the grass. Since this was our first assessment of the 14C content of the grass n-alkanes, we corrected for extraneous carbon derived from PCGC isolation using commercially available single compounds of modern and 14C-free content. Results were consistent across the two extraction methods showing that the C29n-alkane has a fraction modern value that is within 1σ of the bulk value of the grass while C31n-alkane and less abundant n-alkanes have values within 2σ of the bulk value of the grass. C29 and C31n-alkanes were the most abundant n-alkanes in the grass and, as such, the more feasible for collection of sufficient amounts of carbon for accelerator mass spectrometry (AMS) analysis. Our results suggest that choosing a grass n-alkane with an elution time closest to that of the unknowns may be advisable due to possibly greater effect from GC column bleed (14C-free) at later elution times. We conclude that C29 and C31n-alkanes in modern grass of known 14C content can be used as in-house standards to correct for the addition of 14C-free carbon during sample preparation for 14C analysis of n-alkanes.

Free-range birds such as organic broilers may ingest soil and plants during exploration. The estimation of such intakes is of great interest to quantify possible nutritional supplies and also to evaluate the risk of exposure to parasites or to environmental contaminants. Marker-based techniques are now available and would allow to quantify plant and, especially, soil intake in free-range birds, and this quantification was the aim of this study. Methodologically, the proportion of plants in diet intake was determined first using a method based on n-alkanes. Subsequently, the fraction of soil in the total intake was estimated with a second marker, acid-insoluble ash. This approach was carried out to estimate ingested amounts of plants and soil for five successive flocks of organic broilers, exploring grass-covered yards or those under trees, at two time points for each yard: 51 and 64 days of age. Each factor combination (yard type×period=flock number×age) was repeated on two different yards of 750 broilers each.

The birds’ plant intake varied widely, especially on grass-covered yards. The proportion of plant intake was significantly higher on grass-covered plots than under trees and was also affected, but to a lesser extent, by age or flock number. The ingestion of plants would generally not exceed 11 g of DM daily, except two extreme outliers of nearly 30 g. The daily plant intake under trees tended to be lower and never exceeded 7 g of DM. The amount of ingested plants increased significantly for spring flocks. It increased slightly but significantly with age. The proportion of ingested soil was significantly higher under trees than on grass-covered yards. Dry soil intake was generally low with not more than 3 g per day. Only in adverse conditions – that is, older birds exploring yards under trees in winter – soil intake reached the extreme value of nearly 5 g. Broilers on yards under trees ingested significantly more soil than on grass-covered yards with least square means of, respectively, 2.1 and 1.1 g dry soil per day. These quantifications would allow us to evaluate the impact of plant and soil intake in the management of free-range broilers, especially for the management in organic farming systems. Nevertheless, under the two rearing conditions tested in the current study, the quite low proportions of soil intakes would represent a low risk for the safety of the produced food, unless the birds explore yards on heavily contaminated soil.

An experiment was carried out to examine the effect of increasing the proportion of Wimmera ryegrass hay in a lucerne hay-based diet on net transfer of nutrients to the intestine, and on the disappearance of n-alkanes in the reticulo-rumen and the hindgut of sheep. Following a latin square design, four adult ewes were fed 1:0, 0·33:0·67, 0·67:0·33 and 0:1 proportions of legume and grass. Increasing the proportion of ryegrass in the diet linearly decreased the intake of DM (P= 0·017), organic matter (P= 0·021) and N (P= 0·001). However, neutral-detergent fibre intake was not affected (P= 0·148), nor was its digestibility coefficient (P>0·10). Diet had no effect on duodenal flows of nutrients (P>0·10), although the proportion of N intake (NI) recovered at the duodenum as non-NH3 N (NAN) increased linearly with Lolium rigidum in the diet (P= 0·002). Full recovery of NI as NAN was achieved at NH3 concentrations in the rumen below 110 g/l. Microbial N contribution to NAN varied in a quadratic manner (P< 0·05) with the proportion of grass in the diet, although efficiency of microbial synthesis was not affected (P>0·10). Duodenal recovery of consumed n-alkanes was not affected by diet and was complete for those present in higher concentrations in the forages. Isolated rumen bacteria contained significant amounts of n-alkanes, contributing to the duodenal flow of these hydrocarbons in variable proportions depending on the diet consumed.

This study contributes to the paleoenvironmental reconstruction of the loess–paleosol sequence of Nussloch, Germany, by using n-alkanes as plant leaf-wax-derived lipid biomarkers. We found that n-alkane patterns and concentrations in the Saalian loess and the last interglacial Eemian paleosol of Nussloch point to very strong degradation and prevailing deciduous vegetation. Degradation effects in the overlying paleosols and loess layers are less pronounced and allow for the application of an end-member mixing model to estimate vegetation changes semi-quantitatively. Our findings highlight the potential for the interpretation of degradation-corrected n-alkane ratios. n-Alkane modelling results for loess layers, paleosols and an in-filled paleochannel dated to ~ 60–32 ka suggest that up to ~ 50% of the n-alkanes were derived from deciduous trees or shrubs. This finding is in agreement with the abundant occurrence of wood fragments and indicates a highly variable and dynamic landscape dominated by tundra shrubland. On the other hand, deciduous trees or shrubs did not contribute significantly to the soil organic matter in the late Weichselian loess layers and the intercalated Gelic Gleysols (~ 32–18 ka).

The composition of cuticular and internal n-alkanes in Lucilia sericata larvae, pupae, and male and female imagines were studied. The cuticular and internal lipid extracts were separated by HPLC-LLSD, after which the hydrocarbon fraction was identified by GC/MS in selected ion monitoring (SIM) and total ion current (TIC) modes.

The cuticular lipids of the larvae contained seven n-alkanes from C23 to C31. The major n-alkane in L. sericata larvae was C29 (42.1%). The total cuticular n-alkane content in the cuticular lipids was 31.46 μg g−1 of the insect body. The internal lipids of L. sericata larvae contained five n-alkanes ranged from C25 to C31. The most abundant compound was C27 (61.71 μg g−1 of the insect body). Eighteen n-alkanes from C14 to C31 were identified in the cuticular lipids of the pupae. The most abundant n-alkanes ranged from C25 to C31; those with odd-numbered carbon chains were particularly abundant, the major one being C29:0 (59.5%). Traces of eight cuticular n-alkanes were present. The internal lipids of L. sericata pupae contained five n-alkanes, ranging from C25 to C31. The cuticular lipids of female imagines contained 17 n-alkanes from C12 to C30. Among the cuticular n-alkanes of females, C27 (47.5%) was the most abundant compound. Four n-alkanes, with only odd-numbered carbon chains, were identified in the internal lipids of females. The lipids from both sexes of L. sericata had similar n-alkane profiles. The cuticular lipids of adult males contained 16 n-alkanes ranging from C13 to C31. C27 (47.9%) was the most abundant cuticular n-alkanes in males. The same n-alkanes only with odd-numbered carbon chains and in smaller quantities of C27 (0.1%) were also identified in the internal lipids of males.

The highest amounts of total cuticular n-alkanes were detected in males and females of L. sericata (330.4 and 158.93 μg g−1 of the insect body, respectively). The quantities of total cuticular alcohols in larvae and pupae were smaller (31.46 μg g−1 and 42.08 μg g−1, respectively). The internal n-alkane contents of larvae, pupae, and male and female imagines were significantly higher than the cuticular n-alkane contents (153.53, 99.60, 360.06 and 838.76 μg g−1 of the insect body, respectively).

The aim of this study was to compare the n-alkanes and the ytterbium (Yb)/faecal index techniques as two methods for estimating the herbage intake of dairy cows fed indoors on different herbage : supplement ratios and feeding levels. The supplement was a mixture of maize silage and soyabean meal (ratio of 87 : 13 on a dry matter (DM) basis). In all, four treatments were studied. The herbage : supplement ratio in the diet was 25 : 75, 50 : 50, 75 : 25 and 50 : 50 for treatments 1, 2, 3 and 4, respectively. Animals were offered for treatments 1, 2 and 3, 100% of ad libitum intake measured before the experiment and 70% of ad libitum intake for treatment 4. Cows were fed herbage in the morning and supplement in the evening. A total of six lactating Holstein dairy cows were used in a 4 × 4 Latin square with four 14-day periods. Herbage and supplement intakes, faecal output (FO), in vivo organic matter (OM) digestibility and faecal recovery of markers were measured on the last 5 days of each period. Intake was estimated with the two methods and from two faecal sampling techniques, that is, total faecal collection v. grab sampling during milking. Mean herbage intake as fed, or estimated from n-alkanes or from the Yb/faecal index was 7.7, 8.1 and 10.2 kg DM, respectively. The mean prediction error, expressed as a fraction of actual herbage intake, was 0.10 and 0.50 for the n-alkanes and Yb/faecal index methods, respectively. The n-alkanes method clearly showed much better accuracy than the Yb/faecal index method for estimating intake, irrespective of the faecal sampling method, herbage : silage proportion or feeding level. For the n-alkanes method, herbage intake was slightly overestimated (7%) when herbage proportion in the diet was high, due to a ratio of faecal C33 : C32 recovery >1. The high bias for the Yb/faecal index was due to the cumulative effect of overestimation of FO (mean recovery of Yb = 0.92) and underestimation of the diet indigestible fraction (−8%). Between-treatment variations of FO were on average well estimated by Yb. Between-treatment variations of OM digestibility estimated using the faecal index technique were lower than those observed in vivo. It is concluded that intake of grazing dairy cows receiving high levels of maize silage supplement should be estimated using the n-alkanes method.

Plant cuticular n-alkanes have been successfully used as markers to estimate diet composition and intake of grazing herbivores. However, additional markers may be required under grazing conditions in botanically diverse vegetation. This study was conducted to describe the n-alkane profiles and the carbon isotope enrichment of n-alkanes of common plant species from the Mid Rift Valley rangelands of Ethiopia, and evaluate their potential use as nutritional markers. A total of 23 plant species were collected and analysed for long-chain n-alkanes ranging from heptacosane to hexatriacontane (C27 to C36), as well as their carbon isotopic ratio (13C/12C). The analysis was conducted by gas chromatography/combustion isotope ratio mass spectrometry following saponification, extraction and purification. The isotopic composition of the n-alkanes is reported in the delta notation (δ13C) relative to the Vienna Pee Dee Belemnite standard. The dominant n-alkanes in the species were C31 (mean ± s.d., 283 ± 246 mg/kg dry matter) and C33 (149 ± 98 mg/kg dry matter). The carbon isotopic enrichment of the n-alkanes ranged from −19.37‰ to −37.40‰. Principal component analysis was used to examine interspecies differences based on n-alkane profiles and the carbon isotopic enrichments of individual n-alkanes. Large variability among the pasture species was observed. The first three principal components explained most of the interspecies variances. Comparison of the principal component scores using orthogonal procrustes rotation indicated that about 0.84 of the interspecies variances explained by the two types of data sets were independent of each other, suggesting that the use of a combination of the two markers can improve diet composition estimations. It was concluded that, while the n-alkane profile of the pasture species remains a useful marker for use in the study region, the δ13C values of n-alkanes can provide additional information in discriminating diet components of grazing animals.

Whether the rumen microbes are able to synthesize and/or degrade long-chain alkanes in anaerobic conditions remains a question to be answered before these hydrocarbons can be confidently used as duodenal flow or rumen transit markers. In this context, an experiment in vitro was carried out to establish whether within a rumen liquor fermentation system, n-alkanes can be derived from de-waxed structures of the plant or from non-alkane wax components (long-chain fatty alcohols, long-chain fatty acids and esters), or may be metabolized by bacteria to other components or to shorter-chain hydrocarbons. Ryegrass was labelled with 14C in growth chambers under controlled conditions in order to use it as a substrate. The labelled material obtained was separated in three fractions: labelled alkanes, labelled de-waxed plant and labelled wax components without the alkanes. These fractions were used for three different incubations in vitro, which objectives were as follows: 1. To check whether rumen bacteria can synthesize alkanes from carbon structures other than waxes (e.g. sugars). 2. To verify whether rumen bacteria can metabolize the n-alkanes to other compounds. 3. To check whether rumen bacteria can synthesize n-alkanes from other carbon compounds from waxes. The results showed that there was neither bacterial synthesis nor metabolism of the n-alkanes in in vitro conditions.

The n-alkane method was developed in temperate areas as a tool to estimate voluntary intake (VI) at pasture. The present study aimed to investigate the performance of n-alkanes as markers for estimating VI of steers (mean live weight 213 kg) offered a range of tropical grass hays and lucerne. Tropical and temperate forages have different n-alkane profiles and little is known about the issues which affect the accuracy of the method under tropical conditions. In two pen experiments (no. = 20 and no. = 24) n-alkanes were dosed using intraruminal controlled-release devices. Actual mean voluntary dry matter intakes for the diets ranged from 3·12 to 4·60 kg/day and actual mean dry-matter digestibility varied between 439 and 620 g/kg. n-Alkane profiles (C30 to C36) of the diets and the faeces for each animal were determined using gas chromatography. The recovery of each n-alkane was determined for each animal. Recoveries of n-alkanes were highly variable and generally varied between diets and between experiments. When adjacent n-alkanes were used to estimate VI (ratio method), agreement with actual VI was often poor. Despite this, where the recoveries of n-alkane pairs were similar, group mean VI were accurately estimated. From these data, it is concluded that estimation of VI in cattle offered tropical grass hays or lucerne hay, requires measured recoveries of both dosed and natural plant n-alkanes. The dosed and natural n-alkane pairs having the most similar recoveries should be used in the ratio method to estimate VI.