Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Does low phosphorus supply limit seedling establishment and tree growth in groves of ectomycorrhizal trees in a central African rainforest?

In a forest grove at Korup dominated by the ectomycorrhizal species Microberlinia bisulcata, an experiment tested whether phosphorus (P) was a limiting nutrient. P-fertilization of seven subplots 1995-97 was compared with seven controls. It led to large increases in soil P concentrations. Trees were measured in 1995 and 2000. M. bisulcata and four other species were transplanted into the treatments, and a wild cohort of M. bisulcata seedlings was followed in both. Leaf litter fall from trees and seedlings were analysed for nutrients. Growth of trees was not affected by added P. Transplanted seedlings survived better in the controls than added-P subplots: they did not grow better with added-P.M. bisulcata wildlings survived slightly better in the added-P subplots in yr 1 but not later. Litter fall and transplanted survivors had much higher concentrations of P (not N) in the added-P than control subplots. Under current conditions, it appears that P does not limit growth of trees or hinder seedling establishment, especially of M. bisculcata, in these low-P grove soils.

Climate-pollen relationships AD 1901-1996 in two small mires near the forest limit in the northern and central Swiss Alps

Climatic relationships were established in two 210Pb dated pollen sequences from small mires closely surrounded by forest just below actual forest limits (but about 300 m below potential climatic forest limits) in the northern Swiss Alps (suboceanic in climate; mainly with Picea) and the central Swiss Alps (subcontinental; mainly Pinus cembra and Larix) at annual or near-annual resolution from ad 1901 to 1996. Effects of vegetational succession were removed by splitting the time series into early and late periods and by linear detrending. Both pollen concentrations detrended by the depth-age model and modified percentages (in which counts of dominant pollen types are down-weighted) are correlated by simple linear regression with smoothed climatic parameters with one-and two-year timelags, including average monthly and April/September daylight air temperatures and with seasonal and annual precipitation sums. Results from detrended pollen concentrations suggest that peat accumulation is favoured in the northern-Alpine mire either by early snowmelt or by summer precipitation, but in the central-Alpine mire by increased precipitation and cooler summers, suggesting a position of the northern-Alpine mire near the upper altitudinal limit of peat formation, but of the central-Alpine mire near the lower limit. Results from modified pollen percentages indicate that pollen pro duction by plants growing near their upper altitudinal limit is limited by insufficient warmth in summer, and pollen production by plants growing near their lower altitudinal limit is limited by too-high temperatures. Only weakly significant pollen/climate relationships were found for Pinus cembra and Larix, probably because they experience little climatic stress growing 300 m below the potential climatic forest limit.

Uppermost Limit, Extent, and Fluctuations of the Timberline and Treeline Ecocline in the Swiss Central Alps during the past 11,500 Years

Pollen and macrofossils were analyzed at two sites above today's treeline (or tree limit) in the Swiss Central Alps (Gouillé Loéré, 2503 m a.s.l., and Lengi Egga, 2557 m a.s.l.) to test two contrasting hypotheses about the natural formation of timberline (the upper limit of closed forest) in the Alps. Our results revealed that Pinus cembra--Larix decidua forests near timberline were rather closed between 9000 and 2500 B.C. (9600-4000 ¹⁴C yr BP), when timberline fluctuations occurred within a belt 100-150 m above today's tree limit. The treeline ecocline above timberline was characterized by the mixed occurrence of tree, shrub, dwarf-shrub, and herbaceous species, but it did not encompass more than 100-150 altitudinal meters. The uppermost limit reached by timberline and treeline during the Holocene was ca. 2420 and 2530 m, respectively, i.e., about 120 to 180 m higher than today. Between 3500 and 2500 B.C. (4700-4000 ¹⁴C yr BP) timberline progressively sank by about 300 m, while treeline was lowered only ca. 100 m. This change led to an enlargement of the treeline-ecocline belt (by ca. 300 m) after 2500 B.C. (4000 ¹⁴C yr BP). Above the treeline ecocline, natural meadows dominated by dwarf shrubs (e.g., Salix herbacea) and herbaceous species (e.g., Helianthemum, Taraxacum, Potentialla, Leontodon t., Cerastium alpinum t., Cirsium spinosissimum, Silene exscapa t., and Saxifraga stellaris) have been present since at least 11,000 cal yr ago. In these meadows tree and tall shrub species (>0.5 m) never played a major role. These results support the conventional hypothesis of a narrow ecocline with rather sharp upper timberline and treeline boundaries and imply that today's treeless alpine communities in the Alps are close to a natural stage. Pollen (percentages and influx), stomata, and charcoal data may be useful for determining whether or not a site was treeless. Nevertheless, a reliable and detailed record of past local vegetation near and above timberline is best achieved through the inclusion of macrofossil analysis.

Perinatal care at the limit of viability between 22 and 26 completed weeks of gestation in Switzerland. 2011 revision of the Swiss recommendations

Perinatal care of pregnant women at high risk for preterm delivery and of preterm infants born at the limit of viability (22-26 completed weeks of gestation) requires a multidisciplinary approach by an experienced perinatal team. Limited precision in the determination of both gestational age and foetal weight, as well as biological variability may significantly affect the course of action chosen in individual cases. The decisions that must be taken with the pregnant women and on behalf of the preterm infant in this context are complex and have far-reaching consequences. When counselling pregnant women and their partners, neonatologists and obstetricians should provide them with comprehensive information in a sensitive and supportive way to build a basis of trust. The decisions are developed in a continuing dialogue between all parties involved (physicians, midwives, nursing staff and parents) with the principal aim to find solutions that are in the infant's and pregnant woman's best interest. Knowledge of current gestational age-specific mortality and morbidity rates and how they are modified by prenatally known prognostic factors (estimated foetal weight, sex, exposure or nonexposure to antenatal corticosteroids, single or multiple births) as well as the application of accepted ethical principles form the basis for responsible decision-making. Communication between all parties involved plays a central role. The members of the interdisciplinary working group suggest that the care of preterm infants with a gestational age between 22 0/7 and 23 6/7 weeks should generally be limited to palliative care. Obstetric interventions for foetal indications such as Caesarean section delivery are usually not indicated. In selected cases, for example, after 23 weeks of pregnancy have been completed and several of the above mentioned prenatally known prognostic factors are favourable or well informed parents insist on the initiation of life-sustaining therapies, active obstetric interventions for foetal indications and provisional intensive care of the neonate may be reasonable. In preterm infants with a gestational age between 24 0/7 and 24 6/7 weeks, it can be difficult to determine whether the burden of obstetric interventions and neonatal intensive care is justified given the limited chances of success of such a therapy. In such cases, the individual constellation of prenatally known factors which impact on prognosis can be helpful in the decision making process with the parents. In preterm infants with a gestational age between 25 0/7 and 25 6/7 weeks, foetal surveillance, obstetric interventions for foetal indications and neonatal intensive care measures are generally indicated. However, if several prenatally known prognostic factors are unfavourable and the parents agree, primary non-intervention and neonatal palliative care can be considered. All pregnant women with threatening preterm delivery or premature rupture of membranes at the limit of viability must be transferred to a perinatal centre with a level III neonatal intensive care unit no later than 23 0/7 weeks of gestation, unless emergency delivery is indicated. An experienced neonatology team should be involved in all deliveries that take place after 23 0/7 weeks of gestation to help to decide together with the parents if the initiation of intensive care measures appears to be appropriate or if preference should be given to palliative care (i.e., primary non-intervention). In doubtful situations, it can be reasonable to initiate intensive care and to admit the preterm infant to a neonatal intensive care unit (i.e., provisional intensive care). The infant's clinical evolution and additional discussions with the parents will help to clarify whether the life-sustaining therapies should be continued or withdrawn. Life support is continued as long as there is reasonable hope for survival and the infant's burden of intensive care is acceptable. If, on the other hand, the health car...

Exposure dating of Late Glacial and pre-LGM moraines in the Cordon de Doña Rosa, Northern/Central Chile (~ 31°S)

Despite the important role of the Central Andes (15–30° S) for climate reconstruction, knowledge about the Quaternary glaciation is very limited due to the scarcity of organic material for radiocarbon dating. We applied 10Be surface exposure dating (SED) on 22 boulders from moraines in the Cordon de Doña Rosa, Northern/Central Chile (~31° S). The results show that several glacial advances in the southern Central Andes occurred during the Late Glacial between ~14.7±1.5 and 11.6±1.2 ka. A much more extensive glaciation is dated to ~32±3 ka, predating the temperature minimum of the global LGM (Last Glacial Maximum: ~20 ka). Reviewing these results in the paleoclimatic context, we conclude that the Late Glacial advances were most likely caused by an intensification of the tropical circulation and a corresponding increase in summer precipitation. High-latitude temperatures minima, e.g. the Younger Dryas (YD) and the Antarctic Cold Reversal (ACR) may have triggered individual advances, but current systematic exposure age uncertainties limit precise correlations. The absence of LGM moraines indicates that moisture advection was too limited to allow significant glacial advances at ~20 ka. The tropical circulation was less intensive despite the maximum in austral summer insolation. Winter precipitation was apparently also insufficient, although pollen and marine studies indicate a northward shift of the westerlies at that time. The dominant pre-LGM glacial advances in Northern/Central Chile at ~32 ka required lower temperatures and increased precipitation than today. We conclude that the westerlies were more intense and/or shifted equatorward, possibly due to increased snow and ice cover at higher southern latitudes coinciding with a minimum of insolation.

North-south palaeohydrological contrasts in the central Mediterranean during the Holocene: tentative synthesis and working hypotheses

On the basis of a multi-proxy approach and a strategy combining lacustrine and marine records along a north–south transect, data collected in the central Mediterranean within the framework of a collaborative project have led to reconstruction of high-resolution and well-dated palaeohydrological records and to assessment of their spatial and temporal coherency. Contrasting patterns of palaeohydrological changes have been evidenced in the central Mediterranean: south (north) of around 40° N of latitude, the middle part of the Holocene was characterised by lake-level maxima (minima), during an interval dated to ca. 10 300–4500 cal BP to the south and 9000–4500 cal BP to the north. Available data suggest that these contrasting palaeohydrological patterns operated throughout the Holocene, both on millennial and centennial scales. Regarding precipitation seasonality, maximum humidity in the central Mediterranean during the middle part of the Holocene was characterised by humid winters and dry summers north of ca. 40° N, and humid winters and summers south of ca. 40° N. This may explain an apparent conflict between palaeoclimatic records depending on the proxies used for reconstruction as well as the synchronous expansion of tree species taxa with contrasting climatic requirements. In addition, south of ca. 40° N, the first millennium of the Holocene was characterised by very dry climatic conditions not only in the eastern, but also in the central- and the western Mediterranean zones as reflected by low lake levels and delayed reforestation. These results suggest that, in addition to the influence of the Nile discharge reinforced by the African monsoon, the deposition of Sapropel 1 has been favoured (1) by an increase in winter precipitation in the northern Mediterranean borderlands, and (2) by an increase in winter and summer precipitation in the southern Mediterranean area. The climate reversal following the Holocene climate optimum appears to have been punctuated by two major climate changes around 7500 and 4500 cal BP. In the central Mediterranean, the Holocene palaeohydrological changes developed in response to a combination of orbital, ice-sheet and solar forcing factors. The maximum humidity interval in the south-central Mediterranean started ca. 10 300 cal BP, in correlation with the decline (1) of the possible blocking effects of the North Atlantic anticyclone linked to maximum insolation, and/or (2) of the influence of the remnant ice sheets and fresh water forcing in the North Atlantic Ocean. In the north-central Mediterranean, the lake-level minimum interval began only around 9000 cal BP when the Fennoscandian ice sheet disappeared and a prevailing positive NAO-(North Atlantic Oscillation) type circulation developed in the North Atlantic area. The major palaeohydrological oscillation around 4500–4000 cal BP may be a non-linear response to the gradual decrease in insolation, with additional key seasonal and interhemispheric changes. On a centennial scale, the successive climatic events which punctuated the entire Holocene in the central Mediterranean coincided with cooling events associated with deglacial outbursts in the North Atlantic area and decreases in solar activity during the interval 11 700–7000 cal BP, and to a possible combination of NAO-type circulation and solar forcing since ca. 7000 cal BP onwards. Thus, regarding the centennial-scale climatic oscillations, the Mediterranean Basin appears to have been strongly linked to the North Atlantic area and affected by solar activity over the entire Holocene. In addition to model experiments, a better understanding of forcing factors and past atmospheric circulation patterns behind the Holocene palaeohydrological changes in the Mediterranean area will require further investigation to establish additional high-resolution and well-dated records in selected locations around the Mediterranean Basin and in adjacent regions. Special attention should be paid to greater precision in the reconstruction, on millennial and centennial timescales, of changes in the latitudinal location of the limit between the northern and southern palaeohydrological Mediterranean sectors, depending on (1) the intensity and/or characteristics of climatic periods/oscillations (e.g. Holocene thermal maximum versus Neoglacial, as well as, for instance, the 8.2 ka event versus the 4 ka event or the Little Ice Age); and (2) on varying geographical conditions from the western to the eastern Mediterranean areas (longitudinal gradients). Finally, on the basis of projects using strategically located study sites, there is a need to explore possible influences of other general atmospheric circulation patterns than NAO, such as the East Atlantic–West Russian or North Sea–Caspian patterns, in explaining the apparent complexity of palaeoclimatic (palaeohydrological) Holocene records from the Mediterranean area.

Herbivores differentially limit the seedling growth and sapling recruitment of two dominant rain forest trees

Resource heterogeneity may influence how plants are attacked and respond to consumers in multiple ways. Perhaps a better understanding of how this interaction might limit sapling recruitment in tree populations may be achieved by examining species’ functional responses to herbivores on a continuum of resource availability. Here, we experimentally reduced herbivore pressure on newly established seedlings of two dominant masting trees in 40 canopy gaps, across c. 80 ha of tropical rain forest in central Africa (Korup, Cameroon). Mesh cages were built to protect individual seedlings, and their leaf production and changes in height were followed for 22 months. With more light, herbivores increasingly prevented the less shade-tolerant Microberlinia bisulcata from growing as tall as it could and producing more leaves, indicating an undercompensation. The more shade-tolerant Tetraberlinia bifoliolata was much less affected by herbivores, showing instead near to full compensation for leaf numbers, and a negligible to weak impact of herbivores on its height growth. A stage-matrix model that compared control and caged populations lent evidence for a stronger impact of herbivores on the long-term population dynamics of M. bisulcata than T. bifoliolata. Our results suggest that insect herbivores can contribute to the local coexistence of two abundant tree species at Korup by disproportionately suppressing sapling recruitment of the faster-growing dominant via undercompensation across the light gradient created by canopy disturbances. The functional patterns we have documented here are consistent with current theory, and, because gap formations are integral to forest regeneration, they may be more widely applicable in other tropical forest communities. If so, the interaction between life-history and herbivore impact across light gradients may play a substantial role in tree species coexistence.

Late Quaternary history of the Vakinankaratra volcanic field (central Madagascar): insights from luminescence dating of phreatomagmatic eruption deposits

The Quaternary Vakinankaratra volcanic field in the central Madagascar highlands consists of scoria cones, lava flows, tuff rings, and maars. These volcanic landforms are the result of processes triggered by intracontinental rifting and overlie Precambrian basement or Neogene volcanic rocks. Infrared-stimulated luminescence (IRSL) dating was applied to 13 samples taken from phreatomagmatic eruption deposits in the Antsirabe–Betafo region with the aim of constraining the chronology of the volcanic activity. Establishing such a chronology is important for evaluating volcanic hazards in this densely populated area. Stratigraphic correlations of eruption deposits and IRSL ages suggest at least five phreatomagmatic eruption events in Late Pleistocene times. In the Lake Andraikiba region, two such eruption layers can be clearly distinguished. The older one yields ages between 109 ± 15 and 90 ± 11 ka and is possibly related to an eruption at the Amboniloha volcanic complex to the north. The younger one gives ages between 58 ± 4 and 47 ± 7 ka and is clearly related to the phreatomagmatic eruption that formed Lake Andraikiba. IRSL ages of a similar eruption deposit directly overlying basement laterite in the vicinity of the Fizinana and Ampasamihaiky volcanic complexes yield coherent ages of 68 ± 7 and 65 ± 8 ka. These ages provide the upper age limit for the subsequently developed Iavoko, Antsifotra, and Fizinana scoria cones and their associated lava flows. Two phreatomagmatic deposits, identified near Lake Tritrivakely, yield the youngest IRSL ages in the region, with respective ages of 32 ± 3 and 19 ± 2 ka. The reported K-feldspar IRSL ages are the first recorded numerical ages of phreatomagmatic eruption deposits in Madagascar, and our results confirm the huge potential of this dating approach for reconstructing the volcanic activity of Late Pleistocene to Holocene volcanic provinces.

Early-Holocene afforestation processes in the lower subalpine belt of the Central Swiss Alps as inferred from macrofossil and pollen records

To reconstruct the vegetation history of the Upper Engadine, continuous sediment cores covering the past 11 800 years from Lej da Champfer and Lej da San Murezzan (Upper Engadine Valley, c. 1800 m a.s.l., southeastern Switzerland) have been analysed for pollen and plant macrofossils. The chronologies of the cores are based on 16 and 22 radiocarbon dates, respectively. The palaeobotanical records of both lakes are in agreement for the Holocene, but remarkable differences exist between the sites during the period 11 100 to 10 500 cal. BP, when Lej da Champfer was affected by re-sedimentation processes. Macrofossil data suggest that Holocene afforestation began at around 11400 cal. BP. A climatic deterioration, the Preboreal Oscillation, stopped and subsequently delayed the establishment of trees until c. 11000 cal. BP, when first Betula, then Pinus sylvestrislmugo, then Larix 300 years later, and finally Pinus cembra expanded within the lake catchment. Treeline was at c. 1500 m during the Younger Dryas (12 542- 11 550 cal. BP) in the Central Alps. Our results, along with other macrofossil studies from the Alps, suggest a nearly simultaneous afforestation (e.g., by Pinus sylvestris in the lower subalpine belt) between 1500 and 2340 m a.s.l. at around 11 400 to 11 300 cal. BP. We suggest that forest-limit species (e.g., Pinus cembra, Larix decidua) could expand faster at today's treeline (c. 2350 m a.s.l.), than 550 m lower. Earlier expansions at higher altitudes probably resulted from reduced competition with low-altitude trees (e.g. Pinus sylvestris) and herbaceous species. Comparison with other proxies such as oxygen isotopes, residual A14C, glacier fluctuations, and alpine climatic cooling phases suggests climatic sensitivity of vegetation during the early Holocene.

Seven years of annual pollen influx at the forest limit in the Swiss Alps studied by pollen traps: relations to vegetation and climate

Annual pollen influx has been monitored in short transects across the altitudinal tree limit in four areas of the Swiss Alps with the use of modified Tauber traps placed at the ground surface. The study areas are Grindelwald (8 traps), Aletsch (8 traps), Simplon (5 traps), and Zermatt (5 traps). The vegetation around the traps is described. The results obtained are: (1) Peak years of pollen influx (one or two in seven years) follow years of high average air temperatures during June–November of the previous year for Larix and Picea, and less clearly for Pinus non-cembra, but not at all for Pinus cembra and Alnus viridis. (2) At the upper forest limit, the regional pollen influx of trees (trees absent within 100 m of the pollen trap) relates well to the average basal area of the same taxon within 10–15 km of the study areas for Pinus cembra, Larix, and Betula, but not for Picea, Pinus non-cembra, and Alnus viridis. (3) The example of Zermatt shows that pollen influx characterises the upper forest limit, if the latter is more or less intact. (4) Presence/absence of Picea, Pinus cembra, Larix, Pinus non-cembra, and Alnus viridis trees within 50–100 m of the traps is apparent in the pollen influx in peak years of pollen influx but not in other years, suggesting that forest-limit trees produce significant amounts of pollen only in some years. (5) Pollen influx averaged over the study period correlates well with the abundance of plants around the pollen traps for conifer trees (but not deciduous trees), Calluna, Gramineae, and Cyperaceae, and less clearly so Compositae Subfam. Cichorioideae and Potentilla-type. (6) Influx of extra-regional pollen derived from south of the Alps is highest in Simplon, which is open to southerly winds, slightly lower in Aletsch lying just north of Simplon, and lowest in Zermatt sheltered from the south by high mountains and Grindelwald lying north of the central Alps.

Treeline Fluctuations Recorded for 12,500 Years by Soil Profiles, Pollen, and Plant Macrofossils in the Central Swiss Alps

Past treelines can rarely be recorded by pollen percentages alone, but pollen concentration, pollen influx, and plant macrofossils (including stomata of conifers) are more reliable indicators. In addition, ancient forest soils above today's treeline may trace the maximum upper expansion of the forest since the last glaciation. Charcoal in such soil profiles may be radiocarbon dated. Our example from the Central Swiss Alps at the Alpe d'Essertse consists of a plant-macrofossil diagram and pollen diagrams of the pond Gouille Rion at 2343 m a.s.l. and a sequence of soil profiles from 1780 m to 2600 m a.s.l. The area around the pond was forested with LariJc decidua and Pinus cembra between 9500 and 3600 BP. After 4700 BP the forest became more open and Juniperus nana and Alnus viridis expanded (together with Picea abies in the subalpine forest). Between 1700 and 900 BP the Juniperus nana and Alnus viridis scrubs declined while meadows and pastures took over, so that the pond Gouille Rion was definitively above timber­ line. The highest Holocene treeline was at 2400 to 2450 m a.s.l. (i.e. 50 to 100 m higher than the uppermost single specimen of Pinus cembra today) between 9000 and 4700 BP, but it is not yet dated in more detail. The highest charcoal of Pinus cembra at 2380 m a.s.l. has a radiocarbon date of 6010 ± 70 BP. Around 6900 BP a strong climatic deterioration caused an opening of timberline forest. First indicators of anthropogenic influence occurred at 4700 BP, when the forest limit started to move down. The lowering of timberline after 4700 BP was probably due to combined effects of human and climatic impact.