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When sampling animal movement paths, the frequency at which location measurements are attempted is a critical feature for data analysis. Important quantities derived from raw data, e.g. travel distance or sinuosity, can differ largely based on the temporal resolution of the data. Likewise, when movement models are fitted to data, parameter estimates have been demonstrated to vary with sampling rate. Thus, biological statements derived from such analyses can only be made with respect to the resolution of the underlying data, limiting extrapolation of results and comparison between studies. To address this problem, we investigate whether there are models that are robust against changes in temporal resolution. First, we propose a mathematically rigorous framework, in which we formally define robustness as a model property. We then use the framework for a thorough assessment of a range of basic random walk models, in which we also show how robustness relates to other probabilistic concepts. While we found robustness to be a strong condition met by few models only, we suggest a new method to extend models so as to make them robust. Our framework provides a new systematic, mathematically founded approach to the question if, and how, sampling rate of movement paths affects statistical inference.
In this paper, we analyze stochastic dynamic pricing and advertising differential games in special oligopoly markets with constant price and advertising elasticity. We consider the sale of perishable as well as durable goods and include adoption effects in the demand. Based on a unique stochastic feedback Nash equilibrium, we derive closed-form solution formulas of the value functions and the optimal feedback policies of all competing firms. Efficient simulation techniques are used to evaluate optimally controlled sales processes over time. This way, the evolution of optimal controls as well as the firms’ profit distributions are analyzed. Moreover, we are able to compare feedback solutions of the stochastic model with its deterministic counterpart. We show that the market power of the competing firms is exactly the same as in the deterministic version of the model. Further, we discover two fundamental effects that determine the relation between both models. First, the volatility in demand results in a decline of expected profits compared to the deterministic model. Second, we find that saturation effects in demand have an opposite character. We show that the second effect can be strong enough to either exactly balance or even overcompensate the first one. As a result we are able to identify cases in which feedback solutions of the deterministic model provide useful approximations of solutions of the stochastic model.
This paper examines the sale of a finite number of items in a class of stochastic dynamic pricing and advertising models with time-dependent demand elasticities. We prove structural properties of the optimal expected profits with respect to time, inventory level, price impact, advertising impact and different model parameters, such as discount rate, marginal unit costs, and holding costs. We find that the value of an additional item (opportunity costs) is decreasing in the unit costs, the discount rate, the holding cost rate and the number of items left to sell. We also derive structural properties of optimal joint pricing and advertising strategies. This way, we obtain general qualitative insights in the complex interplay and the mutual dependence of optimal pricing and advertising decisions. Among other properties, we show that a higher advertising impact leads to higher optimal prices and lower advertising rates, which in turn implies a lower speed of sale. The results obtained help practitioners to respond to changes in market conditions by adjusting price and advertising accordingly. Our results allow speeding up numerical computations of decisions as the set of possible actions can be reduced significantly. Our analysis implies general results for pure pricing as well as pure advertising models with time-dependent demand elasticities. (C) 2016 Elsevier B.V. All rights reserved.
Robust appraisals of climate impacts at different levels of global-mean temperature increase are vital to guide assessments of dangerous anthropogenic interference with the climate system. The 2015 Paris Agreement includes a two-headed temperature goal: "holding the increase in the global average temperature to well below 2 degrees C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5 degrees C". Despite the prominence of these two temperature limits, a comprehensive overview of the differences in climate impacts at these levels is still missing. Here we provide an assessment of key impacts of climate change at warming levels of 1.5 degrees C and 2 degrees C, including extreme weather events, water availability, agricultural yields, sea-level rise and risk of coral reef loss. Our results reveal substantial differences in impacts between a 1.5 degrees C and 2 degrees C warming that are highly relevant for the assessment of dangerous anthropogenic interference with the climate system. For heat-related extremes, the additional 0.5 degrees C increase in global-mean temperature marks the difference between events at the upper limit of present-day natural variability and a new climate regime, particularly in tropical regions. Similarly, this warming difference is likely to be decisive for the future of tropical coral reefs. In a scenario with an end-of-century warming of 2 degrees C, virtually all tropical coral reefs are projected to be at risk of severe degradation due to temperature-induced bleaching from 2050 onwards. This fraction is reduced to about 90% in 2050 and projected to decline to 70% by 2100 for a 1.5 degrees C scenario. Analyses of precipitation-related impacts reveal distinct regional differences and hot-spots of change emerge. Regional reduction in median water availability for the Mediterranean is found to nearly double from 9% to 17% between 1.5 degrees C and 2 degrees C, and the projected lengthening of regional dry spells increases from 7 to 11%. Projections for agricultural yields differ between crop types as well as world regions. While some (in particular high-latitude) regions may benefit, tropical regions like West Africa, South-East Asia, as well as Central and northern South America are projected to face substantial local yield reductions, particularly for wheat and maize. Best estimate sea-level rise projections based on two illustrative scenarios indicate a 50cm rise by 2100 relative to year 2000-levels for a 2 degrees C scenario, and about 10 cm lower levels for a 1.5 degrees C scenario. In a 1.5 degrees C scenario, the rate of sea-level rise in 2100 would be reduced by about 30% compared to a 2 degrees C scenario. Our findings highlight the importance of regional differentiation to assess both future climate risks and different vulnerabilities to incremental increases in global-mean temperature. The article provides a consistent and comprehensive assessment of existing projections and a good basis for future work on refining our understanding of the difference between impacts at 1.5 degrees C and 2 degrees C warming.
Large-scale transitions in societies are associated with both individual behavioural change and restructuring of the social network. These two factors have often been considered independently, yet recent advances in social network research challenge this view. Here we show that common features of societal marginalization and clustering emerge naturally during transitions in a co-evolutionary adaptive network model. This is achieved by explicitly considering the interplay between individual interaction and a dynamic network structure in behavioural selection. We exemplify this mechanism by simulating how smoking behaviour and the network structure get reconfigured by changing social norms. Our results are consistent with empirical findings: The prevalence of smoking was reduced, remaining smokers were preferentially connected among each other and formed increasingly marginalized clusters. We propose that self-amplifying feedbacks between individual behaviour and dynamic restructuring of the network are main drivers of the transition. This generative mechanism for co-evolution of individual behaviour and social network structure may apply to a wide range of examples beyond smoking.
Sarmentofascis zamparelliae n. sp., a new demosponge from the lower Campanian of southern Italy
(2016)
A new coralline sponge, exhibiting typical "stromatoporoid" bodyplan, is described as Sarmentofascis zamparelliae n. sp. from the lower Campanian of the southern Apennines, Italy. It is differentiated from Sarmentofascis cretacea (Turnsek) (Hauterivian of Montenegro) and Sarmentofascis chabrieri Termier, Termier and Vachard (Santonian of France) above all by its slender arborescent skeleton, exhibiting longitudinally distributed astrorhizae-like canals. S. zamparelliae n. sp. is the youngest representative of the genus and is reported from a period exhibiting a distinct decline of "stromatoporoid" sponges. With its clinogonal microstructure and occurrence in inner platform stromatoporoid-foraminiferan floatstones it can be considered a Late Cretaceous environmental analog to the Late Jurassic Cladocoropsis. (C) 2015 Elsevier Ltd. All rights reserved.
Late Quaternary paleoenvironmental records from the Chatanika River valley near Fairbanks (Alaska)
(2016)
Perennially-frozen deposits are considered as excellent paleoenvironmental archives similar to lacustrine, deep marine, and glacier records because of the long-term and good preservation of fossil records under stable permafrost conditions. A permafrost tunnel in the Vault Creek Valley (Chatanika River Valley, near Fairbanks) exposes a sequence of frozen deposits and ground ice that provides a comprehensive set of proxies to reconstruct the late Quaternary environmental history of Interior Alaska. The multi-proxy approach includes different dating techniques (radiocarbon-accelerator mass spectrometry [AMS C-14], optically stimulated luminescence [OSL], thorium/uranium radioisotope disequilibria [Th-230/U]), as well as methods of sedimentology, paleoecology, hydrochemistry, and stable isotope geochemistry of ground ice. The studied sequence consists of 36-m-thick late Quaternary deposits above schistose bedrock. Main portions of the sequence accumulated during the early and middle Wisconsin periods. The lowermost unit A consists of about 9-m-thick ice-bonded fluvial gravels with sand and peat lenses. A late Sangamon (MIS 5a) age of unit A is assumed. Spruce forest with birch, larch, and some shrubby alder dominated the vegetation. High presence of Sphagnum spores and Cyperaceae pollen points to mires in the Vault Creek Valley. The overlying unit B consists of 10-m-thick alternating fluvial gravels, loess-like silt, and sand layers, penetrated by small ice wedges. OSL dates support a stadial early Wisconsin (MIS 4) age of unit B. Pollen and plant macrofossil data point to spruce forests with some birch interspersed with wetlands around the site. The following unit C is composed of 15-m-thick ice-rich loess-like and organic-rich silt with fossil bones and large ice wedges. Unit C formed during the interstadial mid-Wisconsin (MIS 3) and stadial late Wisconsin (MIS 2) as indicated by radiocarbon ages. Post-depositional slope processes significantly deformed both, ground ice and sediments of unit C. Pollen data show that spruce forests and wetlands dominated the area. The macrofossil remains of Picea, Larix, and Alnus incana ssp. tenuifolia also prove the existence of boreal coniferous forests during the mid-Wisconsin interstadial, which were replaced by treeless tundra-steppe vegetation during the late Wisconsin stadial. Unit C is discordantly overlain by the 2-m-thick late Holocene deposits of unit D. The pollen record of unit D indicates boreal forest vegetation similar to the modern one. The permafrost record from the Vault Creek tunnel reflects more than 90 ka of periglacial landscape dynamics triggered by fluvial and eolian accumulation, and formation of ice-wedge polygons and post depositional deformation by slope processes. The record represents a typical Wisconsin valley-bottom facies in Central Alaska. (C) 2016 Elsevier Ltd. All rights reserved.