In this paper, we review recent advances in stable isotope mixing models (SIMMs) and place them into an overarching Bayesian statistical framework, which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixture. The most widely used application is quantifying the diet of organisms based on the food sources they have been observed to consume. At the centre of the multivariate statistical model we propose is a compositional mixture of the food sources corrected for various metabolic factors. The compositional component of our model is based on the isometric log‐ratio transform. Through this transform, we can apply a range of time series and non‐parametric smoothing relationships. We illustrate our models with three case studies based on real animal dietary behaviour. Copyright © 2013 John Wiley & Sons, Ltd.

The ongoing evolution of tracer mixing models has resulted in a confusing array of software tools that differ in terms of data inputs, model assumptions, and associated analytic products. Here we introduce MixSIAR, an inclusive, rich, and flexible Bayesian tracer (e.g., stable isotope) mixing model framework implemented as an open-source R package. Using MixSIAR as a foundation, we provide guidance for the implementation of mixing model analyses. We begin by outlining the practical differences between mixture data error structure formulations and relate these error structures to common mixing model study designs in ecology. Because Bayesian mixing models afford the option to specify informative priors on source proportion contributions, we outline methods for establishing prior distributions and discuss the influence of prior specification on model outputs. We also discuss the options available for source data inputs (raw data versus summary statistics) and provide guidance for combining sources. We then describe a key advantage of MixSIAR over previous mixing model software—the ability to include fixed and random effects as covariates explaining variability in mixture proportions and calculate relative support for multiple models via information criteria. We present a case study of Alligator mississippiensis diet partitioning to demonstrate the power of this approach. Finally, we conclude with a discussion of limitations to mixing model applications. Through MixSIAR, we have consolidated the disparate array of mixing model tools into a single platform, diversified the set of available parameterizations, and provided developers a platform upon which to continue improving mixing model analyses in the future.

We propose a new and simple continuous Markov monotone stochastic process and use it to make inference on a partially observed monotone stochastic process. The process is piecewise linear, based on additive independent gamma increments arriving in a Poisson fashion. An independent increments variation allows very simple conditional simulation of sample paths given known values of the process. We take advantage of a reparameterization involving the Tweedie distribution to provide efficient computation. The motivating problem is the establishment of a chronology for samples taken from lake sediment cores, i.e. the attribution of a set of dates to samples of the core given their depths, knowing that the age-depth relationship is monotone. The chronological information arises from radiocarbon (-super-14C) dating at a subset of depths. We use the process to model the stochastically varying rate of sedimentation. Copyright (c) 2008 Royal Statistical Society.

The last interglaciation (LIG, 129 to 116 thousand years ago) was the most recent time in Earth's history when global mean sea level was substantially higher than it is at present. However, reconstructions of LIG global temperature remain uncertain, with estimates ranging from no significant difference to nearly 2°C warmer than present-day temperatures. Here we use a network of sea-surface temperature (SST) records to reconstruct spatiotemporal variability in regional and global SSTs during the LIG. Our results indicate that peak LIG global mean annual SSTs were 0.5 ± 0.3°C warmer than the climatological mean from 1870 to 1889 and indistinguishable from the 1995 to 2014 mean. LIG warming in the extratropical latitudes occurred in response to boreal insolation and the bipolar seesaw, whereas tropical SSTs were slightly cooler than the 1870 to 1889 mean in response to reduced mean annual insolation.

The dating of depths in two or more cores is frequently followed by a study of the synchroneity or otherwise of events reflected in the cores. The difficulties most frequently encountered are: (a) determining precisely the depths associated with the events; and (b) determining the ages associated with the depths. There has been much progress in recent years in developing tools for the study of uncertainties in establishing chronologies. This has not yet been matched by similar progress in modelling event/depth relationships. This paper proposes a simple and flexible approach, showing how uncertain events can be married to uncertain chronologies.

The ongoing evolution of tracer mixing models has resulted in a confusing array of software tools that differ in terms of data inputs, model assumptions, and associated analytic products. Here we introduce MixSIAR, an inclusive, rich, and flexible Bayesian tracer (e.g. stable isotope) mixing model framework implemented as an open-source R package. Using MixSIAR as a foundation, we provide guidance for the implementation of mixing model analyses. We begin by outlining the practical differences between mixture data error structure formulations and relate these error structures to common mixing model study designs in ecology. Because Bayesian mixing models afford the option to specify informative priors on source proportion contributions, we outline methods for establishing prior distributions and discuss the influence of prior specification on model outputs. We also discuss the options available for source data inputs (raw data versus summary statistics) and provide guidance for combining sources. We then describe a key advantage of MixSIAR over previous mixing model software—the ability to include fixed and random effects as covariates explaining variability in mixture proportions and calculate relative support for multiple models via information criteria. We present a case study of Alligator mississippiensis diet partitioning to demonstrate the power of this approach. Finally, we conclude with a discussion of limitations to mixing model applications. Through MixSIAR, we have consolidated the disparate array of mixing model tools into a single platform, diversified the set of available parameterizations, and provided developers a platform upon which to continue improving mixing model analyses in the future.

18Relative sea-level changes during the last ~2500 years in New Jersey, USA were reconstructed to test if 19 late Holocene sea level was stable or included persistent and distinctive phases of variability. 20Foraminifera and bulk-sediment δ 13 C values were combined to reconstruct paleomarsh elevation with 21 decimeter precision from sequences of salt-marsh sediment at two sites using a multi-proxy approach. 22The history of sediment deposition was constrained by a composite chronology. An age-depth model 23 developed for each core enabled reconstruction of sea level with multi-decadal resolution. Following 24 correction for land-level change (1.4mm/yr), four successive and sustained (multi-centennial) sea-level 25 trends were objectively identified and quantified using error-in-variables change point analysis to account 26 for age and sea-level uncertainties. From at least 500BC to 250AD sea-level fell at 0.11mm/yr. The 27 second period saw sea-level rise at 0.62mm/yr from 250AD to 733AD. Between 733AD and 1850AD sea 28 level fell at 0.12mm/yr. The reconstructed rate of sea-level rise since ~1850AD was 3.1mm/yr and 29 represents the most rapid period of change for at least 2500 years. This trend began between 1830AD and 30 1873AD and its onset is synchronous with other locations on the U.S. Atlantic coast. Since this change 31 point, reconstructed sea-level rise is in agreement with regional tide-gauge records and exceeds the global 32 average estimate for the 20 th century. These positive and negative departures from background rates 33 demonstrate that the late Holocene sea level was not stable in New Jersey. 34 35

We provide records of relative sea level since A.D. 1500 from two salt marshes in North Carolina to complement existing tide-gauge records and to determine when recent rates of accelerated sea-level rise commenced. Reconstructions were developed using foraminiferabased transfer functions and composite chronologies, which were validated against regional twentieth century tide-gauge records. The measured rate of relative sea-level rise in North Carolina during the twentieth century was 3.0-3.3 mm/a, consisting of a background rate of ~1 mm/a, plus an abrupt increase of 2.2 mm/a, which began between A.D. 1879 and 1915. This acceleration is broadly synchronous with other studies from the Atlantic coast. The magnitude of the acceleration at both sites is larger than at sites farther north along the U.S. and Canadian Atlantic coast and may be indicative of a latitudinal trend.