Stable isotopes are a powerful tool for ecologists, often used to assess contributions of different sources to a mixture (e.g. prey to a consumer). Mixing models use stable isotope data to estimate the contribution of sources to a mixture. Uncertainty associated with mixing models is often substantial, but has not yet been fully incorporated in models. We developed a Bayesian-mixing model that estimates probability distributions of source contributions to a mixture while explicitly accounting for uncertainty associated with multiple sources, fractionation and isotope signatures. This model also allows for optional incorporation of informative prior information in analyses. We demonstrate our model using a predator-prey case study. Accounting for uncertainty in mixing model inputs can change the variability, magnitude and rank order of estimates of prey (source) contributions to the predator (mixture). Isotope mixing models need to fully account for uncertainty in order to accurately estimate source contributions.

Stable isotope mixing models are increasingly used to quantify consumer diets, but may be misused and misinterpreted. We address major challenges to their effective application. Mixing models have increased rapidly in sophistication. Current models estimate probability distributions of source contributions, have user-friendly interfaces, and incorporate complexities such as variability in isotope signatures, discrimination factors, hierarchical variance structure, covariates, and concentration dependence. For proper implementation of mixing models, we offer the following suggestions. First, mixing models can only be as good as the study and data. Studies should have clear questions, be informed by knowledge of the system, and have strong sampling designs to effectively characterize isotope variability of consumers and resources on proper spatio-temporal scales. Second, studies should use models appropriate for the question and recognize their assumptions and limitations. Decisions about source grouping or incorporation of concentration dependence can influence results. Third, studies should be careful about interpretation of model outputs. Mixing models generally estimate proportions of assimilated resources with substantial uncertainty distributions. Last, common sense, such as graphing data before analyzing, is essential to maximize usefulness of these tools. We hope these suggestions for effective implementation of stable isotope mixing models will aid continued development and application of this field.

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.

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Variability in resource use defines the width of a trophic niche occupied by a population. Intra-population variability in resource use may occur across hierarchical levels of population structure from individuals to subpopulations. Understanding how levels of population organization contribute to population niche width is critical to ecology and evolution. Here we describe a hierarchical stable isotope mixing model that can simultaneously estimate both the prey composition of a consumer diet and the diet variability among individuals and across levels of population organization. By explicitly estimating variance components for multiple scales, the model can deconstruct the niche width of a consumer population into relevant levels of population structure. We apply this new approach to stable isotope data from a population of gray wolves from coastal British Columbia, and show support for extensive intra-population niche variability among individuals, social groups, and geographically isolated subpopulations. The analytic method we describe improves mixing models by accounting for diet variability, and improves isotope niche width analysis by quantitatively assessing the contribution of levels of organization to the niche width of a population.

One of the most spectacular phenomena in nature is the annual return of millions of salmon to spawn in their natal streams and lakes along the Pacific coast of North America. The salmon die after spawning, and the nutrients and energy in their bodies, derived almost entirely from marine sources, are deposited in the freshwater ecosystems. This represents a vital input to the ecosystems used as spawning grounds. Salmon-derived nutrients make up a substantial fraction of the plants and animals in aquatic and terrestrial habitats associated with healthy salmon populations. The decline of salmon numbers throughout much of their southern range in North America has prompted concern that the elimination of this "conveyor belt" of nutrients and energy may fundamentally change the productivity of these coastal freshwater and terrestrial ecosystems, and consequently their ability to support wildlife, including salmon. If progress is to be made towards understanding and conserving the connection between migratory salmon and coastal ecosystems, scientists and decisionmakers must explore and understand the vast temporal and spatial scales that characterize this relationship.

Interpopulation variation in dynamics can buffer species against environmental change. We compared population synchrony in a group of threatened Chinook salmon in the highly impacted Snake River basin (Oregon, Washington, Idaho) to that in the sockeye salmon stock complex of less impact Bristol Bay (Alaska). Over the last 40 years, >90% of populations in the Snake River basin became more synchronized with one another. However, over that period, sockeye populations from Alaska did not exhibit systemic changes in synchrony. Coincident with increasing Snake River population synchrony, there was an increase in hatchery propagation and the number of large dams, potentially homogenizing habitats and populations. A simulation using economic portfolio theory revealed that synchronization of Snake River salmon decreased risk-adjusted portfolio performance (the ratio of portfolio productivity to variance) and decreased benefits of population richness. Improving portfolio performance for exploited species, especially given future environmental change, requires protecting a diverse range of populations and the varied habitats upon which they depend.

Summary1. Life-history strategies can buffer individuals and populations from environmental variability. For instance, it is possible that asynchronous dynamics among different life histories can stabilize populations through portfolio effects. 2. Here, we examine life-history diversity and its importance to stability for an iconic migratory fish species. In particular, we examined steelhead (Oncorhynchus mykiss), an anadromous and iteroparous salmonid, in two large, relatively pristine, watersheds, the Skeena and Nass, in north-western British Columbia, Canada. We synthesized life-history information derived from scales collected from adult steelhead (N = 7227) in these watersheds across a decade. 3. These migratory fishes expressed 36 different manifestations of the anadromous life-history strategy, with 16 different combinations of freshwater and marine ages, 7Á6% of fish performing multiple spawning migrations, and up to a maximum of four spawning migrations per lifetime. Furthermore, in the Nass watershed, various life histories were differently prevalent through time -three different life histories were the most prevalent in a given year, and no life history ever represented more than 45% of the population. 4. These asynchronous dynamics among life histories decreased the variability of numerical abundance and biomass of the aggregated population so that it was > 20% more stable than the stability of the weighted average of specific life histories: evidence of a substantial portfolio effect. Year of ocean entry was a key driver of dynamics; the median correlation coefficient of abundance of life histories that entered the ocean the same year was 2Á5 times higher than the median pairwise coefficient of life histories that entered the ocean at different times. Simulations illustrated how different elements of life-history diversity contribute to stability and persistence of populations. 5. This study provides evidence that life-history diversity can dampen fluctuations in population abundances and biomass via portfolio effects. Conserving genetic integrity and habitat diversity in these and other large watersheds can enable a diversity of life histories that increases population and biomass stability in the face of environmental variability.