Brice X. Semmens

Incorporating uncertainty and prior information into stable isotope mixing models.

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.

Quantifying inter- and intra-population niche variability using hierarchical bayesian stable isotope mixing models.

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.

Conservation and management applications of the REEF volunteer fish monitoring program

The REEF Fish Survey Project is a volunteer fish monitoring program developed by the Reef Environmental Education Foundation (REEF). REEF volunteers collect fish distribution and abundance data using a standardized visual method during regular diving and snorkeling activities. Survey data are recorded on preprinted data sheets that are returned to REEF and optically digitized. Data are housed in a publicly accessible database on REEFs Web site (http://www.reef.org). Since the projects inception in 1993, over 40,000 surveys have been conducted in the coastal waters of North America, tropical western Atlantic, Gulf of California and Hawaii. The Fish Survey Project has been incorporated into existing monitoring programs through partnerships with government agencies, scientists, conservation organizations, and private institutions. REEFs partners benefit from the educational value and increased stewardship resulting from volunteer data collection. Applications of the data include an evaluation of fish/habitat interactions in the Florida Keys National Marine Sanctuary, the development of a multi-species trend analysis method to identify sites of management concern, assessment of the current distribution of species, status reports on fish assemblages of marine parks, and the evaluation of no-take zones in the Florida Keys. REEFs collaboration with a variety of partners, combined with the Fish Survey Projects standardized census method and database management system, has resulted in a successful citizen science monitoring program.

Assessing the effects of large mobile predators on ecosystem connectivity.

Large predators are often highly mobile and can traverse and use multiple habitats. We know surprisingly little about how predator mobility determines important processes of ecosystem connectivity. Here we used a variety of data sources drawn from Palmyra Atoll, a remote tropical marine ecosystem where large predators remain in high abundance, to investigate how these animals foster connectivity. Our results indicate that three of Palmyras most abundant large predators (e.g., two reef sharks and one snapper) use resources from different habitats creating important linkages across ecosystems. Observations of cross-system foraging such as this have important implications for the understanding of ecosystem functioning, the management of large-predator populations, and the design of conservation measures intended to protect whole ecosystems. In the face of widespread declines of large, mobile predators, it is important that resource managers, policy makers, and ecologists work to understand how these predators create connectivity and to determine the impact that their depletions may be having on the integrity of these linkages.

Observations of a Nassau grouper, Epinephelus striatus, Spawning Aggregation Site in Little Cayman, Cayman Islands, Including Multi-Species Spawning Information

Mass spawning aggregations of Caribbean grouper species are a conservation priority because of declines due to over-fishing. Previous studies have documented five historical aggregation sites in the Cayman Islands. Today, three of these sites are inactive or commercially extinct. In January 2002, the Reef Environmental Education Foundation led an expedition to Little Cayman Island to document a recently re-discovered spawning aggregation of Nassau grouper, Epinephelus striatus. A team of divers estimated the abundance, color phase composition, and courtship and spawning behavior of the aggregating grouper. The color phase composition of the aggregation shifted both during the course of each evening and throughout the 10-day project. Divers documented atypical coloration and courtship behavior in 10 additional fish species, of which five were seen spawning. Artisanal fishing occurred daily on the aggregation. The Cayman Islands Department of the Environment collected landings data and sampled catches to obtain length and sex ratios. The Cayman fishing fleet, while small, had a significant impact on the aggregation with a harvest of almost 2 000 Nassau grouper during the 10-day project. The study site supports the largest known Nassau grouper aggregation in the Cayman Islands. The relatively large size of fish and the high proportion of males indicate that this site supports a relatively healthy aggregation compared to other Nassau grouper aggregation sites throughout the Caribbean.

Using Stable Isotope Analysis to Understand the Migration and Trophic Ecology of Northeastern Pacific White Sharks (Carcharodon carcharias)

The white shark (Carcharodon carcharias) is a wide-ranging apex predator in the northeastern Pacific (NEP). Electronic tagging has demonstrated that white sharks exhibit a regular migratory pattern, occurring at coastal sites during the late summer, autumn and early winter and moving offshore to oceanic habitats during the remainder of the year, although the purpose of these migrations remains unclear. The purpose of this study was to use stable isotope analysis (SIA) to provide insight into the trophic ecology and migratory behaviors of white sharks in the NEP. Between 2006 and 2009, 53 white sharks were biopsied in central California to obtain dermal and muscle tissues, which were analyzed for stable isotope values of carbon (δ13C) and nitrogen (δ15N). We developed a mixing model that directly incorporates movement data and tissue incorporation (turnover) rates to better estimate the relative importance of different focal areas to white shark diet and elucidate their migratory behavior. Mixing model results for muscle showed a relatively equal dietary contribution from coastal and offshore regions, indicating that white sharks forage in both areas. However, model results indicated that sharks foraged at a higher relative rate in coastal habitats. There was a negative relationship between shark length and muscle δ13C and δ15N values, which may indicate ontogenetic changes in habitat use related to onset of maturity. The isotopic composition of dermal tissue was consistent with a more rapid incorporation rate than muscle and may represent more recent foraging. Low offshore consumption rates suggest that it is unlikely that foraging is the primary purpose of the offshore migrations. These results demonstrate how SIA can provide insight into the trophic ecology and migratory behavior of marine predators, especially when coupled with electronic tagging data.

Habitat structure determines resource use by zooplankton in temperate lakes

While the importance of terrestrial linkages to aquatic ecosystems is well appreciated, the degree of terrestrial support of aquatic consumers remains debated. Estimates of terrestrial contributions to lake zooplankton have omitted a key food source, phytoplankton produced below the mixed layer. We used carbon and nitrogen stable isotope data from 25 Pacific Northwest lakes to assess the relative importance of particulate organic matter (POM) from the mixed layer, below the mixed layer and terrestrial detritus to zooplankton. Zooplankton and deep POM were depleted in ¹³C relative to mixed layer POM in lakes that can support deep primary production. A Bayesian stable isotope mixing model estimated that terrestrial detritus contributed <5% to zooplankton production, and confirms the role of lake optical and thermal properties; deep POM accounted for up to 80% of zooplankton production in the clearest lakes. These results suggest terrestrial support of lake zooplankton production is trivial.

Including source uncertainty and prior information in the analysis of stable isotope mixing models.

Stable isotope mixing models offer a statistical framework for estimating the contribution of multiple sources (such as prey) to a mixture distribution. Recent advances in these models have estimated the source proportions using Bayesian methods, but have not explicitly accounted for uncertainty in the mean and variance of sources. We demonstrate that treating these quantities as unknown parameters can reduce bias in the estimated source contributions, although model complexity is increased (thereby increasing the variance of estimates). The advantages of this fully Bayesian approach are particularly apparent when the source geometry is poor or sample sizes are small. A second benefit to treating source quantities as parameters is that prior source information can be included. We present findings from 9 lake food-webs, where the consumer of interest (fish) has a diet composed of 5 sources: aquatic insects, snails, zooplankton, amphipods, and terrestrial insects. We compared the traditional Bayesian stable isotope mixing model with fixed source parameters to our fully Bayesian model-with and without an informative prior. The informative prior has much less impact than the choice of model-the traditional mixing model with fixed source parameters estimates the diet to be dominated by aquatic insects, while the fully Bayesian model estimates the diet to be more balanced but with greater importance of zooplankton. The findings from this example demonstrate that there can be stark differences in inference between the two model approaches, particularly when the source geometry of the mixing model is poor. These analyses also emphasize the importance of investing substantial effort toward characterizing the variation in the isotopic characteristics of source pools to appropriately quantify uncertainties in their contributions to consumers in food webs.

Quasi-extinction risk and population targets for the Eastern, migratory population of monarch butterflies ( Danaus plexippus )

The Eastern, migratory population of monarch butterflies (Danaus plexippus), an iconic North American insect, has declined by ~80% over the last decade. The monarch’s multi-generational migration between overwintering grounds in central Mexico and the summer breeding grounds in the northern U.S. and southern Canada is celebrated in all three countries and creates shared management responsibilities across North America. Here we present a novel Bayesian multivariate auto-regressive state-space model to assess quasi-extinction risk and aid in the establishment of a target population size for monarch conservation planning. We find that, given a range of plausible quasi-extinction thresholds, the population has a substantial probability of quasi-extinction, from 11–57% over 20 years, although uncertainty in these estimates is large. Exceptionally high population stochasticity, declining numbers, and a small current population size act in concert to drive this risk. An approximately 5-fold increase of the monarch population size (relative to the winter of 2014–15) is necessary to halve the current risk of quasi-extinction across all thresholds considered. Conserving the monarch migration thus requires active management to reverse population declines, and the establishment of an ambitious target population size goal to buffer against future environmentally driven variability.

A quantitative approach to combine sources in stable isotope mixing models

Stable isotope mixing models, used to estimate source contributions to a mixture, typically yield highly uncertain estimates when there are many sources and relatively few isotope elements. Previously, ecologists have either accepted the uncertain contribution estimates for individual sources or addressed the problem in an ad hoc way by combining either related sources prior to analysis or the estimated proportions of related sources following analysis. Neither of these latter approaches explicitly account for uncertainty in source combinations within the likelihood framework. In this paper we incorporate uncertainty in both the number of source groups and group assignment within a formal Bayesian mixing model framework. By dynamically exploring model complexity due to aggregating sources based on shared proportional contributions, we can estimate posterior probabilities of alternative group configurations, and construct posterior dendrograms of group membership. We apply this method to simulated data, and illustrate applications to two consumer datasets (rainbow trout, coastal mink). Our results demonstrate that estimating, rather than fixing, the number of proportional contributions in a mixing model can improve model inference and reduce bias in estimates of source contributions to a mixture.