Scholarly Work - Mathematical Sciences

Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/8719

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    Evaluating and presenting uncertainty in model‐based unconstrained ordination
    (2019-12) Hoegh, Andrew; Roberts, David W.
    Variability in ecological community composition is often analyzed by recording the presence or abundance of taxa in sample units, calculating a symmetric matrix of pairwise distances or dissimilarities among sample units and then mapping the resulting matrix to a low‐dimensional representation through methods collectively called ordination. Unconstrained ordination only uses taxon composition data, without any environmental or experimental covariates, to infer latent compositional gradients associated with the sampling units. Commonly, such distance‐based methods have been used for ordination, but recently there has been a shift toward model‐based approaches. Model‐based unconstrained ordinations are commonly formulated using a Bayesian latent factor model that permits uncertainty assessment for parameters, including the latent factors that correspond to gradients in community composition. While model‐based methods have the additional benefit of addressing uncertainty in the estimated gradients, typically the current practice is to report point estimates without summarizing uncertainty. To demonstrate the uncertainty present in model‐based unconstrained ordination, the well‐known spider and dune data sets were analyzed and shown to have large uncertainty in the ordination projections. Hence to understand the factors that contribute to the uncertainty, simulation studies were conducted to assess the impact of additional sampling units or species to help inform future ordination studies that seek to minimize variability in the latent factors. Accurate reporting of uncertainty is an important part of transparency in the scientific process; thus, a model‐based approach that accounts for uncertainty is valuable. An R package, UncertainOrd, contains visualization tools that accurately represent estimates of the gradients in community composition in the presence of uncertainty.
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    Identifying occupancy model inadequacies: can residuals separately assess detection and presence?
    (2019-04) Wright, Wilson J.; Irvine, Kathryn M.; Higgs, Megan D.
    Occupancy models are widely applied to estimate species distributions, but few methods exist for model checking. Thorough model assessments can uncover inadequacies and allow for deeper ecological insight by exploring structure in the observed data not accounted for by a model. We introduce occupancy model residual definitions that utilize the posterior distribution of the partially latent occupancy states. Residual-based assessments are valuable because they can target specific assumptions and identify ways to improve a model, such as adding spatial correlation or meaningful covariates. Our approach defines separate residuals for occupancy and detection, and we use simulation to examine whether missing structure for modeling detection probabilities can be distinguished from that for occupancy probabilities. In many scenarios, our residual diagnostics were able to separate inadequacies at the different model levels successfully, but we describe other situations when this may not be the case. Applying Moran\'s I residual diagnostics to assess models for silver-haired (Lasionycteris noctivagans) and little brown (Myotis lucifugus) bats only provided evidence of residual spatial correlation among detections. Targeting specific model assumptions using carefully chosen residual diagnostics is valuable for any analysis, and we remove previous barriers for occupancy analyses-lack of examples and practical advice.
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    When a habitat freezes solid: Microorganisms over-winter within the ice column of a coastal Antarctic lake
    (2011-03) Foreman, Christine M.; Dieser, Markus; Greenwood, Mark C.; Cory, R. M.; Laybourn-Parry, Johanna; Lisle, John T.; Jaros, C.; Miller, P. L.; Chin, Yu-Ping; McKnight, Diane M.
    A major impediment to understanding the biology of microorganisms inhabiting Antarctic environments is the logistical constraint of conducting field work primarily during the summer season. However, organisms that persist throughout the year encounter severe environmental changes between seasons. In an attempt to bridge this gap, we collected ice core samples from Pony Lake in early November 2004 when the lake was frozen solid to its base, providing an archive for the biological and chemical processes that occurred during winter freezeup. The ice contained bacteria and virus-like particles, while flagellated algae and ciliates over-wintered in the form of inactive cysts and spores. Both bacteria and algae were metabolically active in the ice core melt water. Bacterial production ranged from 1.8 to 37.9 μg C L−1 day−1. Upon encountering favorable growth conditions in the melt water, primary production ranged from 51 to 931 μg C L−1 day−1. Because of the strong H2S odor and the presence of closely related anaerobic organisms assigned to Pony Lake bacterial 16S rRNA gene clones, we hypothesize that the microbial assemblage was strongly affected by oxygen gradients, which ultimately restricted the majority of phylotypes to distinct strata within the ice column. This study provides evidence that the microbial community over-winters in the ice column of Pony Lake and returns to a highly active metabolic state when spring melt is initiated.
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    Physicochemical and biological dynamics in a coastal Antarctic lake as it transitions from frozen to open water
    (2013-03) Dieser, Markus; Foreman, Christine M.; Jaros, C.; Lisle, John T.; Greenwood, Mark C.; Laybourn-Parry, Johanna; Miller, P. L.; Chin, Yu-Ping; McKnight, Diane M.
    Pony Lake, at Cape Royds, Antarctica, is a shallow, eutrophic, coastal lake that freezes solid in the winter. Changes in Pony Lake's physicochemical parameters and microbial community were studied during the transition from ice to open water. Due to rising water temperatures, the progressive melt of the ice column and the gradual mixing of basal brines into the remaining water column, Pony Lake evolved physically and chemically over the course of the summer, thereby affecting the microbial community composition. Temperature, pH, conductivity, nutrients and major ion concentrations reached their maximum in January. Pony Lake was colonized by bacteria, viruses, phytoflagellates, ciliates, and a small number of rotifers. Primary and bacterial production were highest in mid-December (2.66 mg C 1-1 d-1 and 30.5 µg C 1-1 d-1, respectively). A 16S rRNA gene analysis of the bacterioplankton revealed 34 unique sequences dominated by members of the ß- and y-proteobacteria lineages. Cluster analyses on denaturing gradient gel electrophoresis (DGGE) banding patterns and community structure indicated a shift in the dominant members of the microbial community during the transition from winter ice, to early, and late summer lakewater. Our data demonstrate that temporal changes in physicochemical parameters during the summer months determine community dynamics and mediate changes in microbial species composition.
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    A multi-scale assessment of animal aggregation patterns to understand increasing pathogen seroprevalence
    (Ecological Society of America, 2014-10) Brennan, Angela; Cross, Paul C.; Higgs, Megan D.; Edwards, W. Henry; Scurlock, Brandon M.; Creel, Scott
    Understanding how animal density is related to pathogen transmission is important to develop effective disease control strategies, but requires measuring density at a scale relevant to transmission. However, this is not straightforward or well-studied among large mammals with group sizes that range several orders of magnitude or aggregation patterns that vary across space and time. To address this issue, we examined spatial variation in elk (Cervus canadensis) aggregation patterns and brucellosis across 10 regions in the Greater Yellowstone Area where previous studies suggest the disease may be increasing. We hypothesized that rates of increasing brucellosis would be better related to the frequency of large groups than mean group size or population density, but we examined whether other measures of density would also explain rising seroprevalence. To do this, we measured wintering elk density and group size across multiple spatial and temporal scales from monthly aerial surveys. We used Bayesian hierarchical models and 20 years of serologic data to estimate rates of increase in brucellosis within the 10 regions, and to examine the linear relationships between these estimated rates of increase and multiple measures of aggregation. Brucellosis seroprevalence increased over time in eight regions (one region showed an estimated increase from 0.015 in 1991 to 0.26 in 2011), and these rates of increase were positively related to all measures of aggregation. The relationships were weaker when the analysis was restricted to areas where brucellosis was present for at least two years, potentially because aggregation was related to disease-establishment within a population. Our findings suggest that (1) group size did not explain brucellosis increases any better than population density and (2) some elk populations may have high densities with small groups or lower densities with large groups, but brucellosis is likely to increase in either scenario. In this case, any one control method such as reducing population density or group size may not be sufficient to reduce transmission. This study highlights the importance of examining the density-transmission relationship at multiple scales and across populations before broadly applying disease control strategies.
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