Occupancy Models for Monitoring Marine Fish: A Bayesian Hierarchical Approach to Model Imperfect Detection with a Novel Gear Combination

Occupancy models using incidence data collected repeatedly at sites across the range of a population are increasingly employed to infer patterns and processes influencing population distribution and dynamics. While such work is common in terrestrial systems, fewer examples exist in marine applications. This disparity likely exists because the replicate samples required by these models to account for imperfect detection are often impractical to obtain when surveying aquatic organisms, particularly fishes. We employ simultaneous sampling using fish traps and novel underwater camera observations to generate the requisite replicate samples for occupancy models of red snapper, a reef fish species. Since the replicate samples are collected simultaneously by multiple sampling devices, many typical problems encountered when obtaining replicate observations are avoided. Our results suggest that augmenting traditional fish trap sampling with camera observations not only doubled the probability of detecting red snapper in reef habitats off the Southeast coast of the United States, but supplied the necessary observations to infer factors influencing population distribution and abundance while accounting for imperfect detection. We found that detection probabilities tended to be higher for camera traps than traditional fish traps. Furthermore, camera trap detections were influenced by the current direction and turbidity of the water, indicating that collecting data on these variables is important for future monitoring. These models indicate that the distribution and abundance of this species is more heavily influenced by latitude and depth than by micro-scale reef characteristics lending credence to previous characterizations of red snapper as a reef habitat generalist. This study demonstrates the utility of simultaneous sampling devices, including camera traps, in aquatic environments to inform occupancy models and account for imperfect detection when describing factors influencing fish population distribution and dynamics.     

Evaluating Multi-Level Models to Test Occupancy State Responses of Plethodontid Salamanders

Plethodontid salamanders are diverse and widely distributed taxa and play critical roles in ecosystem processes. Due to salamander use of structurally complex habitats, and because only a portion of a population is available for sampling, evaluation of sampling designs and estimators is critical to provide strong inference about Plethodontid ecology and responses to conservation and management activities. We conducted a simulation study to evaluate the effectiveness of multi-scale and hierarchical single-scale occupancy models in the context of a Before-After Control-Impact (BACI) experimental design with multiple levels of sampling. Also, we fit the hierarchical single-scale model to empirical data collected for Oregon slender and Ensatina salamanders across two years on 66 forest stands in the Cascade Range, Oregon, USA. All models were fit within a Bayesian framework. Estimator precision in both models improved with increasing numbers of primary and secondary sampling units, underscoring the potential gains accrued when adding secondary sampling units. Both models showed evidence of estimator bias at low detection probabilities and low sample sizes; this problem was particularly acute for the multi-scale model. Our results suggested that sufficient sample sizes at both the primary and secondary sampling levels could ameliorate this issue. Empirical data indicated Oregon slender salamander occupancy was associated strongly with the amount of coarse woody debris (posterior mean = 0.74; SD = 0.24); Ensatina occupancy was not associated with amount of coarse woody debris (posterior mean = -0.01; SD = 0.29). Our simulation results indicate that either model is suitable for use in an experimental study of Plethodontid salamanders provided that sample sizes are sufficiently large. However, hierarchical single-scale and multi-scale models describe different processes and estimate different parameters. As a result, we recommend careful consideration of study questions and objectives prior to sampling data and fitting models.     

Estimating the Occupancy Rate of Spatially Rare or Hard to Detect Species: A Conditional Approach

Summary We consider the problem of estimating the occupancy rate of a target species in a region divided in spatial units (called quadrats); this quantity being defined as the proportion of quadrats occupied by this species. We mainly focus on spatially rare or hard to detect species that are typically detected in very few quadrats, and for which estimating the occupancy rate (with an acceptable precision) is problematic. We develop a conditional approach for estimating the quantity of interest; we condition on the presence of the target species in the region of study. We show that conditioning makes identifiable the occurrence and detectability parameters, regardless of the number of visits made in the sampled quadrats. Compared with an unconditional approach, it proves to be complementary, in that this allows us to deal with biological questions that cannot be addressed by the former. Two Bayesian analyses of the data are performed: one is noninformative, and the other takes advantage of the fact that some prior information on detectability is available. It emerges that taking such a prior into account significantly improves the precision of the estimate when the target species has been detected in few quadrats and is known to be easily detectable.     

Variational Bayes Analysis of a Photon-Based Hidden Markov Model for Single-Molecule FRET Trajectories

Single-molecule fluorescence resonance energy transfer (smFRET) measurement is a powerful technique for investigating dynamics of biomolecules, for which various efforts have been made to overcome significant stochastic noise. Time stamp (TS) measurement has been employed experimentally to enrich information within the signals, while data analyses such as the hidden Markov model (HMM) have been successfully applied to recover the trajectories of molecular state transitions from time-binned photon counting signals or images. In this article, we introduce the HMM for TS-FRET signals, employing the variational Bayes (VB) inference to solve the model, and demonstrate the application of VB-HMM-TS-FRET to simulated TS-FRET data. The same analysis using VB-HMM is conducted for other models and the previously reported change point detection scheme. The performance is compared to other analysis methods or data types and we show that our VB-HMM-TS-FRET analysis can achieve the best performance and results in the highest time resolution. Finally, an smFRET experiment was conducted to observe spontaneous branch migration of Holliday-junction DNA. VB-HMM-TS-FRET was successfully applied to reconstruct the state transition trajectory with the number of states consistent with the nucleotide sequence. The results suggest that a single migration process frequently involves rearrangement of multiple basepairs.     

Bayesian Approach to Proportional Odds Models for Survival Analysis

In this paper Bayesian approach is adopted to develop inferences about parameters in proportional odds models. Bayesian posterior intervals for coefficients in proportional odds models are derived by using approximation given in Pregibon (1981). The results are illustrated by using the lung cancer survival data reported by Prentice (1973).     

A Complex Network Approach to Distributional Semantic Models

A number of studies on network analysis have focused on language networks based on free word association, which reflects human lexical knowledge, and have demonstrated the small-world and scale-free properties in the word association network. Nevertheless, there have been very few attempts at applying network analysis to distributional semantic models, despite the fact that these models have been studied extensively as computational or cognitive models of human lexical knowledge. In this paper, we analyze three network properties, namely, small-world, scale-free, and hierarchical properties, of semantic networks created by distributional semantic models. We demonstrate that the created networks generally exhibit the same properties as word association networks. In particular, we show that the distribution of the number of connections in these networks follows the truncated power law, which is also observed in an association network. This indicates that distributional semantic models can provide a plausible model of lexical knowledge. Additionally, the observed differences in the network properties of various implementations of distributional semantic models are consistently explained or predicted by considering the intrinsic semantic features of a word-context matrix and the functions of matrix weighting and smoothing. Furthermore, to simulate a semantic network with the observed network properties, we propose a new growing network model based on the model of Steyvers and Tenenbaum. The idea underlying the proposed model is that both preferential and random attachments are required to reflect different types of semantic relations in network growth process. We demonstrate that this model provides a better explanation of network behaviors generated by distributional semantic models.     

A Computational Approach to Developing Mathematical Models of Polyploid Meiosis

Mathematical models of meiosis that relate offspring to parental genotypes through parameters such as meiotic recombination frequency have been difficult to develop for polyploids. Existing models have limitations with respect to their analytic potential, their compatibility with insights into mechanistic aspects of meiosis, and their treatment of model parameters in terms of parameter dependencies. In this article I put forward a computational approach to the probabilistic modeling of meiosis. A computer program enumerates all possible paths through the phases of replication, pairing, recombination, and segregation, while keeping track of the probabilities of the paths according to the various parameters involved. Probabilities for classes of genotypes or phenotypes are added, and the resulting formulas are simplified by the symbolic-computation system Mathematica. An example application to autotetraploids results in a model that remedies the limitations of previous models mentioned above. In addition to the immediate implications, the computational approach presented here can be expected to be useful through opening avenues for modeling a host of processes, including meiosis in higher-order ploidies.     

A Network Extension of Species Occupancy Models in a Patchy Environment Applied to the Yosemite Toad (Anaxyrus canorus)

A central challenge of conservation biology is using limited data to predict rare species occurrence and identify conservation areas that play a disproportionate role in regional persistence. Where species occupy discrete patches in a landscape, such predictions require data about environmental quality of individual patches and the connectivity among high quality patches. We present a novel extension to species occupancy modeling that blends traditional predictions of individual patch environmental quality with network analysis to estimate connectivity characteristics using limited survey data. We demonstrate this approach using environmental and geospatial attributes to predict observed occupancy patterns of the Yosemite toad (Anaxyrus (= Bufo) canorus) across >2,500 meadows in Yosemite National Park (USA). A . canorus , a Federal Proposed Species, breeds in shallow water associated with meadows. Our generalized linear model (GLM) accurately predicted ~84% of true presence-absence data on a subset of data withheld for testing. The predicted environmental quality of each meadow was iteratively ‘boosted’ by the quality of neighbors within dispersal distance. We used this park-wide meadow connectivity network to estimate the relative influence of an individual Meadow’s ‘environmental quality’ versus its ‘network quality’ to predict: a) clusters of high quality breeding meadows potentially linked by dispersal, b) breeding meadows with high environmental quality that are isolated from other such meadows, c) breeding meadows with lower environmental quality where long-term persistence may critically depend on the network neighborhood, and d) breeding meadows with the biggest impact on park-wide breeding patterns. Combined with targeted data on dispersal, genetics, disease, and other potential stressors, these results can guide designation of core conservation areas for A . canorus in Yosemite National Park.     

Mechanics of Constriction during Cell Division: A Variational Approach

During symmetric division cells undergo large constriction deformations at a stable midcell site. Using a variational approach, we investigate the mechanical route for symmetric constriction by computing the bending energy of deformed vesicles with rotational symmetry. Forces required for constriction are explicitly computed at constant area and constant volume, and their values are found to be determined by cell size and bending modulus. For cell-sized vesicles, considering typical bending modulus of , we calculate constriction forces in the range . The instability of symmetrical constriction is shown and quantified with a characteristic coefficient of the order of , thus evidencing that cells need a robust mechanism to stabilize constriction at midcell.     

Consistency Analysis of Genome-Scale Models of Bacterial Metabolism: A Metamodel Approach

Genome-scale metabolic models usually contain inconsistencies that manifest as blocked reactions and gap metabolites. With the purpose to detect recurrent inconsistencies in metabolic models, a large-scale analysis was performed using a previously published dataset of 130 genome-scale models. The results showed that a large number of reactions (~22%) are blocked in all the models where they are present. To unravel the nature of such inconsistencies a metamodel was construed by joining the 130 models in a single network. This metamodel was manually curated using the unconnected modules approach, and then, it was used as a reference network to perform a gap-filling on each individual genome-scale model. Finally, a set of 36 models that had not been considered during the construction of the metamodel was used, as a proof of concept, to extend the metamodel with new biochemical information, and to assess its impact on gap-filling results. The analysis performed on the metamodel allowed to conclude: 1) the recurrent inconsistencies found in the models were already present in the metabolic database used during the reconstructions process; 2) the presence of inconsistencies in a metabolic database can be propagated to the reconstructed models; 3) there are reactions not manifested as blocked which are active as a consequence of some classes of artifacts, and; 4) the results of an automatic gap-filling are highly dependent on the consistency and completeness of the metamodel or metabolic database used as the reference network. In conclusion the consistency analysis should be applied to metabolic databases in order to detect and fill gaps as well as to detect and remove artifacts and redundant information.     

A Many-Body Field Theory Approach to Stochastic Models in Population Biology

Background

Many models used in theoretical ecology, or mathematical epidemiology are stochastic, and may also be spatially-explicit. Techniques from quantum field theory have been used before in reaction-diffusion systems, principally to investigate their critical behavior. Here we argue that they make many calculations easier and are a possible starting point for new approximations.

Methodology

We review the many-body field formalism for Markov processes and illustrate how to apply it to a ‘Brownian bug’ population model, and to an epidemic model. We show how the master equation and the moment hierarchy can both be written in particularly compact forms. The introduction of functional methods allows the systematic computation of the effective action, which gives the dynamics of mean quantities. We obtain the 1-loop approximation to the effective action for general (space-) translation invariant systems, and thus approximations to the non-equilibrium dynamics of the mean fields.

Conclusions

The master equations for spatial stochastic systems normally take a neater form in the many-body field formalism. One can write down the dynamics for generating functional of physically-relevant moments, equivalent to the whole moment hierarchy. The 1-loop dynamics of the mean fields are the same as those of a particular moment-closure.     

Ranking Mahalanobis Distance Models for Predictions of Occupancy From Presence-Only Data

ABSTRACT The Mahalanobis distance statistic (D²) has emerged as an effective tool to identify suitable habitat from presence data alone, but there has been no mechanism to select among potential habitat covariates. We propose that the best combination of explanatory variables for a D² model can be identified by ranking potential models based on the proportion of the entire study area that is classified as potentially suitable habitat given that a predetermined proportion of occupied locations are correctly classified. In effect, our approach seeks to minimize errors of commission, or maximize specificity, while holding the omission error rate constant. We used this approach to identify potentially suitable habitat for the Olympic marmot (Marmota olympus), a declining species endemic to Olympic National Park, Washington, USA. We compared models built with all combinations of 11 habitat variables. A 7-variable model identified 21,143 ha within the park as potentially suitable for marmots, correctly classifying 80% of occupied locations. Additional refinements to the 7-variable model (e.g., eliminating small patches) further reduced the predicted area to 18,579 ha with little reduction in predictive power. Although we sought a model that would allow field workers to find 80% of Olympic marmot locations, in fact, <3% of 376 occupied locations and <9% of abandoned locations were >100 m from habitat predicted by the final model, suggesting that >90% of occupied marmot habitat could be found by observant workers surveying predicted habitat. The model comparison procedure allowed us to identify the suite of covariates that maximized specificity of our model and, thus, limited the amount of less favorable habitat included in the final prediction area. We expect that by maximizing specificity of models built from presence-only data, our model comparison procedure will be useful to conservation practitioners planning reintroductions, searching for rare species, or identifying habitat for protection.     

Occupancy Models of Nesting-Season Habitat Associations of Red-Shouldered Hawks in Central Minnesota

ABSTRACT Red-shouldered hawks (Buteo lineatus) are a species of special conservation concern in much of the Great Lakes region, and apparent population declines are thought to be primarily due to habitat loss and alteration. To evaluate red-shouldered hawk-habitat associations during the nesting season and at the landscape scale, we conducted repeated call-broadcast surveys in central Minnesota, USA, across 3 landscapes that represented a range of landscape conditions as a result of differing management practices. In 2004, we conducted repeated call-broadcast surveys at 131 locations in 2 study areas, and in 2005, we surveyed 238 locations in 3 study areas. We developed models relating habitat characteristics at 2 spatial scales to red-shouldered hawk occupancy and assessed support for these models in an information-theoretic framework. Overall, a small proportion of nonforest (grass, clear-cut area, forest <5 yr old), and a large proportion of mature deciduous forest (>40 yr old), had the strongest association with red-shouldered hawk occupancy (proportion of sites occupied) at both spatial scales. The landscape conditions we examined appeared to contain a habitat transition important to red-shouldered hawks. We found, in predominately forest landscapes, the amount of open habitat was most strongly associated with red-shouldered hawk occupancy, but in landscapes that included slightly less mature forest and more extensive open habitats, the extent of mature deciduous forest was most strongly associated with red-shouldered hawk occupancy. Our results suggested that relatively small (<5 ha) patches of open habitat (clear-cuts) in otherwise forested landscapes did not appear to influence red-shouldered hawk occupancy. Whereas, in an otherwise similar landscape, with smaller amounts of mature deciduous forest and larger (>15 ha) patches of open habitat, red-shouldered hawk occupancy decreased, suggesting a threshold in landscape composition, based on both the amount of mature forest and open area, is important in managing forest landscapes for red-shouldered hawks. Our results show that during the nesting season, red-shouldered hawks in central Minnesota occupy at similar rates landscapes with different habitat compositions resulting from different management strategies and that management strategies that create small openings may not negatively affect red-shouldered hawk occupancy.     

Assessing Differential Expression in Two-Color Microarrays: A Resampling-Based Empirical Bayes Approach

Microarrays are widely used for examining differential gene expression, identifying single nucleotide polymorphisms, and detecting methylation loci. Multiple testing methods in microarray data analysis aim at controlling both Type I and Type II error rates; however, real microarray data do not always fit their distribution assumptions. Smyth''s ubiquitous parametric method, for example, inadequately accommodates violations of normality assumptions, resulting in inflated Type I error rates. The Significance Analysis of Microarrays, another widely used microarray data analysis method, is based on a permutation test and is robust to non-normally distributed data; however, the Significance Analysis of Microarrays method fold change criteria are problematic, and can critically alter the conclusion of a study, as a result of compositional changes of the control data set in the analysis. We propose a novel approach, combining resampling with empirical Bayes methods: the Resampling-based empirical Bayes Methods. This approach not only reduces false discovery rates for non-normally distributed microarray data, but it is also impervious to fold change threshold since no control data set selection is needed. Through simulation studies, sensitivities, specificities, total rejections, and false discovery rates are compared across the Smyth''s parametric method, the Significance Analysis of Microarrays, and the Resampling-based empirical Bayes Methods. Differences in false discovery rates controls between each approach are illustrated through a preterm delivery methylation study. The results show that the Resampling-based empirical Bayes Methods offer significantly higher specificity and lower false discovery rates compared to Smyth''s parametric method when data are not normally distributed. The Resampling-based empirical Bayes Methods also offers higher statistical power than the Significance Analysis of Microarrays method when the proportion of significantly differentially expressed genes is large for both normally and non-normally distributed data. Finally, the Resampling-based empirical Bayes Methods are generalizable to next generation sequencing RNA-seq data analysis.     

Use of Occupancy Models to Estimate the Influence of Previous Live Captures on DNA-Based Detection Probabilities of Grizzly Bears

Abstract: Large carnivores potentially change their behavior following physical capture, becoming less responsive to the attractants that resulted in their capture, which can bias population estimates where the change in behavior is not appropriately modeled. We applied occupancy models to efficiently estimate and compare detection probabilities of previously collared grizzly bears (Ursus arctos) with bears captured at DNA hair-snag sites that were not previously collared. We found that previously captured bears had lower detection probabilities, although their detection probabilities were still >0, implying that they were still visible to be sampled via the DNA hair-snag grid, which was able to detect finer differences in capture probabilities of previously collared bears compared with Huggins closed-captures population models. To obtain relatively unbiased population estimates for DNA surveys, heterogeneity caused by previous live capture should be accounted for in the population estimator. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):589–595; 2008)     

A Structured Approach to LCA Improvement Analysis

The third stage of life-cycle assessment, interpretation analysis (and improvement analysis, one of its components), has received relatively modest attention from LCA developers, especially as regards approaches for effecting improvements. However, this latter step is crucial if the LCA is to produce environmental benefits. A structured approach to improvement analysis is proposed, in which it is recognized that decisions regarding the recommendations that flow from the first two LCA stages are based not only on the environmental aspects of the recommended actions but also on such factors as technical feasibility, economic benefit, implications for product management, and effects on customer perception. A prioritization technique based on these factors is developed, as are two prioritization diagrams, one segmented by action agent and one segmented by life stage.     

A Mathematical Approach to the Analysis of Multiplex DNA Profiles

Multiplex DNA profiles are used extensively for biomedical and forensic purposes. However, while DNA profile data generation is automated, human analysis of those data is not, and the need for speed combined with accuracy demands a computer-automated approach to sample interpretation and quality assessment. In this paper, we describe an integrated mathematical approach to modeling the data and extracting the relevant information, while rejecting noise and sample artifacts. We conclude with examples showing the effectiveness of our algorithms.     

A Data-Driven Approach to Reverse Engineering Customer Engagement Models: Towards Functional Constructs

Online consumer behavior in general and online customer engagement with brands in particular, has become a major focus of research activity fuelled by the exponential increase of interactive functions of the internet and social media platforms and applications. Current research in this area is mostly hypothesis-driven and much debate about the concept of Customer Engagement and its related constructs remains existent in the literature. In this paper, we aim to propose a novel methodology for reverse engineering a consumer behavior model for online customer engagement, based on a computational and data-driven perspective. This methodology could be generalized and prove useful for future research in the fields of consumer behaviors using questionnaire data or studies investigating other types of human behaviors. The method we propose contains five main stages; symbolic regression analysis, graph building, community detection, evaluation of results and finally, investigation of directed cycles and common feedback loops. The ‘communities’ of questionnaire items that emerge from our community detection method form possible ‘functional constructs’ inferred from data rather than assumed from literature and theory. Our results show consistent partitioning of questionnaire items into such ‘functional constructs’ suggesting the method proposed here could be adopted as a new data-driven way of human behavior modeling.     

A Modified Chi-squared Approach for Fitting WEIBULL Models to Synthetic Life Tables1

WEIBULL models are fitted to synthetic life table data by applying weighted least squares analysis to log log functions which are constructed from appropriate underlying contingency tables. As such, the resulting estimates and test statistics are based on the linearized minimum modified X²₁-criterion and thus have satisfactory properties in moderately large samples. The basic methodology is illustrated in terms of an example which is bivariate in the sense of involving two simultaneous, but non-competing, vital events. For this situation, the estimation of WEIBULL model parameters is described for both marginal as well as certain conditional distributions either individually or jointly.