Computationally Efficient Statistical Differential Equation Modeling Using Homogenization

Hooten, Mevin B.; Garlick, Martha; Powell, James A.

doi:10.1007/s13253-013-0147-9

Cited by 29 publications

(60 citation statements)

References 58 publications

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“…each year), temporal replication of images can be incorporated into each survey using randomization, or model‐based optimization (e.g. Hooten, Wikle, Sheriff, & Rushin, ; Wikle & Royle, ). Alternatively, if detection probability is not likely to change through time, a pilot study could be conducted to examine availability bias, and then used as an informative prior distribution for future aerial surveys, precluding the necessity to conduct replicate surveys during each sampling period.…”

Section: Discussionmentioning

confidence: 99%

Estimating occupancy and abundance using aerial images with imperfect detection

et al. 2017

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Species distribution and abundance are critical population characteristics for efficient management, conservation, and ecological insight. Point process models are a powerful tool for modelling distribution and abundance, and can incorporate many data types, including count data, presence‐absence data, and presence‐only data. Aerial photographic images are a natural tool for collecting data to fit point process models, but aerial images do not always capture all animals that are present at a site. Methods for estimating detection probability for aerial surveys usually include collecting auxiliary data to estimate the proportion of time animals are available to be detected. We developed an approach for fitting point process models using an N‐mixture model framework to estimate detection probability for aerial occupancy and abundance surveys. Our method uses multiple aerial images taken of animals at the same spatial location to provide temporal replication of sample sites. The intersection of the images provide multiple counts of individuals at different times. We examined this approach using both simulated and real data of sea otters (Enhydra lutris kenyoni) in Glacier Bay National Park, southeastern Alaska. Using our proposed methods, we estimated detection probability of sea otters to be 0.76, the same as visual aerial surveys that have been used in the past. Further, simulations demonstrated that our approach is a promising tool for estimating occupancy, abundance, and detection probability from aerial photographic surveys. Our methods can be readily extended to data collected using unmanned aerial vehicles, as technology and regulations permit. The generality of our methods for other aerial surveys depends on how well surveys can be designed to meet the assumptions of N‐mixture models.

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Section: Discussionmentioning

confidence: 99%

Estimating occupancy and abundance using aerial images with imperfect detection

et al. 2017

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“…; Hooten et al . ). As a result of the variable residence times, the spatial distribution of u ( s , t ) is heterogeneous and captures local variability and abrupt changes in population densities (or disease prevalence) that occurs at the transition between habitat types.…”

Section: Methodsmentioning

confidence: 97%

When mechanism matters: Bayesian forecasting using models of ecological diffusion

et al. 2017

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Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

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“…; n t ðs n ÞÞ 0 . 7) is advantageous for development and facilitation of numerical techniques for efficient implementation (e.g., homogenization; Garlick et al 2011, Hooten et al 2013, Hefley et al 2017. For example, a common specification of Eq.…”

Section: Models Of Ecological Diffusion and Statistical Uncertaintymentioning

confidence: 99%

“…To facilitate computation, we used homogenization to implement the model (Garlick et al 2011, Hooten et al 2013, Hefley et al 2017, Williams et al 2017b). We fit the model described in Eq.…”

Section: Forecast U ðKþmentioning

confidence: 99%

Monitoring dynamic spatio‐temporal ecological processes optimally

Williams

Hooten

Womble

et al. 2018

Ecology

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Population dynamics vary in space and time. Survey designs that ignore these dynamics may be inefficient and fail to capture essential spatio-temporal variability of a process. Alternatively, dynamic survey designs explicitly incorporate knowledge of ecological processes, the associated uncertainty in those processes, and can be optimized with respect to monitoring objectives. We describe a cohesive framework for monitoring a spreading population that explicitly links animal movement models with survey design and monitoring objectives. We apply the framework to develop an optimal survey design for sea otters in Glacier Bay. Sea otters were first detected in Glacier Bay in 1988 and have since increased in both abundance and distribution; abundance estimates increased from 5 otters to >5,000 otters, and they have spread faster than 2.7 km/yr. By explicitly linking animal movement models and survey design, we are able to reduce uncertainty associated with forecasting occupancy, abundance, and distribution compared to other potential random designs. The framework we describe is general, and we outline steps to applying it to novel systems and taxa.

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Computationally Efficient Statistical Differential Equation Modeling Using Homogenization

Cited by 29 publications

References 58 publications

Estimating occupancy and abundance using aerial images with imperfect detection

Estimating occupancy and abundance using aerial images with imperfect detection

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Monitoring dynamic spatio‐temporal ecological processes optimally

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