Source Reconstruction for Spatio-Temporal Physical Statistical Models

In many applications, a signal is deformed by well-understood dynamics before it can be measured. For example, when a pollutant enters a river, it immediately begins dispersing, flowing, settling, and reacting. If the pollutant enters at a single point, its concentration can be measured before it enters the complex dynamics of the river system. However, in the case of a non-point source pollutant, it is not clear how to efficiently measure its source. One possibility is to record concentration measurements in the river, but this signal is masked by the fluid dynamics of the river. Specifically, concentration is governed by the advection-diffusion-reaction PDE, with an unknown source term. We propose a method to statistically reconstruct a source term from these PDE-deformed measurements. Our method is general and applies to any linear PDE. This method has important applications in the study of environmental DNA and non-point source pollution.Comment: 28 pages, 8 figures, 2 table

Large-scale movement behavior in a reintroduced predator population

Understanding movement behavior and identifying areas of landscape connectivity is critical for the conservation of many species. However, collecting fine-scale movement data can be prohibitively time consuming and costly, especially for rare or endangered species, whereas existing data sets may provide the best available information on animal movement. Contemporary movement models may not be an option for modeling existing data due to low temporal resolution and large or unusual error structures, but inference can still be obtained using a functional movement modeling approach. We use a functional movement model to perform a population-level analysis of telemetry data collected during the reintroduction of Canada lynx to Colorado. Little is known about southern lynx populations compared to those in Canada and Alaska, and inference is often limited to a few individuals due to their low densities. Our analysis of a population of Canada lynx fills significant gaps in the knowledge of Canada lynx behavior at the southern edge of its historical range. We analyzed functions of individual-level movement paths, such as speed, residence time, and tortuosity, and identified a region of connectivity that extended north from the San Juan Mountains, along the continental divide, and terminated in Wyoming at the northern edge of the Southern Rocky Mountains. Individuals were able to traverse large distances across non-boreal habitat, including exploratory movements to the Greater Yellowstone area and beyond. We found evidence for an effect of seasonality and breeding status on many of the movement quantities and documented a potential reintroduction effect. Our findings provide the first analysis of Canada lynx movement in Colorado and substantially augment the information available for conservation and management decisions. Th e functional movement framework can be extended to other species and demonstrates that information on movement behavior can be obtained using existing data sets

When to be discrete: the importance of time formulation in understanding animal movement

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.Fil: McClintock, Brett T.. National Marine Mammal Laboratory; Estados UnidosFil: Johnson, Devin S.. National Marine Mammal Laboratory; Estados UnidosFil: Hooten, Mevin B.. State University Of Colorado - Fort Collins; Estados UnidosFil: Ver Hoef, Jay M.. National Marine Mammal Laboratory; Estados UnidosFil: Morales, Juan Manuel. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche. Laboratorio de Ecotono; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte. Instituto de Investigación en Biodiversidad y Medioambiente; Argentin

Interchangeable punishments during aversive conditioning in Drosophila

Using Drosophila melanogaster larvae we asked whether distinct aversive stimuli have a common neuralrepresentation during associative learning. We tested the interchangeability of heat shock and electroshock punishments when used within a single olfactory associative conditioning experiment. We find that compared to animals trained with the repetitive use of a single punishment, the use of two alternating punishments results in similar associative learning. Additionally, the two punishments are shown to have different sensory origins. Therefore, while punishments are processed differently by the larvae of Drosophila melanogaster, the value of the stimulus is preserved

Inferring invasive species abundance using removal data from management actions

Evaluation of the progress of management programs for invasive species is crucial for demonstrating impacts to stakeholders and strategic planning of resource allocation. Estimates of abundance before and after management activities can serve as a useful metric of population management programs. However, many methods of estimating population size are too labor intensive and costly to implement, posing restrictive levels of burden on operational programs. Removal models are a reliable method for estimating abundance before and after management using data from the removal activities exclusively, thus requiring no work in addition to management. We developed a Bayesian hierarchical model to estimate abundance from removal data accounting for varying levels of effort, and used simulations to assess the conditions under which reliable population estimates are obtained. We applied this model to estimate site-specific abundance of an invasive species, feral swine (Sus scrofa), using removal data from aerial gunning in 59 site/time-frame combinations (480–19,600 acres) throughout Oklahoma and Texas, USA. Simulations showed that abundance estimates were generally accurate when effective removal rates (removal rate accounting for total effort) were above 0.40. However, when abundances were small