Models for bounded systems with continuous dynamics.

Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. Often, the scientist has preferred to model the underlying dynamical processes (i.e., theoretical mechanisms) in continuous time. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty associated with the models in the presence of observations. That is, given discrete observations arising from the underlying continuous process, the unobserved process can be formally described while accounting for multiple sources of uncertainty (e.g., measurement error, model choice, and inherent stochasticity of process parameters). In addition to continuity, natural processes are often bounded; specifically, they tend to have nonnegative support. Various techniques have been implemented to accommodate nonnegative processes, but such techniques are often limited or overly compromising. This article offers an alternative to common differential modeling practices by using a bias-corrected truncated normal distribution to model the observations and latent process, both having bounded support. Parameters of an underlying continuous process are characterized in a Bayesian hierarchical context, utilizing a fourth-order Runge-Kutta approximation.

Short-Term Space-Use Patterns of Translocated Mojave Desert Tortoise in Southern California.

Increasingly, renewable energy comprises a larger share of global energy production. Across the western United States, public lands are being developed to support renewable energy production. Where there are conflicts with threatened or endangered species, translocation can be used in an attempt to mitigate negative effects. For the threatened Mojave desert tortoise (Gopherus agassizii), we sought to compare habitat- and space-use patterns between short-distance translocated, resident, and control groups. We tested for differences in home range size based on utilization distributions and used linear mixed-effects models to compare space-use intensity, while controlling for demographic and environmental variables. In addition, we examined mean movement distances as well as home range overlap between years and for male and female tortoises in each study group. During the first active season post-translocation, home range size was greater and space-use intensity was lower for translocated tortoises than resident and control groups. These patterns were not present in the second season. In both years, there was no difference in home range size or space-use intensity between control and resident groups. Translocation typically resulted in one active season of questing followed by a second active season characterized by space-use patterns that were indistinguishable from control tortoises. Across both years, the number of times a tortoise was found in a burrow was positively related to greater space-use intensity. Minimizing the time required for translocated tortoises to exhibit patterns similar to non-translocated individuals may have strong implications for conservation by reducing exposure to adverse environmental conditions and predation. With ongoing development, our results can be used to guide future efforts aimed at understanding how translocation strategies influence patterns of animal space use.