Extracting more out of relocation data: building movement models as mixtures of random walks

We present a framework for fitting multiple random walks to animal movement paths consisting of ordered sets of step lengths and turning angles. Each step and turn is assigned to one of a number of random walks, each characteristic of a different behavioral state. Behavioral state assignments may be inferred purely from movement data or may include the habitat type in which the animals are located. Switching between different behavioral states may be modeled explicitly using a state transition matrix estimated directly from data, or switching probabilities may take into account the proximity of animals to landscape features. Model fitting is undertaken within a Bayesian framework using the WinBUGS software. These methods allow for identification of different movement states using several properties of observed paths and lead naturally to the formulation of movement models. Analysis of relocation data from elk released in east-central Ontario, Canada, suggests a biphasic movement behavior: elk are either in an "encamped" state in which step lengths are small and turning angles are high, or in an "exploratory" state, in which daily step lengths are several kilometers and turning angles are small. Animals encamp in open habitat (agricultural fields and opened forest), but the exploratory state is not associated with any particular habitat type.

Effects of Externally Applied, Cyclical, Low Magnitude Forces on Orthodontic Tooth Movement in Rats

Orthodontic tooth movement requires external orthodontic forces to be converted to cellular signals that result in the coordinated removal of bone on one side of the tooth (compression side) by osteoclasts, and the formation of new bone by osteoblasts on the other side (tension side). The length of orthodontic treatment can take several years, leading to problems of caries, periodontal disease, root resorption, and patient dissatisfaction. It appears that the velocity of tooth movement is largely dependent on the rate of alveolar bone remodeling. Pharmacological approaches to increase the rate of tooth movement are limited due to patient discomfort, severe root resorption, and drug-induced side effects. Recently, externally applied, cyclical, low magnitude forces (CLMF) have been shown to cause an increase in the bone mineral density of long bones, and in the growth of craniofacial structures in a variety of animal models. In addition, CLMF is well tolerated by the patient and produces no known adverse effects. However, its application in orthodontic tooth movement has not been specifically determined. Since factors that increase alveolar bone remodeling enhance the rate of orthodontic tooth movement, we hypothesized that externally applied, cyclical, low magnitude forces (CLMF) will increase the rate of orthodontic tooth movement. In order to test this hypothesis we used an in vivo rat orthodontic tooth movement model. Our specific aims were: Specific Aim 1: To develop an in vivo rat model for tooth movement. We developed a tooth movement model based upon two established rodent models (Ren and Yoshimatsu et al, See Figure 1.). The amount of variation of tooth movement in rats exposed to 25-60 g of mesial force activated viii from the first molar to the incisor for 4 weeks was calculated. Specific Aim 2: To determine the frequency dose response of externally applied, cyclical, low magnitude forces (CLMF) for maximal tooth movement and osteoclast numbers. Our working hypothesis for this aim was that the amount of tooth movement would be dose dependent on the frequency of application of the CLMF. In order to test this working hypothesis, we varied the frequency of the CLMF from 30, 60, 100, and 200 Hz, 0.4N, two times per week, for 10 minutes for 4 weeks, and measured the amount of tooth movement. We also looked at the number of osteoclasts for the different frequencies; we hypothesized an increase in osteoclasts for the dose respnse of different frequencies. Specific Aim 3: To determine the effects of externally applied, cyclical, low magnitude forces (CLMF) on PDL proliferation. Our working hypothesis for this aim was that PDL proliferation would increase with CLMF. In order to test this hypothesis we compared CLMF (30 Hz, 0.4N, two times per week, for 10 minutes for 4 weeks) performed on the left side (experimental side), to the non-CLMF side, on the right (control side). This was an experimental study with 24 rats in total. The experimental group contained fifteen (15) rats in total, and they all received a spring plus a different frequency of CLMF. Three (3) received a spring and CLMF at 30 Hz, 0.4N for 10 minutes. Six (6) received a spring and CLMF at 60 Hz, 0.4N for 10 minutes. Three (3) received a spring and CLMF at 100 Hz, 0.4N for 10 minutes. Three (3) received a spring and CLMF at 200 Hz, 0.4N for 10 minutes. The control group contained six (6) rats, and received only a spring. An additional ix three (3) rats received CLMF (30 Hz, 0.4N, two times per week, for 10 minutes for 4 weeks) only, with no spring, and were used only for histological purposes. Rats were subjected to the application of orthodontic force from their maxillary left first molar to their left central incisor. In addition some of the rats received externally applied, cyclical, low magnitude force (CLMF) on their maxillary left first molar. micro-CT was used to measure the amount of orthodontic tooth movement. The distance between the maxillary first and second molars, at the most mesial point of the second molar and the most distal point of the first molar (1M-2M distance) were used to evaluate the distance of tooth movement. Immunohistochemistry was performed with TRAP staining and BrdU quantification. Externally applied, cyclical, low magnitude forces (CLMF) do appear to have an effect on the rate, while not significant, of orthodontic tooth movement in rats. It appears that lower CLMF decreases the rate of tooth movement, while higher CLMF increases the rate of tooth movement. Future studies with larger sample sizes are needed to clarify this issue. CLMF does not appear to affect the proliferation in PDL cells, and has no effect on the number of osteoclasts.

The Devil’s Calculus: Mathematical Models of Civil War

In spite of the movement to turn political science into a real science, various mathematical methods that are now the staples of physics, biology, and even economics are thoroughly uncommon in political science, especially the study of civil war. This study seeks to apply such methods - specifically, ordinary differential equations (ODEs) - to model civil war based on what one might dub the capabilities school of thought, which roughly states that civil wars end only when one side’s ability to make war falls far enough to make peace truly attractive. I construct several different ODE-based models and then test them all to see which best predicts the instantaneous capabilities of both sides of the Sri Lankan civil war in the period from 1990 to 1994 given parameters and initial conditions. The model that the tests declare most accurate gives very accurate predictions of state military capabilities and reasonable short term predictions of cumulative deaths. Analysis of the model reveals the scale of the importance of rebel finances to the sustainability of insurgency, most notably that the number of troops required to put down the Tamil Tigers is reduced by nearly a full order of magnitude when Tiger foreign funding is stopped. The study thus demonstrates that accurate foresight may come of relatively simple dynamical models, and implies the great potential of advanced and currently unconventional non-statistical mathematical methods in political science.