Particle Statistics and Population Dynamics

We study a master equation system modelling a population dynamics problem in a lattice. The problem is the calculation of the minimum size of a refuge that can protect a population from hostile external conditions, the so called critical patch size problem. We analize both cases in which the particles are considered fermions and bosons and show using exact analitical methods that, while the Fermi-Dirac statistics leads to certain extinction for any refuge size, the Bose-Eistein statistics allows survival even for the minimal refuge

Population: Basic Statistics

This lesson reinforces the idea that Earth's population, including the population of the United States, is gowing at a dramatic rate. It discusses some of the basics of demography, the study of population and its changes, and introduces key terms used to describe a population. The lesson inlcudes an activity in which students use an online reference to look up some population statistics and answer questions related to them. Educational levels: Undergraduate lower division, High school

Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization

We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size.Comment: 26 page

Surveys, Astrometric Follow-up & Population Statistics

Asteroid surveys are the backbone of asteroid science, and with this in mind we begin with a broad review of the impact of asteroid surveys on our field. We then provide a brief history of asteroid discoveries so as to place contemporary and future surveys in perspective. Surveys in the United States have discovered the vast majority of the asteroids and this dominance has been consolidated since the publication of Asteroids III. Our descriptions of the asteroid surveys that have been operational since that time are focussed upon those that have contributed the vast majority of asteroid observations and discoveries. We also provide some insight into upcoming next-generation surveys that are sure to alter our understanding of the small bodies in the inner solar system and provide evidence to untangle their complicated dynamical and physical histories. The Minor Planet Center, the nerve center of the asteroid discovery effort, has improved its operations significantly in the past decade so that it can manage the increasing discovery rate, and ensure that it is well-placed to handle the data rates expected in the next decade. We also consider the difficulties associated with astrometric follow-up of newly identified objects. It seems clear that both of these efforts must operate in new modes in order to keep pace with expected discovery rates of next-generation ground- and space-based surveys.Comment: Chapter to appear in the book ASTEROIDS IV, (University of Arizona Press) Space Science Series, edited by P. Michel, F. DeMeo and W. Bottk

Cram\'{e}r-type large deviations for samples from a finite population

Cram\'{e}r-type large deviations for means of samples from a finite population are established under weak conditions. The results are comparable to results for the so-called self-normalized large deviation for independent random variables. Cram\'{e}r-type large deviations for the finite population Student $t$-statistic are also investigated.Comment: Published at http://dx.doi.org/10.1214/009053606000001343 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the two-phase framework for joint model and design-based inference

We establish a mathematical framework that formally validates the two-phase ``super-population viewpoint'' proposed by Hartley and Sielken [Biometrics 31 (1975) 411--422] by defining a product probability space which includes both the design space and the model space. The methodology we develop combines finite population sampling theory and the classical theory of infinite population sampling to account for the underlying processes that produce the data under a unified approach. Our key results are the following: first, if the sample estimators converge in the design law and the model statistics converge in the model, then, under certain conditions, they are asymptotically independent, and they converge jointly in the product space; second, the sample estimating equation estimator is asymptotically normal around a super-population parameter.Comment: Published at http://dx.doi.org/10.1214/009053605000000651 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Waitomo District: Demographic profile 1986-2031

This report outlines the demographic changes that have occurred in Waitomo Region, as well as what trends are expected in the future