From Marginals to Array Structure with the Shuttle Algorithm

In many statistical problems there is the need to analyze the structure of an unknown n-dimensional array given its marginal distributions. The usual method utilized to solve the problem is linear programming, which involves a large amount of computational time when the original array is large. Alternative solutions have been proposed in the literature, especially to find less time consuming algorithms. One of these is the shuttle algorithm introduced by Buzzigoli and Giusti [1] to calculate lower and upper bounds of the elements of an n-way array, starting from the complete set of its (n-1)-way marginals. The proposed algorithm, very easy to implement with a matrix language, shows interesting properties and possibilities of application. The paper presents the algorithm, analyses its properties and describes its disadvantages. It also suggests possible applications in some statistical fields and, in particular, in Symbolic Data Analysis and, finally, shows the results of some simulations on randomly generated arrays

From Marginals to Array Structure with the Shuttle Algorithm

In many statistical problems there is the need to analyze the structure of an unknown n-dimensional array given its marginal distributions. The usual method utilized to solve the problem is linear programming, which involves a large amount of computational time when the original array is large. Alternative solutions have been proposed in the literature, especially to find less time consuming algorithms. One of these is the shuttle algorithm introduced by Buzzigoli and Giusti [1] to calculate lower and upper bounds of the elements of an n-way array, starting from the complete set of its (n-1)-way marginals. The proposed algorithm, very easy to implement with a matrix language, shows interesting properties and possibilities of application. The paper presents the algorithm, analyses its properties and describes its disadvantages. It also suggests possible applications in some statistical fields and, in particular, in Symbolic Data Analysis and, finally, shows the results of some simulations on randomly generated arrays

Combinatorics and Geometry of Transportation Polytopes: An Update

A transportation polytope consists of all multidimensional arrays or tables of non-negative real numbers that satisfy certain sum conditions on subsets of the entries. They arise naturally in optimization and statistics, and also have interest for discrete mathematics because permutation matrices, latin squares, and magic squares appear naturally as lattice points of these polytopes. In this paper we survey advances on the understanding of the combinatorics and geometry of these polyhedra and include some recent unpublished results on the diameter of graphs of these polytopes. In particular, this is a thirty-year update on the status of a list of open questions last visited in the 1984 book by Yemelichev, Kovalev and Kravtsov and the 1986 survey paper of Vlach.Comment: 35 pages, 13 figure

Responses of Upland Herpetofauna to the Restoration of Carolina Bays and Thinning of Forested Bay Margins

Research on the effects of wetland restoration on reptiles and amphibians is becoming more common, but almost all of these studies have observed the colonization of recently disturbed habitats that were completely dry at the time of restoration. In a similar manner, investigations herpetofaunal responses to forest management have focused on clearcuts, and less intensive stand manipulations are not as well studied. To evaluate community and population responses of reptiles and amphibians to hydrology restoration and canopy removal in the interior of previously degraded Carolina bays, I monitored herpetofauna in the uplands adjacent to six historically degraded Carolina bays in the at the Savannah River Site (SRS) in South Carolina for four years after restoration. To evaluate the effects of forest thinning on upland herpetofauna, forests were thinned in the margins of three of these bays. I used repeated measures ANOVA to compare species richness and diversity and the abundance of selected species and guilds between these bays and with those at three reference bays that were not historically drained and three control bays that remained degraded. I also used Non-metric Multidimensional Scaling (NMDS) to look for community-level patterns based treatments I did not detect any differences in diversity or overall abundance of reptiles or amphibians between the four treatments, and NMDS did not indicate any patterns of community structure based on treatment. I captured eleven South Carolina species of conservation concern at the twelve bays, including juvenile Carolina gopher frogs (Rana capito) at two restored bays. Adult gopher frogs have only rarely been documented on the SRS despite intensive, long-term sampling at several wetlands, and successful recruitment is even rarer. Southern toads (Bufo terrestris) responded quickly to bay restoration, and gopher frog recruitment can be considered an indication of habitat quality. Because many of these species are highly philopatric and have limited dispersal ability, four years may be too soon to see changes in the herpetofaunal community, especially since restoration improved existing habitat rather than restoring uninhabitable sites. Pre-restoration sampling and long-term monitoring would allow more firm conclusions to be made. Forest thinning reduced the most common reptile, the green anole (Anolis carolinensis), a generalist lizard not especially sensitive to an open canopy or to harvest operations. Increased red imported fire ant (Solenopsis invicta) populations in disturbed areas and open canopies could be a factor, though more research is needed on the effects of fire ants on herpetofauna

Responses of Upland Herpetofauna to the Restoration of Carolina Bays and Thinning of Forested Bay Margins

Research on the effects of wetland restoration on reptiles and amphibians is becoming more common, but almost all of these studies have observed the colonization of recently disturbed habitats that were completely dry at the time of restoration. In a similar manner, investigations herpetofaunal responses to forest management have focused on clearcuts, and less intensive stand manipulations are not as well studied. To evaluate community and population responses of reptiles and amphibians to hydrology restoration and canopy removal in the interior of previously degraded Carolina bays, I monitored herpetofauna in the uplands adjacent to six historically degraded Carolina bays in the at the Savannah River Site (SRS) in South Carolina for four years after restoration. To evaluate the effects of forest thinning on upland herpetofauna, forests were thinned in the margins of three of these bays. I used repeated measures ANOVA to compare species richness and diversity and the abundance of selected species and guilds between these bays and with those at three reference bays that were not historically drained and three control bays that remained degraded. I also used Non-metric Multidimensional Scaling (NMDS) to look for community-level patterns based treatments I did not detect any differences in diversity or overall abundance of reptiles or amphibians between the four treatments, and NMDS did not indicate any patterns of community structure based on treatment. I captured eleven South Carolina species of conservation concern at the twelve bays, including juvenile Carolina gopher frogs (Rana capito) at two restored bays. Adult gopher frogs have only rarely been documented on the SRS despite intensive, long-term sampling at several wetlands, and successful recruitment is even rarer. Southern toads (Bufo terrestris) responded quickly to bay restoration, and gopher frog recruitment can be considered an indication of habitat quality. Because many of these species are highly philopatric and have limited dispersal ability, four years may be too soon to see changes in the herpetofaunal community, especially since restoration improved existing habitat rather than restoring uninhabitable sites. Pre-restoration sampling and long-term monitoring would allow more firm conclusions to be made. Forest thinning reduced the most common reptile, the green anole (Anolis carolinensis), a generalist lizard not especially sensitive to an open canopy or to harvest operations. Increased red imported fire ant (Solenopsis invicta) populations in disturbed areas and open canopies could be a factor, though more research is needed on the effects of fire ants on herpetofauna

Estimating multistate transition rates from population distributions

The ability to estimate transition rates (or probabilities) from population distributions has many potential applications in demography. Iterative Proportional Fitting (IPF) has been used for such estimation, but lacks a meaningful behavioral, or demographic, foundation. Here a new approach, Relative State Attractiveness (RSA), is advanced. It assumes that states become more (or less) attractive, and that rates respond accordingly. The RSA estimation procedure is developed and applied to model and actual data where the underlying rates are known. Results show that RSA provides accurate estimates under a wide range of conditions, usually yielding values similar to those produced by IPF. Both methods are then applied to U.S. data to provide new estimates of interregional migration between the years 1980 and 1990.entropy, estimation techniques, iterative proportional fitting, multistate models

mipfp: An R Package for Multidimensional Array Fitting and Simulating Multivariate Bernoulli Distributions

This paper explains the mipfp package for R with the core functionality of updating an d-dimensional array with respect to given target marginal distributions, which in turn can be multi-dimensional. The implemented methods include the iterative proportional fitting procedure (IPFP), the maximum likelihood method, the minimum chi-square and least squares procedures. The package also provides an application of the IPFP to simulate data from a multivariate Bernoulli distribution. The functionalities of the package are illustrated through two practical examples: the update of a 3-dimensional contingency table to match the targets for a synthetic population and the estimation and simulation of the joint distribution of the binary attribute impaired pulmonary function as used by Qaqish, Zink, and Preisser (2012)

Carnivore Competition and Resource use in the Serengeti Ecosystem of Tanzania

Coexisting ungulate-eating carnivores--lion, spotted hyena, cheetah, leopard, African wild dog, black-backed jackal, common jackal, and six species of vulture--are examined in East Africa\u27s Serengeti ecosystem. Niche similarities year-round, by season, and by location are described using food, habitat, time of hunting, and other variables. Intraspecific niches of cheetah sex, age, and social groups show that male coalitions differ most from the others in hunting behavior and habitat use. Tests using the carnivore data failed to support hypotheses about niche breadth variation, niche overlap variation, range of food items, and niche inclusion. Densities of the five largest Carnivora in the 35,500 square kilometer ecosystem are 0.513/sq km; including the two jackals gives a density of 1.55/sq km. Their prey--30 ungulate species--are 84 .85/sq km. Prey and predator ratios suggest that the Serengeti Plains in 1977 had a three-fourths decrease in relative abundance of prey to predators from wet season to dry season . Year-round the Ngorongoro Crater had a prey:predator ratio slightly larger than that of the dry season Serengeti Plains. Literature review suggests that cleptoparasitism and direct killing are very important forms of interference competition among and within carnivore species . Evidence for exploitation competition i s scant, but is inferred because local environments are unpredictable f or carnivores. Analysis of body sizes fails to support the hypothesized ratios of 2.0 for body weigh t and 1.28 for linear dimensions . Three methods of calculating multidimensional niche metrics (product, summation, and projection) are compared. Apparently the Serengeti\u27s carnivores coexist because of their behavioral flexibility in an unpredictable environment . Niche descriptions were of little he l p in assessing the foci for potential and real competition among carnivores . Only the direct observations of interference competition in long-term field studies identified where competitive interactions are occurring with sufficient intensity to provide a numerical response in a population. Spotted hyenas some times competitively exclude African wild dogs locally . Management f or a high abundance and diversity of carnivores probably requires maintaining high densities of prey and varied habitats. Specific recommendations are made for cheetah and African wild dog conservation