A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

The Effects of Smolt Stocking Strategies on Migratory Path Selection of Adult Atlantic Salmon in the Penobscot River, Maine

Understanding the homing behavior of Atlantic salmon Salmo salar is vital to the restoration program employed on the Penobscot River, Maine. To produce significant adult returns, managers currently stock hatchery-raised smolts in specific river sections, providing smolts the opportunity to imprint on chemical signals and enabling their return to productive spawning and rearing habitat as adults. In this study, we used observational evidence from passive integrated transponder telemetry to determine whether adults returning from smolt stockings behaved in a way that suggested strong homing to smolt stocking locations. Adults returning from smolt stocking locations located in or at the mouth of the Piscataquis River were more likely to be detected as entering the Piscataquis River than were adults returning from the upper Penobscot River smolt stocking locations. In general, returning adult Atlantic salmon that had been stocked near or in tributaries as smolts chose a path more quickly than those that had been stocked in more downstream or main-stem locations. These results suggest that Atlantic salmon smolts should be stocked at specific sites with superior habitat for spawning kind juvenile survival to capitalize on the strong homing tendency in adults. This technique call also be utilized to allow for natural selection and the development of localized stocks.

Modeling the Effects of Size on Patch Dynamics of an Inert Tracer

Mesoscale iron enrichment experiments have revealed that additional iron affects the phytoplankton productivity and carbon cycle. However, the role of initial size of fertilized patch in determining the patch evolution is poorly quantified due to the limited observational capability and complex of physical processes. Using a three-dimensional ocean circulation model, we simulated different sizes of inert tracer patches that were only regulated by physical circulation and diffusion. Model results showed that during the first few days since release of inert tracer, the calculated dilution rate was found to be a linear function with time, which was sensitive to the initial patch size with steeper slope for smaller size patch. After the initial phase of rapid decay, the relationship between dilution rate and time became an exponential function, which was also size dependent. Therefore, larger initial size patches can usually last longer and ultimately affect biogeochemical processes much stronger than smaller patches.

Implications of Longterm Diameter-Limit Harvesting: Effects on Radial Growth of Red Spruce (Picea rubens) and Genetic Diversity of White Pine (Pinus strobus)

For over 3 centuries, diameter-limit harvesting has been a predominant logging method in the northeastern United States. Silvicultural theory asserts that such intensively selective harvesting can lead to genetic degradation. A decrease in softwood productivity has recently been reported in Maine - has a long history of dysgenic selection degraded the genetic resources of Maine softwoods, contributing to a decrease in growth and productivity? This study examines two aspects of potential implications of diameter-limit harvesting: effects on residual phenotypes of red spruce and impacts on genetic diversity of white pine. Radial growth of residual red spruce trees in stands experiencing 50 years of fixed diameter-limit harvesting was measured using annual increment rings and compared with residual red spruce trees in positive selection stands. Trees remaiaing after several rounds of diameter-limit harvesting exhibited sigdicantl y smaller radial sizes throughout their lives, and displayed significantly slower growth rates for the first 80 years of measured growth. These results strongly suggest that the largest and fastest-growing genotypes and their respective gene complexes determining good radial growth have been removed from the diameter-limit stand. Dysgenic selection can be observed in fixed diarneter-limit stands, resulting in a diminished genetic resource and decreased residual stand value. To examine more direct genetic implications of long-term diameter-limit harvesting, microsatellite DNA markers were implemented to study genetic diversity of eastern white pine in Maine. Three age groups of trees were studied: mature trees older than 200 years, juvenile trees 5-30 years old, and embryos. Trees were genotyped at 10 microsatellite loci. Overall genetic diversity levels of eastern white pine in Maine were extremely high, with an average observed heterozygosity of 0.762. Genetic differentiation was minimal among and between all three age groups, although an excess of heterozygotes was shown in the mature and juvenile groups that was not reflected in the embryo group, which actually had a slight heterozygote deficiency. Allele frequencies did not differ significantly between age groups, but did reveal more rare and low frequency alleles in the embryo groups than in the mature group. Overall, low frequency alleles comprise the largest portion of alleles in the sample population, with no common alleles evident overall. These results suggest that significant genetic degradation has either not occurred for white pine, or that the results of dysgenic selection have not yet emerged. It is clear, however, that selective harvesting could result in a loss of low frequency alleles, which are a primary reserve of evolutionary potential in a species. Implications of these studies affect industrial forestry, regional economics, and ecological concerns for the northeast. Long-term diameter-limit harvesting can lead to a degradation of residual phenotypes, and an overall decrease in stand quality. Potentially, a loss of low frequency, locally adapted alleles could result in a decrease of allelic richness and degradation of the regidnal genetic resource. Decreased genetic variation can lead to seriously limited evolutionary potential of species and ecosystems, particularly in rapidly changing environments. Based on these findings, I recommend a reassessment of any harvesting prescription that includes fixed diameter-limit removals, particularly for species that have low natural genetic diversity levels or a limited natural range, such as red spruce. Maintenance of a healthy genetic reserve can avoid effects of dysgenic harvesting.