Randall George Binks, Bifurcation in Natural Convection in Horizontal Cylindrical Annuli using Spectral Expansions.

Allison Kimber DeLong, A Habitat Fragmentation Model for the Ovenbird.

Abstract: Deforestation and fragmentation of the breeding habitat in North America has resulted in significant declines of many species of forest interior, neotropical migrant birds. In this paper, we develop a mathematical model to examine the relationship between the landscape characteristics and the population dynamics of these birds. Hopefully, the results of the model can be used to help determine the forest area requirements necessary to sustain viable populations of these birds.

We allow habitat selection to be based upon movement toward more suitable breeding territories and away from high densities. We allow fitness to be a function of density. We ran the model over two landscapes. The first was built to approximate the land surrounding the Ozark mountains in Missouri. The second landscape represents a section of the midwestern landscape from Missouri to Minnesota.

The results indicate that further deforestation within the regions containing the most suitable breeding territory can result in extinction of the Ovenbird throughout a large geographic region. Our model shows that dispersal from the more suitable sub-habitats into less desirable breeding territories increases the minimum forested area requirement to sustain viable populations. As a result, when considering possible management strategies, a thorough analysis should be done of both the population growth rates across the habitat and the dispersal patterns among sub-habitats.

Margaret I. Martin, A Model for the Relationship Between the Population Dynamics of Hippopotamus Amphibious and River Flow Rates in Kruger National Park, South America.

Abstract: The Hippopotamus amphibious is one of the last megaherbivoures in the world. It is dependent on water for a diurnal home. The rivers of Kruger National Park in South Africa are being threatened by withdrawal of water for agricultural and recreational purposes. The lowering of the levels in these rivers is beginning to stress the hippo populations. Data from Kruger indicates the populations are in decline.

A discrete, stochastic model was developed to simulate populations of hippos on the rivers of Kruger. A 24-km section of the Sabie river was chosen for the simulations.

Three different scenarios were investigated. Hippo pools in the first scenario were initialized at different depths, ranging from 1 m to 2.5 m. In the second scenario, the pools were set at the same initial depth (2.5 m) and then allowed to fluctuate. In the third scenario, a constant pool depth was set for 30 years.

River low rates below 1.1 m^3/sec appear to have the most influence on pool levels. They were at their lowest at this rate. Flow rates of 1.2 m^3/sec to to 3.5 m^3/sec have been suggested by O’keefe and Davies (1991). The lower end of these flow rates appears to be too low.

Philip M. Zastrow, Tribal Extinction: A Model for the Long-term Consequences of Tribal Enrollment Rules.

Abstract: The Hoopa Valley Tribe is only one of a number of American Indian tribes caught between its unique traditional work and the onslaught of federal policy. These policies through replete with good intentions, may bring about the eventual extinction of Indian tribes. This paper examines the federal policy that takes the form of enrollment rules and requires a certain blood degree for enrollment in the tribe.

A mathematical model has been designed to investigate the effects of several factors on the long term population of the Hoopa Valley Tribe. The foremost of these is the affinity factor; the tendency of one tribal member to choose another tribal member as a mating partner. The effects are reported in the following statistics: total population, available mates, and average blood degree. The model projects a steep decline in the population of the tribe given the initial conditions and certain assumptions. Also, the average blood degree is projected to fall from approximately 0.45 to 0.32 in the next 100 years. Due to the nature of the model these figures are the maximum expected.

Several options are suggested to alleviate the declines mentioned above, although all options come with critical changes that may need to be made. This paper is offered to open discussion on the solutions necessary to prevent the model outcomes from becoming reality.