10 research outputs found
Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments
This article provides an exposition of recent methodologies for nonparametric
analysis of digital observations on images and other non-Euclidean objects.
Fr\'echet means of distributions on metric spaces, such as manifolds and
stratified spaces, have played an important role in this endeavor. Apart from
theoretical issues of uniqueness of the Fr\'echet minimizer and the asymptotic
distribution of the sample Fr\'echet mean under uniqueness, applications to
image analysis are highlighted. In addition, nonparametric Bayes theory is
brought to bear on the problems of density estimation and classification on
manifolds
The Effect of Structural Complexity, Prey Density, and âPredator-Free Spaceâ on Prey Survivorship at Created Oyster Reef Mesocosms
Interactions between predators and their prey are influenced by the habitat they occupy. Using created oyster (Crassostrea virginica) reef mesocosms, we conducted a series of laboratory experiments that created structure and manipulated complexity as well as prey density and âpredator-free spaceâ to examine the relationship between structural complexity and prey survivorship. Specifically, volume and spatial arrangement of oysters as well as prey density were manipulated, and the survivorship of prey (grass shrimp, Palaemonetes pugio) in the presence of a predator (wild red drum, Sciaenops ocellatus) was quantified. We found that the presence of structure increased prey survivorship, and that increasing complexity of this structure further increased survivorship, but only to a point. This agrees with the theory that structural complexity may influence predator-prey dynamics, but that a threshold exists with diminishing returns. These results held true even when prey density was scaled to structural complexity, or the amount of âpredator-free spaceâ was manipulated within our created reef mesocosms. The presence of structure and its complexity (oyster shell volume) were more important in facilitating prey survivorship than perceived refugia or density-dependent prey effects. A more accurate indicator of refugia might require âpredator-free spaceâ measures that also account for the available area within the structure itself (i.e., volume) and not just on the surface of a structure. Creating experiments that better mimic natural conditions and test a wider range of âpredator-free spaceâ are suggested to better understand the role of structural complexity in oyster reefs and other complex habitats