Biomedical subjects

P G Blackwell

Publications and source records attributed to P G Blackwell.

5 recordsLinked to original sources

PubMed2002

Group formation games with reappraisal.

The formation of a social group, such as the group of individuals sharing a territory, depends on the interaction between choices made by individuals to stay or disperse. The process can be modelled as a multi-player variant of the well-known War of Attrition in evolutionary game theory, as shown by Blackwell (1997; J. Theor. Biol.189, 175-181). In this paper, we extend the set of strategies defined there by allowing reappraisal during the game. We give a formal analysis of the evolutionarily stable strategy, where one exists, and illustrate it with an example based on badger (Meles meles) territoriality. The results predict that group size will be well adapted to, and very sensitive to, the precise conditions under which the game is played, and give an indication of the potential for parent-offspring conflict.

Animals↗

PubMed2002

Impact of landmark reliability on the planar Procrustes analysis of tooth shape.

In a recent study, the ideas of Procrustes analysis were introduced to the study of tooth shape for teeth represented as configurations of 'landmarks' from digital images. This study aimed to establish how well the method could be expected to perform (in its standard form) when used on surfaces from a variety of tooth types and, in particular, how much impact inconsistencies in the positioning of landmarks would have on investigations of shape. Using four different operators' images and landmarks from 10 different surfaces from each of 20 patients, the consequences of location inconsistency are evaluated by calculating its effect on the recorded variation in Procrustes fits, obtained for each set of multiple representations. The proportion of variation in shape attributable to actual differences between patients, rather than other sources of error, ranged from only 36 to 65% for the five buccal-surfaces considered and was no more than 30% for any of the five occlusal surfaces. Further examination of these results indicated that consistent orientation differences before imaging might be a particular source of error in obtaining any occlusal-landmark data, as might location ambiguities around the edges of the teeth. Orientation effects were also suggested for the buccal-surfaces of the molar teeth. In contrast, the relatively flatter buccal-surfaces of the incisors and canines produced the most reliable data. Methods of analysis need to accommodate these problems if landmark data are to be used to describe variations in tooth shape. Different surfaces each present their own particular difficulties and so a variety of solutions may be required.

Female↗

PubMed2001

Planar Procrustes analysis of tooth shape.

Accurate quantification of variation in tooth shape is important in studies of dental development, which typically have involved measuring distances between subjectively identified landmarks, key points of correspondence on teeth. An established statistical framework now exists for the analysis of shape when objects are represented as configurations of landmark coordinates; allowing work with the full geometry of objects, which is otherwise lost. This approach was introduced here to the study of tooth morphology, demonstrating how after optimally matching shapes to account for the unwanted effects of location, scale and rotation, most standard descriptive and inferential statistical techniques can be adapted and applied successfully. The techniques are illustrated using a sample of buccal-surface images of central incisors from patients with hypodontia; a significant difference is found in mean buccal-surface shape (Hotelling's two-sample T(2)-test; P=0.004) when compared to a corresponding control group. Successful implementation of these methods depends on the accuracy and reliability with which the landmarks are collected; issues and problems to be addressed are discussed.

Algorithms↗

PubMed2001

Bayesian inference for a random tessellation process.

This article describes an inhomogeneous Poisson point process in the plane with an intensity function based on a Dirichlet tessellation process and a method for using observations on the point process to make fully Bayesian inferences about the underlying tessellation. The method is implemented using a Markov chain Monte Carlo approach. An application to modeling the territories of clans of badgers, Meles meles, is described.

Animals↗

PubMed1997

The n-player war of attrition and territorial groups.

The choices made by juveniles, in territorial species, between dispersing and remaining in the natal territory, can be modelled as a simple multi-player evolutionary game, related to the well-known War of Attrition [Maynard Smith, J. (1974) J. theor. Biol. 47, 209-221; Haigh J. & Cannings, C. (1989) Acta Applicandae Mathematicae 14, 59-74]. The game is shown to have a unique evolutionarily stable strategy, involving a random choice between dispersing early in the game and staying indefinitely. An example is given, involving badgers (Meles meles), in which the key factor affecting the pay-off in the game is the possibility of inheriting the territory on the death of the current holders. The example indicates the sensitivity of the size of the group occupying the territory to the mortality rate among dispersers.

Animals↗