Statistical Techniques In Stereology

Stereology typically concerns estimation of properties of a geometric structure from plane section information. This paperprovides a brief review of some statistical aspects of this rapidly developing field, with some reference to applications in the earth sciences. After an introductory discussion of the scope of stereology, section 2 briefly mentions results applicable when no assumptions can be made about the stochastic nature of the sampled matrix, statistical considerations then arising solelyfrom the ‘randomness’ of the plane section. The next two sections postulate embedded particles of specific shapes, the particular case of spheres being discussed in some detail. References are made to results for ‘thin slices’ and other prob-ing mechanisms. Randomly located convex particles, of otherwise arbitrary shape, are discussed in section 5 and the review concludes with a specific application of stereological ideas to some data on neolithic mining.

Statistical Procedure For Estimating Grey Seal Pup Production From A Single Census

The variable start and duration of the Grey seal breeding season makes the estimation of total pup production from a single census very difficult. Classifying the count into morphological age classes enables the form and timing of the birth rate curve and estimates of pup mortality rates to be elucidated. A simulation technique is described which enables the duration of each morphological stage to be determined from a series of such classified counts taken over one season. A further statistical technique uses these estimates to calculate the mean timing and duration of the breeding season from a single classified count taken from similar populations in subsequent years. This information allows total pup production to be calculated for any appropriate breeding colony. Some guidance is given as to the optimal timing of that single census which would yield the best estimate of production, although the precise date is not critical to the success of the technique. Results from single census estimates obtained in this way are compared with known production data from more detailed surveys for a number of different colonies.

An innovative statistical approach to constructing a readily comprehensible food web for a demersal fish community

Many food webs are so complex that it is difficult to distinguish the relationships between predators and their prey. We have therefore developed an approach that produces a food web which clearly demonstrates the strengths of the relationships between the predator guilds of demersal fish and their prey guilds in a coastal ecosystem. Subjecting volumetric dietary data for 35 abundant predators along the lower western Australia coast to cluster analysis and the SIMPROF routine separated the various species x length class combinations into 14 discrete predator guilds. Following nMDS ordination, the sequence of points for these predator guilds represented a 'trophic' hierarchy. This demonstrated that, with increasing body size, several species progressed upwards through this hierarchy, reflecting a marked change in diet, whereas others remained within the same guild. A novel use of cluster analysis and SIMPROF then identified each group of prey that was ingested in a common pattern across the full suite of predator guilds. This produced 12 discrete groups of taxa (prey guilds) that each typically comprised similar ecological/functional prey, which were then also aligned in a hierarchy. The hierarchical arrangements of the predator and prey guilds were plotted against each other to show the percentage contribution of each prey guild to the diet of each predator guild. The resultant shade plot demonstrates quantitatively how food resources are spread among the fish species and revealed that two prey guilds, one containing cephalopods and teleosts and the other small benthic/epibenthic crustaceans and polychaetes, were consumed by all predator guilds.