In this paper we examine the use of the minimum message length criterion in the process of evaluating alternative models of data when the samples are serially ordered in space and implicitly in time. Much data from vegetation studies can be arranged in a sequence and in such cases the user may elect to constrain the clustering by zones, in preference to an unconstrained clustering. We use the minimum message length principle to determine if such a choice provides an effective model of the data. Pollen data provide a suitably organised set of samples, but have other properties which make it desirable to examine several different models for the distribution of palynomorphs within the clusters. The results suggest that zonation is not a particularly preferred model since it captures only a small part of the patterns present. It represents a user expectation regarding the nature of variation in the data and results in some patterns being neglected. By using unconstrained clustering within zones, we can recover some of this overlooked pattern. We then examine other evidence for the nature of change in vegetation and finally discuss the usefulness of the minimum message length as a guiding principle in model choice and its relationship to other possible criteria.
Many methods of cluster analysis do not explicitly account for correlation between attributes. In this paper we explicitly model any correlation using a single factor within each cluster: i.e., the correlation of atributes within each cluster is adequately described by a single component axis. However, the use of a factor is not required in every cluster. Using a Minimum Message Length criterion, we can determine the number of clusters and also whether the model of any cluster is improved by introducing a factor. The technique allows us to seek clusters which reflect directional changes rather than imposing a zonation constrained by spatial (and implicitly temporal) position. Minimal message length is a means of utilising Okham’s Razor in inductive analysis. The ‘best’ model is that which allows most compression of the data, which results in a minimal message length for the description. Fit to the data is not a sufficient criterion for choosing models because more complicated models will almost always fit better. Minimum message length combines fit to the data with an encoding of the model and provides a Bayesian probability criterion as a means of choosing between models (and classes of model). Applying the analysis to a pollen diagram from Southern Chile, we find that the introduction of factors does not improve the overall quality of the mixture model. The solution without axes in any cluster provides the most parsimonious solution. Examining the cluster with the best case for a factor to be incorporated in its description shows that the attributes highly loaded on the axis represent a contrast of herbaceous vegetation and dominant forests types. This contrast is also found when fitting the entire population, and in this case the factor solution is the preferred model. Overall, the cluster solution without factors is much preferred. Thus, in this case classification is preferred to ordination although more data are desirable to confirm such a conclusion.
In this paper, we use decision trees to construct models for predicting vegetation types from environmental attributes in a salt marsh. We examine a method for evaluating the worth of a decision tree and look at seven sources of uncertainty in the models produced, namely algorithmic, predictive, model, scenario, objective, context and scale. The accuracy of prediction of types was strongly affected by the scenario and scale, with the most dynamically variable attributes associated with poor prediction, while more static attributes performed better. However, examination of the misclassified samples showed that prediction of processes was much better, with local vegetation type-induced patterns nested within a broader environmental framework.
In this paper we examine the impact of runnelling on the vegetation of a salt marsh. Runnelling is a form of habitat modification used for mosquito control in Australia. Defining the states of the system through unsupervised clustering of vegetation records using the minimum message length principle, 11 states (or classes) were identified. The runnelled sites have a greater diversity of states present than the unrunnelled ones. The states at each time for each site were then used to develop transition matrices. From these, two different pathways were identified, indicating the patterns of change. The method of showing changes relied on pictures that represent average species size and density. Both the two main pathways of change started with the dominant grass (Sporobolus). One led to a reduction in Sporobolous and ended in bare ground; the other included changes involving variation in the size and density of a mix of Sporobolus and Sarcocornia. The effects can be interpreted in terms of the increased access of seawater to the marsh resulting in an extension of the lower marsh. We note, however, that this methodology does not distinguish between changes of state within a single process and changes associated with a change in the actual processes operating.
We examine monitoring data for 28 years of change in a sub-tropical salt marsh where the hydrology had been minimally modified for mosquito control. This extends the work previously published in 2002 for 14 years of data, analysed by Mike Dale (Dale and Dale 2002 Community Ecol. 3: 19–29). The Minimum Message Length method was used in an unsupervised classification to determine the optimum classes, based on the characteristics of the two dominant plant species: Sporobolus virginicus and Sarcocornia quinqueflora. A question at that time was whether the observed changes were only those of state (or condition) or if they were associated with a change in the underlying saltmarsh processes (dynamics). In the 28-year analysis we have been able to address this issue. The classes were generally similar to those in the 2002 analysis. However, class extinctions occurred over the 28 years and only four classes remained: three were stands of Sporobolus and the other was bare mud. The latter, with mangrove pneumatophores, represented the encroachment of Avicennia mangroves into salt marsh. We suggest that the class extinctions and the final loss of most of the plants represent a change in the processes operating in the marsh. The observed changes may be related to sea level and/or climate changes but future research would be needed to assess this
Authors:L. Hulett, John Dale, H. Dunn, and P. Murty
The purpose of this paper is to demonstrate that complicated mixtures of solids can be characterized to a rather high degree
if a coordinated examination by non-destructive methods is used. The techniques discussed are X-ray fluorescence, scanning
electron microscopy, photoelectron spectroscopy, transmission electron microscopy, electron diffraction and X-ray diffraction.
The application of these methods to the characterization of corrosion scale on an inconel coupon is illustrated. The types
of information accumulated were elemental composition, chemical forms of elements, special distributions of elements and compounds
in the scale, sizes of particles that made up the scale, variations in composition of particle surfaces from that of their
interiors, and composition of scale-alloy interface.