Point patterns of forest fire locations

In this paper I demonstrate some of the techniques for the analysis of spatial point patterns that have become available due to recent developments in point process modelling software. These developments permit convenient exploratory data analysis, model fitting, and model assessment. Efficient model fitting, in particular, makes possible the testing of statistical hypotheses of genuine interest, even when interaction between points is present, via Monte Carlo methods. The discussion of these techniques is conducted jointly with and in the context of some preliminary analyses of a collection of data sets which are of considerable interest in their own right. These data sets (which were kindly provided to me by the New Brunswick Department of Natural Resources) consist of the complete records of wildfires which occurred in New Brunswick during the years 1987 through 2003. In treating these data sets I deal with data-cleaning problems, methods of exploratory data analysis, means of detecting interaction, fitting of statistical models, and residual analysis and diagnostics. In addition to demonstrating modelling techniques, I include a discussion on the nature of statistical models for point patterns. This is given with a view to providing an understanding of why, in particular, the Strauss model fails as a model for interpoint attraction and how it has been modified to overcome this difficulty. All actual modelling of the New Brunswick fire data is done only with the intent of illustrating techniques. No substantive conclusions are or can be drawn at this stage. Realistic modelling of these data sets would require incorporation of covariate information which I do not so far have available.

Intertype mark correlation function: A new tool for the analysis of species interactions

The spatial pattern of the different species in complex ecosystems reflects the underlying ecological processes. In this paper a second order moment function is proposed and tested to analyse the spatial distribution of a mark, which could be a tree characteristic such as diameter or height, between two different types of points, which could be two different tree species. The proposed function was a conditional density function based on the intertype K_rs(d) function, incorporating as test function the correlation of the marks between pairs composed of points of different types. The results obtained in simulated and real plots prove that the function is capable of revealing the scale at which spatial correlation of the mark between two types of points exists. The proposed function allows the spatial association between individuals of different species at different life stages to be identified. This analysis may reveal information on species ecology and interspecific interactions in forest ecosystems.     

Ontogenetic and spatio-temporal patterns of induced volatiles in <Emphasis Type="Italic">Glycine max</Emphasis> in the light of the optimal defence hypothesis

Summary. Plants attacked by herbivorous insects emit a blend of volatile compounds that serve as important host location cues for parasitoid wasps. Variability in the released blend may exist on the whole-plant and withinplant level and can affect the foraging efficiency of parasitoids. We comprehensively assessed the kinetics of herbivore-induced volatiles in soybean in the context of growth stage, plant organ, leaf age, and direction of signal transport. The observed patterns were used to test the predictions of the optimal defence hypothesis (OD). We found that plants in the vegetative stage emitted 10-fold more volatiles per biomass than reproductive plants and young leaves emitted >2.6 times more volatiles than old leaves. Systemic induction in single leaves was stronger and faster by one day in acropetal than in basipetal direction while no systemic induction was found in pods. Herbivore-damaged leaves had a 200-fold higher release rate than pods. To some extent these findings support the OD: i) indirect defence levels were increased in response to herbivory and ii) young leaves, which are more valuable, emitted more volatiles. However, the fact that reproductive structures emitted no constitutive or very few inducible volatiles is in seeming contrast to the OD predictions. We argue that in case of volatile emission the OD can only partially explain the patterns of defence allocation due to the peculiarity that volatiles act as signals not as toxins or repellents.