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A stochastic cellular automaton for modelling the dynamics of a two-species fungal microcosm is presented. The state of each cell in the automaton depends on the state of a predefined neighbourhood via a set of conditional probabilities derived from experiments conducted on pairwise combinations of species. The model is tested by detailed comparison with larger-scale experimental microcosms. By employing different hypotheses which relate the pairwise data to the conditional probabilities in the model, the nature of the local and non-local interactions in the community is explored. The hypothesis that the large-scale dynamics are a consequence of independent interactions between species in a local neighbourhood can be excluded at the 5% significance level. The form of the interdependencies is determined and it is shown that the outcome of the interactions at the local neighbourhood-scale depends on the community-scale patterning of individuals. The dynamics of the microcosm are therefore an emergent property of the system of interacting mycelia that cannot be deduced from a study of the components in isolation.

The community dynamics of two- and three-fungal species interactions derived for a tessellated agar model system are described. The microcosm allows for the varied prescription of: (1) the number of fungal species interacting; (2) the spatial configuration (patchiness) of the distribution of individuals; (3) the magnitude of scale of spatial occupation by different fungal individuals; and (4) the operation of antagonistic mechanisms based on contact or longer range diffusible components. Stepwise logistic regressions for two-species interactions are used to inform the design of the multi-species interaction tessellations. The model prescribes and investigates complex parameters, such as spatiotemporal heterogeneity and microcosm scale (e.g. population patchiness and crossing times). Data are quantified as proportion, interface class and state transition class of viable fungal species. Spatiotemporal heterogeneity is represented using a novel application of principal component analysis which shows good intuitive agreement with visual assessment of the interaction outcome patterns, and allows effective comparison of the data as a whole. The model demonstrates the influence of the complex and coordinated behaviour of fungal mycelia on community development: interaction outcome of three-species interactions cannot be directly extrapolated from the relevant binary component interactions; interaction outcomes of the multi-species tessellations appears to be neither random nor fully deterministic; a degree of stochasticity is apparent in all tessellation arrangements; the smaller scale tessellations produce more consistent interaction outcome results, probably because experimental scale affects the duration of transient behaviour; and different initial spatial configurations of inoculum (irrespective of inoculum quantity or proportion) influence community development and reproducibility.

Consequences of initial spatial organisation of model fungal communities upon their spatio-temporal development were investigated. Dynamics of prescribed two- and three-species 'communities' developing on tessellated agar tile model systems were analysed in terms of literal maps, principal component analyses, or as the proportion of species extant within tiles. It was established that for two-species interactions of equal patch size, large-scale (i.e. many constituent tiles) behaviour could be extrapolated from the relevant small-scale (i.e. pairs of tiles) interactions. However, relative patch sizes (scale) of species within tessellations influenced the times taken by individuals to colonise tiles and, hence, temporal behaviour of the system. Outcome of arrangements involving three species of equal patch size and inoculum potential, and prescribed with different mixing patterns, could not be directly extrapolated by reference to the outcome of pair-wise interactions between constituent species. Three-species arrangements attempt to limit assembly of lateral aggregates of individuals (patch size) and hence any effects of tile colonisation times, so as to reveal effects of nearest neighbour context within the complex community. Such arrangements indicate that spatial configuration of inoculum influences community development and reproducibility. They also suggest that spatial distribution of species affects persistence of individuals, which would otherwise be expected to be eliminated from the system. Two-species interactions appeared generally more reproducible than those comprising three species, and the sensitivity of fungal community development to temperature was not solely associated with influence on colony extension rate.

APE, an Animated Programming Environment, is an interactive, graphical, program design and development system, that embodies structured programming and top-down design. The system supports the development of programs for a variety of block structured languages whilst working conceptually at the level of Jackson diagrams. Formal methods are applied to validate and verify the implementation. We discuss some of our experiences in successfully applying formal methods to the APE system and outline the benefits of a similar approach to existing software in general. The evaluation of the system was based on responses to a questionnaire and a comparison with conventional methods of generating code. The results from the user trials, summarized in this paper, suggest that the APE system helps to produce standard quality products and reduces the dependence on the experience and ability of the practitioner.

Experience gained in successfully applying formal methods to an animated programming environment (APE) is reported. These techniques were applied to specify precisely some features of the APE system. The benefits of applying formal methods particularly to existing software are described, as is the specification process itself. Axiomatic specifications are written and a prototype of a module in the APE system is developed in Standard ml. The formal specification was developed by interrogating the implementation and documentation. A number of problems, exposed as a consequence, are presented.