Finite 2D lattice digraphs as the life cycle graphs of clonal plant species: The reproduction core and reproductive uncertainty

When considered as a life cycle graph for a single-species plant population, a finite 2D lattice digraph represents a sample of polyvariant ontogeny, meaning the diversity of pathways that individual plants may go in their development. Botanists regard polyvariant ontogeny as the major mechanism of adaptation at the local population level, while the corresponding matrix model provides for a quantitative measure of adaptation as the dominant eigenvalue of the model matrix, a popular tool in comparative demography. Practical application of these concepts suggests matrix calibration on structured population data, and this paper concerns the data gained in recent case studies of Calamagrostis spp., perennial grasses propagating vegetatively to colonize open areas, such as forest clear-cuts or meadow habitats. To overcome uncertainty in data, calibration is reduced to a constraint maximization problem, with the constraints ensuing from the data and expert knowledge, under a hypothesis of maximal adaptation. A general existence-uniqueness theorem provides for the solution at a vertex of the polyhedral of constraints, which helps test any computational solution. The hypothesis is verified on the data gained from the excavation of the whole root system, and recommendations are formulated on the calibration without this laborious kind of data.