Computational convergence of the path integral for real dendritic morphologies

Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures

Cohort aggregation modelling for complex forest stands: Spruce-aspen mixtures in British Columbia

Mixed-species growth models are needed as a synthesis of ecological knowledge and for guiding forest management. Individual-tree models have been commonly used, but the difficulties of reliably scaling from the individual to the stand level are often underestimated. Emergent properties and statistical issues limit their effectiveness. A more holistic modelling of aggregates at the whole stand level is a potentially attractive alternative. This work explores methodology for developing biologically consistent dynamic mixture models where the state is described by aggregate stand-level variables for species or age/size cohorts. The methods are demonstrated and tested with a two-cohort model for spruce-aspen mixtures named SAM. The models combine single-species submodels and submodels for resource partitioning among the cohorts. The partitioning allows for differences in competitive strength among species and size classes, and for complementarity effects. Height growth reduction in suppressed cohorts is also modelled. SAM fits well the available data, and exhibits behaviors consistent with current ecological knowledge. The general framework can be applied to any number of cohorts, and should be useful as a basis for modelling other mixed-species or uneven-aged stands.Comment: Accepted manuscript, to appear in Ecological Modellin

Effects of Lightning on Trees: A Predictive Model Based on in situ Electrical Resistivity

The effects of lightning on trees range from catastrophic death to the absence of observable damage. Such differences may be predictable among tree species, and more generally among plant life history strategies and growth forms. We used field‐collected electrical resistivity data in temperate and tropical forests to model how the distribution of power from a lightning discharge varies with tree size and identity, and with the presence of lianas. Estimated heating density (heat generated per volume of tree tissue) and maximum power (maximum rate of heating) from a standardized lightning discharge differed 300% among tree species. Tree size and morphology also were important; the heating density of a hypothetical 10 m tall Alseis blackiana was 49 times greater than for a 30 m tall conspecific, and 127 times greater than for a 30 m tall Dipteryx panamensis. Lianas may protect trees from lightning by conducting electric current; estimated heating and maximum power were reduced by 60% (±7.1%) for trees with one liana and by 87% (±4.0%) for trees with three lianas. This study provides the first quantitative mechanism describing how differences among trees can influence lightning–tree interactions, and how lianas can serve as natural lightning rods for trees