An integrative framework for stochastic, size-structured community assembly.

We present a theoretical framework to describe stochastic, size-structured community assembly, and use this framework to make community-level ecological predictions. Our model can be thought of as adding biological realism to Neutral Biodiversity Theory by incorporating size variation and growth dynamics, and allowing demographic rates to depend on the sizes of individuals. We find that the species abundance distribution (SAD) is insensitive to the details of the size structure in our model, demonstrating that the SAD is a poor indicator of size-dependent processes. We also derive the species biomass distribution (SBD) and find that the form of the SBD depends on the underlying size structure. This leads to a prescription for testing multiple, intertwined ecological predictions of the model, and provides evidence that alternatives to the traditional SAD are more closely tied to certain ecological processes. Finally, we describe how our framework may be extended to make predictions for more general types of community structure.

Reliable short-term memory in the trion model: toward a cortical language and grammar.

It has previously been shown that Hebb learning in a single column in the trion model of cortical organization occurs by selection. Motivated by von Neumann's solution for obtaining reliability and by models of circulating cortical activity, we introduce Hebb intercolumnar couplings to achieve dramatic enhancements in reliability in the firing of connected columns. In order for these enhancements to occur, specific temporal phase differences must exist between the same inherent spatial-temporal memory patterns in connected columns. We then generalize the criteria of large enhancements in the global firing of the entire connected columnar network to investigate the case when different inherent memory patterns are in the columns. The spatial rotations as well as the temporal phases now are crucial. Only certain combinations of inherent memory patterns meet these criteria with the symmetry properties playing a major role. The columnar order of these memory patterns not in the same symmetry family can be extremely important. This yields the first higher-level architecture of a cortical language and grammar within the trion model. The implications of this result with regard to an innate human language and grammar are discussed.

Self-similarity and the relationship between abundance and range size.

Patterns in the relationships among the range, abundance, and distribution of species within a biome are of fundamental interest in ecology. A self-similarity condition, imposed at the community level and previously demonstrated to lead to the power-law form of the species-area relationship, is extended to the species level and shown to predict testable power-law relationships between range size and both species abundance and area of census cell across scales of spatial resolution. The predicted slopes of plots of log(range size) versus log(abundance) are shown to be in good agreement with data from British breeding bird and mammal censuses and with data on the distribution of fern species in old-growth forest. The predicted slopes of plots of log(range size) versus log (area of census cell) are consistent with the limited available data for British plant species. Self-similarity provides a testable theoretical framework for a unified understanding of patterns among the range, abundance, and distribution of species.