On variability in the density of corticocortical and thalamocortical connections

Variability is an important but neglected aspect of connectional neuroanato my. The quantitative density of the 'same' corticocortical or thalamocortic al connection may vary by over two orders of magnitude between different in jections of the same tracer. At present, however, the frequency distributio n of connection densities is unknown. Therefore, it is unclear what kind of sampling strategies or statistical methods are appropriate for quantitativ e studies of connectivity. Nor is it clear if the measured variability repr esents differences between subjects, or if it is simply a consequence of in tra-individual differences resulting from experimental technique and the ex act placement of tracers relative to local spatial and laminar variation in connectivity. We used quantitative measurements of the density of a large number of corti cocortical and thalamocortical connections from our own laboratories and fr om the literature. Variability in the density of given corticocortical and thalamocortical connections is high, with the standard deviation of density proportional to the mean. The frequency distribution is close to exponenti al. Therefore, analysis methods relying on the normal distribution are not appropriate. We provide an appendix that gives simple statistical guidance for samples drawn from exponentially distributed data. For a given corticocortical or thalamocortical connection density, between- individual standard deviation is 0.85 to 1.25 times the within-individual s tandard deviation. Therefore, much of the variability reported in conventio nal neuroanatomical studies (with one tracer deposited per animal) is due t o within-individual factors. We also find that strong, but not weak, cortic ocortical connections are substantially more variable than thalamocortical connections. We propose that the near exponential distribution of connectio n densities is a simple consequence of 'patchy' connectivity. We anticipate that connection data will be well described by the negative binomial, a cl ass of distribution that applies to events occurring in clumped or patchy s ubstrates. Local patchiness may be a feature of all corticocortical connect ions and could explain why strong corticocortical connections are more vari able than strong thalamocortical connections. This idea is supported by the columnar patterns of many corticocortical but few thalamocortical connecti ons in the literature.