Neutral behavior of shared polymorphism

Several cases have been described in the literature where genetic polymorphism appears to be shared between a pair of species. Here we examine the distribution of times to random loss of shared polymorphism in the context of the neutral Wright–Fisher model. Order statistics are used to obtain the distribution of times to loss of a shared polymorphism based on Kimura’s solution to the diffusion approximation of the Wright–Fisher model. In a single species, the expected absorption time for a neutral allele having an initial allele frequency of ½ is 2.77 N generations. If two species initially share a polymorphism, that shared polymorphism is lost as soon as either of two species undergoes fixation. The loss of a shared polymorphism thus occurs sooner than loss of polymorphism in a single species and has an expected time of 1.7 N generations. Molecular sequences of genes with shared polymorphism may be characterized by the count of the number of sites that segregate in both species for the same nucleotides (or amino acids). The distribution of the expected numbers of these shared polymorphic sites also is obtained. Shared polymorphism appears to be more likely at genetic loci that have an unusually large number of segregating alleles, and the neutral coalescent proves to be very useful in determining the probability of shared allelic lineages expected by chance. These results are related to examples of shared polymorphism in the literature.

Spatially independent activity patterns in functional MRI data during the Stroop color-naming task

A method is given for determining the time course and spatial extent of consistently and transiently task-related activations from other physiological and artifactual components that contribute to functional MRI (fMRI) recordings. Independent component analysis (ICA) was used to analyze two fMRI data sets from a subject performing 6-min trials composed of alternating 40-sec Stroop color-naming and control task blocks. Each component consisted of a fixed three-dimensional spatial distribution of brain voxel values (a “map”) and an associated time course of activation. For each trial, the algorithm detected, without a priori knowledge of their spatial or temporal structure, one consistently task-related component activated during each Stroop task block, plus several transiently task-related components activated at the onset of one or two of the Stroop task blocks only. Activation patterns occurring during only part of the fMRI trial are not observed with other techniques, because their time courses cannot easily be known in advance. Other ICA components were related to physiological pulsations, head movements, or machine noise. By using higher-order statistics to specify stricter criteria for spatial independence between component maps, ICA produced improved estimates of the temporal and spatial extent of task-related activation in our data compared with principal component analysis (PCA). ICA appears to be a promising tool for exploratory analysis of fMRI data, particularly when the time courses of activation are not known in advance.