Exact moment calculations for genetic models with migration, mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. in addition, we provide closed form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.

Behavioral Implications of Knockout for the Dyslexia-Risk Gene Dcdc2 in Mice

Several genetic linkage and epidemiological studies have provided strong evidence that DCDC2 is a candidate gene for developmental dyslexia, a disorder that impairs a person’s reading ability despite adequate intelligence, education, and socio-economic status. Studies investigating embryonic intra-ventricular RNA interference (RNAi) of Dcdc2, a rat homolog of the DCDC2 gene in humans, indicate disruptions in neuronal migration in the rat cortex during development. Interestingly, these anatomical anomalies are consistent with post mortem histological analysis of human dyslexic patients. Other rodent models of cortical developmental disruption have shown impairment in rapid auditory processing and learning maze tasks in affected subjects. The current study investigates the rapid auditory processing abilities of mice heterozygous for Dcdc2 (one functioning Dcdc2 allele) and mice with a homozygous knockout of Dcdc2 (no functioning Dcdc2 allele). It is important to note that this genetic model for behavioral assessment is still in the pilot stage. However, preliminary results suggest that mice with a genetic mutation of Dcdc2 have impaired rapid auditory processing, as well as non-spatial maze learning and memory ability, as compared to wildtypes. By genetically knocking out Dcdc2 in mice, behavioral features associated with Dcdc2 can be characterized, along with other neurological abnormalities that may arise due to the loss of the functioning gene.