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.

Breaking Points: Mutiny in the Continental Army

The mutinies of the Continental Army during the American Revolution threatened both the integrity of the army and the viability of the Revolution itself. They were complex phenomena, stemming from numerous underlying physical and psychological causes. Having slowly developed over the course of the war, the problems confronting the Continental Army eventually brought it to the breaking point. No less than four major mutinies, involving soldiers or officers, occurred between 1780-1783. This essay focuses on the reasons for the mutinies and how the participants justified their actions. It also examines responses from General Washington and other senior officers, and what effects these actions had on the army. Finally, this essay addresses the question of why so few major mutinies occurred given the miserable state of the Continental Army.