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.

Nitrate leaching from Kentucky bluegrass soil columns predicted with anion exchange membranes

Ideal nitrogen (N) management for turfgrass supplies sufficient N for high-quality turf without increasing N leaching losses. A greenhouse study was conducted during two 27-week periods to determine if in situ anion exchange membranes (AEMs) could predict nitrate (NO3-N) leaching from a Kentucky bluegrass (Poa pratensis) turf grown on intact soil columns. Treatments consisted of 16 rates of N fertilizer application, from 0 to 98 kg N ha-1 mo-1. Percolate water was collected weekly and analysed for NO3-N. Mean flow-weighted NO3-N concentration and cumulative mass in percolate were exponentially related (pseudo-R2=0.995 and 0.994, respectively) to AEM desorbed soil NO3-N, with a percolate concentration below 10 mg NO3-N L-1 corresponding to an AEM soil NO3-N value of 2.9 micro g cm-2 d-1. Apparent N recovery by turf ranged from 28 to 40% of applied N, with a maximum corresponding to 4.7 micro g cm-2 d-1 AEM soil NO3-N. Turf colour, growth, and chlorophyll index increased with increasing AEM soil NO3-N, but these increases occurred at the expense of increases in NO3-N leaching losses. These results suggest that AEMs might serve as a tool for predicting NO3-N leaching losses from turf.