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.

Validation of a Spatially Continuous EDEN Water-Surface Model for the Everglades, Florida

The Everglades Depth Estimation Network (EDEN) is an integrated network of realtime water-level monitoring, ground-elevation modeling, and water-surface modeling that provides scientists and managers with current (2000-present), online water-stage and water-depth information for the entire freshwater portion of the Greater Everglades. Continuous daily spatial interpolations of the EDEN network stage data are presented on grid with 400-square-meter spacing. EDEN offers a consistent and documented dataset that can be used by scientists and managers to: (1) guide large-scale field operations, (2) integrate hydrologic and ecological responses, and (3) support biological and ecological assessments that measure ecosystem responses to the implementation of the Comprehensive Everglades Restoration Plan (CERP) (U.S. Army Corps of Engineers, 1999). The target users are biologists and ecologists examining trophic level responses to hydrodynamic changes in the Everglades. The first objective of this report is to validate the spatially continuous EDEN water-surface model for the Everglades, Florida developed by Pearlstine et al. (2007) by using an independent field-measured data-set. The second objective is to demonstrate two applications of the EDEN water-surface model: to estimate site-specific ground elevation by using the validated EDEN water-surface model and observed water depth data; and to create water-depth hydrographs for tree islands. We found that there are no statistically significant differences between model-predicted and field-observed water-stage data in both southern Water Conservation Area (WCA) 3A and WCA 3B. Tree island elevations were derived by subtracting field water-depth measurements from the predicted EDEN water-surface. Water-depth hydrographs were then computed by subtracting tree island elevations from the EDEN water stage. Overall, the model is reliable by a root mean square error (RMSE) of 3.31 cm. By region, the RMSE is 2.49 cm and 7.77 cm in WCA 3A and 3B, respectively. This new landscape-scale hydrological model has wide applications for ongoing research and management efforts that are vital to restoration of the Florida Everglades. The accurate, high-resolution hydrological data, generated over broad spatial and temporal scales by the EDEN model, provides a previously missing key to understanding the habitat requirements and linkages among native and invasive populations, including fish, wildlife, wading birds, and plants. The EDEN model is a powerful tool that could be adapted for other ecosystem-scale restoration and management programs worldwide.