Incorporating parametric uncertainty into population viability analysis models

Uncertainty in parameter estimates from sampling variation or expert judgment can introduce substantial uncertainty into ecological predictions based on those estimates. However, in standard population viability analyses, one of the most widely used tools for managing plant, fish and wildlife populations, parametric uncertainty is often ignored in or discarded from model projections. We present a method for explicitly incorporating this source of uncertainty into population models to fully account for risk in management and decision contexts. Our method involves a two-step simulation process where parametric uncertainty is incorporated into the replication loop of the model and temporal variance is incorporated into the loop for time steps in the model. Using the piping plover, a federally threatened shorebird in the USA and Canada, as an example, we compare abundance projections and extinction probabilities from simulations that exclude and include parametric uncertainty. Although final abundance was very low for all sets of simulations, estimated extinction risk was much greater for the simulation that incorporated parametric uncertainty in the replication loop. Decisions about species conservation (e.g., listing, delisting, and jeopardy) might differ greatly depending on the treatment of parametric uncertainty in population models.     

Incorporating variance uncertainty into a power analysis of monitoring designs

Power calculations usually assume that the components of the population variance are known, but it is frequently the case that they are estimated using data from a pilot study. Imprecision in the estimates is then ignored and a single value for power is generated. We present a method that incorporates the error in the estimates of any number of variance components into the power calculations. We show that, by sampling values for the variance components from the residual likelihood function of the pilot data, our method can approximate the distribution of powers expected given the uncertainty in the variance components. Alternative summary measures of power can then be derived: we strongly recommend treating a minimum acceptable power as a quality standard and summarizing power in terms of the probability that this quality standard is attained. The method is illustrated by application to counts of common guillemots (Uria aalge) on the Isle of May in Scotland to assess the power of detecting long-term trends in abundance using a model for random variation with seven parameters.     

Incorporating LASSO effects into a mixed model for quantitative trait loci detection

The identification of quantitative trait loci (QTL) can be viewed as a subset selection problem. In a simulation study the least absolute selection and shrinkage operator (LASSO) is shown to be a useful and powerful tool for QTL identification. LASSO effects are embedded into a mixed model allowing simultaneous modeling of genetic and experimental effects. This provides the flexibility to model the experiment in conjunction with the power of LASSO QTL identification. Estimation is performed using an approximation to the restricted likelihood and modified Gaussian elimination. The extended mixed model is used to analyze a cattle gene mapping dataset.     

A statistical framework to combine multivariate spatial data and physical models for Hurricane surface wind prediction

Storm surge is the onshore rush of seawater associated with hurricane force winds. Storm surge can compound the effects of inland flooding caused by rainfall, leading to loss of property and loss of life for residents of coastal areas. Numerical ocean models are essential for predicting which coastal areas are most likely to be impacted by storm surge. These numerical physics-based models are driven primarily by the surface wind forcings which are currently specified by a deterministic formula. Although these equations incorporate important physical knowledge about the structure of hurricane surface wind fields, they cannot always capture the asymmetric and dynamic nature of a hurricane. This article develops a new multivariate spatial statistical framework to improve the estimation of these wind field inputs while accounting for potential bias in the observations. We find that this spatial model consistently improves parameter estimation and prediction for surface wind data for a case study of Hurricane Charley of 2004 when compared to the original physical model. These methods are also shown to improve storm surge estimates when used as the forcing fields for a numerical three-dimensional coastal ocean model.     

Incorporating uncertainty about species’ potential distributions under climate change into the selection of conservation areas with a case study from the Arctic Coastal Plain of Alaska

This analysis presents a conservation planning framework for decisions under uncertainty and applies it to the Arctic Coastal Plain of Alaska. Uncertainty arises from variable distributional shifts of species’ ranges due to climate change. The planning framework consists of a two-stage optimization model that selects a nominal conservation area network in the first stage and evaluates its performance under the climate scenarios in the second stage. The model is applied to eleven at-risk species in Alaska including the threatened Spectacled Eider and Steller’s Eider sea ducks and the polar bear. The 109th United States Congress and 2008 federal budget proposed opening for oil and gas development the “1002 Area” of the Arctic National Wildlife Refuge, which intersects the Plain. This analysis finds that, if Arctic Alaska experiences 1.5 °C of warming by 2040 (as predicted by the Intergovernmental Panel on Climate Change’s A2 scenario), then potential habitat will decrease significantly for eight of these at-risk species, including the polar bear. This analysis also shows that there is synergism between oil and gas development and climate change. For instance, climate change accompanied by no development of the 1002 Area results in an increase of potential habitat for Steller’s Eider. However, if development accompanies climate change, then there is a 20% decrease in that area. Further, this analysis quantifies the tradeoff between development and maintenance of suitable habitat for at-risk species.