Lisa Madsen

Models for Estimating Abundance from Repeated Counts of an Open Metapopulation

Using only spatially and temporally replicated point counts, Royle (2004b, Biometrics 60, 108-115) developed an N-mixture model to estimate the abundance of an animal population when individual animal detection probability is unknown. One assumption inherent in this model is that the animal populations at each sampled location are closed with respect to migration, births, and deaths throughout the study. In the past this has been verified solely by biological arguments related to the study design as no statistical verification was available. In this article, we propose a generalization of the N-mixture model that can be used to formally test the closure assumption. Additionally, when applied to an open metapopulation, the generalized model provides estimates of population dynamics parameters and yields abundance estimates that account for imperfect detection probability and do not require the closure assumption. A simulation study shows these abundance estimates are less biased than the abundance estimate obtained from the original N-mixture model. The proposed model is then applied to two data sets of avian point counts. The first example demonstrates the closure test on a single-season study of Mallards (Anas platyrhynchos), and the second uses the proposed model to estimate the population dynamics parameters and yearly abundance of American robins (Turdus migratorius) from a multi-year study.

Effects of lidar pulse density and sample size on a model-assisted approach to estimate forest inventory variables

Using lidar in an area-based model-assisted approach to forest inventory has the potential to increase estimation precision for some forest inventory variables. This study documents the bias and precision of a model-assisted (regression estimation) approach to forest inventory with lidar-derived auxiliary variables relative to lidar pulse density and the number of sample plots. For managed forests on the Lewis portion of the Lewis-McChord Joint Base (35025 ha, 23290 forested) in western Washington state, we evaluated a regression estimator for combinations of pulse density (.05–3 pulses/m2) and sample size (15–105 plots) to estimate five forest yield variables: basal area, volume, biomass, number of stems, and Loreys height. The results indicate that there is almost no loss in precision in using as few as .05 pulses/m2 relative to 3 pulses/m2. We demonstrate that estimation precision declined quickly for reduced sample sizes (as expected from sampling theory); but of more importance we demonstrate that sample size has a dramatic effect on the validity of inferences. Our investigations indicate that for our test dataset that central limit theorem based confidence intervals were too small on average for sample sizes smaller than 55. The results from this study can aid in identifying design components for forest inventory with lidar which satisfy users’ objectives.

Stream temperature change detection for state and private forests in the Oregon Coast Range

[1] Oregon’s forested coastal watersheds support important cold-water fisheries of salmon and steelhead (Oncorhynchus spp.) as well as forestry-dependent local economies. Riparian timber harvest restrictions in Oregon and elsewhere are designed to protect stream habitat characteristics while enabling upland timber harvest. We present an assessment of riparian leave tree rule effectiveness at protecting streams from temperature increases in the Oregon Coast Range. We evaluated temperature responses to timber harvest at 33 privately owned and state forest sites with Oregon’s water quality temperature antidegradation standard, the Protecting Cold Water (PCW) criterion. At each site we evaluated stream temperature patterns before and after harvest upstream, within, and downstream of harvest units. We developed a method for detecting stream temperature change between years that adhered as closely as possible to Oregon’s water quality rule language. The procedure provided an exceedance history across sites that allowed us to quantify background and treatment (timber harvest) PCW exceedance rates. For streams adjacent to harvested areas on privately owned lands, preharvest to postharvest year comparisons exhibited a 40% probability of exceedance. Sites managed according to the more stringent state forest riparian standards did not exhibit exceedance rates that differed from preharvest, control, or downstream rates (5%). These results will inform policy discussion regarding the sufficiency of Oregon’s forest practices regulation at protecting stream temperature. The analysis process itself may assist other states and countries in developing and evaluating their forest management and water quality antidegradation regulations.

Joint Regression Analysis for Discrete Longitudinal Data

We introduce an approximation to the Gaussian copula likelihood of Song, Li, and Yuan (2009, Biometrics 65, 60-68) used to estimate regression parameters from correlated discrete or mixed bivariate or trivariate outcomes. Our approximation allows estimation of parameters from response vectors of length much larger than three, and is asymptotically equivalent to the Gaussian copula likelihood. We estimate regression parameters from the toenail infection data of De Backer et al. (1996, British Journal of Dermatology 134, 16-17), which consist of binary response vectors of length seven or less from 294 subjects. Although maximizing the Gaussian copula likelihood yields estimators that are asymptotically more efficient than generalized estimating equation (GEE) estimators, our simulation study illustrates that for finite samples, GEE estimators can actually be as much as 20% more efficient.

Simulating dependent discrete data

This article describes a method for simulating n-dimensional multivariate non-normal data, with emphasis on count-valued data. Dependence is characterized by either Pearson correlations or Spearman correlations. The simulation is accomplished by simulating a vector of correlated standard normal variates. The elements of this vector are then transformed to achieve the target marginal distributions. We prove that the method corresponds to simulating data from a multivariate Gaussian copula. The simulation method does not restrict pairwise dependence beyond the limits imposed by the marginal distributions and can achieve any Pearson or Spearman correlation within those limits. Two examples are included. In the first example, marginal means, variances, Pearson correlations, and Spearman correlations are estimated from the epileptic seizure data set of Diggle et al. [P. Diggle, P. Heagerty, K.Y. Liang, and S. Zeger, Analysis of Longitudinal Data, Oxford University Press, Oxford, 2002]. Data with these means and variances are simulated to first achieve the estimated Pearson correlations and then achieve the estimated Spearman correlations. The second example is of a hypothetical time series of Poisson counts with seasonal mean ranging between 1 and 9 and an autoregressive(1) dependence structure.

Estimating Open Population Site Occupancy from Presence–Absence Data Lacking the Robust Design

Many animal monitoring studies seek to estimate the proportion of a study area occupied by a target population. The study area is divided into spatially distinct sites where the detected presence or absence of the population is recorded, and this is repeated in time for multiple seasons. However, when occupied sites are detected with probability p < 1, the lack of a detection does not imply lack of occupancy. MacKenzie et al. (2003, Ecology 84, 2200-2207) developed a multiseason model for estimating seasonal site occupancy (ψt ) while accounting for unknown p. Their model performs well when observations are collected according to the robust design, where multiple sampling occasions occur during each season; the repeated sampling aids in the estimation p. However, their model does not perform as well when the robust design is lacking. In this paper, we propose an alternative likelihood model that yields improved seasonal estimates of p and Ψt in the absence of the robust design. We construct the marginal likelihood of the observed data by conditioning on, and summing out, the latent number of occupied sites during each season. A simulation study shows that in cases without the robust design, the proposed model estimates p with less bias than the MacKenzie et al. model and hence improves the estimates of Ψt . We apply both models to a data set consisting of repeated presence-absence observations of American robins (Turdus migratorius) with yearly survey periods. The two models are compared to a third estimator available when the repeated counts (from the same study) are considered, with the proposed model yielding estimates of Ψt closest to estimates from the point count model.

Estimation and simulation for geospatial porosity and permeability data

Reservoir simulation of

Supplement 1. R code to calculate posterior distribution of M, total fatality at a wind facility when zero carcasses are observed.

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