Lyman L. McDonald

Estimating Uncertainty in Population Growth Rates: Jackknife vs. Bootstrap Techniques

Although per capita rates of increase (r) have been calculated by population biologists for decades, the inability to estimate uncertainty (variance) associated with r values has until recently precluded statistical comparisons of population growth rates. In this study, we used two computer- intensive techniques, Jackknifing and Bootstrapping, to estimate bias, standard errors, and sampling distributions of r for real and hypothetical populations of cladocerans. Results generated using the two techniques, using data on laboratory cohorts of Daphnia pulex, were almost identical, as were results for a hypothetical D. pulex population whose sampling distribution was approximately normal. However, for another hypothetical population whose sampling distribution was negatively skewed due to high juvenile mortality, Bootstrap and full-sample estimates of r were negatively biased by 3.3 and 1.8%, respectively. A bias adjustment reduced the bias in the Bootstrap estimate and produced estimates of r and SE(r) almost identical to those ofthe Jackknife technique. In general, our simulations show that the Jackknife will provide more cost-effective point and interval estimates of r for cladoceran populations, except when juvenile mortality is high (at least >25%). Coefficients of variation in the mean of r within laboratory cohorts of D. pulex were one-half to one-third the magnitude of the corresponding coefficients of variation in the mean of total reproduction and in the mean day to death (range of values of cv(r) = 1.6 to 3.8%). This suggests that extremes in reproductive output and survival of individuals tend to be dampened at the population level, and that within-cohort variability in r is not explosive. Moreover, between-cohort variability in r can be much greater than within-cohort variability, as indicated by a statistically significant difference of 30% (P <c; .01) between the high and low r values that were computed for four cohorts of D. pulex born during a 1 -mo period from the same laboratory stock population. Based on variability in per capita rates of increase that have been estimated for several cladoceran species, we suggest that the precision for reporting r values should in most cases be limited to two significant figures.

Relating populations to habitats using resource selection functions.

Habitat use can be characterized by resource selection functions (RSFs) that are proportional to the probability of an area being used by an animal. We highlight two procedures that have recently been used to relate RSFs to population density, dependent upon which field procedures are practical for a species. These new developments allow RSF models to be interfaced with geographical information systems (GIS) to map the probability of use, and ultimately populations, across landscapes.

Assessing habitat selection when availability changes

We present a method of comparing data on habitat use and availability that allows availability to differ among observations. This rnethod is applicable when habitats change over time and when animals are unable to move throughout a predeter- mined study area between observations. We used maximum-likelihood techniques to de- rive an index that estimates the probability that each habitat type would be used if all were equally available. We also demonstrate how these indices can be used to compare relative use of available habitats, assign them ranks, and assess statistical differences between pairs of indices. The set of these indices for all habitats can be compared between groups of animals that represent different seasons, sex or age classes, or experimental treatments. This method allows quantitative comparisons among types and is not affected by arbitrary decisions about which habitats to include in the study. We provide an example by comparing the availability of four categories of sea ice concentration to their use by adult female polar bears (Ursus maritimus), whose movements were monitored by satellite radio tracking in the Bering and Chukchi Seas during 1990. Use of ice categories by bears was nonrandom, and the pattern of use differed between spring and late summer seasons.

Winter Habitat Selection of Mule Deer Before and During Development of a Natural Gas Field

Abstract Increased levels of natural gas exploration, development, and production across the Intermountain West have created a variety of concerns for mule deer (Odocoileus hemionus) populations, including direct habitat loss to road and well-pad construction and indirect habitat losses that may occur if deer use declines near roads or well pads. We examined winter habitat selection patterns of adult female mule deer before and during the first 3 years of development in a natural gas field in western Wyoming. We used global positioning system (GPS) locations collected from a sample of adult female mule deer to model relative frequency or probability of use as a function of habitat variables. Model coefficients and predictive maps suggested mule deer were less likely to occupy areas in close proximity to well pads than those farther away. Changes in habitat selection appeared to be immediate (i.e., year 1 of development), and no evidence of well-pad acclimation occurred through the course of the study; rather, mule deer selected areas farther from well pads as development progressed. Lower predicted probabilities of use within 2.7 to 3.7 km of well pads suggested indirect habitat losses may be substantially larger than direct habitat losses. Additionally, some areas classified as high probability of use by mule deer before gas field development changed to areas of low use following development, and others originally classified as low probability of use were used more frequently as the field developed. If areas with high probability of use before development were those preferred by the deer, observed shifts in their distribution as development progressed were toward less-preferred and presumably less-suitable habitats.

Analysis of count data from before-after control-impact studies

Before-after control-impact (BACI) studies are common observational studies conducted to determine environmental impacts of accidents or potential disturbances. In this paper, we present a practical guide to analysis of BACI studies when response variables are counts. Two commonly used analyses and one less common, but more appropriate, analysis are covered. The two common analyses fundamentally compare differences of differences, one using original units, the other using log-transformed units. The third analysis, which is less common, consists of estimating interaction effects in a quasi-likelihood generalized linear model with correlated errors (i.e., a generalized linear mixed model). We conclude that the two common analyses are of marginal utility when analyzing count data due to questions regarding interpretation of parameter estimates and treatment of zeros. These questions do not arise under the quasi-likelihood generalized linear model method, and it is the recommended approach. We illustrate the three techniques by analyzing data similar to that collected by an observational study of seabird counts on oiled and unoiled sites before and after the Exxon Valdez oil spill. Example data and SAS(r) code to conduct the three analyses are given.

Survey and Comparison of Methods for Study of Resource Selection

Wildlife management studies often compare relative use and availability of resources (e.g., habitats). When resources. are used disproportionately to availability, use is said to be selective. Designs and analyses for resource selection studies are reviewed and compared with respect to the type of data collected, underlying assumptions, weighting of observations, distributional requirements and usefulness in comparing selection among subgroups or time periods. Common misuses of analyses are noted. Practical problems in studying resource selection, such as which resources to consider, the choice of study area, and spatial and temporal dependencies, are discussed and suggestions for future development are given.

NINE YEARS AFTER THE EXXON VALDEZ OIL SPILL: EFFECTS ON MARINE BIRD POPULATIONS IN PRINCE WILLIAM SOUND, ALASKA

Abstract We compared post Exxon Valdez oil-spill densities of marine birds in Prince William Sound from 1989–1991, 1993, 1996, and 1998 to pre-spill densities from 1984–1985. Post-spill densities of several species of marine birds were lower than expected in the oiled area of Prince William Sound when compared to densities in the unoiled area. These negative effects continued through 1998 for five taxa: cormorants, goldeneyes, mergansers, Pigeon Guillemot (Cepphus columba), and murres. Black Oystercatchers (Haematopus bachmani) and Harlequin Ducks (Histrionicus histrionicus) exhibited negative effects in 1990 and 1991. Loons showed a weak negative effect in 1993. Black-legged Kittiwakes (Rissa tridactyla) showed relative decreases in 1989, 1996, and 1998 which may have been caused by shifts in foraging distribution rather than declines in populations. Glaucous-winged Gulls (Larus glaucescens) showed positive effects in most post-spill years. Murrelets and terns showed relative increases in 1993, 1996, and 1998. Generally, taxa that dive for their food were negatively affected, whereas taxa that feed at the surface were not. Effects for some taxa were dependent upon the spatial scale at which they were analyzed. Movements of birds and the mosaic pattern of oiling reduced our ability to detect oil-spill effects, therefore our results may be conservative. Several marine bird species were negatively affected at the population level and have not recovered to pre-spill levels nine years after the oil spill. The reason for lack of recovery may be related to persistent oil remaining in the environment and reduced forage fish abundance.

Maximum Likelihood Estimation for the Double-Count Method With Independent Observers

influenced the detection probabilities included perpendicular distance of bear groups from the flight line and the number of individuals in the groups. A series of models were considered which vary from (1) the simplest, where the probability of detection was the same for both observers and was not affected by either distance from the flight line or group size, to (2) models where probability of detection is different for the two observers and depends on both distance from the transect and group size. Estimation procedures are developed for the case when additional variables may affect detection probabilities. The methods are illustrated using data from the pilot polar bear survey and some recommendations are given for design of a survey over the larger Chukchi Sea between Russia and the United States.

A Nonrandomized Unconditional Test for Comparing Two Proportions in 2×2 Contingency Tables

It is shown that the “usual” nonrandomized, conditional test for comparing proportions using independent binomial samples, is very conservative in the sense that the actual significance level attributable to an outcome is often one-fourth to one-half of the anticipated value. A nonrandomized unconditional test is proposed, and for sample sizes up to 15, tables are given in an appendix which specify one-sided critical regions of size less than or equal to the nominal values 0.05, and 0.01 (two-sided critical regions are also given). Numerical examples illustrating the use of the tables and a brief description of the algorithm used to generate the tables are included.

Estimating habitat selection when GPS fix success is less than 100

Inferences about habitat selection by animals derived from sequences of relocations obtained with global positioning system (GPS) collars can be influenced by GPS fix success. Environmental factors such as dense canopy cover or rugged terrain can reduce GPS fix success, making subsequent modeling problematic if fix success depends on the selected habitat. Ignoring failed fix attempts may affect estimates of model coefficients and lead to incorrect conclusions about habitat selection. Here, we present a habitat selection model that accounts for missing locations due to habitat-induced data losses, called a resource selection function (RSF) for GPS fix success. The models formulation is similar to adjusting estimates of probability of occupancy when detection is less than 100% in patch occupancy sampling. We demonstrate use of the model with GPS data collected from an adult female mule deer (Odocoileus hemionus) and discuss how to analyze data from multiple animals. In the simulations presented, our habitat selection model was generally unbiased for GPS data sets missing up to 50% of the locations.