Brian M. Steele

Usefulness of molecular markers for detecting population bottlenecks via monitoring genetic change

It is important to detect population bottlenecks in threatened and managed species because bottlenecks can increase the risk of population extinction. Early detection is critical and can be facilitated by statistically powerful monitoring programs for detecting bottleneck‐induced genetic change. We used Monte Carlo computer simulations to evaluate the power of the following tests for detecting genetic changes caused by a severe reduction in a populations effective size (Ne): a test for loss of heterozygosity, two tests for loss of alleles, two tests for change in the distribution of allele frequencies, and a test for small Ne based on variance in allele frequencies (the ‘variance test’). The variance test was most powerful; it provided an 85% probability of detecting a bottleneck of size Ne = 10 when monitoring five microsatellite loci and sampling 30 individuals both before and one generation after the bottleneck. The variance test was almost 10‐times more powerful than a commonly used test for loss of heterozygosity, and it allowed for detection of bottlenecks before 5% of a populations heterozygosity had been lost. The second most powerful tests were generally the tests for loss of alleles. However, these tests had reduced power for detecting genetic bottlenecks caused by skewed sex ratios. We provide guidelines for the number of loci and individuals needed to achieve high‐power tests when monitoring via the variance test. We also illustrate how the variance test performs when monitoring loci that have widely different allele frequency distributions as observed in five wild populations of mountain sheep (Ovis canadensis).

Genetic rescue of an insular population of large mammals

Natural populations worldwide are increasingly fragmented by habitat loss. Isolation at small population size is thought to reduce individual and population fitness via inbreeding depression. However, little is known about the time-scale over which adverse genetic effects may develop in natural populations or the number and types of traits likely to be affected. The benefits of restoring gene flow to isolates are therefore also largely unknown. In contrast, the potential costs of migration (e.g. disease spread) are readily apparent. Management for ecological connectivity has therefore been controversial and sometimes avoided. Using pedigree and life-history data collected during 25 years of study, we evaluated genetic decline and rescue in a population of bighorn sheep founded by 12 individuals in 1922 and isolated at an average size of 42 animals for 10–12 generations. Immigration was restored experimentally, beginning in 1985. We detected marked improvements in reproduction, survival and five fitness-related traits among descendants of the 15 recent migrants. Trait values were increased by 23–257% in maximally outbred individuals. This is the first demonstration, to our knowledge, of increased male and female fitness attributable to outbreeding realized in a fully competitive natural setting. Our findings suggest that genetic principles deserve broader recognition as practical management tools with near-term consequences for large-mammal conservation.

Power of Sign Surveys to Monitor Population Trends

The urgent need for an effective monitoring scheme for grizzly bear (Ursus arctos) populations led us to investigate the effort required to detect changes in populations of low-density dispersed animals, using sign (mainly scats and tracks) they leave on trails. We surveyed trails in Glacier National Park for bear tracks and scats during five consecutive years. Using these data, we modeled the occurrence of bear sign on trails, then estimated the power of various sampling schemes. Specifically, we explored the power of bear sign surveys to detect a 20% decline in sign occurrence. Realistic sampling schemes appear feasible if the density of sign is high enough, and we provide guidelines for designs with adequate replication to monitor long-term trends of dispersed populations using sign occurrences on trails.

Combining Multiple Classifiers: An Application Using Spatial and Remotely Sensed Information for Land Cover Type Mapping

This article discusses two new methods for increasing the accuracy of classifiers used land cover mapping. The first method, called the product rule, is a simple and general method of combining two or more classification rules as a single rule. Stacked regression methods of combining classification rules are discussed and compared to the product rule. The second method of increasing classifier accuracy is a simple nonparametric classifier that uses spatial information for classification. Two data sets used for land cover mapping of Landsat TM scenes from Idaho and Montana illustrate the new methods. For these examples, the product rule compared favorably to the more complex stacked regression methods. The spatial classifier produced substantial increases in estimated accuracy when combined with one or more additional classifiers that used remotely sensed variables for classification. These results suggest that the product rule may produce increases in map accuracy with little additional expense or effort. The spatial classifier may be useful for increasing accuracy when patterns exist in the spatial distribution of land cover.

A MODIFIED EM ALGORITHM FOR ESTIMATION IN GENERALIZED MIXED MODELS

Application of the EM algorithm for estimation in the generalized mixed model has been largely unsuccessful because the E-step cannot be determined in most instances. The E-step computes the conditional expectation of the complete data log-likelihood and when the random effect distribution is normal, this expectation remains an intractable integral. The problem can be approached by numerical or analytic approximations; however, the computational burden imposed by numerical integration methods and the absence of an accurate analytic approximation have limited the use of the EM algorithm. In this paper, Laplaces method is adapted for analytic approximation within the E-step. The proposed algorithm is computationally straightforward and retains much of the conceptual simplicity of the conventional EM algorithm, although the usual convergence properties are not guaranteed. The proposed algorithm accommodates multiple random factors and random effect distributions besides the normal, e.g., the log-gamma distribution. Parameter estimates obtained for several data sets and through simulation show that this modified EM algorithm compares favorably with other generalized mixed model methods.

A method of exploiting spatial information for improving classification rules : application to the construction of polygon-based land cover maps

This article proposes a method of exploiting spatial information to improve classification rules constructed by automated methods such as k-nearest neighbour or linear discriminant analysis. The method is intended for polygonbased, land cover type mapping using remote sensing information in a GIS. Our approach differs from contextual allocation methods used in lattice- or pixel-based mapping because it does not rely on spatial dependence models. Instead, the method uses a Bayes-type formula to modify the estimated posterior probabilities of group membership produced by automated classifiers. The method is found to substantially improve classification accuracy estimates in areas where there is a moderate or greater degree of physiographic variation across the map extent.

Exact bootstrap k-nearest neighbor learners

Bootstrap aggregation, or bagging, is a method of reducing the prediction error of a statistical learner. The goal of bagging is to construct a new learner which is the expectation of the original learner with respect to the empirical distribution function. In nearly all cases, the expectation cannot be computed analytically, and bootstrap sampling is used to produce an approximation. The k-nearest neighbor learners are exceptions to this generalization, and exact bagging of many k-nearest neighbor learners is straightforward. This article presents computationally simple and fast formulae for exact bagging of k-nearest neighbor learners and extends exact bagging methods from the conventional bootstrap sampling (sampling n observations with replacement from a set of n observations) to bootstrap sub-sampling schemes (with and without replacement). In addition, a partially exact k-nearest neighbor regression learner is developed. The article also compares the prediction error associated with elementary and exact bagging k-nearest neighbor learners, and several other ensemble methods using a suite of publicly available data sets.

Ideal bootstrap estimation of expected prediction error for k-nearest neighbor classifiers: Applications for classification and error assessment

Euclidean distance k-nearest neighbor (k-NN) classifiers are simple nonparametric classification rules. Bootstrap methods, widely used for estimating the expected prediction error of classification rules, are motivated by the objective of calculating the ideal bootstrap estimate of expected prediction error. In practice, bootstrap methods use Monte Carlo resampling to estimate the ideal bootstrap estimate because exact calculation is generally intractable. In this article, we present analytical formulae for exact calculation of the ideal bootstrap estimate of expected prediction error for k-NN classifiers and propose a new weighted k-NN classifier based on resampling ideas. The resampling-weighted k-NN classifier replaces the k-NN posterior probability estimates by their expectations under resampling and predicts an unclassified covariate as belonging to the group with the largest resampling expectation. A simulation study and an application involving remotely sensed data show that the resampling-weighted k-NN classifier compares favorably to unweighted and distance-weighted k-NN classifiers.

Sampling Design and Statistical Inference for Ecological Assessment

The success of ecological assessment depends on relevant and accurate information about the ecosystem or landscape under study. Data collected by sampling are a primary source of information about ecosystems and usually the only source of information that is specific to the ecosystem. The information value of sample data cannot be overestimated: these data directly reflect the processes and organisms constituting the system and are independent of human-held assumptions and theories. There are three general approaches to using sample data to describe ecosystems and ecosystem processes: (1) often important ecosystem components can be assessed by analyzing a few summary statistics; (2) ecosystem monitoring makes use of sample data for trend estimation and uses hypothesis testing for change detection; and (3) occasionally, ecological assessment involves the modeling of ecosystem processes, and sample data are used for model estimation and prediction.