Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

Spatial methods for plot-based sampling of wildlife populations

Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version of block kriging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging. FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1) FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK allows nonrandom sampling designs.

Double-Observer Line Transect Methods: Levels of Independence

Double-observer line transect methods are becoming increasingly widespread, especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain. The resulting data supplement conventional distance sampling data with two-sample mark–recapture data. Like conventional mark–recapture data, these have inherent problems for estimating abundance in the presence of heterogeneity. Unlike conventional mark–recapture methods, line transect methods use knowledge of the distribution of a covariate, which affects detection probability (namely, distance from the transect line) in inference. This knowledge can be used to diagnose unmodeled heterogeneity in the mark–recapture component of the data. By modeling the covariance in detection probabilities with distance, we show how the estimation problem can be formulated in terms of different levels of independence. At one extreme, full independence is assumed, as in the Petersen estimator (which does not use distance data); at the other extreme, independence only occurs in the limit as detection probability tends to one. Between the two extremes, there is a range of models, including those currently in common use, which have intermediate levels of independence. We show how this framework can be used to provide more reliable analysis of double-observer line transect data. We test the methods by simulation, and by analysis of a dataset for which true abundance is known. We illustrate the approach through analysis of minke whale sightings data from the North Sea and adjacent waters.

Seeking a Second Opinion: Uncertainty in Disease Ecology

Analytical methods accounting for imperfect detection are often used to facilitate reliable inference in population and community ecology. We contend that similar approaches are needed in disease ecology because these complicated systems are inherently difficult to observe without error. For example, wildlife disease studies often designate individuals, populations, or spatial units to states (e.g., susceptible, infected, post-infected), but the uncertainty associated with these state assignments remains largely ignored or unaccounted for. We demonstrate how recent developments incorporating observation error through repeated sampling extend quite naturally to hierarchical spatial models of disease effects, prevalence, and dynamics in natural systems. A highly pathogenic strain of avian influenza virus in migratory waterfowl and a pathogenic fungus recently implicated in the global loss of amphibian biodiversity are used as motivating examples. Both show that relatively simple modifications to study designs can greatly improve our understanding of complex spatio-temporal disease dynamics by rigorously accounting for uncertainty at each level of the hierarchy.

Compressed Air, Wooden Clappers, and Other Non-Traditional Methods for Dispersing European Starlings from an Urban Roost

During autumn 2003, several thousand European starlings (Sturnus vulgaris) began roosting on exposed I-beams in a newly constructed, decorative glass canopy that covered the passenger pick-up area at the terminal building for Cleveland Hopkins International Airport, Ohio. The use of lethal control or conventional dispersal techniques, such as pyrotechnics and fire hoses, were not feasible in the airport terminal area. The design and aesthetics of the structure precluded the use of netting and other exclusion materials. In January 2004, an attempt was made to disperse the birds using recorded predator and distress calls broadcast from speakers installed in the structure. This technique failed to disperse the birds. In February 2004, we developed a technique using compressed air to physically and audibly harass the birds. We used a trailer-mounted commercial air compressor producing 185 cubic feet per minute of air at 100 pounds per square inch pressure and a 20-foot long, 1-inch diameter PVC pipe attached to the outlet hose. One person slowly (< 5 mph) drove a pick-up truck through the airport terminal at dusk while the second person sat on a bench in the truck bed and directed the compressed air from the pipe into the canopy to harass starlings attempting to enter the roost site. After 5 consecutive nights of compressed-air harassment, virtually no starlings attempted to roost in the canopy. Once familiar with the physical effects of the compressed air, the birds dispersed at the sound of the air. Only occasional harassment at dusk was needed through the remainder of the winter to keep the canopy free of starlings. Similar harassment with the compressor was conducted successfully in autumn 2004 with the addition of a modified leaf blower, wooden clappers, and laser. In conclusion, we found compressed air to be a safe, unobtrusive, and effective method for dispersing starlings from an urban roost site. This technique would likely be applicable for other urban-roosting species such as crows, house sparrows, and blackbirds.

METHODS OF CONTROLLING COYOTES, BOBCATS, AND FOXES

In reviewing methods of predator control, it would first seem appropriate to define what is meant "by "methods" and what is meant by "control." Taking the last term first, control, as applied to the predatory coyotes, bobcats, and foxes, may be defined as regulating the numbers of these animals to the point where the economic losses for which they are responsible will be reduced to a practicable minimum. In some situations, area control, i.e., limiting the numbers of the offending predator over wide areas, may be necessary for satisfactory reduction of economic losses; in other situations, spot control or localized reduction of numbers of a certain predator may be called for; in still other situations, elimination of an individual animal may be all the control that is needed. In no sense is control, as applied to coyotes, bobcats, and foxes, intended to mean extermi¬nation of a species. The term "methods" is interpreted as meaning the procedures employed against coyotes, bobcats, and foxes, and not the broader systems of predator control such as the paid hunter system, the extension system, or the much-discredited bounty system. For an excellent review of the systems of predator control, see Latham (l).

HAWAIIAN SUGAR CANE RAT CONTROL METHODS AND PROBLEMS

The problem of rats in our Hawaiian sugar cane fields has been with us for a long time. Early records tell of heavy damage at various times on all the islands where sugar cane is grown. Many methods were tried to control these rats. Trapping was once used as a control measure, a bounty was used for a time, gangs of dogs were trained to catch the rats as the cane was harvested. Many kinds of baits and poisons were used. All of these methods were of some value as long as labor was cheap. Our present day problem started when the labor costs started up and the sugar industry shifted to long cropping. Until World War II cane was an annual crop. After the war it was shifted to a two year crop, three years in some places. Depending on variety, location, and soil we raise 90 to 130 tons of sugar cane per acre, which produces 7 to 15 tons of sugar per acre for a two year crop. This sugar brings about $135 dollars per ton. This tonnage of cane is a thick tangle of vegetation. The cane grows erect for almost a year, as it continues to grow it bends over at the base. This allows the stalk to rest on the ground or on other stalks of cane as it continues to grow. These stalks form a tangled mat of stalks and dead leaves that may be two feet thick at the time of harvest. At the same time the leafy growing portion of the stalk will be sticking up out of the mat of cane ten feet in the air. Some of these individual stalks may be 30 feet long and still growing at the time of harvest. All this makes it very hard to get through a cane field as it is one long, prolonged stumble over and through the cane. It is in this mat of cane that our three species of rats live. Two species are familiar to most people in the pest control field. Rattus norvegicus and Rattus rattus. In the latter species we include both the black rat and the alexandrine rats, their habits seem to be the same in Hawaii. Our third rat is the Polynesian rat, Rattus exlans, locally called the Hawaiian rat. This is a small rat, the average length head to tip of tail is nine inches and the average body weight is 65 grams. It has dark brownish fur like the alexandrine rats, and a grey belly. It is found in Indonesia, on most of the islands of Oceania and in New Zealand. All three rats live in our cane fields and the brushy and forested portions of our islands. The norway and alexandrine rats are found in and around the villages and farms, the Polynesian rat is only found in the fields and waste areas. The actual amount of damage done by rats is small, but destruction they cause is large. The rats gnaw through the rind of the cane stalk and eat the soft juicy and sweet tissues inside. They will hollow out one to several nodes per stalk attacked. The effect to the cane stalk is like ringing a tree. After this attack the stalk above the chewed portion usually dies, and sometimes the lower portion too. If the rat does not eat through the stalk the cane stalk could go on living and producing sugar at a reduced rate. Generally an injured stalk does not last long. Disease and souring organisms get in the injury and kill the stalk. And if this isn't enough, some insects are attracted to the injured stalk and will sometimes bore in and kill it. An injured stalk of cane doesn't have much of a chance. A rat may only gnaw out six inches of a 30 foot stalk and the whole stalk will die. If the rat only destroyed what he ate we could ignore them but they cause the death of too much cane. This dead, dying, and souring cane cause several direct and indirect tosses. First we lose the sugar that the cane would have produced. We harvest all of our cane mechanically so we haul the dead and souring cane to the mill where we have to grind it with our good cane and the bad cane reduces the purity of the sugar juices we squeeze from the cane. Rats reduce our income and run up our overhead.

METHODS OF CONTROLLING STARLINGS AND BLACKBIRDS

Most people have accepted the fact that all living things can be beneficial to mankind in some way or other. This is especially true of our wild birds, since they provide enjoyment and wholesome recreation for most of us, regardless of whether we live on farms or in the city. But despite the fact that wild birds are for the most part beneficial, at times individuals or populations of certain species can seriously affect man's interests. When such situations occur, some measures of relief are desirable and usually eagerly sought. This report is not intended to answer all the questions that may arise concerning problems with blackbirds and starlings; instead, it is merely a summary of measures used to protect agricultural crops from these birds.

BIRD CONTROL METHODS AND DEVICES--COMMENTS OF THE NATIONAL PEST CONTROL ASSOCIATION

It may be useful to review some of the considerations that go into recommendations concerning bird management. Later I will make some comments concerning specific methods and devices being used in or promoted for bird control work regardless of whether or not they are new. Members of the National Pest Control Association provide a variety of services, such as fumigation, termite control and general pest control which includes rodent control. There are eight such categories listed in our roster, but only one member in five provides every service listed. Bird control is a rather recent development and is the newest category of service to be listed in the NPCA roster where it appeared for the first time in 1959. As of September 1, 1966, 45% of our members' offices indicated that they were prepared to offer bird control service. Less than 40% did so in 1964. Why is it that more of our members do not declare themselves as ready to do bird control work? I believe the most common answer you would find is that bird control is not yet sufficiently established that they can provide a service comparable in quality to that which is provided against termites or cockroaches or rats. Our members simply do not want to jeopardize their reputation on methods that are not certain or are too complex. Others recognize the emotional reaction evidenced by much of the population concerning control of birds and do not want to become involved in work that might offend some of their clientele. Still others simply do not agree that birds are their responsibility.