Overexploitation threatens the future of many large vertebrates. In the ocean, tunas and sea turtles are current conservation concerns because of this intense pressure. The status of most shark species, in contrast, remains uncertain. Using the largest data set in the Northwest Atlantic, we show rapid large declines in large coastal and oceanic shark populations. Scalloped hammerhead, white, and thresher sharks are each estimated to have declined by over 75% in the past 15 years. Closed-area models highlight priority areas for shark conservation, and the need to consider effort reallocation and site selection if marine reserves are to benefit multiple threatened species.

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Collapse and Conservation of Shark Populations in the Northwest Atlantic

We present several modifications of the Poisson and negative binomial models for count data to accommodate cases in which the number of zeros in the data exceed what would typically be predicted by either model. The excess zeros can masquerade as overdispersion. We present a new test procedure for distinguishing between zero inflation and overdispersion. We also develop a model for sample selection which is analogous to the Heckman style specification for continuous choice models. An application is presented to a data set on consumer loan behavior in which both of these phenomena are clearly present.

Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models

Modelling the abundance of rare species: statistical models for counts with extra zeros

Poisson regression models provide a standard framework for the analysis of count data. In practice, however, count data are often overdispersed relative to the Poisson distribution. One frequent manifestation of overdispersion is that the incidence of zero counts is greater than expected for the Poisson distribution and this is of interest because zero counts frequently have special status. For example, in counting disease lesions on plants, a plant may have no lesions either because it is resistant to the disease, or simply because no disease spores have landed on it. This is the distinction between structural zeros, which are inevitable, and sampling zeros, which occur by chance. In recent years there has been considerable interest in models for count data that allow for excess zeros, particularly in the econometric literature. These models complement more conventional models for overdispersion that concentrate on modelling the variance-mean relationship correctly. Application areas are diverse and have included manufacturing defects (Lambert, 1992), patent applications (Crepon & Duguet, 1997), road safety (Miaou, 1994), species abundance (Welsh et al., 1996; Faddy, 1998), medical consultations

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Models for count data with many zeros

This paper develops a negative binomial model of recreation demand that corrects for both truncation and endogenous stratification. This approach recovers the demand associated with the general population, not just the users of the site. This model demonstrates the importance of the joint nature of the population's latent demand for trips and the consumer surplus associated with those trips. The empirical results provide an estimate of the willingness-to-pay by Washington state residents for hiking opportunities in the Cascade Mountain Range. These results are used to forecast total trips and willingness-to-pay over the next forty years. Copyright 1995 by MIT Press.

Estimating social welfare using count data models: an application to long-run recreation demand under conditions of endogenous stratification and truncation

SUMMARY This paper examines a class of maximum-likelihood regression estimators for count data from truncated samples. Estimators for the truncated Poisson and negative binomial distributions are illustrated. Simulation results are given to illustrate the magnitude of the bias that may result from the failure to account for overdispersion in truncated samples. An empirical application based upon the number of recreational fishing trips taken by a sample of Alaskan fishermen is provided. the number of bus trips taken per week and other variables which might be related to that behaviour, such as attitudinal and demographic variables. Given these data we seek to construct a model of the number of weekly bus trips taken as a function of various exogenous variables, some of which are under the control of the public transit authority. Due to the choice-based sampling scheme employed, no observations are made of individuals making zero bus trips, since a criterion for sample inclusion is that at least one bus trip be made. The dependent variable in our model, the number of bus trips taken that week, is truncated at zero, taking on only positive values. More generally, two common types of sampling schemes are likely to give rise to samples of truncated counts: surveys which ask 'participants' about the number of 'participation occasions' and samples drawn from administrative records where inclusion in such a database is predicated on having engaged in the activity of interest. Examples of the first type include on-site sampling plans, surveys of owners of a particular home appliance (e.g. from warranty

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J. T. Grogger

Papers

Models for truncated counts