848 Transactions of the American Fisheries Society 130:848–856, 2001  Copyright by the American Fisheries Society 2001 A Simple Test for Nonmixing in Multiyear Tagging Studies: Application to Striped Bass Tagged in the Rappahannock River, Virginia ROBERT J. LATOUR,* JOHN M. HOENIG, AND JOHN E. OLNEY Department of Fisheries Science, Virginia Institute of Marine Science, College of William and Mary, Gloucester Point, Virginia 23062, USA KENNETH H. POLLOCK Biomathematics Graduate Program, Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, USA Abstract.—The Brownie-type models for multiyear tagging studies allow the estimation of age- specific and year-specific total survival. An important assumption of these models is that the tagged cohorts are thoroughly mixed, or more specifically, that they have identical spatial distributions. We propose a chi-square test to assess the validity of this assumption and apply the method to striped bass tagging data from the Rappahannock River, Virginia. The current protocol for esti- mating striped bass survival involves fitting a suite of Brownie-type models to tag recovery data. Because moderate levels of nonmixing can induce significant bias, we examined tagging data for two size ranges of fish to determine if the well-mixed assumption was violated. We suggest that examining spatial patterns of recaptures should be a routine part of analyzing tagging data from multiyear studies. For the striped bass data, the analysis showed little evidence of assumption violation, but in some cases the power of the test was probably low because the number of recaptures was small. Brownie et al. (1985) developed a series of sim- ple multiyear tagging models to estimate age- specific and year-specific survival and tag recov- ery rates. These models generalize early work by Seber (1970) and Youngs and Robson (1975) and have been applied frequently to wildlife banding studies. Recent extensions and modifications of the Brownie models have rendered this class of models more applicable to fisheries tagging studies. Pol- lock et al. (1991) and Hoenig et al. (1998a) showed that tag recovery rates may be converted to fishing exploitation rates when information on tag reten- tion, tag-induced mortality, and tag reporting rate is available. Instantaneous rates of fishing and nat- ural mortality may be determined if additional in- formation on the seasonal distribution of fishing intensity is known at least approximately (Ricker 1975). Brownie-type models are extremely useful. An important and fundamental, but often overlooked, assumption of these models is that the cohorts of tagged animals are thoroughly mixed. Hoenig et al. (1998b) demonstrated that modest amounts of nonmixing between previously and newly tagged animals could cause serious bias and that, when * Corresponding author: latour@vims.edu Received May 24, 2000; accepted March 14, 2001 nonmixing is present, tagging data should be an- alyzed using models that explicitly account for nonmixing. Hoenig et al. (1998b) also suggested use of a likelihood ratio test of nonmixing, but this test requires comparing the fit of both a mixed and nonmixed model and is specific to only one class of models (i.e., those models presented by Hoenig et al. 1998a, 1988b). Also, the likelihood ratio test does not make use of any additional information that may be available by knowing the recapture locations. Here, we propose a new and general chi-square test of nonmixing that can be performed before fitting a Brownie-type tagging model. The test is based on the principle that mixing of tagged co- horts implies that the cohorts have the same spatial distribution. The procedure consists of creating a spatial grid for the recaptures and comparing the distribution of tag recoveries from the cohorts over space. For illustrative purposes, the chi-square test is applied to data from a hypothetical tagging study and is subsequently followed by an application of the test to newly and previously tagged striped bass Morone saxatilis in the Rappahannock River, Virginia. Development of the Method The chi-square test we propose can be derived by generalizing the Brownie et al. (1985) multi-