Brodziak et al. 195 We offer this rejoinder to Gilbert’s (2002) discussion of our analyses of stock–recruitment data for several New England groundfish stocks (Brodziak et al. 2001). The first point that Gilbert makes—that our choice of prior probabilities affects the calculated posterior probabilities—is of course true of all Bayesian analyses. The prior odds ratio of a density-dependent stock–recruitment model being true over the range of observed data was assumed to be 2.0 in Brodziak et al. (2001) because this value was consistent with our beliefs in the relative credibility of the six stock– recruitment models examined. Based on the results of Myers and Barrowman (1996), an empirical Bayesian analysis could make an alternative argument that the prior odds ratio used by Brodziak et al. (2001) for density-independent stock–recruitment models was too ecologically optimistic. Regardless, we must point out that for 7 of the 11 stocks examined, the posterior odds ratio of a density-dependent stock–recruitment model being true over the range of observed data either increased to above 2.0 or decreased slightly to 1.78 (see table 1 of Gilbert 2002). This fact indicates that our assumed prior odds ratio was consistent with the observed data and also shows that for these stock– recruitment data, density dependence was more likely than density independence in the majority of stocks. Nonetheless, we concur with Gilbert’s implicit point that a key step in applying Bayesian analyses to natural resource management issues is selecting public policy priors. Furthermore, we submit that if Gilbert’s (1997) “recruitment-states hypothesis” is to be a credible prior belief for a specific system during a specific time period, then data and mechanisms should be presented to conclude that physical oceanographic change implies a change in fish stock dynamics (e.g., Baumann 1998). Unfortunately, Gilbert (2002) offers neither in his discussion. The second point that Gilbert (2002) makes is that the frequentist odds ratio analyses of Brodziak et al. (2001) are invalid because they do not account for the possibility that Gilbert’s recruitment-states hypothesis (or other unspecified mechanisms) could be true for the time period and system examined. This is a seemingly persuasive argument, because if the odds ratio analyses are valid, then any mediumor longer-term changes, such as a regime shift in oceanic conditions, could not have occurred under the implicit assumption that groundfish recruitment strength changes substantially from one average state to another following such a shift. Simply denying that the odds ratio analyses are valid without providing evidence of such a regime shift is a fallacy, however. If changes had occurred in the continental shelf waters off New England during the time period of our investigation, we would expect that important environmental forcing processes, such as water temperature, would have changed substantially in an obvious directional manner. Instead, water temperature anomalies for this region exhibit short-term variation on the order of a few years but do not show interdecadal time trends (Fig. 1). Furthermore, longerterm forcing variables, such as the North Atlantic Oscillation (NAO), appear to have had a limited influence on the dynamics of fish populations within the northeast United States continental shelf ecosystem in comparison to fishing activities (Link et al. 2001). Although oceanographic conditions can substantially affect recruitment of New England groundfish in any given year (see, for example, Polacheck et al. 1992), there is no conclusive evidence of any medium-term change or a sustained regime shift in the continental shelf waters off New England that would support the recruitmentstates hypothesis during the time period of our investigation. Thus, Gilbert’s rejection of our frequentist odds ratio results is not valid. We conclude by noting that our assumption that recruitment is constant over the range of observed stock sizes is not equiva-
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Mar 1, 2006
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