A reply to Lombardi & Hurlbert

Alas, our study of bluegill cognition (Dugatkin & Wilson 1992) has become the latest exemplar of pseudoreplication. In addition, the entire journal and editorial system has been implicated because our reply to a previous critique (Dugatkin & Wilson 1994; Lamprecht & Hofer 1994) survived the review process. In our reply to Lombardi & Hurlbert (1996), we will first re-analyse our data the way that they suggest and then comment briefly on some general issues concerning pseudoreplication. As with Lombardi & Hurlbert’s (1996) critique, the reader will need to consult the original paper to follow our reply. We re-analysed our data as recommended by Lombardi & Hurlbert (1996) (Table I). We cannot re-analyse the first comparison because we have misplaced our data on fish size. The original correlation was not significant, however, and therefore will remain so when the degrees of freedom are reduced. In general, the recommended analyses involve fewer degrees of freedom than our original analyses, resulting in higher P values. For two comparisons (3, 5), results that we reported as statistically significant become non-significant. Thus, solo fish may not take longer to capture their first prey than paired fish and there may be no relationship between feeding success and aggression, rather than a ‘significantly positive, but very weak’ relationship as we reported in our original paper. We did not ascribe much biological significance to either of these comparisons in any case. The most important results of our study were that (1) bluegill prefer to associate with partners that they foraged best in association with over the previous 7-week period (comparisons 6, 7, 8, 10), and (2) bluegill preferred familiar over unfamiliar partners (comparison 11). These results remain statistically significant even with the reduced degrees of freedom recommended by Lombardi & Hurlbert (1996). Thus, the statistical scrutiny that our study has received should not obscure the biological results: bluegill sunfish possess the cognitive abilities to employ strategic behaviour. Individuals can remember their feeding success with as many as five associates and use this information to prefer or avoid those associates in the future. In addition, bluegills prefer familiar to unfamiliar associates. These results are statistically significant according to our original analysis and the recommendations of Lamprecht & Hofer (1994) and Lombardi & Hurlbert (1996). In addition to disagreeing with our own analysis, Lombardi & Hurlbert (1996) also apparently disagree with the analysis suggested by Lamprecht & Hofer (1994). Their ‘proper procedure[s]’ for our original analysis and for Lamprecht & Hofer’s (1994) analysis differ from each other, making it difficult to know which to choose. We have elected to follow Lombardi & Hurlbert’s (1996) proper procedure for our original analysis (comparison 7). Now that we have followed Lombardi & Hurlbert’s (1996) advice, we would like to comment on some basic statistical issues. We certainly do not regard ourselves as authorities on these subjects and think that we have much to learn from people such as Lombardi and Hurlbert. Pseudoreplication is a pervasive problem and we are not trying to defend all aspects of our original analysis. Nevertheless, we feel that the problem of pseudoreplication is not as black and white as implied by Lombardi & Hurlbert’s (1996) critique of our study. We therefore pose the following basic questions. Correspondence: D. S. Wilson, Department of Biology, Binghamton University, State University of New York, Binghamton, NY 13902-6000, U.S.A. (email: dwilson@ bingsuns.cc.binghamton.edu). L. A. Dugatkin is at Department of Biology, University of Louisville, Louisville, KY 40292, U.S.A.