Anim. Behav., 1998, 55, 241–244 Confounded correlations: a reply to Lifjeld et al. and Wagner et al. BART KEMPENAERS* & BEN C. SHELDON² *Konrad Lorenz Institute for Comparative Ethology, Vienna ² Department of Z oology, Uppsala University ( R eceived 13 June 1997; initial acceptance 4 A ugust 1997; final acceptance 4 September 1997; M S. number: -1111) Both Lifjeld et al. (1998) and Wagner et al. (1998) feel that we have been unduly harsh in our whole- sale rejection of studies that report the correlation between paternity and paternal care as a test of optimality models of paternal investment in the face of variation in paternity (Kempenaers & Sheldon 1997). Wagner et al. suggest that negative results (here meaning the absence of a correlation) may reveal something useful, and argue that this is particularly the case with their study of purple martins, Progne subis (Wagner et al. 1996). Lifjeld et al. also make some further suggestions about experimental approaches to this problem. We deal with some of the latter points later, but first, are we in danger of throwing the baby out with the bath water in our rejection of correlational studies? As we tried to make clear in our original commentary (Kempenaers & Sheldon 1997)a particular problem with paternal care is that there are so many potentially confounding variables (e.g. see Clutton-Brock 1991) that could mask any relationship between paternity and paternal care, or even generate a relationship when no causal relationship exists. Many of the potentially con- founding factors we discussed (e.g. differential investment by females in response to mate attrac- tiveness, the dependence of one pair member’s level of care on that of the other) have a solid base in empirical studies of bird populations (Wright & Cuthill 1990; de Lope & Møller 1993; Petrie & Williams 1993), and as far as is known may occur commonly. We could have constructed yet other examples where paternity–paternal care correla- tions arose from the influence of other variables, but felt that we had made the point extensively enough in our original commentary. Thus, far from there being a ‘possibility of the relationships being confounded’, we believe that a conscientious researcher should start by assuming the worst (i.e. that the relationships are very probably con- founded), and attempt to remove the influence of confounding variables. This cannot be done by correlational studies. Lifjeld et al. suggest that the publication of correlational studies of the kind that we criticize is valuable because it allows evaluation of the role of confounding variables. However, they offer no suggestions as to how this might be accomplished, and in the majority of studies published so far there is little attempt to do so. A notable exception is the study by Yezerinac et al. (1996) which takes the sensible alternative approach of asking whether the biology of their species is such that a reduction in paternal effort in response to lower certainty of paternity would be expected. Thus, although Lifjeld et al. state that ‘a further increase in the number of studies showing no relationship will weaken the arguments about confounding factors and strengthen the idea that the two variables are generally not causally re- lated’, we do not agree. In our view, these studies provide no useful information about causality, and we would hold this view whether the next 50 studies in this area produce positive, negative or any mixture of relationships. However, our com- mentary should not be taken as an attack on correlational studies in general, as Lifjeld et al. suggest. It was specifically addressed at one par- ticular area. Lifjeld et al. also state that we imply that the significance of correlation coefficients is what matters, and themselves imply that we are suggesting that only the studies reporting non- significant correlations should be ignored. On the other hand, Wagner et al. suggest that our criti- cisms ‘largely pertain to studies in which a positive relationship was found’. Both are mistaken; our entire argument was that any correlation is Correspondence: B. C. Sheldon, Department of Zoology, Uppsala University, Villava ¨gen 9, S-752 36 Uppsala, Sweden (email: ben.sheldon@zoologi.uu.se). B. Kempenaers is at KLIVV, Savoyenstrasse 1a, A-1160 Vienna, Austria. 0003–3472/98/010241+ 04 $25.00/0/ar970607  1998 The Association for the Study of Animal Behaviour 241