## General comments

It has been plainly stated that Adaptive Dynamics is ‘not a scientific theory, but a mathematical framework’ (Metz, 2005); it is a ‘method but not a model’ (Kisdi & Gyllenberg, 2005). From a completely pragmatic point of view, there is, then, only one question that evolutionary biologists need to ask: Is Adaptive Dynamics a useful way of approaching problems? The 14 Commentaries present a variety of different views, indicating that there is no consensus in the answer to this question. Indeed, we view the previous pages, consisting of the Target Review and the 14 Commentaries, as a part of a much larger public discussion on Adaptive Dynamics, and we thank the other authors for their contributions to the discussion.

We feel it necessary to acknowledge that the wording of our comment in Question 6 of our Target Review (Waxman & Gavrilets, 2005) concerning ‘hidden limitations and unconscious or implicit assumptions’ was not optimal. It was not our intention to imply that limitations and assumptions of Adaptive Dynamics are hidden or unconsciously made by practitioners of Adaptive Dynamics. Rather, the statement was intended for biologists who use Adaptive Dynamics, or who wish to understand the biological implications of its mathematical results, and may not be aware of the underlying limitations and assumptions. These limitations and assumptions are not, in our opinion, sufficiently emphasised in the literature and, equally importantly, the consequences of their violation are not made clear. The Commentary of Geritz & Gyllenberg (2005) makes it admirably clear what these limitations are but not the consequences of their violation. The Commentaries of Abrams (2005), Barton & Polechová (2005), Kokko (2005), Spencer & Feldman (2005), Butlin & Tregenza (2005), and Van Dooren (2005) provide additional discussion of the issue.

We also feel it necessary to clarify our wording about the treatment of genetic drift in Adaptive Dynamics. In the second paragraph of Question 4.3, we said an implicit assumption of Adaptive Dynamics is that all beneficial mutations will always initially increase in frequency. However in the first paragraph, we noted that in the work of Dieckmann & Law (1996), fixation of new alleles occurs at a rate proportional to the probability of fixation of a mutant. Since the probability of fixation of all mutants is not unity, the two paragraphs are clearly inconsistent. Our reading of the Adaptive Dynamics literature, however, leads us to believe that it is *common* to make the assumption that beneficial mutations always initially increase in frequency (see Meszéna, 2005). We are also of the opinion that the treatment of genetic drift, when included in Adaptive Dynamics, has not been particularly realistic. As an example, the probability of invasion of a deleterious mutation is invariably taken as zero in Adaptive Dynamics (Geritz & Gyllenberg, 2005; Meszéna, 2005). However, if a mutation is deleterious, but only very slightly so, and the population is finite, then such near neutral mutants can invade and become fixed in the population (Kimura, 1957).

At the end of our Review, we stated our earnest and legitimate wish to see more details of numerical simulations, but this was somehow interpreted, in some Commentaries, as an attempt to denigrate Adaptive Dynamics, because of the lack of analytical results, or to attach specific significance to simulations in Adaptive Dynamics. This was not our intention.

Although we appreciate all of the Commentaries made, we will not answer them directly. Rather we discuss three controversial points raised in more than one Commentary. A separate response is, however, also necessary for a number of peripheral points raised by Dieckmann & Doebeli (2005). Our response to these points is contained in Appendix B.