J. Math. Biol. (2010) 61:165–169 DOI 10.1007/s00285-009-0300-9 Mathematical Biology PERSPECTIVES IN MATHEMATICAL BIOLOGY Adaptive dynamics: a framework to model evolution in the ecological theatre Éva Kisdi · Stefan A. H. Geritz Published online: 24 September 2009 © Springer-Verlag 2009 The astonishing diversity of life has evolved over many millions of years of natural selection. Yet natural selection, as often taught in introductory courses and textbooks on population genetics, seems to explain why diversity should not exist: the survival of the fittest is the loss of everything else. Simple models of natural selection predict the fixation of the best allele in every locus. 1 Yet the Earth (or any part of it) is not ruled by a single Darwinian monster. Frequency-dependent selection (the advantage of an allele being rare, regardless of which allele it is) solves the problem of diversity, but then solves it all too well: by choosing the frequency-dependent fitness function appropriately, the model can produce any conceivable result and, hence, lacks predictive power. 2 In between the survival of the fittest and the survival of anybody, the problem of adaptive diversity slips away. The solution to this paradox of classical population genetics is in the Ecology text- books. Fitness describing survival and reproduction must be derived from realistic ecological interactions, 3 which explain how different genotypes or species coexist. 1 Save heterozygote superiority, which explains only within-species variation, is likely to be transient in long-term evolution, and is rare in fact. 2 We used somewhat extreme words for clarity, but this extreme view is maintained in recent textbooks of population genetics (Hartl and Clark 2007, p. 230; Ewens 2004, p. 54). 3 This point was also emphasised by the article of Lambert (2009) in this series of Perspectives in Mathe- matical Biology. Contributed by the European Society for Mathematical and Theoretical Biology. É. Kisdi (B ) · S. A. H. Geritz Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland e-mail: eva.kisdi@helsinki.fi S. A. H. Geritz e-mail: stefan.geritz@helsinki.fi 123