# 20 Questions on Adaptive Dynamics

Adaptive dynamics is a tool used of studying phenotypic changes in evolving populations over time^{1}. Adaptive dynamics approach is different from population genetic Fisher’s model^{2}. Fisher’s population under natural selection will additively increase its population fitness, where as an adaptive dynamics population of unfit individuals are replace by fitter ones but the average individual reproduces just enough to replace itself, the population maintains a mean fitness unity^{2,3}. Adaptive dynamics assumes that organisms are asexual and initially are monomorphic, where mutations are rare and have little effect on the population’s phenotypic value^{1}. Fitness functions are the ability of a mutant to invade the resident population, invasive fitness. The invasive fitness can be visually shown as an invasion fitness landscape or a slice of the landscape, a pairwise invasibility plot (PIP). Highlighted by Kirkpatrick and Rousset since Wright introduced the metaphor of adaptive landscapes and PIP’s have been use in adaptive dynamics, these visual tools have sometimes taken priority over equations and assumptions^{4-6}.

In the review by Waxmen and Gavrilets they examine the basic adaptive dynamics questions, assumptions and problems. As Waxmen and Gavrilets are population geneticists, they intentionally reduced the level of maths which was extremely useful, as it makes the topic more digestible to non-mathematicians.

The adaptive dynamics assumptions that are workable under are that populations are large, mutations are at a low rate, and mutant types can occur and change the composition of the population^{8}. The new successful mutant becomes resident, returning to an equilibrium state^{8}.

The strengths of adaptive dynamics are that it has shown that, in some ecological interactions, evolution occurs through a sequence of fixation of mutations where genetic variation is maintained^{1}. Therefore polymorphism can be maintained providing more general conditions compared to the restrictive limitations of standard population genetic approaches^{1}. Adaptive dynamics also can have intermediate genotypes included^{1}. The evolution of assortative mating has been examined with adaptive dynamics showing that successful invasions of mutants can establish branching in alleles associated with mating^{9-10}. Waxmen and Gavrilets highlighted that adaptive dynamics has been used to examine the plausibility of sympatric speciation due to the maintenance of genetic variation under strong disruptive selection^{1}.

Adaptive dynamics like the use of any modelling scenario needs to be strip down to the essential parts but with assumptions, there are violations. Barton and Polechova discussed the limitation of adaptive dynamics highlighting that populations should be strictly asexual (or sex with only a single type) and populations should exist around discrete phenotypes^{11}. They also exclaimed that adaptive dynamics doesn’t actually model evolution under mutation and selection^{11}. The first assumption WG discussed is smooth fitness functions of mutant frequencies which isn’t justified in nature^{1}. Mutations are assumed to exist in a continuum and never happened before but the most likely assumption to be violated, by natural systems, is that differences between the mutant and resident population are small, suggesting that polymorphism can’t be maintained. Waxmen and Gavrilets posed that the question that can’t be answered, “How small must the effect of a mutation to be, for adaptive dynamics results to accurately apply?”^{1}.

Genetic drift is not treated in adaptive dynamics, the fate of rare mutations in large population are assumed to be beneficial. But when included in fisher model, significant mutations had intermediate sized effects^{1,2}. Further research to investigate genetic drift’s effect is needed^{1}. Adaptive dynamics in most work assumes an asexual population of individuals but a large proportion of species mate sexually, so aren’t applicable to be examined by adaptive dynamics. The only exception is the one locus model where the one locus, multi-allele diploid population is mathematically same as the asexual haploid population^{1}.

Kokko highlighted the fact when researchers apply their favourite models; they ignored and dismissed alternative approaches^{3}. WG highlighted that to improve adaptive dynamics understanding they suggest the future acknowledgement of recent relevant work of alternative approaches, old concepts and clear understanding of the simplifications and assumptions by practitioners is essential for development of adaptive dynamics ^{1,3}. Further research should test empirical data and compare results with predictions of adaptive dynamics ^{1}.Work still needs to be done by modellers to apply testable prediction to evolutionary understanding.

Metz describes adaptive dynamics as a “simple, understandable, robust and beautiful”^{3}way of using a mathematical framework for examining natural problems by simplifying by a set of assumptions^{7}. WG and others express how useful, influential and significant from the theoretical point of view adaptive dynamics can be but with simplicity of the approach is a cost^{1,8}.

References

- Waxman, D. & Gavrilets, S. 2005. 20 Questions on adaptive dynamics. J. Evol. Biol. 18:1139–1154.
- Fisher, R.A., 1930. The Genetical Theory of Natural Selection. Oxford University Press, Oxford.
- Kokko, H., 2005. Useful ways of being wrong. J. Evol. Biol. 18: 1155-1157.
- Kirkpatrick M. & Rousset F., 2005. Wright meets AD: not all landscapes are adaptive, J. Evol. Biol. 18: 1166-1169.
- Wright, S. 1932. The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Proceedings of the Sixth International Congress on Genetics (Jones, ed.), Austin, TX, Vol. 1, pp. 356–366.
- Wright, S. 1988. Surfaces of selective value revisited. Am. Nat. 131: 115–123
*.* - Metz J. A. J., 2005. Eight personal rules for doing science, J. Evol. Biol. 18: 1178-1181
- van Dooren T. J. M., 2005.The future of a mutation-limited tool-box. J. Evol. Biol. 18: 1158-1161.
- van Doorn, G.S., Luttikhuizen, P.C. & Weissing, F.J. 2001. Sexual selection at the protein level drives the extraordinary divergence of sex-related genes during sympatric speciation. Proc. R. Soc. Lond. B 268: 2155–2161.
- Gavrilets, S. & Waxman, D. 2002. Sympatric speciation by sexual conflict. Proc. Natl Acad. Sci. USA 99: 10533–10538
- Barton N. H. & Polechová J., 2005. The limitations of adaptive dynamics as a model of evolution, J. Evol. Biol. 18: 1186-1190.