Abstract
Two questions are raised for Grafen’s formal darwinism project of aligning evolutionary dynamics under natural selection with the optimization of phenotypes for individuals of a population. The first question concerns mean fitness maximization during frequency-dependent selection; in such selection regimes, not only is mean fitness typically not maximized but it is implausible that any parameter closely related to fitness is being maximized. The second question concerns whether natural selection on inclusive fitness differences can be regarded as individual selection or whether it leads to a departure from the central motivation that led to the formal darwinism project, viz., to show that “Darwinian” evolution through individual selection leads to “good design” or phenotypic adaptation through trait optimization.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
This means that, formally, the problem is one of constrained optimization.
Grafen seems to accept this requirement insofar as he notes that conditionals can be “trivially” and, thus, irrelevantly satisfied if the antecedent is false (“Inclusive fitness)” section. In his discussion of problematic cases, he makes it clear that at least one of his four “links” must hold non-trivially.
In fact, this is why I take it that the formal darwinism project accepts the accessibility condition of the last paragraph.
For instance: frequency-dependence can maintain polymorphism in a population indefinitely (this insight goes back to a pioneering paper by Haldane and Jayakar 1963); an infinite number of alternative frequency-dependent fitness sets give rise to the same allele trajectory (Lachmann-Tarkhanov and Sarkar 1994), etc. Some of the many dynamical complexities that may arise from frequency-dependent selection are mentioned later in the text.
In particular, especially if—contrary to the models discussed in these remarks—the dynamical evolution is probabilistic, it would probably be universally acceptable if all that is excluded is a set of initial states that has measure 0.
For an introduction to these issues, see the work of Okasha (e.g., 2006). What is relevant is whether different types of group selection can be coherently distinguished. There is another interesting issue here: suppose that groups are defined in such a way that the criteria intended to distinguish them entirely exclude relatedness. Then, such group selection cannot make any evolutionary difference because of absent heritability—I owe this point to Mark Kirkpatrick in conversation.
There does not seem to be a systematic analysis of this question in the literature.
A more restricted definition (that of Sarkar 2008) which would also disallow frequency-dependence would prevent all frequency-dependent selection from being individual selection. In this case, the arguments of “Frequency-dependent selection” section questioning the formal darwinism project would become irrelevant. Though this would seem to be an argument in favor of the formal darwinism project, it would be a somewhat pyrrhic victory. The scope of the project would become restricted to uninteresting situations in which individuals within a populations are precluded from all direct interaction.
I am presuming that any definition of inclusive fitness will invoke r. (I am not aware of exceptions.) However, using the fitnesses of other individuals in a definition is sufficient for the present purpose.
Indeed, this is the consensus view about Darwin. However, it is also correct that Darwin invoked group selection to account for altruism. But, presumably because Grafen views inclusive fitness as an individual property, and accepts that kin selection explains altruism, Darwin’s apparent departure from individual selection is not supposed to constitute a problem for the formal darwinism project.
From a purely formal point of view, this process can obviously be recast as an optimization problem. Simply define a function that has value 1 if the phenotype reaches the satisficing level, and 0 otherwise and let the problem be to maximize this function. The point is that such a formal move hardly coheres with the idea of good design in any strong sense.
References
Altenberg L (1991) Chaos from linear frequency-dependent selection. Am Nat 138:51–68
Behera N (1996) Variational principles in evolution. Bull Math Biol 58(1):175–202
Charlesworth B, Charlesworth D (2010) Elements of evolutionary genetics. Roberts & Co., Greenwood Village, CO
Ewens WJ (2004) Mathematical population genetics: I. Theoretical introduction, 2nd edn. Springer, Berlin
Fisher RA (1930) The genetical theory of natural selection. Clarendon Press, Oxford
Garson J, Wang L, Sarkar S (2003) How development may direct evolution. Biol Philos 18(2):353–370
Grafen A (2007) The formal Darwinism project: a mid-term report. J Evol Biol 20(4):1243–1254
Hagedoorn AL, Hagedoorn-Vorstheuvella Brand AC (1921) The relative value of the processes causing evolution. Martinus–Nijhoff, Hague
Haldane JBS, Jayakar SD (1963) Polymorphism due to selection depending on the composition of a population. J Genet 58(3):318–323
Koonin EV (2012) The logic of chance: the nature and origin of biological evolution. Pearson Education, Upper Saddle River, NJ
Lachmann-Tarkhanov M, Sarkar S (1994) The alternative fitness sets which preserve allele trajectories: a general treatment. Genetics 138(4):1323–1330
Lynch M (2007) The origins of genome architecture. Sinauer, Sunderland, MA
Matessi C, Schneider KA (2009) Optimization under frequency-dependent selection. Theor Popul Biol 76:1–12
Moran PAP (1964) On the non-existence of adaptive topographies. Ann Hum Genet 27:383–393
Ohta T (1996) Development of neutral and nearly neutral theories. Theor Popul Biol 49:128–142
Okasha S (2006) Evolution and the levels of selection. Oxford University Press, Oxford
Sarkar S (2005) Maynard Smith, optimization, and evolution. Biol Philos 20(5):951–966
Sarkar S (2007a) Doubting Darwin? Creationist designs on evolution. Blackwell Press, Oxford
Sarkar S (2007b) Haldane and the emergence of modern evolutionary theory. In: Matthen M, Stephens C (eds) Handbook of the philosophy of biology. Elsevier, New York, pp 49–86
Sarkar S (2008) A note on frequency-dependence and the levels/units of selection. Biol Philos 23:217–228
Schneider KA (2006) A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J Math Biol 52(4):483–523
Schneider KA (2008) Maximization principles for frequency-dependent selection i: the one-locus two-allele case. Theor Popul Biol 74(3):251–262
Schneider KA (2010) Maximization principles for frequency-dependent selection ii: the one-locus multiallele case. J Math Biol 61(1):95–132
Trotter MV, Spencer HG (2009) Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection. Theor Popul Biol 76(4):292–298
Wright S (1931) Evolution in Mendelian populations. Genetics 16:97–159
Wright S (1949) Adaptation and selection. In: Jepson GL, Simpson GG, Mayr E (eds) Genetics, paleonotoloy, and evolution. Princeton University Press, Princeton, NJ, pp 365–389
Acknowledgments
Thanks are due to Mark Kirkpatrick for discussions and Samir Okasha for critical comments on an earlier version of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sarkar, S. Formal Darwinism. Biol Philos 29, 249–257 (2014). https://doi.org/10.1007/s10539-013-9416-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10539-013-9416-9