Abstract
The most consistent definition of fitness makes it a static property of organisms. However, this is not how fitness is used in many evolutionary models. In those models, fitness is permitted to vary with an organism’s circumstances. According to this second conception, fitness is dynamic. There is consequently tension between these two conceptions of fitness. One recently proposed solution suggests resorting to conditional properties. We argue, however, that this solution is unsatisfactory. Using a very simple model, we show that it can lead to incompatible fitness values and indecision about whether selection actually occurs.
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Notes
See Beatty and Finsen (1989) for more about the so-called “operationalist fallacy.”
For details, see Equation 4 on p.862 of Pence and Ramsey (2013).
Op. 860-861 of Pence and Ramsey (2013). What follows draws very heavily on Pence and Ramsey’s wording.
The adjective “God’s-eye-view” is not intended as pejorative. It is illustrative rather than evaluative. There is nothing philosophically untoward about attempting to establish metaphysical foundations for evolutionary theorizing.
Although studies involving trait types feature prominently, it is worth remembering that this contingent fact is a matter of “occupational necessity” designed to prevent the conflation of individual fitness (as a propensity or propensity-like property) with realized individual fitness. It can be argued that biologists aim to determine the fitness of token organisms, which can only be approximated by way of indirect inferences that rely on selectively relevant trait types. On this point, compare Sober (2013) and Pence and Ramsey (2015).
It is worth noting that models for the evolution of altruism rely on a form of frequency-dependent selection.
Pence and Ramsey are clearly aware of the difficulties raised in this section. They explicitly state, “Our Equation (4) is the density-independent, non-chaotic limit of this more sophisticated work [in adaptive dynamics]” (2013, p.863).
Astute readers will recognize that this is a slightly modified version of Abrams’s (2009a) example involving carotenoids.
See Brandon (pp.60-64, 1990) for details about, what he calls, the “selective environment.”
Epistasis occurs when alleles at two or more genetic loci interact non-additively to determine the phenotype.
Pleiotropy occurs when one genetic locus affects more than one phenotypic trait, which causes a genetic correlation.
In other words, the fitness distributions for the character states are identical.
This local interpretation or “fine-grained partitioning” is equivalent to situation in which there is a metapopulation consisting of two subpopulations of equal size and there is no migration or mutation.
We do not mean to imply that Abrams is oblivious to this problem. See, especially, Abrams (2009b) for a suggested resolution to, what he calls, “the problem of the reference environment.”
Op.20 (Abrams, 2014): “What matters to natural selection is not this or that organism’s particular circumstances and particular fate, but the sorts of conditions that individuals in the population are likely to encounter repeatedly.”
It also threatens to blur the distinction between drift and natural selection, an outcome that runs counter to the intuitions of most biologists and philosophers (Brandon, 2005). If your mathematical expectations differ substantially, then so, too, will your views about which outcomes are due to selection (i.e., are adaptions) and drift (i.e., departure from expectation).
“Second scenario: Imagine a single environment in which sand color varies in patches whose average diameter is about a meter. The random assignment of pigeons to a background sand color is then determined by where pigeons happen to land. In either case, we suppose that the pigeons are not selective about sand color” (Abrams, 2013, p.295-296).
“I argue for the stronger claim that it’s plausible that: [1] Different descriptions of a biological population sometimes pick out distinct effects, and [2] There are distinct causes producing these effects. This is a claim about causation rather than explanation. Causal relations exist independently of how the population is characterized, though our way of describing the population can, indeed, focus on one or another of these causal relations” (Abrams, 2013, p.295). Later in the same paper, he claims that: “My view implies that a researcher’s description is able to pick out different causal relationships, but allows that these causal relationships exist, realized by some the of same parts of the world, independent of the choice of causal relationships on which to focus” (p. 300).
In an earlier paper, Abrams says the following: “Rather than an organism’s fitness literally changing when an effect C occurs, there is instead a relationship between conditional probabilities: a type’s fitness conditional on the occurrence of C is different from its fitness conditional on C’s non-occurrence” (2009a, p.493).
On this point, Abrams (2013, p.296, emphasis added) says the following: “It should be clear, though, that if what we are concerned with is the evolution of the pigeon population over several generations […] then any relevant sense of fitness and selection must take into account probabilities of pigeons being found on light or dark sand when hawks are overhead.”
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Peter Takacs’s research was supported under Australian Research Council's Discovery Projects funding scheme (project number FL170100160).
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Appendix
Appendix
Statistical measures (e.g., relative fitness inequalities) in Table 1 are based on the following data
Individuals by Trait Type | Number of Offspring | Statistics | |||
|---|---|---|---|---|---|
Local Partition E1 | Global Partition (Union of E1 and ~ E1) | ||||
A | 11 | Arithmetic Mean for A in E1 | 10 | ||
A | 9 | ||||
A | 10 | ||||
A | 9 | Arithmetic Mean for B in E1 | 6 | ||
A | 11 | Variance for A in E1 | 0.8 | ||
B | 7 | Variance for B in E1 | 0.8 | ||
B | 5 | Geometric Mean for A in E1 | 9.96 | ||
B | 6 | Geometric Mean for B in E1 | 5.93 | Arithmetic Mean for A | 8 |
B | 5 | Arithmetic Mean for B | 8 | ||
B | 7 | Variance for A | 4.8 | ||
Local Partition ~ E1 | Variance for B | 4.8 | |||
A | 7 | Arithmetic Mean for A in ~E1 | 6 | Geometric Mean for A | 7.69 |
A | 5 | Geometric Mean for B | 7.69 | ||
A | 6 | ||||
A | 5 | Arithmetic Mean for B in ~E1 | 10 | ||
A | 7 | Variance for A in ~E1 | 0.8 | ||
B | 11 | Variance for B in ~E1 | 0.8 | ||
B | 9 | Geometric Mean for A in ~E1 | 5.93 | ||
B | 10 | Geometric Mean for B in ~E1 | 9.96 | ||
B | 9 | ||||
B | 11 | ||||
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Takacs, P., Bourrat, P. Fitness: static or dynamic?. Euro Jnl Phil Sci 11, 112 (2021). https://doi.org/10.1007/s13194-021-00430-0
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DOI: https://doi.org/10.1007/s13194-021-00430-0