Optimality Models and the Propensity Interpretation of Fitness


The propensity account of fitness intends to solve the classical tautologicity issue by identifying fitness with a disposition, the ability to survive and reproduce. As proponents recognized early on, this account requires operational independence from actual reproductive success to avoid circularity and vacuousness charges. They suggested that operational independence is achieved by measuring fitness values through optimality models. Our goal in this article is to develop this suggestion. We show that one plausible procedure by which these independent operationalizations could be thought to take place, and which is in accordance with what is said in the optimality literature, is unsound. We provide two independent lines of reasoning to show this. We then provide a sketch of a more adequate account of the role of optimality models in evolutionary contexts and draw some consequences.

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Fig. 1

(Taken from Holling (1964) and modified)

Fig. 2
Fig. 3

(Taken from Holling (1964))

Fig. 4


  1. 1.

    This is only a schematic presentation of the PNS. The “tend to” here only means that fitter organisms do not always actually have a greater reproductive success than less fit organisms. This can be made more precise in different ways. For example, the “tend to” may be interpreted probabilistically, as a ceteris paribus clause, etc. There are more specific versions of the PNS in the literature (see Rosenberg and Bouchard 2015). Since the way in which one spells this out precisely is not directly relevant to our point, we stick to this more general presentation.

  2. 2.

    For more precisions on this, see Sect. 2, where we give a more complete characterization of the PIF.

  3. 3.

    We do not claim, however, that nothing has been written on the topic, but only that existing proposals (e.g. Maynard Smith 1978; Parker and Maynard Smith 1990; see below for more references) are not sufficiently precise or well-developed to constitute a complete account, specifically for cases where the currency of the model is a proxy for fitness. See below for more on this.

  4. 4.

    Standard (both classical and contemporary) presentations of the PIF assume that fitness is a property of individuals. This idea has been criticized, e.g. in Sober (2013), who takes fitness to be a property of traits (he actually reaches similar conclusions to ours regarding quantitative predictions from optimality models, although parting from different starting points, and not developing them to the extent that we do, see Sober 2013, p. 338). Since our goal is to make an internal critique to this standard version of the PIF, we follow their own presentation.

  5. 5.

    The same point applies to inferences from similar cases, which need not necessarily be past states of the same population.

  6. 6.

    We thank an anonymous reviewer for bringing this possible response to our attention.

  7. 7.

    Note that, even though Beatty takes this position, proponents of the PIF do not need to claim that, in general, optimality models contain a proxy for fitness as currency. All they need to claim is that fitness values are measurable through optimality models in at least some cases (not necessarily all of them).

  8. 8.

    We should also note that we are assuming (for the sake of simplicity and consistency) that we are in a situation like that described by Holling, where the only relevant prey variable is size. There are other, more complex models in the optimal foraging theory literature (for instance, Schoener 1974) that incorporate more variables. For instance, in Schoener’s model, larger prey may be less abundant and more difficult to catch, and thus a predator could prefer smaller prey (even if it is mechanically possible for it to catch the larger prey).

  9. 9.

    In fact, Parker and Maynard Smith show that, in some special cases, when the correlation between functions is not linear (see what follows below) the optimum value and the fittest value may not coincide. For simplicity, we will leave this problem aside. We will show that even if one makes this assumption, there are still problems in thinking that currency values can be directly used to measure fitness values.

  10. 10.

    One might reply here that, although quantitative fitness differences cannot be established, a qualitative ordering or ranking can be. This point will be addressed in the next section.

  11. 11.

    We are utilizing a very basic textbook population genetic model, in which fitness is interpreted as the probability of survival to adulthood. For our criticism to be more accurate, we should associate each diet with a probability distribution of leaving n offspring, and then some mathematical way of converting each distribution into a scalar. The first option was chosen for the sake of simplicity and clarity.

  12. 12.

    For a similar conclusion regarding OFT, although argued from different premises, the reader may see Bolduc and Cézilly (2012, pp. 860–861).

  13. 13.

    That the currency is a good proxy for fitness could perhaps be inferred from similar cases, not necessarily from the same population, or even the same species. However, as stated in footnote 5, we would still need to have measured the fitnesses in that other population or species beforehand. Thus, we would not have a measurement of fitness that is independent of actual reproductive success.

  14. 14.

    Notice that we are not claiming here that the PIF advocates are mistaken because the PNS is not a priori or analytical. What we did show in the previous sections is that their own claim that fitness has to be determinable independently from fitness, through the use of optimality models, should lead them to reject the idea that evolutionary theory is nothing more than applied probability (because, as we showed, if this inference can be made, then it is much more indirect than thought and presupposes more than pure probability and the direct inference principle).


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This work has been funded by the research projects PUNQ 1401/15 and SAI 827-223/19 (National University of Quilmes, Argentina), UNTREF 32/15 255 (Universidad Nacional Tres de Febrero, Argentina) and UBACyT 20020170200106BA (Universidad de Buenos Aires, Argentina).

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Roffé, A.J., Ginnobili, S. Optimality Models and the Propensity Interpretation of Fitness. Acta Biotheor 68, 367–385 (2020). https://doi.org/10.1007/s10441-019-09369-5

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  • Fitness
  • Natural selection
  • Optimality models
  • Propensity interpretation of fitness
  • Population genetics
  • Optimal foraging theory