The central analogy here is that optimizing apes for inclusive genetic fitness (IGF) doesn’t make the resulting humans optimize mentally for IGF.
This analogy gets brought out a lot, but has anyone actually spelled it out explicitly? Because it’s not clear to me that it holds if you try to explicitly work out the argument.
In particular, I don’t quite understand what it would mean for evolution to optimize the species for fitness, given that fitness is defined as a measure of reproductive success within the species. A genotype has a high fitness, if it tends to increase in frequency relative to other genotypes in that species.
To be more precise, there is a measure of “absolute fitness” that refers to a specific genotype’s success from one generation to the next: if a genotype has 100 individuals in one generation and 80 individuals in the next generation, then it has an absolute fitness of 0.8. But AFAIK evolutionary biology generally focuses on relative fitness—on how well a genotype performs relative to others in the species. If genotype A has an absolute fitness of 1.2 and genotype B has an absolute fitness of 1.5, then genotype B will tend to become more common than A, even though both have fitness > 1.
Although absolute fitness is easy to think about, evolutionary geneticists almost always use a different summary statistic, relative fitness. The relative fitness of a genotype, symbolized w, equals its absolute fitness normalized in some way. In the most common normalization, the absolute fitness of each genotype is divided by the absolute fitness of the fittest genotype 11, such that the fittest genotype has a relative fitness of one. We can also define a selection coefficient, a measure of how much worse the A2 allele is than A1. Mathematically, w2 = 1−s. Just as before, we can calculate various statistics characterizing relative fitness. We can, for instance, find the mean relative fitness ( = pw1 + qw2), as well as the variance in relative fitness. [...]
It is the relative fitness of a genotype that almost always matters in evolutionary genetics. The reason is simple. Natural selection is a differential process: there are winners and losers. It is, therefore, the difference in fitness that typically matters.
Going with our previous example, genotype A would have a fitness of 0.8 and genotype B would have a fitness of 1.
The most natural interpretation of the “fitness of the species” would be as the mean relative fitness of the species:
In late 1960s and early 1970s, Alan Robertson 24 and George Price 25 independently showed that the amount by which any trait, X, changes from one generation to the next is given by the genetic covariance between the trait and relative fitness. (The relevant covariance here is the “additive genetic covariance,” a statistic that disentangles the additive from dominance and epistatic effects of alleles 26) If a trait strongly covaries with relative fitness, it will change a good deal from one generation to the next; if not, not. This result is now known as the Secondary Theorem of Natural Selection 27, 28.
If the trait, X, is relative fitness itself, the additive genetic covariance between X and fitness collapses into the additive genetic variance in relative fitness, VA (w). Theory allows us to predict, therefore, how much the average relative fitness of a population will change from one generation to the next under selection: it will change by VA (w). Because a variance cannot be negative, the mean relative fitness of a population either increases or does not change under natural selection (the latter possibility could occur if, for instance, the population harbors no genetic variation). This finding, the Fundamental Theorem of Natural Selection, was first derived by Ronald A. Fisher 29 early in the history of evolutionary genetics. Despite the misleading nomenclature, the Fundamental Theorem is clearly a special case of the Secondary Theorem. It is the Secondary Theorem that is more fundamental.
However, it seems to me that—given that the mean relative fitness is defined by reference to the trait with the highest fitness within the genotype, that implies that the definition of the mean relative fitness changes over time. If the highest-fitness trait changes over time—because the environment changes (due to changes in the climate, other species, etc.), or because of the emergence of a new trait—then the mean relative fitness of the species also changes. The species might also be spread across different regions, with the same trait having different fitness in different regions:
A genotype’s fitness might vary spatially. Within a generation, a genotype might enjoy high fitness if it resides in one region but lower fitness if it resides in other regions. In diploids, spatial variation in fitness can, under certain conditions, maintain genetic variation in a population, a form of so-called balancing selection. The conditions required depend on the precise way in which natural selection acts.
In one scenario, different regions, following viability selection, contribute a fixed proportion of adults to a large random-mating population. This scenario involves “soft selection”: selection acts in a way that changes genotype frequencies within a region but that does not affect the number of adults produced by the region. [...]
In another scenario, different regions, following viability selection, contribute variable proportions of adults to a large random-mating population, depending on the genotypes (and thus fitnesses) of individuals within a region. This scenario involves “hard selection”: selection acts in a way that changes genotype frequencies within a region and affects the number of adults produced by the region.
Also:
The Fundamental Theorem of Natural Selection implies that the mean relative fitness, of a population generally increases through time and specifies the amount by which it will increase per small unit of time. This suggests a tempting way to think about natural selection: it is a process that increases mean relative fitness.
While attractive and often powerful, it should be emphasized that— surprisingly— the mean fitness of a population does not always increase under natural selection. Population geneticists have identified a number of scenarios in which selection acts but [mean relative fitness] does not increase. These include frequency dependent selection (wherein the fitness of a genotype depends on its frequency in a population) and, in sexual species, certain forms of epistasis (wherein the fitness of a genotype depends on non-additive effects over multiple loci). Put differently, these findings show that the Fundamental Theorem of Natural Selection does not invariably hold.
The paper does note that one can define alternative definitions of fitness under which the fundamental theorem does hold, but that the “relevant literature is forbidding”. The general takeaway that I would draw from this is that fitness is not the kind of clear-cut, “carves reality at joints” kind of a measure that evolution would directly optimize in a similar kind of sense as you directly optimize, say, the amount of correct classifications that a neural net gets on MNIST.
Rather it’s a theoretical fiction or an abstract measure that can be defined in different ways, and which is defined in different ways in different contexts, depending on what kind of an aim one wants to achieve. But that’s a simplifying interpretation imposed on complex process for the purpose of modeling it, rather than something that the process actually has an explicit optimization target. So there are ways in which you could view evolution as if it was optimizing for something, but it’s not clear to me that it can be said to actually be optimizing for anything in particular—at least not in the sense in which we talk about a machine learning system being optimized for a particular goal.
‘Fitness’ is a very overloaded term, as you’ve delved into above. I’d like to attempt to describe a few carvings which help me to firm things up and avoid equivocation in my own thinking.
The original pretheoretic term ‘fitness’ meant ‘being fitted/suitable/capable (relative to a context)’, and this is what Darwin and co were originally pointing to. (Remember they didn’t have genes or Mendel until decades later!)
The modern technical usage of ‘fitness’ very often operationalises this, for organisms, to be something like number of offspring, and for alleles/traits to be something like change in prevalence (perhaps averaged and/or normalised relative to some reference).
So natural selection is the ex post tautology ‘that which propagates in fact propagates’.
If we allow for ex ante uncertainty, we can talk about probabilities of selection/fixation and expected time to equilibrium and such. Here, ‘fitness’ is some latent property, understood as a distribution over outcomes.
If we look at longer timescales, ‘fitness’ is heavily bimodal: in many cases a particular allele/trait either fixes or goes extinct[1]. If we squint, we can think of this unknown future outcome as the hidden ground truth of latent fitness, about which some bits are revealed over time and over generations.
How can we reconcile this claim with the fact that the operationalised ‘relative fitness’ often walks approximately randomly, at least not often sustainedly upward[2]? Well, it’s precisely because it’s relative—relative to a changing series of fitness landscapes over time. Those landscapes change in part as a consequence of abiotic processes, partly as a consequence of other species’ changes, and often as a consequence of the very trait changes which natural selection is itself imposing within a population/species!
So, I think, we can say with a straight face that natural selection is optimising (weakly) for increased fitness, even while a changing fitness landscape means that almost by definition relative fitness hovers around a constant for most extant lineages. I don’t think it’s optimising on species, but on lineages (which sometimes correspond).[3]
In cases where the relative fitness of a trait corresponds with its prevalence, there can be a dynamic equilibrium at neither of these modes. Consider evolutionary stable strategies. But the vast majority of mutations ever have hit the ‘extinct’ attractor, and a lot of extant material is of the form ‘ancestor of a large proportion of living organisms’.
Though note we do see (briefly?) sustained upward fitness in times of abundance, as notably in human population and in adaptive radiation in response to new resources, habitats, and niches becoming available.
Now, if the earlier instances of now-extinct lineages were somehow evolutionarily ‘frozen’ and periodically revived back into existence, we really would see that natural selection pushes for increased fitness. But because those lineages aren’t (by definition) around any more, the fitness landscape’s changes over time are under no obligation to be transitive, so in fact a faceoff between a chicken and a velociraptor might tell a different story.
This analogy gets brought out a lot, but has anyone actually spelled it out explicitly? Because it’s not clear to me that it holds if you try to explicitly work out the argument.
In particular, I don’t quite understand what it would mean for evolution to optimize the species for fitness, given that fitness is defined as a measure of reproductive success within the species. A genotype has a high fitness, if it tends to increase in frequency relative to other genotypes in that species.
To be more precise, there is a measure of “absolute fitness” that refers to a specific genotype’s success from one generation to the next: if a genotype has 100 individuals in one generation and 80 individuals in the next generation, then it has an absolute fitness of 0.8. But AFAIK evolutionary biology generally focuses on relative fitness—on how well a genotype performs relative to others in the species. If genotype A has an absolute fitness of 1.2 and genotype B has an absolute fitness of 1.5, then genotype B will tend to become more common than A, even though both have fitness > 1.
Quoting from this Nature Reviews Genetics article:
Going with our previous example, genotype A would have a fitness of 0.8 and genotype B would have a fitness of 1.
The most natural interpretation of the “fitness of the species” would be as the mean relative fitness of the species:
However, it seems to me that—given that the mean relative fitness is defined by reference to the trait with the highest fitness within the genotype, that implies that the definition of the mean relative fitness changes over time. If the highest-fitness trait changes over time—because the environment changes (due to changes in the climate, other species, etc.), or because of the emergence of a new trait—then the mean relative fitness of the species also changes. The species might also be spread across different regions, with the same trait having different fitness in different regions:
Also:
The paper does note that one can define alternative definitions of fitness under which the fundamental theorem does hold, but that the “relevant literature is forbidding”. The general takeaway that I would draw from this is that fitness is not the kind of clear-cut, “carves reality at joints” kind of a measure that evolution would directly optimize in a similar kind of sense as you directly optimize, say, the amount of correct classifications that a neural net gets on MNIST.
Rather it’s a theoretical fiction or an abstract measure that can be defined in different ways, and which is defined in different ways in different contexts, depending on what kind of an aim one wants to achieve. But that’s a simplifying interpretation imposed on complex process for the purpose of modeling it, rather than something that the process actually has an explicit optimization target. So there are ways in which you could view evolution as if it was optimizing for something, but it’s not clear to me that it can be said to actually be optimizing for anything in particular—at least not in the sense in which we talk about a machine learning system being optimized for a particular goal.
Somewhat relevant comment thread
‘Fitness’ is a very overloaded term, as you’ve delved into above. I’d like to attempt to describe a few carvings which help me to firm things up and avoid equivocation in my own thinking.
The original pretheoretic term ‘fitness’ meant ‘being fitted/suitable/capable (relative to a context)’, and this is what Darwin and co were originally pointing to. (Remember they didn’t have genes or Mendel until decades later!)
The modern technical usage of ‘fitness’ very often operationalises this, for organisms, to be something like number of offspring, and for alleles/traits to be something like change in prevalence (perhaps averaged and/or normalised relative to some reference).
So natural selection is the ex post tautology ‘that which propagates in fact propagates’.
If we allow for ex ante uncertainty, we can talk about probabilities of selection/fixation and expected time to equilibrium and such. Here, ‘fitness’ is some latent property, understood as a distribution over outcomes.
If we look at longer timescales, ‘fitness’ is heavily bimodal: in many cases a particular allele/trait either fixes or goes extinct[1]. If we squint, we can think of this unknown future outcome as the hidden ground truth of latent fitness, about which some bits are revealed over time and over generations.
A ‘single step’ of natural selection tries out some variations and promotes the ones which in fact work (based on a realisation of the ‘ex ante’ uncertain fitness). This indeed follows the latent fitness gradient in expectation.
In this ex ante framing it becomes much more reasonable to treat natural selection as an optimisation/control process similar to gradient descent. It’s shooting for maximising the hidden ground truth of latent fitness over many iterations, but it’s doing so based on a similar foresight-free local heuristic like gradient descent, applied many times.
How can we reconcile this claim with the fact that the operationalised ‘relative fitness’ often walks approximately randomly, at least not often sustainedly upward[2]? Well, it’s precisely because it’s relative—relative to a changing series of fitness landscapes over time. Those landscapes change in part as a consequence of abiotic processes, partly as a consequence of other species’ changes, and often as a consequence of the very trait changes which natural selection is itself imposing within a population/species!
So, I think, we can say with a straight face that natural selection is optimising (weakly) for increased fitness, even while a changing fitness landscape means that almost by definition relative fitness hovers around a constant for most extant lineages. I don’t think it’s optimising on species, but on lineages (which sometimes correspond).[3]
In cases where the relative fitness of a trait corresponds with its prevalence, there can be a dynamic equilibrium at neither of these modes. Consider evolutionary stable strategies. But the vast majority of mutations ever have hit the ‘extinct’ attractor, and a lot of extant material is of the form ‘ancestor of a large proportion of living organisms’.
Though note we do see (briefly?) sustained upward fitness in times of abundance, as notably in human population and in adaptive radiation in response to new resources, habitats, and niches becoming available.
Now, if the earlier instances of now-extinct lineages were somehow evolutionarily ‘frozen’ and periodically revived back into existence, we really would see that natural selection pushes for increased fitness. But because those lineages aren’t (by definition) around any more, the fitness landscape’s changes over time are under no obligation to be transitive, so in fact a faceoff between a chicken and a velociraptor might tell a different story.