Suppose that each individual in a species of a given sex has some real-valued variable X, which is observable by the other sex. Suppose that, absent considerations about sexual selection by potential mates for the next generation, the evolutionarily optimal value for X is 0. How could we end up with a positive feedback loop involving sexual selection for positive values of X, creating a new evolutionary equilibrium with an optimal value X=1 when taking into account sexual selection? First the other sex ends up with some smaller degree of selection for positive values of X (say selecting most strongly for X=.5). If sexual selection by the next generation of potential mates were the only thing that mattered, then the optimal value of X to select for is .5, since that’s what everyone else is selecting for. That’s stability, not positive feedback. But sexual selection by the next generation of potential mates isn’t the only thing that matters; by stipulation, different values of X have effects on evolutionary fitness other than through sexual selection, with values closer to 0 being better. So, when choosing a mate, one must balance the considerations of sexual selection by the next generation (for which X=.5 is optimal) and other considerations (for which X=0 is optimal), leading to selection for mates with 0<X<.5 being evolutionarily optimal. That’s negative feedback. How do you get positive feedback?

In the context of your model, I see two potential ways that Fisherian runaway might occur:

Within each generation, males that survive with higher X are consistently fitter on average than males that survive with lower X because the fitness required to survive monotonically increases with X. Therefore, in every generation, choosing males with higher X is a good proxy for local improvements in fitness. However, the performance detriments of high X “off-distribution” are never signalled. In an ML context, this is basically distributional shift via proxy misalignment.

Positive feedback that negatively impacts fitness “on-distribution” might occur temporarily if selection for higher X is so strong that it has “acquired momentum” that ensures females will select for higher X males for several generations past the point the trait becomes net costly for fitness. This is possible if the negative effects of the trait take longer to manifest selection pressure than the time window during which sexual selection boosts the trait via preferential mating. This mechanism is temporary, however, but I can see search processes halting prematurely in an ML context.

By “optimal”, I mean in an evidential, rather than causal, sense. That is, the optimal value is that which signals greatest fitness to a mate, rather than the value that is most practically useful otherwise. I took Fisherian runaway to mean that there would be overcorrection, with selection for even more extreme traits than what signals greatest fitness, because of sexual selection by the next generation. So, in my model, the value of X that causally leads to greatest chance of survival could be −1, but high values for X are evidence for other traits that are causally associated with survivability, so X=0 offers best evidence of survivability to potential mates, and Fisherian runaway leads to selection for X=1. Perhaps I’m misinterpreting Fisherian runaway, and it’s just saying that there will be selection for X=0 in this case, instead of over-correcting and selecting for X=1? But then what’s all this talk about later-generation sexual selection, if this doesn’t change the equilibrium?

Ah, so if we start out with an average X=−10, standard deviation 1, and optimal X=0, then selecting for larger X has the same effect as selecting for X closer to 0, and that could end up being what potential mates do, driving X up over the generations, until it is common for individuals to have positive X, but potential mates have learned to select for higher X? Sure, I guess that could happen, but there would then be selection pressure on potential mates to stop selecting for higher X at this point. This would also require a rapid environmental change that shifts the optimal value of X; if environmental changes affecting optimal phenotype aren’t much faster than evolution, then optimal phenotypes shouldn’t be so wildly off the distribution of actual phenotypes.

I think it’s important to distinguish between “fitness as evaluated on the training distribution” (i.e. the set of environments ancestral peacocks roamed) and “fitness as evaluated on a hypothetical deployment distribution” (i.e. the set of possible predation and resource scarcity environments peacocks might suddenly face). Also important is the concept of “path-dependent search” when fitness is a convex function on X which biases local search towards X=1, but has global minimum at X=−1.

In this case, I’m imagining that Fisherian runaway boosts X as long as it still indicates good fitness on-distribution. However, it could be that X=1 is the “local optimum for fitness” and in reality X=−1 is the global optimum for fitness. In this case, the search process has chosen an intiial X-direction that biases sexual selection towards X=1. This is equivalent to gradient descent finding a local minima.

I think I agree with your thoughts here. I do wonder if sexual selection in humans has reached a point where we are deliberately immune to natural selection pressure due to such a distributional shift and acquired capabilities.

Fisherian runaway doesn’t make any sense to me.

Suppose that each individual in a species of a given sex has some real-valued variable X, which is observable by the other sex. Suppose that, absent considerations about sexual selection by potential mates for the next generation, the evolutionarily optimal value for X is 0. How could we end up with a positive feedback loop involving sexual selection for positive values of X, creating a new evolutionary equilibrium with an optimal value X=1 when taking into account sexual selection? First the other sex ends up with some smaller degree of selection for positive values of X (say selecting most strongly for X=.5). If sexual selection by the next generation of potential mates were the only thing that mattered, then the optimal value of X to select for is .5, since that’s what everyone else is selecting for. That’s stability, not positive feedback. But sexual selection by the next generation of potential mates isn’t the only thing that matters; by stipulation, different values of X have effects on evolutionary fitness other than through sexual selection, with values closer to 0 being better. So, when choosing a mate, one must balance the considerations of sexual selection by the next generation (for which X=.5 is optimal) and other considerations (for which X=0 is optimal), leading to selection for mates with 0<X<.5 being evolutionarily optimal. That’s negative feedback. How do you get positive feedback?

In the context of your model, I see two potential ways that Fisherian runaway might occur:

Within each generation, males that survive with higher X are consistently fitter on average than males that survive with lower X because the fitness required to survive monotonically increases with X. Therefore, in every generation, choosing males with higher X is a good proxy for local improvements in fitness. However, the performance detriments of high X “off-distribution” are never signalled. In an ML context, this is basically distributional shift via proxy misalignment.

Positive feedback that negatively impacts fitness “on-distribution” might occur temporarily if selection for higher X is so strong that it has “acquired momentum” that ensures females will select for higher X males for several generations past the point the trait becomes net costly for fitness. This is possible if the negative effects of the trait take longer to manifest selection pressure than the time window during which sexual selection boosts the trait via preferential mating. This mechanism is temporary, however, but I can see search processes halting prematurely in an ML context.

By “optimal”, I mean in an evidential, rather than causal, sense. That is, the optimal value is that which signals greatest fitness to a mate, rather than the value that is most practically useful otherwise. I took Fisherian runaway to mean that there would be overcorrection, with selection for even more extreme traits than what signals greatest fitness, because of sexual selection by the next generation. So, in my model, the value of X that causally leads to greatest chance of survival could be −1, but high values for X are evidence for other traits that are causally associated with survivability, so X=0 offers best evidence of survivability to potential mates, and Fisherian runaway leads to selection for X=1. Perhaps I’m misinterpreting Fisherian runaway, and it’s just saying that there will be selection for X=0 in this case, instead of over-correcting and selecting for X=1? But then what’s all this talk about later-generation sexual selection, if this doesn’t change the equilibrium?

Ah, so if we start out with an average X=−10, standard deviation 1, and optimal X=0, then selecting for larger X has the same effect as selecting for X closer to 0, and that could end up being what potential mates do, driving X up over the generations, until it is common for individuals to have positive X, but potential mates have learned to select for higher X? Sure, I guess that could happen, but there would then be selection pressure on potential mates to stop selecting for higher X at this point. This would also require a rapid environmental change that shifts the optimal value of X; if environmental changes affecting optimal phenotype aren’t much faster than evolution, then optimal phenotypes shouldn’t be so wildly off the distribution of actual phenotypes.

I think it’s important to distinguish between “fitness as evaluated on the training distribution” (i.e. the set of environments ancestral peacocks roamed) and “fitness as evaluated on a hypothetical deployment distribution” (i.e. the set of possible predation and resource scarcity environments peacocks might suddenly face). Also important is the concept of “path-dependent search” when fitness is a convex function on X which biases local search towards X=1, but has global minimum at X=−1.

In this case, I’m imagining that Fisherian runaway boosts X as long as it still indicates good fitness on-distribution. However, it could be that X=1 is the “local optimum for fitness” and in reality X=−1 is the global optimum for fitness. In this case, the search process has chosen an intiial X-direction that biases sexual selection towards X=1. This is equivalent to gradient descent finding a local minima.

I think I agree with your thoughts here. I do wonder if sexual selection in humans has reached a point where we are deliberately immune to natural selection pressure due to such a distributional shift and acquired capabilities.