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.

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.