> The question I don't think he could really answer was 'how do the cells know when to stop?'
I'm likely missing something obvious but I'll ask anyway out of curiosity. How is this not handled by the well understood chemical gradient mechanisms covered in introductory texts on this topic? Essentially cells orient themselves within multiple overlapping chemical gradients. Those gradients are constructed iteratively, exhibiting increasingly complex spatial behavior at each iteration.
Textbook models typically simulate normal development of an embryo, e.g. A-P and D-V (anterior-posterior and dorsal-ventral) patterning. The question Levin raises is how a perturbed embryo manages to develop normally, both "picasso tadpoles" where a scrambled face will re-organize into a normal face, and tadpoles with eyes transplanted to their tails, where an optic nerve forms across from the tail to the brain and a functional eye develops.
I haven't thoroughly read all of Levin's papers, so I'm not sure to what extent they specifically address the issue of whether textbook models of morphogen gradients can or cannot account for these experiments. I'd guess that it is difficult to say conclusively. You might have to use one of the software packages for simulating multi-cellular development, regulatory logic, and morphogen gradients/diffusion, if you wanted to argue either "the textbook model can generate this behavior" or that the textbook model cannot.
The simulations/models that I'm familiar with are quite basic, relative to actual biology, e.g. models of drosophila eve stripes are based on a few dozen genes or less. But iiuc, our understanding of larval development and patterning of C Elegans is far behind that of drosophila (the fly embryo starts as a syncytium, unlike worms and vertebrates, which makes fly segmentation easier to follow). I haven't read about Xenopus (the frogs that Levin studies), but I'd guess that we are very far from being able to simulate all the way from embryo to facial development in the normal case, let alone the abnormal picasso and "eye on tail" tadpoles.
I'm not an expert on the actual biological mechanisms, but, it makes intuitive sense to me that both of those effects would occur in the situation you described from simple cells working on gradients: I was one of the authors on this paper during my undergrad[1] and the generalized idea of an eye being placed on a tail and having nerves routed successfully through the body via pheromone gradient is exactly the kind of error I watched occur a dozen times while collecting the population error statistics for this paper. Same thing with the kind of error of a face re-arranging itself. The "ants" in this paper have no communication except chemical gradients similar to the ones talked about with morphogen gradients. I'm not claiming it's a proof of it working that way, ofc, but, even simpler versions of the same mechanism can result in the same kind of behavior and error.
I'm likely missing something obvious but I'll ask anyway out of curiosity. How is this not handled by the well understood chemical gradient mechanisms covered in introductory texts on this topic? Essentially cells orient themselves within multiple overlapping chemical gradients. Those gradients are constructed iteratively, exhibiting increasingly complex spatial behavior at each iteration.