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I'm looking for help in finding the 'big ideas' behind a project I'm beginning and want to make sure I'm not missing anything since I wasn't trained in Biology.

My idea is investigating constrained selective breeding, say, a farmer who wants to balance crop yield with artificially selecting a desired trait (can't select too strongly because this will reduce yield). I've found many models for selection and found Haldane's classic useful but I'm not sure how to incorporate a constraint.

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I believe that you are talking about "multidimensional selection".

E.g. you are selecting on not one trait (yield) only but more than one (yield+some other trait). There's quite a bit of work done on this in crop science for example.

See e.g.

Figure 3 from the last talks about this in terms of evolution by reproductive isolation, which is pretty much the same thing except it's natural rather than artificial selection.

enter image description here

The most important thing practically is to try to measure the correlations of the traits in question. If they are positively correlated or uncorrelated, it shouldn't be too hard. If they are negatively correlated then you might have some difficulties due to constraints on the kinds of phenotypes that can exist.

For a recent technical treatment with good references, see here.

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