Reddit mentions of How Economics Shapes Science

So the thing to remember that alot of the different things that you talk about, such as the general use of maths, came from the hard sciences first and were transferred over to economics. Thus I don't think that there is much mathematics that economics can teach to the hard sciences in terms of mathematical techniques and analysis. Use of game theory in evolutionary biology might be the exception. And much of convex optimization was probably inspired by economics, though I'm not sure.

What economics potentially can transfer over is certain economics concepts. For example, the concept of a market might be useful in explaining certain biological interactions. I came across this paper looking at gut microbes:

https://www.pnas.org/content/111/4/1237

Perhaps you might be interested in some areas where economics needs to account for natural systems, like ecological economics or the economics of climate change.

There also is looking at how economic forces shape how science is conducted. I came across that idea in this book:

https://www.amazon.co.uk/Economics-Shapes-Science-Paula-Stephan/dp/0674088166/ref=sr_1_1?keywords=how+economics+shapes+science&qid=1565834193&s=gateway&sr=8-1

Otherwise, that's all I know in my limited knowledge of how economics interacts with science. I'm sure there's plenty more.

Sure. This was the report from the NIH work group: http://acd.od.nih.gov/biomedical_research_wgreport.pdf

The first author, Shirley Tilghman, is a molecular biologist and has been one of the main advocates for reform, so you may be able to find other stuff from her on this topic such as this shorter paper in PNAS: http://www.pnas.org/content/111/16/5773.full

The book I was thinking of is How Economics Shapes Science by Paula Stephan (who is an economist): https://www.amazon.com/Economics-Shapes-Science-Paula-Stephan/dp/0674088166