The significance of a Ph.D. degree is that you can do much more than excellent research. You can also think of what questions to ask. You know how to push at the most important unknowns. You can read the literature of a field and see not just what is there, but also what is missing. You can tell which missing pieces are important and which are details. You also have a sense of what is feasible and what is not. If there is a new tool developed in this or another discipline, you are quickly able to apply it in new ways to answer things that were previously unanswerable. You are amazing, at least for that brief well-read time when you are embarking on a specific project, before your days are filled with censusing, pipetting, counting, or whatever other routine tedium comes with actually testing hypotheses.
So how can you become amazing if you do a project handed to you by someone else? If you never need to sink or swim according to what your own intellect has discovered, how can you own a field? If you are a cog in someone else’s research machine, even if you get out all the papers, even if you learn well how to do a complex project, have you really learned what it takes for a degree called Doctor of Philosophy, literally from the Latin, philosophiae doctor? I think not, but it depends on the details.
What is the optimum balance between independence and guidance? The answer is less clear than you might think. At one extreme you might be a nearly completely independent agent, working in a place, on an organism, and on a question separate from your mentor. He might work on grasshoppers, or butterflies, or even Drosophila, asking questions of speciation, crypsis, or population genetics in South Africa, Costa Rica, or Hawaii while you work on Texas wasps with questions of social behavior. Why would you do this? How will you be gently guided between better and worse approaches? How will you learn new techniques or even know what they might be for your field? How will you fund your research? Honestly, this extreme level of independence makes no sense to me.
Yet a few decades ago it was practically the norm in ecology and evolution. I suppose it was only possible because the techniques were few and cheap and science was booming. Yet this system left a lot of people floundering, often leaving the program before finishing, though I can’t say I have any numbers to indicate that this has changed. Some people still adhere to this extreme independence idea, perhaps to justify their own hands-off mentoring, perhaps because it worked for them.
The other extreme is to be given a project that is very specific. It might be one of the aims of a research proposal an adviser wrote. It might be a gap in what the rest of the lab is doing. It might even be heavy on technique development. Is this a terrible thing? Will it keep you from being a Ph.D. in the full sense of the word? I think it depends on how independently you then approach the question. This kind of project can be excellent. It might be the only kind expensive work in a difficult system allows. After all, you might take three years learning some complex cell biology techniques and approaches. If it is your problem, you can learn what it takes.
So, in my opinion, the problem comes in if you are micro-managed, or not allowed to explore your own solutions to the system, even a very specific one. But too close a project assignment has a risk. The risk is that it might not feel like your own. It might not mesh well with your ever evolving interests. Even if you own it, if you don’t love it, it won’t be optimal.
Where does the balance lie? I like to think it is best to do a project in the general area of your mentor’s interests and expertise. What I like to do is to give a new student our papers and our funded grant proposals and suggest that they find in this rich soil something that entrances. It does not have to be something that we directly proposed, though that would be fine. But it should be directly relevant to our general area of expertise and what the rest of the lab is doing. That way help, sympathy, and collaboration are more likely. If someone wants, we are always happy to suggest two or three things to do for a first project. Then the student can soar on their own, having shepherded a project all the way through.
Once we had a student working on stingless bees, on a project central to our interests for which we had funding. Her work went exceptionally well. She published a series of important papers. But the rest of the lab were working on either wasps or social amoebae, so she did not have a team helping her think about bees. I know she felt a bit isolated, though leaving bees was never what she wanted.
So think hard about the program you choose for graduate school. You need to learn a lot to own a field. Mentors can help, but only if they are neither too restricting nor too hands off. It might seem like a delicate balance, but it is one that is often successfully achieved.