At VIMS, we don't accept a student unless there is a professor who agrees to be the advisor and who agrees to provide funding (unless the student declares s/he doesn't need money, which never happens). When you submit an application, you must identify the professor or professors with whom you are interested in working. Although you don't have to contact them, your chances are much better if you do.
There are many reasons why you may be turned down. You should not take rejection personally. For example, if someone from Harvard with a 3.8 grade point average and GRE scores of 1560 indicated he or she wanted to work with me and had already picked the research topic of "evolution of kidney function across crossopterygian taxa" … I would have to turn that person down. The topic might be fascinating but I am not a specialist in evolution, kidney morphology, physiology, or taxonomy. I simply wouldn't be able to give the student the kind of help he or she would need. Thus, a professor may turn down a student because the professor does not have interest or expertise in the area identified by the student, may not be able to fund the student, or may not have time to take on responsibility for another person.
What if you have low GRE scores or low grades? The three pieces of advice I give students about the GREs are:
If you wind up with a low score, take the exam again. I know people who have jumped 100 points higher in each part of the exam the second time around. Also, recognize that some professors think the GREs are tremendously important while others attach little importance to them. So, one professor may be interested in you while another isn't.
If you have a low grade point average, that suggests either lack of ability (and knowledge) or lack of maturity (disinterest in your studies or lack of discipline). You'll have to convince a potential advisor that you are capable and you now have maturity. One way to do this is to work for a year or two to gain professional experience and to take some advanced courses to demonstrate your abilities and dedication. Naturally, the more difficult the course the more impressive it is.
What should you tell a prospective advisor? You should represent your interests fairly and accurately and indicate the degree to which you are flexible in the choice of research topic. Suppose you're truly interested in shark behavior. Say so. But, what if the professor has a project involving sea turtle behavior - would that satisfy you? What if the professor had a project involving behavior of sea trout, or blue crab? If you only want to work on shark behavior, say so. If your interests are broader and you'd be happy with any interesting project involving behavior, say so. But, don't make the mistake of specifying broader interests than you truly have. That's likely to lead to a series of uninteresting projects being offered to you and frustration on both sides. I believe it works best when you identify the kinds of things that interest you, and those that don't, and you then shop around to see what kinds of projects may be available. One student told me she was interested in conservation, field work, and economics. I thought about her interests and was able to find a suitable research opportunity that capitalized on all of these interests.
By all means, talk about your relevant experiences with your prospective advisor. One professor at VIMS does all his research at sea and he looks for students with experience at sea; others couldn't care less if you've been to sea or not. Discuss your experiences, but make it clear whether or not you expect to continue in those areas, e.g., whether you require a research project that takes you to sea, whether experience at sea would be particularly appealing, or whether you're indifferent or opposed to going to sea.
The more research you do on prospective advisors the better. It's not that by demonstrating familiarity with a professor's work you flatter his/her ego. Rather, if you look over the research you get some idea of the types of things you might be doing if you work with this person. If you're still interested in working with the professor you'll have a more lively and enthusiastic discussion with him/her about opportunities at VIMS.
Many times prospective students tell me they share my research interests but they have not, in fact, read any of my papers. They base their statement on the descriptions on my webpage of my research highlights and of the species I study. These students have little idea what my work entails and they do not have much credibility when they say they share my interests. A prospective student need not read the papers of a potential advisor carefully. They are, after all, highly technical and may require substantial specialized knowledge in order to understand them fully. But, the student can get an idea of what is involved in the research and perhaps see why the research is significant. For example, you can get an impression of whether the prospective advisor is field oriented, lab oriented, or perhaps interested in mathematical models. And, you can see what kinds of techniques and instruments the professor and his/her students use in the field and in the lab.
How do you do research on a professor? First, look at his/her website. Some have really good websites. Others have lousy ones. That may be because they're too busy doing science, helping students, etc. to worry about the webpage. Or, it may be that they don't have much to say. Don't stop after a glance at the webpage. You can use Google Scholar to search for publications by the professor. Or, your library may have access online to Web of Science (also known as: Science Citation Index or ISI Web of Science) which indexes peer-reviewed publications. Both of these sources will identify (some of) the professor's publications and also provide you with information on how many times the papers have been cited. You'd be surprised how many papers never get cited more than once or twice. One thing I would suggest is researching the professor's recent graduates. Have they published their work? And are the papers interesting? You may also wish to investigate the professor's funding. At some universities, grants are listed on the webpage of the Office of Sponsored Programs. However, be a little careful. Sometimes only one investigator is listed as receiving the grant when there are several co-principal investigators. Alternatively, one investigator may have the lion's share of a grant with another professor just getting a small piece of it. Another way to determine sources of funding is to look at the acknowledgments section of the professor's publications. The funding agencies are generally acknowledged. Of course, you can also ask the professor your questions directly. You may also wish to contact the professor's current students or recent graduates and ask them what it's like to work with the professor. Are they concerned about continuation of their funding? Is the professor accessible and sober? Does he or she provide much guidance? Too much guidance?
Characteristics of a good advisor. You might think that mentoring students is important enough that some attention would have been devoted to identifying characteristics of top notch advisors. And, you'd be right. A recent article in Nature (Lee, A., C. Dennis and P. Campbell. 2007. Nature's guide for mentors. Nature v. 447, 14 June 2007, p. 791-797) tabulated the traits listed in nominations for Nature's mentoring awards. Among the traits cited were being: