Since my work spans ecology, evolution, epidemiology, mathematics, statistics, and computation, my ideal prospective student/postdoc knows something about all of those topics. You shouldn’t be discouraged if you don’t know all that stuff yet (I didn’t when I started!), but knowing something about some of it will definitely encourage me to accept you as a student, for two reasons:
My ‘lab’ size is approximately 1-2 undergraduates, 1-2 master’s students, 1-2 PhD students, maybe a postdoc. (I take relatively few undergraduate and master’s students because I don’t need people to do grunt-work/have to invest a lot in each student.)
I would expect to hear from prospective graduate students sometime May-October for admission the following September, and prospective undergraduate thesis students in March-April for thesis projects starting the following September.
I like prospective students to have some idea what topics they would like to work on. More detailed proposals are welcome, but in my experience most incoming students have a hard time identifying a good, feasible project. Check the ideas page and some of my recent papers for general areas of interest.