I probably sent about 20 emails to prospective advisors, all from different universities. There was only one person I didn’t hear back from, and I later learned that person was no longer allowed by their university to take graduate students due to a culture of bullying in their lab (as an aside, do your due diligence into your prospective advisors and how they treat their students). Despite a high return rate on emails, there were no more than three or four potential advisors I emailed that had funding to take on a PhD student. However, because I detailed my experience and research interests in my original email, several connected me to other potential advisors who they thought would be a good fit. Funding in the sciences can be very limited, especially in certain fields. My niche was highly specific, so it isn’t surprising that few openings were available to me. This is definitely something to consider as you apply.
Last step, and this is very important – for any responses you receive, whether the person is taking students or not, always respond back thanking them for their time in getting back to you. As someone just starting in academia, I can attest to the fact that potential advisors are very busy, and responding to prospective student emails isn’t a requirement, but is generally out of kindness. Make sure they know it is appreciated!
Best of luck with your networking!
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My experience has solely been within the field of marine science in the United States. As with all my advice on this platform, the suggestions here are based on that and may not be applicable to other fields or other countries.