Here is my recommended reading list for students just starting a PhD in some aspect of quantitative ecology. I’ve written this reading list to keep in mind that many new PhDs may not have a lot of math or stats from their earlier degrees.
Chapters 1 and 2 give a general introduction to the modern philosophy of science, with a focus on statistics, cause and correlation. This is a great introduction to how we use correlation to infer causation in modern science, and how science often progresses by building evidence for or against multiple competing hypotheses.
Chapters 3 onwards are more focused on the methods of structural equation modelling and will be of most interest to students who will be using statistical models such as GLMs.
The first few chapters are worth reading for an excellent introduction to the philosophy of science. Later chapters focus on theory and application of Bayesian statistical methods.
If you are going to be doing anything with Bayesian methods, then this book is gold. McElreath uses easily understood analogies to break down the jargon and complexity of Bayesian models and make them accessible to a general science audience.
You can even watch this whole book in his lecture series on YouTube.
I’d recommend the first few chapters for everyone again, because they will give you a good overview of what modelling is about. Later chapters will be good for students who will be specifically using process models (e.g. with differential equations) in their PhD.
There are lots of great books on this topic, but one of my favourites is Cairo, The Truthful Art.
Cairo uses really compelling examples to show how we can use data visualisation and simple statistics to accurately communicate scientific knowledge.
You can’t go past Gardiner and Kearn’s books. There’s a whole bunch to recommend here, but the Seven Secrets is probably a good place to start.
You should of course be also reading papers in your specific field of study. A few tips for finding these are:
Look in the top review journals, like Trends in Ecology and Evolution and Biological Reviews, for recent articles in your general area of interest. These journals in particular have high communication standards and articles are pitched at a more general audience than in specialist journals.
Search (e.g. with web of science) for review articles on your topic in discipline specific journals. For instance, if its conservation planning, then look in Conservation Letters, Conservation Biology and Biological Conservation.
Make sure you read the new and old literature. One way to identify very influential older papers is to sort results of a lit search by citation count. When you start your PhD you have your chance to read some of the classics. You probably won’t feel you have time to read this sort of thing later on (though don’t let me hold you back if you want to!).
Ask your peers for their favourite papers to read.
Follow up on citations. For instance, if you see an article that is repeatedly cited