I often see place or species names shortened in scientific journal articles and would like to know what the correct protocol is.
Can I shorten "Gough Island" to just "Gough"? Or "leatherback turtle" to "leatherback"?
Typically, if we are going to introduce any shorthand for a long name (including initializing it), the first time we use it in full and then note the shorter name we will use throughout: This can just be the shortened name in parentheses if no worded explanation is needed; (xxx) implies "hereinafter xxxx". Or it can be an actual sentence to introduce it.
The experiments took place on Gough Island (Gough),
The primary experiments were performed on leatherback turtles (leatherbacks),
The most time-consuming element of this computation is the third Hessenberg Factorization of the outer product. We call this the 'outer HF'.
Measuring the Inter-Element Coupling Factor (IECF) is the focus of our concern in this study,
Precision is more important than word count!
Don't abbreviate just for having fewer words.
Also, follow the conventions of specific fields. For scientific nomenclature, for example, genus name can be abbreviated to one letter when the genus is understood:
P. semiperverens, P. australis and P. aromata are found only in North America.
The examples in the question, in my mind, are not ideal. Using generic terms is better than using truncated terms. In other words, I'd shorten "Gough Island" to "the island" on subsequent mentions, and use "turtles" rather than "leatherbacks."
However, there are much worse examples of abbreviations used in technical and academic writing, so use whatever you prefer without resorting to non-words -- like "LT" for "leatherback turtle."
As always, check a reliable style guide for particular fields of study and organizations. Check Strunk & White for the best overview of clear, concise writing.