A Foray into the World of Animals and Humans is a good place to start), or even anything by Deleuze on Peirce and semiotics can be quite good (see THIS dissertation, for example, Toward a Material Concept of the Sign). Deleuze, Whitehead, Peirce, von Uexkull all have biosemiotical theories that can stand as introductions.
See also these below.
"What is biosemiotics?" Alexei Sharov
"Biosemiotics" Soren Brier
Biosemiotics (Living Book About Life)
"Theses on Biosemiotics" Kalevi Kull
Jesper Hoffmeyer academia.edu page
Jesper Hoffmeyer presentation (below)