Fundamental turns in biological understanding can be interpreted as replacements of deep models that organise the biological knowledge. Three deep models distinguished here are a holistic ladder model that sees all levels of nature being complete (from Aristotle to the 18th century), a modernist tree model that emphasises progress and evolution (from Enlightenment to the recent times), and a web model that evaluates diversity (since the 20th century). The turn from the tree model to the web model in biology includes (1) a transfer from modern to postmodern approaches, (2) a shift of semiotic threshold to the border of life, and (3) building the semiotic models of living systems, i.e., the rise of biosemiotics.