Sophisticated algorithms in biological systems
There are many examples of biological systems doing computation, according to my understanding:


Regulatory networks encode decision trees of significant complexity: wikipedia.
Alan Turing did significant work on organismal morphogenesis showing how simple chemical patterns of inducers can lead to complex outcomes, "Turing patterns".
All of organismal development, cell division, etc. are tightly regulated procedures of gene regulation and morphogenesis.
The inspiration for neural networks is brains.