Every living organism has -- to our knowledge -- only a finite amount of resources available. So no, they can not be Turing-complete.
That said, there is quite a number of bio-inspired models of computation that can be studied formally. Sticker systems , for instance -- an abstraction of recombining DNA fragments -- can be shown to reach Turing-power ...
The computer's operating system keeps track of which pieces of memory make up which program. The partition into programs is entirely arbitrary, and the only reason a section of memory counts as program is because there is a specially designated piece of memory that keeps a list of all "programs" and their memory locations.
This paper[] recommends the following Swarm Intelligence algorithms:
Ant colony optimization
Particle swarm optimization
: "A Brief Review of Nature-Inspired Algorithms for Optimization"
Adding on Tom van der Zanden's answer, for most existing artificial evolution systems (for sure Tierra) a program is a sequence of instructions subject to strict limitations.
limitations to preserve the organism (program) structural integrity (cellularity-constraints in Tierra). E.g.
each organism has exclusive write privilege to its own code;
an organism ...
In order to complement some answers here, here are other approaches related to Computer Vision without using neural networks:
3D reconstruction for achieving 3D models of imaged objects (although I am starting to see some PhD opportunities that try to make use of deep learning here)
Text detection (and possible recognition) in natural imagery. (I am ...
Yes there are a number of computer vision algorithms that do not involve AI in the sense they do not 'learn'. In certain use cases these approaches can be more efficient than a neural net approach.
These algorithms work by extracting features (like histograms, edge detection, etc.) from an image, then using an algorithm to compare these features.
I think you could use some type of probabilistic model to solve this issue. I might be completely wrong, though, as I do not know a lot about probabilistic models.
Some time ago, I made use of Markov chains to generate levels for a game called Mega Man, and I remember that the results were promising, so I looked up "Markov Chains and face recognition" and ...
Recently, optimization algorithms are being suggested based on the network dynamics of a slime mold called Physarum polycephalum. For certain problems, these algorithms provably construct optimal solutions. Have a look into the following paper for further pointers.
Yahui Sun. Physarum-inspired Network Optimization: A Review. arXiv: 1712.02910
You may want to check the IEEE Congress on Evolutionary Computation as new algorithms are published there every year. Not sure if the answer is still helpful though. You may check here link for the 2018 publications.
There are many bio-inspired models of computation. As Raphael has already stated, real implementations would always have the limitation of finite resources. This aside, Membrane Computing uses abstractions of cells with their compartments as the computing hardware. However, they use the quantities of different objects/molecules in the different compartments ...