As an example programmers can understand, machine learning is a better model for this than a logistic map. Natural selection is basically gradient descent with

As an example programmers can understand, machine learning is a better model for this than a logistic map. Natural selection is basically gradient descent with random walk as the "step" algorithm rather than back propagation. At each step, you randomly adjust the weights by a small amount. You do this with like 100 candidates and pick the best one that lowers the cost function the most. This is one generation, and you "selected" the best mutation that can proceed to the next generation of your learning algorithm. It's essentially an extremely accurate model of evolution. When you let gradient descent run in-definitely the weights will eventually converge on a minimum in general. By "in general" I mean that these weights will only converge within the vicinity of the local minimum. Keeping the learning algorithm running with random walk... what you will find is that the algorithm travels randomly all around the minimum and stays within a certain "equilibrium zone." This is exactly what happens in biology. A more accurate example would be adversarial neural networks, when you have two networks competing. What you will find is that for adversial networks you ALSO get convergence within the vicinity of a local minimum. The logistic map you present here is simply not an accurate model of evolution. I don't think an accurate model actually exists. The most accurate models are the algorithms we to do genetic programming and these models are simply simulations where we have a sort of "feel" for how the algorithm will converge. There is no closed form understanding of it. Our knowledge of these algorithms accurately reflects our knowledge of natural selection itself in the sense that you can't simply pull a random logistic map formula out of nowhere and claim it applies. It doesn't.