Double post because it’s been 3 months and this is about something different.
I was rereading the Auto-Evo thread on the dev forum and found a little error in the math. I know Nick has been in hibernation for the past year but this post will be here when he (hopefully) comes back.
The Distance per Hunt isn’t calculated correctly. In his equation, Nick assumes that adding more creatures would decrease the average distance to a food source, but this is incorrect. Since each creature has to get his calories individually, it does not actually matter how many other creatures there are. If you look at the picture with the triceratopses you’ll find that the distance from a triceratops to a fern is still the same regardless of how many triceratopses there are, even if there was only one triceratops. Only the size of the patch and the amount of ferns matter. This is likely part of the reason why time per hunt is so low right now.
Let’s look at the equation Nick gives and how to correct it:
Distance per Hunt = (0.66 * Patch Length) * (1 - (4 * Predator Population Density * Prey Population Density))
Nick expresses doubt about this, but he is right about the (0.66 * Patch Length) part. The rest of the equation just looks like guesswork to me. I have to be honest here: I don’t know how to mathematically prove anything about this either, but I managed to brute force this by using a simulation:
Distance = (0.6617 * Patch Length) / (Food Sources^0.35)
I have verified with the simulation that this is roughly accurate for anywhere from 1 to 5000 food sources.