Optimizing Random Searches in High Density Environments

We explore possible ways that a forager performing a random walk can optimize their chances of finding a resource in a resource dense environment. We specifically look at varying how the forager chooses their path lengths, by drawing them from different probability distributions. It is known that for low resource dense environments an optimal foraging strategy is one where the walker chooses step lengths according to a power-law distribution (Viswanathan et al., 1999). It has also been observed that in nature animals act like brownian walkers when in dense resource environments (Calich et al., 2021; Heinrich, 1979; Viswanathan et al., 2011). This is why both of these random walks were tested, along with a uniform distribution as a control, to see if one strategy would be more optimal than another. To do this we first tested the distributions against themselves using different constants that would morph their shape to find which constants were most optimal. Then we used those constants and compared the distributions against each other. In our simulations we found that there was no significant difference in the search efficiencies of the different distributions