Bugs may or may not be randomly distributed under boards. If the bugs are randomly distributed, then the counts of the bugs under the boards should be Poisson distributed. If individuals are attracted or repulsed by each other, we could fit them by a Lagrangian Poisson Distribution or LGP.

λ2 > 0: organisms may form large-number clusters more than expected by chance λ2 < 0: organisms are more likely to be repulsed by one another than expected by chance

1. The Poisson distribution with the same mean as the spider counts was plotted along with the data *The Poisson distribution fits the spider data, so we conclude that the spiders are randomly distributed. λ2 = 0 for spiders because it fits the Poisson data.
2. The Poisson distribution with the same mean as the sowbug counts was plotted along with the data. A curve was added that shows the LGP distribution with the parameter hint for the sowbug counts. *The Poisson distribution does not fit the sowbug data, so the insects are not randomly distributed. λ2 > 1 for sowbugs because these bugs are more likely to be found in clusters.
3. The Poisson distribution with the same mean as the weevil egg counts was plotted along with the data. A curve was added that shows the LGP distribution with the parameter hint for the weevil egg counts. *The Poisson distribution fits the weevil egg data, so we conclude that the weevils are randomly distributed. λ2 = 0 for weevils because it fits the Poisson data.