# Probabilistic Models

The nice thing about a probability is that (in an normal world) it must range between 0 and 1, and also never really exactly equal either. These bounds on probabilities are satisfying to me because they give a scaled indication of the likelihood of a particular biological event, process, or pattern happening. In fact, that’s what a probability is in any context, not just biology. I think ecologists (and other biologists) could make greater use of basic probability “theory” in their research and investigation into natural processes and patterns. By this I mean that often times a probabilistic model can take the place of a statistical test (and all its various assumptions). Also ecologists could learn to think more clearly about their study systems and processes in a probability-based framework even apart from the collection of data to test hypotheses. To some extent and in some situations, the outcome(s) of a particular process or the manifestation of a pattern can be determined with some known probability (or range of probabilities) derived from the basics of probability and some prior knowledge of the study system.  Analytical/mathematical solutions to biological questions are not going to replace data and statistical tests but they can help us see more clearly the range of possible outcomes and the most likely outcome.

One of my research interests is to promote the use of probability and math (rather than strictly statistics) in the conduct of ecological research. I first started thinking about this perspective on ecological research after reading “Chance in Biology: Using Probability to Explore Nature” by Mark Denny and Steve Gaines (Princeton University Press, 2000). In my own research since then, this perspective is best represented by my work on the probabilistic model of species co-occurrence. I have also been influenced by the Random Placement Model of Coleman and colleagues (Coleman_et_al_1982). To me, this paper presents a brilliant solution to the number of species expected in an area of a specified size (e.g., an island or habitat fragment) and given the abundances of the species available to colonize the area, under the condition in which the species (individuals) are randomly placed or distributed to the area and other areas. That is what is most important about the model: it is giving the random expectation.  Observed empirical patterns can then be compared to the random expectation so as to gain ecological knowledge and insight.  Related to this, I also have developed null models and continue to use them in my research for precisely this reason: they give the null or random expectation against which to compare observed patterns.