Dealing with frequency distribution data is something that we as ecologists haven’t typically done in a very sophisticated way. This isn’t really our fault. Proper methods aren’t typically taught in undergraduate statistics courses or in the graduate level classes targeted at biologists. That said, as ecology becomes a more quantitative science it becomes increasingly important to analyze data carefully so that we can understand its precise quantitative structure and its relationship to theoretical predictions.
Frequency distribution data is basically any data that you would think about making a histogram out of. Any time you have a single value that you (or someone else) has measured, for example the size or abundance of a species, and you are interested in how the number of occurrences changes as a function of that value, for example – are there more small species than large species or more small patches than large patches, then you are talking about a frequency distribution. Technically what we’re often interested in is the probability distribution underlying the data and you will often have more luck using this term when looking for information. Many major ecological patterns are probability/frequency distributions including the species-abundance distribution, species size distribution (also known as the body size distribution), individual size distribution (also known as the size spectrum), Levy flights, and many others.
Last year I wrote a paper with Jessica Green and Brian Enquist on one of the problems that can result from the approaches to this kind of data typically employed by ecologists and the more sophisticated methods available for addressing the question. As a result I’ve been receiving a fair bit of email recently about related problems; enough that I thought it might be worth a couple of posts to lay out some of the basic ideas regarding the analysis of frequency distribution data. Over the next week or so I’ll try to cover what I’ve learned about basic data visualization, parameter estimation, and comparing the fits of different models to the data. Along the way I may have a couple of things to say about some recently published papers that have the potential to cause confusion with respect to these subject.
Please keep in mind that I am not a professionally trained statistician and that this is not intended to be an authoritative treatment of the subject. I’m just hoping to provide folks with an entryway into thinking about what to do with this kind of data and I’ll try to point to useful references to help take you further if you’re interested.