Perhaps this book is my attempt to hold a conversation with Banquo? He would be a fierce critic of the scientific stature of plant ecology, judging from this quote, and I doubt that I could get him to speak at all. He demands, not only predictive ability, but a very fine-grained level of predictive ability. In this book I attempt to develop a predictive theory of plant community assembly. By “predictive” I mean that the theory should be able to quantitatively tell us the relative abundance of each species in the local community under natural field conditions and based on information that can be collected in practice. By “theory” I mean a formal method of both performing such predictions and also of being able logically to deduce why such predictions actually hold in nature based on known biological processes – in this case, the process of natural selection.

I warn you at the outset that the predictive theory presented in this book would not satisfy Banquo even if it were to succeed. Such fine-scale predictive ability – being able to “say which grain will grow and which will not” – is likely forever beyond our grasp. The reason for this is explained in Chapter 2. We must remain forever mute before Banquo.

The previous chapter described a verbal model of community assembly: trait-based environmental filtering. This conceptual model views the environmental conditions of a site as a series of “filters” consisting of various selection pressures. These selection pressures reflect the probability of a given species being able to immigrate into the site and then to survive and reproduce. Such demographic probabilities vary between species because each species has a unique set of functional traits and because such functional traits bias these probabilities. The problem with this verbal model is that we don't know how to formally link traits with such probabilities. We now have to build such formal links.

With a chapter title including the words “Bayesian statistics”, “information theory” and the “Maximum Entropy Formalism” you might be tempted to skip to the next one. Please resist this understandable temptation because, although this chapter is more statistical than ecological, it will develop the statistical and mathematical methods upon which the ecological theory is based. If you are a typical reader then you will be reading this book in order to learn about the links between organismal traits and ecological communities. If so then, for you, the theoretical content of the book is only a means to an end. In order to convince you that reading this chapter will be worthwhile let's be clear about what we are trying to accomplish and, equally important, what we are trying to avoid.

When you look at vegetation, you can concentrate on the things you see (plants or species) or on the properties of these things (the traits of plants). As the previous chapter has emphasized, most ecologists working at the population and community levels have concentrated on the things, not their properties, and, because of this conceptual framework, the process of community assembly has usually been seen as a demographic one. Despite this majority tradition there has always been, even from the beginnings of plant ecology as a scientific discipline, two minority approaches in the study of plant communities. The first minority approach, used especially by plant geographers, concentrated on morphological properties of plants and how, on average, such morphologies change as a function of major climatic variables such as temperature and precipitation (Warming and Vahl 1909, DuRietz 1931, Raunkiaer 1934, Holdridge 1947, Box 1981, 1995, 1996). In fact Warming, who can reasonably be called the father of plant ecology, had an explicitly trait-based approach. A small group of American prairie ecologists applied this approach to the regional, rather than the global, scale during the first half of the twentieth century but without much impact on community ecology (Steiger 1930, DuRietz 1931, Dykserhuis 1949, Knight 1965). A second minority approach is based on the notion of ecological “strategies” (Southwood 1977). Grime's CSR scheme (Grime 1974, 1977) is perhaps best known to contemporary plant ecologists but Grime (2001, page 5) documents a continuous history dating back to MacLeod (1894).

I approach this chapter with trepidation. Since the model proposed in this book is rather different from traditional models in community ecology, I want to discuss those aspects of model-building that will allow you to judge it relative to others. It might be fun to embark on a long-winded discussion about the philosophy of modeling in ecology, but only on a Friday afternoon, only if accompanied by cool beer and good friends, and especially if done in moderation. Since these conditions are not present (except, I hope, for the presence of friends) I will be brief.

Another reason why I am uneasy with this chapter is that I want to avoid giving the impression that I view previous modeling attempts in community ecology to be useless. On the contrary, these previous attempts were inspired (and have inspired me) and are of high quality. At the same time, it is important that I contrast my approach with previous ones. It is important that you understand both the differences with other models and also why I think that previous modeling approaches have failed, at least by the criteria that I am using. After all, if even I don't think that the approach is an advance over previous attempts then why should you invest your time in reading this book? I reconcile these two contradictory messages by appealing to the nature of scientific research.