Comments on Wilson's Null Model

We agree with several of Wilson's general observations concerning the difficulties and pitfalls of this approach to distributional ecology. We disagree on two of his main points, however. First, he has not correctly discussed our own procedure. Second, the model he has produced contains a serious flaw. Related to this second point, we find his analysis of the Vanuatu data to be unconvincing. Therefore, we stand behind our earlier work (Diamond and Gilpin 1982; Gilpin and Diamond 1982, 1984). Wilson claims to have tested our method for the generation of a null distribution against purely random data (see his Scheme 1). Finding an inconsistency, he concludes: "a method that finds significant coocurrence in random numbers is inappropriate." There are two very serious problems with Wilson's criticism of our method. One involves test implementation, the other involves test strategy. First, and very importantly, Wilson has not actually used our method, which is iterative and algorithmic, and which is embodied in a VAX-11 BASIC program that he does not possess (we would have given him a copy had he asked). Because he does not understand our approach, he repeats two false charges made previously by Connor and Simberloff, that is, that our p?j values can be greater than 1 and that our formula for the S.D. is inappropriate. The strategic flaw in Wilson's critique requires more explanation. It involves the question of how one tests a method against "random numbers.". Disregarding for the moment our various criticisms of the null model approach, accept that it might be useful for detecting biogeographic pattern in taxonomically-broad data bases. To do this, one must start from something real. We start from the actual presence/absence matrix that contains Is and Os, where a 1 denotes the presence of a species on an island. From this matrix, one produces a randomization against which the original matrix can be tested. Wilson does something new: he pretends that one can actually start this process from a knowledge that all species are equally likely on every island. He assumes a probability of 0.3333; below we assume, with no loss of generality, a probability of 0.5. Such uniform colonization probabilities for all species are biologically absurd, but, accepting them, the epistemological problem is that unless we had vary large numbers of such replicate archipelagos, or an extremely long time series of species occurrences, it is impossible to have such knowledge of the actual porobabilities. Hence, this approach cannot be carried out in practice. In any case, Wilson takes the seeming innocuous step of realizing these probabilities by drawing an actual matrix of 1 s and Os. For example, starting from a matrix of 0.5 probabilities, Scheme 1 A, some possible realizations are shown in Scheme 1 B-D. All of these are supposedly produced by "random numbers" and, by Wilson's argument, should not be seen as containing pattern, but it is obvious at a glance that Scheme 1 B, C do contain pattern. Our method does detect both negative cooccurrence and positive cooccurrence in the matrices of Scheme 1 B, C. The reason our method does so is that it commences from the actual realized presence/absence matrix, not from some privileged and impossible knowledge of the probability distribution function that underlies the distribution.