Humped pattern of diversity: fact or artifact?

Fact or Artifact? Molino and Sabatier (1) claimed to have evidence for validation of the intermediate disturbance hypothesis (2) in a tropical rainforest. Here, we demonstrate that the humped pattern of species diversity in a gradient of disturbance [figure 2 in (1)] is a methodological artifact arising from the manner in which the relationship was constructed. Molino and Sabatier estimated environmental disturbance as the proportion of pioneer or heliophilic species in the plots studied. They justified this approach by noting that “[b]ecause pioneer species establish only in gaps, their occurrence and density should record the recent history of canopy gap openings.” The approach is well founded biologically but will always produce a statistically humped pattern. For any pool of species classified into two groups, it is possible to calculate the expected richness of a sample of n individuals that contains a proportion P of individuals from either of the two groups. The total expected richness will be the sum of the expected richness in a sample of P n individuals from one group, plus the expected richness of a sample of (1– P) n individuals from the other group. Considering a parent distribution formed by N (i) individuals, distributed among S(i) species with m(i) abundance, the expected richness can be calculated with a rarefaction procedure (3). With this procedure, we estimated the expected richness as a function of the proportion of species from one group. We assumed that individuals among species may be distributed normally (curve a in Fig. 1), uniformly (curve b), or lognormally (curve c). In all cases, the expected pattern has a markedly humped distribution. The humped pattern is statistically generated without the need to invoke any biological process. The only requirement is variation among samples in the relative number of individuals from one species group. Variation of species proportions could result from disturbance; differences in recruitment, mortality, soil texture, or nutrient levels; or by chance. Regardless of the cause of variation, a plot that relates the proportion of individuals from one group to total species richness will always result in a humped pattern of diversity. Molino and Sabatier offered good arguments for using the proportion of heliophilic or pioneer species as a measure of disturbance; nevertheless, all variation in the abundance of these species, whether related to disturbance or not, will tend to validate the hypothesis. Their methodology forces the occurrence of a humped pattern in total richness and thus should not be used as a validation of the intermediate disturbance hypothesis. We hope that further studies on this topic will remind researchers that the null expectation for trends of diversity along a gradient defined by the proportional representation of species is humped rather than horizontal.