The species–accumulation curve and estimation of species richness

Summary One of the general characteristics of ecological communities is that the number of species accumulates with increasing area sampled. However, it is important to distinguish between the species–area relationship and species accumulation curves. The species–area relationship is concerned with the number of species in areas of different size irrespective of the identity of the species within the areas, whereas the species accumulation curve is concerned with accumulation rates of new species over the sampled area and depends on species identity. We derive an exact analytical expression for the expectance and variance of the species–accumulation curve in all random subsets of samples from a given area. The analytical species accumulation curve may be approximated by a semilog curve. Both the exact accumulation curve and its semilog approximation are independent of the underlying species abundance distributions, but are influenced strongly by the distribution of species among the samples and the spatial relationship of the samples that are randomized. To estimate species richness in larger areas than that sampled we take account of the spatial relationship between samples by dividing the sampled area into subareas. First a species–accumulation curve is obtained for randomized samples of all the single subareas. Then the species–accumulation curve for all combinations of two subareas is calculated and the procedure is repeated for all subareas. From these curves a new total species (T–S) curve is obtained from the terminal point of the subarea plots. The T–S curve can then be extrapolated to estimate the probable total number of species in the area studied. Data from the Norwegian continental shelf show that extrapolation of the traditional species–accumulation curve gave a large underestimate of total species richness for the whole shelf compared with that predicted by the T–S curve. Application of non‐parametric methods also gave large underestimates compared with actual data obtained from more extensive sampling than the data analysed here. Although marine soft sediments sampled in Hong Kong were not as variable as those from the Norwegian shelf, nevertheless here the new method also gave higher estimates of total richness than the traditional species–accumulation approaches. Our data show that both the species–accumulation curve and the accompanying T–S curve apply to large heterogeneous areas varying in depth and sediment properties as well as a relatively small homogeneous area with small variation in depth and sediment properties.