Species accumulation curves analysed by a class of null models discovered by Arrhenius

• Published in: Oikos 2005-02, Vol.108 (2), p.263-274
• Main Authors: Ugland, Karl I., Gray, John S., Lambshead, P. John D.
• Format: Article
• Language: English
• Subjects: Animal, plant and microbial ecology; Approximation; Arrhenius, Svante; Biological and medical sciences; Biological taxonomies; Datasets; Ecological modeling; Ecology; Fundamental and applied biological sciences. Psychology; General aspects. Techniques; Habitats; Mathematical models; Methods and techniques (sampling, tagging, trapping, modelling...); Modeling; Null set; Parametric models; Species; Stock prices; Synecology
• ISSN: 0030-1299; 1600-0706
• DOI: 10.1111/j.0030-1299.2005.13532.x

Arrhenius is mainly given credit for his discovery of the log-log relationship between number of species and area, but in 1921 he invented the technique of analysing the data with a null model. This achievement, which Arrhenius explicitly stated was more important than the empirical species-area relationship, has been overlooked in the scientific literature. We suggest here that analysis of large communities should be done by a successive addition of predefined subsets of samples. Plotting the resulting accumulation curves in a common diagram usually will reveal heterogeneity between subsamples. We believe that this is a general feature of a counting process, (over space or time), that keeps record of new objects being generated by an unobservable process. We show this by two nonbiological time series: examination scores at the University of Oslo and stock prices on the Oslo stock market. We then apply these ideas to the analysis of the nested accumulation plots obtained from two unusually large community samples, the benthos of the Norwegian continental shelf and of marine areas of Hong Kong. Discontinuities in the accumulation curves can be explained by changes in habitat heterogeneity. These changes may be interpreted as variations in the parameter values in the class of null models discovered by Arrhenius. By selecting appropriate parameter values, the observed accumulation curves (calculated by an analytical expression giving exact values) can be approximated by null curves. This procedure makes it possible to identifying the major factors responsible for the shape of the curves in the accumulation plots.