Seriation is a term invented probably by the archaeologists who use it to name the procedure of putting the samples of artifacts into the correct (relative) chronological order. On the other hand, the ecologists use the term ordination for "putting things into order", i.e., arranging samples, usually in several dimensions, so that the pattern included within the data becomes visible. One of these dimensions may, but need not be, time. Any other variable is appropriate. I use the term "seriation" here simply for topological (preserving only order, not distances) ordination in one dimension.
The underlying idea upon which seriation is based has been formulated perhaps as early as in 1899 by Flinders-Petrie... In archaeology, it is generally supposed that any type of an artifact, after being invented, spreads and gains popularity, thus being produced (and discarded) in greater and greater numbers. Then, its popularity declines, as new types are invented and coming to use. Thus, the number of produced artifacts of certain type per time unit forms a unimodal curve along the time. This process has clear analogies in biostratigraphy (an invading / radiating species occurs in low numbers first, then establishes itself reaching the maximum population density, and declines as well, being outcompeted by a fitter species) as well as in (paleo)ecology (there, a species has its realized niche on a gradient of an environmental variable, reaching the maximum population density at the proper optimum, declining on both directions towards the niche margins.
Seriation is founded upon this assumption of humped unimodal "response curves". This assumption is central to seriation. The task might seem trivial at first glance: take a species' abundance matrix, where samples are represented by rows and species by columns, and permute its rows until the humped pattern appears in columns. Unfortunately, the number of permutations increases with $n!/2$, where $n$ is the number of samples. Thus, having to seriate 20 samples by exhaustive search means to evaluate 1216451004088320000 different permutations.
What seriation does is illustrated in the following series of figures. Suppose that the species assemblages formed under prevailing influence of a single environmental variable, say, temperature. The temperature varied in time, but we cannot access its direct record. Instead, we want to deduce past temperatures from assemblages alone, even without a knowledge of the species' temperature optima and tolerances.
This figure shows twenty random (= uninformed) samples of assemblages (total 50 species). Abundances of individual species, hopefuly related linearly to their population densities, vary without exhibiting any pattern.
After successful seriation, a humped pattern emerges. Note that the curves are not strictly unimodal: the "noise" is inherent to the colonization / fossilization / sampling process. This noise is inevitable, and a good ordination method is supposed to be robust to it. In this step, seriation reveals the species' temperature optima and tolerances.
Now, suppose that the samples were originally numbered according to their stratigraphic position, i.e. their order represents time. By plotting the sample scores (reflecting their position on the reconstructed gradient) against time we get reconstructed relative temperatures in the past.
Comments & reactions are most welcome at cej@cejchan.gli.cas.cz
Fri Dec 17 16:53:33 1999