CR_notes - Incidence data In this scenario we collect...

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Incidence data In this scenario we collect species occurrence or incidence data on several different sampling “occasions,” or from several different lists; this is also known as capture- recapture, multiple recapture, or multiple list data. For example, the Table 2 shows 10 different samples or lists, which yielded a combined total of 15 observed species. (This is a subset of a larger dataset with 46 samples and 3717 observed species, extracted from GenBank at the 90% similarity level (Epstein and Bunge 2008).) Each row represents the “capture history” of a particular species (arbitrary species ID numbers are assigned), and each column represents the list of species observed on a given sampling occasion. Note that on each occasion, the only presence or absence – the “incidence” – of each species is recorded, where 1 indicates that the given species was observed on the given occasion (0 otherwise). The right-most column gives the total number of observations for each (observed) species. Analysis of such data has a long history and immense literature, dating back at least as far as the 18 th century (Borchers et al. 2002, Chao and Huggins 2005); here we attempt only a sketch from a particular point of view. Sample Species ID 1 2 3 4 5 6 7 8 9 10 Total 1 0 1 0 0 0 0 0 0 1 0 2 2 0 0 0 0 0 0 0 0 1 0 1 3 1 1 1 0 0 0 0 0 1 0 4 4 0 0 1 0 0 0 0 0 0 0 1 5 1 0 0 0 0 0 1 1 1 0 4 6 0 0 0 0 0 1 0 0 0 0 1 7 1 1 1 0 0 1 0 0 1 0 5 8 0 0 1 0 0 0 0 0 1 0 2 9 0 0 0 0 0 1 0 0 1 0 2 10 0 0 0 0 0 1 0 0 0 0 1 11 0 1 0 0 0 0 1 0 1 0 3 12 0 0 0 0 0 0 0 0 0 1 1 13 0 0 0 0 0 0 0 0 1 0 1 14 0 0 0 0 0 0 0 0 1 0 1 15 0 0 0 0 0 0 0 1 0 0 1 Table 2: Example multiple recapture data We note that in some cases the actual “abundance” or number of observations of a given species on a given occasion may be recorded, leading to integer entries greater than 1; this may be called “multiple abundance data,” although there is no standard terminology in this case. Clearly multiple incidence data can be derived from multiple abundance data, but not the reverse. Note also that frequency-count data
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can be derived from the marginal totals, but the full table cannot be recovered from the frequency-count data. In this example the latter is (1,8), (2,3), (3,1), (4,2), (5,1). Here the maximum possible frequency is equal to the number of samples. It is possible to apply frequency-count methods to such data if the number of samples is large enough; we return to this issue below. Multiple incidence data is more highly structured than frequency-count data, and its statistical analysis admits more variations; here we only attempt an outline of the areas we see as especially relevant to microbial ecology. Much of the literature in this area originated with population size estimation for macro-fauna – birds, mammals, fish – and in this application a row in the table represents the capture history for a particular animal. A certain taxonomy of models has emerged from
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CR_notes - Incidence data In this scenario we collect...

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