How To Plot A Rarefaction Curve In Excel
Sanora Ngueyn
We have seen how a sample can be represented by either an accumulating ora rarefying approach. But before representing data, we need to collect it, i.e.we need to sample it.
For some datasets, information is collected from observed individuals (as previously).Often surveys on vertebrates are obtained in this manner, recording the speciesidentity for the first observed animal, then the identity for the second observedanimal and so on. In such situation, the only accumulation / rarefaction curvethat can be calculated is an individual-based curve. Such a sampling approachis called individual-based collection.
Alternatively, one could establish a series of squares (equivalent to samples,used for reasons of clarity) in each plot, record the number and identity ofall the organisms (e.g. trees) within each square, and accumulate the totalnumber of species as additional squares. This is an example of a sample-based collection.
The difference between the individual-based and sample-based species accumulation(as can be seen in figure 3) is a result of the fact that species are not distributedrandomly over the sites. Remember that individual-based species accumulationis based on randomly selecting individuals from the entire set of individualsnot taking site information into account. If both curves have similar patterns,you can conclude that species are distributed at random over the sites.
The rarefaction.shared command willgenerate inter-sample rarefaction curves using a re-sampling withoutreplacement approach. The traditional way that ecologists userarefaction is not to randomize the sampling order within a sample,rather between samples. For instance, if we wanted to know the number ofOTUs in the human colon, we might sample from various sites within thecolon, and sequence a bunch of 16S rRNA genes. By determining the numberof OTUs in each sample and comparing the composition of those samples itis possible to determine how well you have sampled the biodiversitywithin the individual. mothur has the ability to generate data forinter-sample rarefaction curves for the number of observed species. Forthis tutorial you should download and decompress Patient70Data.zip
The rarefaction curve of annotated species richness is a plot (seeFigure 5.11 of the total number of distinctspecies annotations as a function of the number of sequences sampled.The slope of the right-hand part of the curve is related to the fractionof sampled species that are rare. On the left, a steep slope indicatesthat a large fraction of the species diversity remains to be discovered.If the curve becomes flatter to the right, a reasonable number ofindividuals is sampled: more intensive sampling is likely to yield onlyfew additional species. Sampling curves generally rise quickly at firstand then level off toward an asymptote as fewer new species are foundper unit of individuals collected.
The rarefaction curve is derived from the protein taxonomic annotationsand is subject to problems stemming from technical artifacts. Theseartifacts can be similar to the ones affecting amplicon sequencing(Reeder and Knight 2009), but the process of inferring species fromprotein similarities may introduce additional uncertainty.
The rarefaction view is available only for taxonomic data. Therarefaction curve of annotated species richness is a plot (see Figure5.18) of the total numberof distinct species annotations as a function of the number of sequencessampled. As shown in Figure5.18, multiple data setscan be included.
The slope of the right-hand part of the curve is related to the fractionof sampled species that are rare. When the rarefaction curve is flat,more intensive sampling is likely to yield only a few additionalspecies. The rarefaction curve is derived from the protein taxonomicannotations and is subject to problems stemming from technicalartifacts. These artifacts can be similar to the ones affecting ampliconsequencing (Reeder and Knight 2009), but the process of inferringspecies from protein similarities may introduce additional uncertainty.
Sampling curves generally rise very quickly at first and then level offtoward an asymptote as fewer new species are found per unit ofindividuals collected. These rarefaction curves are calculated from thetable of species abundance. The curves represent the average number ofdifferent species annotations for subsamples of the the completedataset.
Button Taxa (see above) recalls the taxa of the table, with some parameters.Five (editable) columns contain:
- One letter of life form (decisive for pollen sum, AP/NAP diagram and so on). The letters are defined by the user, however, we use t-trees, h-herbs, s-shrubs, d-dwarf shrubs, l-local, n-non pollen, i-indicator, and x
- Sequential number of taxon for diagram (see also Set of taxa)
- One letter of color or pattern symbol for the curve
- Taxon name to be printed above the curve (no limitations for that text, may be anything, of any length)
- Miscellaneous information (letter b or p results in plotting Betula and Pinus pollen curves in form of circles, on the AP/NAP diagram; the text: %20 means that curve is to be exactly of 20% width)
In order to plot the curves of absolute concentration of pollen the counts of the indicator are necessary. The program recognize the indicator taxon by the life form "i". In case of plotting diagram without use of the list of taxa, i.e. only with the pollen table, the life form of proper taxon (for example Lycopodium) is to be changed to i (see figure below).
Some buttons are visible only if available. For example Taxa is invisible when spreadsheet with taxa names is actually displayed. Test one curve The program is fast, however, memory demanding, so try at first one curve (indicated on the spreadsheet with taxa)Diagram Pressing that produces diagram for all taxa chosen in taxa spreadsheetBest quality. Normal (1/2). Draft (1/5) Try at fist to produce smaller diagram (2 or 5 times smaller). The final, Best quality diagram is large, in sense of file size (kB). In case of difficulties in producing Best quality diagram try: (1) Normal diagram (may be good enough), (2) use smaller vertical or horizontal scale, (3) use smaller font, (4) change in Windows settings color precision to 256 colors only, (5) plot diagram in a few separate parts (for example: trees, herbs, others) to be united later, in some graphical program or in Sum_d.exe.Taxa Recalls spreadsheet with taxa names and parameters Multi diagram When selected, next diagrams or single curves are added to previously plotted. New pollen table may be loaded, for comparison of, for example Quercus curves.no grey Enlargements of curves will by white, no grey (if no color is applied) what means that diagram would be b&w, and so much smaller in sizeProject
Save diagram Shows Save dialog to save bitmap producedParameters Shows small dialog with All parametersLayout That menu is described belowTaxa arrangement That menu is described belowNumerical analysis See Numerical analysisView diagram Shows window with the entire diagram visible. Note, that diagram shown is of poor quality, what has nothing in common with its real qualityLayoutSum (define pollen sum) Shows dialog where pollen sum may be defined (it is the sequence of letters, here is: tsdh (trees+shrubs+dwarf shrubs+herbs)). To obtain concentration diagram the indicator taxon with life form "i" is necessary. Amount of indicator added is defined in Parameters/Added indicator=10000. Option Numbers (1:1) means that row counts will be plotted.Scales (of % and of cm) Shows dialog where scales may be adjusted. There are two ways to define the vertical scale. Simply setting the number of pixels per depth unit (or age unit) used in the pollen table, or by defining the aspect ratio of the diagram. Which way is used is indicated by the white color of the field. The number in the field Proportion is the ratio of pollen curve height to the 100% curve width. Fragment of profile Shows dialog where you may decide to plot only some part of diagram.AP/NAP Switch on/off diagram of type AP/NAP (with all curves "added")Histogram/macro Switch on/off rectangular diagram. Below: the first diagram is obtained with: Histogram=20 the second: Histogram=50 the last: Histogram=Cyclogram (pie) Switch on/off cyclogram instead of typical diagramSample depths Switch on/off printing depthsLithology Click these manu option to show Lithology tab of Parameters dialog (see Fig. below). Type or paste (Ctrl-V) description of lithology column to the large field at the left of the dialog. The format of the text is precisely defined. In each row there is: upper depth - space or tab - type of sediment - space or tab - lower depth. (The same unit of depth (or age) as used in the table.) The type of sediment is according to Troll-Smith; two letters (the first is capital) followed by the number 1, 2, or 3. Which types of sediment are available is given in the dialog. The width of the lithology column is defined automatically, however, it can be defined by parameter Lithol Width=. More than one type of sediment can be plotted at the same depths (see the small diagram below; 250-300 cm). Name of the column can be changed in the dialog shown below (default is 'Lithology').Vertical axis See the diagram above - the column "depth". The scale is plotted automatically, however, the amount of numbers can by adjusted by the parameter Vertical scale, how dense (0-1)=. The name for the axis is defined by the parameter Vertical axis name= (default is 'depth').Print values of sums Switch on/off printing sums (next to the last curve)Font Shows dialog where font size may be changed as well as proportion of font of taxa names size to that of depths. Also skewed taxa names may be chosen. Try to select the check box Test on one curve. Note that more font parameters are available after clicking Parameters (All).Colors/Patterns Shows dialog where the available colors are presented, with the letter symbols assigned to them. New colors may be created here and assigned to the letter symbols and/or to the taxa/sample font. Colors may be adjusted using scroll bars. When the proper color is obtained select the letter and press the button Assign to. Exaggerations in color Switch on/off gray color for enlarged curve. Switching it off may result in much smaller bitmapColor to all taxa (F6) Click it to assign color (defined in Parameters/Color for all=) to all taxa.Smoothing Switch on/off Gaussian smoothing (averaging) of pollen curves. Degree of smoothing is defined by Parameters/Smoothing=10 (below: curves on the left are obtained with Smoothing=10 on the right with Smoothing=30)Taxa arrangement10, 20, 30,...Assigns to the sequence of taxa numbers like: 10, 20, 30, ...Set of taxa (paste from Clipboard)Pastes from Clipboard set of taxa (previously copied (Ctrl-C) to the Clipboard from Excel, Word, Notepad...). Taxa will get numbers according to the order of taxa in Set of taxa (taxa not included in the Set will not be plotted).Set of taxa (load from file)Shows dialog Open, where text file containing set of taxa may be chosen and loaded.Exclude all Clears all the column (no taxon will be plotted)10 first Good for trialsSearch for summed up Search for the first taxon from group of summed up taxa (in order to modify that taxon name)Manually 10, 20, 30,... Try it, after switching it on, click on the second columnManually 10, 10, 10... Try it, click on the second columnManually remove Try it, click on the second columnAccording to life form assign numbers according to Parameters/ nr 10=... For example, in case of nr 10=ts, nr 20=dh all taxa with life form t or s (trees, shrubs) will get number 10, and will be summed up, while dwarf shrubs and herbs will get 20, and also will be summed up. It is the way to prepare taxa for AP/NAP diagram.Stratigraphically arranges taxa in stratigraphical order, only taxa which already posses numbers are taken into accountExclude if too few grains If the sum of pollen grains in the taxon is lower or equal to the number given in the All Parameters (Exclude if too few grains=...), the taxon position number for the diagram is cleared.Change numbers to "X" Exchanges numbers to "X", to mark taxa already plottedSave chosen taxa as Set Shows dialog Save as to save taxa currently selected for diagram plotting as set of taxa, for future use. Parameter Set of taxa save with=n (n-names, 1-numbers, c-codes) decides if set of taxa will be saved in text file using full taxa names (n), taxa numbers (1) or short taxa codes (c).Text description of samplesAt the left part of the Text tab of Parameters dialog, there are options for placing text instead of sample depths.ZonesAt the right part of the Text tab of Parameters dialog (see figure above), there are options for adding zones description at the end of the diagram. The text of zones definition has the following structure. In each row there is: depth - tabulator - letter s or d or nothing - tabulator - zone name. It is impossible to type tabulator into the proper field in the dialog, so the text is to be prepared in Excel, Word, or Notepad.
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