How Do I Upload a Library Vegan
Table of Contents
Section: Ordination analysis
RDA, tb-RDA, CCA & db-RDA (constrained ordination)
Example 1: How much variation explain soil pH and soil depth in the Vltava valley vegetation? (tb-RDA)
In this instance, we will utilise constrained ordination (tb-RDA) on Vltava river valley dataset. We will enquire how much variance in species composition can be explained by two variables, soil pH and soil depth. Both are of import factors for plant growth, and moreover, in the study area, they are somewhat correlated (shallower soils have lower pH since the prevailing geological substrate is acrid).
First, upload the Vltava river valley data:
vltava.spe <- read.delim ( 'https://raw.githubusercontent.com/zdealveindy/anadat-r/master/data/vltava-spe.txt', row.names = 1 ) vltava.env <- read.delim ( 'https://raw.githubusercontent.com/zdealveindy/anadat-r/master/data/vltava-env.txt' ) spe <- vltava.spe # rename variables to make them shorter env <- vltava.env [, c ( 'pH', 'SOILDPT' ) ] # select only two explanatory variables
Upload library vegan and calculate tb-RDA based on Hellinger pre-transformed species composition data. Annotation that since the original data stand for estimates of percent cover, it is better to log transform these values first earlier Hellinger transformation is washed (using function log1p, which calculates log (x+one) to avoid log (0)):
library (vegan) spe.log <- log1p (spe) # species data are in per centum scale which is strongly rightskewed, better to transform them spe.hell <- decostand (spe.log, 'hell' ) # we are planning to do tb-RDA, this is Hellinger pre-transformation tbRDA <- rda (spe.hell ~ pH + SOILDPT, data = env) # calculate tb-RDA with two explanatory variables tbRDA
The result printed by rda office is the following:
Call: rda(formula = spe.hell ~ pH + SOILDPT, data = env) Inertia Proportion Rank Total 0.70476 1.00000 Constrained 0.06250 0.08869 ii Unconstrained 0.64226 0.91131 94 Inertia is variance Eigenvalues for constrained axes: RDA1 RDA2 0.04023 0.02227 Eigenvalues for unconstrained axes: PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 0.07321 0.04857 0.04074 0.03144 0.02604 0.02152 0.01917 0.01715 (Showed only eight of all 94 unconstrained eigenvalues)
and, the aforementioned with comments:
The two variables explain 8.9% of the variance (the row Constrained and cavalcade Proportion in the table to a higher place, tin be calculated also as the sum of eigenvalues for the constrained axes divided by full variance (inertia): (0.04023+0.02227) /0.70476=0.08869. The beginning constrained axis (RDA1) explains 0.04023/0.70476=5.7% of the variance, while the second (RDA2) explains 0.02227/0.70476=3.two%. Note that the first unconstrained axis (PC1) represents 0.07321/0.70476=10.iv% of the total variance, which is more the variance explained by both explanatory variables together; the first two unconstrained explain (0.07321+0.04857)/0.70476=17.3%. This means that the dataset may be structured by some strong environmental variable(southward) different from pH and soil depth (we will check this below).
The relationship between the variation represented past private (constrained and unconstrained) ordination axes tin can be displayed using the barplot of percentage variance explained past individual axes (ie their eigenvalue divided by total inertia):
constrained_eig <- tbRDA$CCA$eig/tbRDA$tot.chi * 100 unconstrained_eig <- tbRDA$CA$eig/tbRDA$tot.chi * 100 expl_var <- c (constrained_eig, unconstrained_eig) barplot (expl_var[ 1 : 20 ], col = c ( rep ( 'cerise', length (constrained_eig) ), rep ( 'blackness', length (unconstrained_eig) ) ), las = two, ylab = '% variation' )
(annotation that all information about the eigenvalues and full inertia is in the object calculated by vegan's ordination function (rda in this case, stored in the list tbRDA), you just need to search a bit within to find it - consider using the function str to check the structure of tbRDA showtime).
Let'south run across the ordination diagram:
ordiplot (tbRDA)
Example two: What may be an ecological meaning of unconstrained axes in constrained ordination? (tb-RDA)
This example is a direct continuation of Example ane above.
When checking results of tb-RDA on Vltava data, calculated in Example 1 using tb-RDA, 1 may notice that the commencement and 2d unconstrained ordination axes represent considerably more variation than the 2 constrained axes:
vltava.spe <- read.delim ( 'https://raw.githubusercontent.com/zdealveindy/anadat-r/master/data/vltava-spe.txt', row.names = 1 ) vltava.env <- read.delim ( 'https://raw.githubusercontent.com/zdealveindy/anadat-r/main/data/vltava-env.txt' ) spe <- vltava.spe # rename variables to make them shorter env <- vltava.env [, c ( 'pH', 'SOILDPT' ) ] # select only 2 explanatory variables library (vegan) spe.log <- log1p (spe) spe.log.hell <- decostand (spe.log, 'hell' ) tbRDA <- rda (spe.log.hell ~ pH + SOILDPT, data = env) head ( summary (tbRDA) ) # prints first lines of the summary of tbRDA
Call: rda(formula = spe.log.hell ~ pH + SOILDPT, data = env) Partitioning of variance: Inertia Proportion Total 0.7048 one.00000 Constrained 0.0625 0.08869 Unconstrained 0.6423 0.91131 Eigenvalues, and their contribution to the variance Importance of components: RDA1 RDA2 PC1 PC2 PC3 PC4 PC5 PC6 Eigenvalue 0.04023 0.02227 0.07321 0.04857 0.04074 0.03144 0.02604 0.02152 Proportion Explained 0.05709 0.03160 0.10388 0.06891 0.05781 0.04461 0.03695 0.03054 Cumulative Proportion 0.05709 0.08869 0.19257 0.26149 0.31929 0.36391 0.40086 0.43139 ...
From the output above, you tin can see (rows "Proportion Explained" that the first and the second constrained axes (RDA1, RDA2), explain 5.7 and 3.1% of the variation, respectively, while the kickoff and second unconstrained axes (PC1, PC2) stand for ten.4 and 6.9% of the variation, respectively. This indicates that after accounting for soil pH and soil depth (the two variables used equally explanatory), there is all the same quite a considerable variation in species composition left, possibly calling for interpretation.
1 matter we can do is to create an ordination diagram with the outset and 2nd unconstrained ordination axis (PC1, PC2), and project species into it, and promise that they can aid u.s.a. to empathize what environmental variables may be behind these gradients. Of course, this expects that you have at least marginal knowledge about the ecological behaviour of these species (I recollect I exercise, since I spent several years working on the vegetation of these valleys, and then let's endeavor).
ordiplot (tbRDA, brandish = 'species', choices = c ( 3,four ), type = 'n' ) orditorp (tbRDA, display = 'species', choices = c ( iii,4 ), pcol = 'grey', pch = '+' )
At that place is 274 species in the Vltava dataset, so I used orditorp function to draw simply some of them (run across Ordination diagrams > Examples for details on how to employ this office). Also, since RDA is a linear office, the species should be displayed by vectors, not every bit centroids, but if we want to brandish only some of the species, this choice in R is not so simple (you may demand to use envfit function to project vectors of species onto the ordination diagram). Species are displayed by their abbreviation, where the first four letters are from the genus name, the last four letters from species name, and the numbers point the layer (1 for herb layer, 23 for merged shrub and tree layer; for example, Tilicor23 is an abbreviation of Tilia cordata in shrub and tree layer).
When interpreting the first (horizontal) unconstrained centrality (PC1), we tin run into that the left role (negative scores) is related to high abundances of Quercus petraea (Querpet23) and Pinus sylvestris (Pinusyl23) in the shrub and tree layer, and Avenella flexuosa in the herb layer (Avefle1), while the right part (positive scores) is related to high abundances of Abies alba in shrub and tree layer (Abiealb23), and Dryopteris filix-mas (Dryofil1), Galeobdolon montanum (Galemon1) and Lunaria rediviva (Lunared1) in the herb layer. These species seem to bespeak opposite ends of the gradient of light (light-demanding species on the left, shade-tolerant on the correct) and nutrient availability (nutrient demanding species on the correct, and species of oligotrophic site on the right). When interpreting the 2d (vertical) unconstrained axis (PC2), the lower part (negative scores) is related to loftier abundances of Impatiens glandulifera (Impagla1), Lycopus europaeus (Lycoeur1) and Aegopodium podagrarium (Aegopod1) in the herb layer, while the upper part (positive scores) are related to high abundances of Tilia cordata (Tilicor23) and Fagus sylvatica (Fagusyl23) in the shrub and tree layer, and Poa nemoralis (Poa.nem1), Luzula luzuloides (Luzuluz1) and Convalaria majalis (Convmaj1) in the herb layer; this centrality seem to negatively correlate with the slope of moisture, with species indicating wet soil of the alluvial forest at the lower part of the axis and mesic species in the upper office.
If we are not familiar with ecological requirements of the species, but accept their tabulated Ellenberg-type indicator values in paw (unremarkably for soil pH, moisture, nutrients, air temperature, light availability and continentality), nosotros can use them to calculate mean indicator values for each plot, representing their estimated ecological weather condition. Vltava dataset (vltava.env) includes such calculated mEIV (hateful Ellenberg indicator values), and these can be used as supplementary in the ordination diagram of the start and second unconstrained ordination axes:
ordiplot (tbRDA, choices = c ( iii,four ), type = 'n' ) points (tbRDA, choices = c ( three,four ), display = 'sites', pch = equally.grapheme (vltava.env$GROUP), col = vltava.env$GROUP) ef <- envfit (tbRDA, vltava.env [,23 : 28 ], choices = c ( 3,4 ), permutations = 0 ) plot (ef)
ef
***VECTORS PC1 PC2 r2 LIGHT -0.93135 -0.36411 0.6282 TEMP -0.97246 -0.23305 0.2352 CONT -0.86643 -0.49929 0.0885 MOIST 0.44495 -0.89556 0.4706 REACT 0.95614 -0.29291 0.1166 NUTR 0.94383 -0.33044 0.4519
The highest R2 of the regression with the outset two axes have light, moisture and nutrients, with low-cal and nutrients associated mostly with the commencement unconstrained centrality and the moisture more often than not with the 2d. It seems that these ecological factors, not related to soil pH and soil depth, are important for the studied vegetation, but were not measured. This interpretation fits well with the interpretation based on the human relationship between axes and abundances of species listed to a higher place.
Notation one more thing: when applying the function envfit on hateful Ellenberg indicator values, I did non test for the significance (I set the argument permutation = 0). This has a pregnant: both hateful Ellenberg indicator values and sample scores on ordination axes are calculated from the same matrix of species limerick, and to directly exam their relationship would be wrong (since they are not independent, it is piece of cake to reject the zip hypothesis stating that these variables are contained). Check the section Analysis of species attributes for a detailed explanation on how to solve this. 
Example three: How different are cookies from pastries and pizzas (CCA)?
This case is using Divergence between cookies, pastries and pizzas dataset, which I found on reddit.com, posted by author everest4ever. As the postal service on reddit.com goes, the author attended the Christmas political party at his function with "Christmas cookie competition", which sparked a "huge debate well-nigh what are eligible entries for the cookie contest (eastward.chiliad. are mini-pizzas cookies?)". The writer decided to approach the give-and-take rigorously and did the following: "I scraped 1931 recipes from the Food Network that contain the keywords cookies (my grouping of involvement), pastry, or pizza (two command groups). Side by side, I extracted the ingredient list and pooled similar ingredients together (e.g. salt, seasalt, Kosher salt), coming up with a full of 133 unique ingredients. I ended upwardly with a 1931×133 matrix, where each row is one recipe, and each column is whether this recipe contains a sure ingredient (0 or 1)". The writer did PCA analysis on the information accompanied by some clustering and predictions, only to show that "NO IAN AND JOSEPH YOUR FUCKING EGG TARTS AREN'T COOKIES, NO MATTER HOW GOOD THEY WERE!!". I think we can also use this dataset for a simple constrained ordination do. First import the data:
recipes.ingr <- read.delim ( 'https://raw.githubusercontent.com/zdealveindy/anadat-r/primary/information/cookie_dataset_everest4ever_composition.txt', row.names = i ) recipes.type <- read.delim ( 'https://raw.githubusercontent.com/zdealveindy/anadat-r/master/data/cookie_dataset_everest4ever_type.txt', row.names = i )
Data stand for a matrix of presence/absence of different ingredients in individual recipes (each row of recipes.ingr matrix is a recipe, each column i ingredients). To know which recipe is classified how, nosotros need a variable type_of_food in the data frame recipes.blazon.
To get familiar with data, allow's first summate DCA:
library (vegan) DCA <- decorana (recipes.ingr ) DCA
Call: decorana(veg = recipes.ingr) Detrended correspondence assay with 26 segments. Rescaling of axes with 4 iterations. DCA1 DCA2 DCA3 DCA4 Eigenvalues 0.5633 0.2598 0.2224 0.2185 Decorana values 0.5918 0.2622 0.2352 0.2138 Axis lengths 6.2276 4.1302 5.6396 three.5449
The output shows that the length of the first axis is half dozen.two S.D. units, then unimodal ordination methods is advisable. The ordination diagram which displays recipes of cookies, pastries and pizzas by different symbols and colours, is more than informative:
type_num <- every bit.numeric ( equally.cistron (recipes.type$type_of_food) ) ordiplot (DCA, type = 'n' ) points (DCA, display = 'sites', col = type_num, pch = type_num) legend ( 'topright', col = 1 : 3, pch = 1 : iii, legend = levels ( as.factor (recipes.type$type_of_food) ) )
(the variable type_num contains numerical values one, 2 and iii in place of Cookies, Pastries and Pizzas from the original type_of_food variable in recipes.type data frame, and then as nosotros can utilize these values every bit colors and symbols in ordination diagram).
Information technology seems that pizzas are somewhat different from the rest (although a part of the pastries is somewhat close), while pastries and cookies class a cloud with a big overlap. Let's attempt to ask the following question: tin can the nomenclature of a recipe into cookies/pastries/pizzas (done largely subjectively past authors of those recipes based on their stance how each category item should expect like) explain the difference in "ingredients composition" of individual recipes? This is a task for constrained ordination. Since the first DCA centrality has length 6.2 S.D. (ie longer than iv S.D.), nosotros use CCA for constrained ordination, with recipes as dependent variable and consignment into the type as explanatory variables. Note that explanatory variable is chiselled with three levels (pastry, cookie, pizza):
blazon <- recipes.type$type_of_food CCA <- cca (recipes.ingr ~ type) CCA
Call: cca(formula = recipes.ingr ~ type) Inertia Proportion Rank Full 14.28961 i.00000 Constrained 0.60311 0.04221 2 Unconstrained 13.68650 0.95779 132 Inertia is scaled Chi-square Eigenvalues for constrained axes: CCA1 CCA2 0.4649 0.1382 Eigenvalues for unconstrained axes: CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 0.30447 0.28409 0.26249 0.25278 0.23942 0.21521 0.21069 0.20674 (Showed simply viii of all 132 unconstrained eigenvalues)
(note that I saved the cavalcade type_of_food from the data frame recipes.type into a variable blazon, not really because I want to simplify the cca (it would need to be CCA <- cca (recipes.ingr ~ type_of_food, data = recipes.type), just that is even so fine), but because this will get in simple to display individual cistron levels onto ordination diagram (the levels are displayed every bit the Name_of_variableName_of_category, which would be besides long with the original names).
Nosotros got two constrained axes (explanatory variable is qualitative with iii cistron levels -> number of contrained axes = number of levels - ane), the first exlaining more than than iii fourth dimension more than than the 2d (eigCCA1 = 0.4649, eigCCA2 = 0.1382, which ways that the start axis represents 0.4649/xiv.28961 = iii.3 % of variance (eigenvalue/total inertia), while the second 0.1382/14.28961 = one.0%. Ordination diagram shows that the offset axis is mostly separating pizzas (right) and cookies+pastries (left), while the second axis is generally separating cookies (up) from pastries (bottom):
ordiplot (CCA, display = c ( 'si', 'cn' ), type = 'n' ) points (CCA, brandish = 'si', col = type_num, pch = type_num) text (CCA, brandish = 'cn', col = 'navy', cex = i.five ) legend ( 'topright', col = 1 : 3, pch = 1 : iii, legend = levels ( as.factor (recipes.type$type_of_food) ) )
Few more than things. First, we should ask whether the CCA ordination is meaning and whether information technology is worth interpreting it:
anova (CCA)
Permutation examination for cca under reduced model Permutation: gratuitous Number of permutations: 999 Model: cca(formula = recipes.ingr ~ type) Df ChiSquare F Pr(>F) Model 2 0.6031 42.479 0.001 *** Residual 1928 xiii.6865 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.one ' ' one
Indeed, information technology is. And how nigh private axes, are they both pregnant? We will use the argument past = "axis" in the function anova - encounter this explanation what it ways:
anova (CCA, by = 'axis' )
Permutation test for cca under reduced model Frontwards tests for axes Permutation: free Number of permutations: 999 Model: cca(formula = recipes.ingr ~ type) Df ChiSquare F Pr(>F) CCA1 1 0.4649 65.493 0.001 *** CCA2 1 0.1382 19.465 0.001 *** Residual 1928 xiii.6865 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' ane
Both axes are significant, which means that even the distinction between cookies and pastries along the second axis is important. So I would say, without farther testing, that not only pizza is (quite obviously) different from cookies, but also much more than ambiguous category pastries are different regarding ingredients they utilise. Btw, permit's meet these ingredients (display species in CCA ordination diagram):
ordiplot (CCA, display = c ( 'sp', 'cn' ), type = 'n' ) orditorp (CCA, display = 'sp', priority = colSums (recipes.ingr ) )
Note that I did not display all 133 ingredients ("species"); otherwise, the diagram gets also cluttered. I used the low-level graphical office orditorp which is adding but some labels and draws others equally symbols. It has argument priority (the species with the highest priority volition exist more likely plotted as text, with lower equally symbols, if there is non enough space); the priority here is the overall frequency of ingredients in the dataset (colSums practical on the recipes.ingr data frame). The diagram shows a clear triangle, with each corner representing one blazon of nutrient. There is a gradient of ingredients connecting pizzas with pastries and pastries with cookies, simply near no ingredients connecting pizzas and cookies (except pine nuts, which tin can perhaps brand it in both pizzas and cookies - but I have no thought). Some ingredients are shared among all three (obviously water and seems that besides honey), some are only for that blazon of food (basil for pizza, puff pastry for pastries and cookies(??) and ice foam for cookies. Please, run across the diagram and guess which particular in your stance should be where (carrots in pastry? non sure...).
Source: https://www.davidzeleny.net/anadat-r/doku.php/en:rda_cca_examples
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