Both year: CSP soil and vegetation analysis
July 2024
Data exploration
We collected three soil samples at 2, 5 and 8 meters of the 10-m-length transect. We did so for 62 vegetation transects done during spring 2022 and 2024.
From soil sampling, We measured the following soil physico-chemical variables:
Dataset features explained
wetanddry weightphweightand volume of stones (v_stones) within the cylinders. We have the weight just for the soil sampling of 2024.bulk.density: Soil bulk density (\(\frac{g}{cm^{3}}\))depth: Soil depth (cm)soil compaction: just for the soil sampling of 2024.HCL Test:Limestone : In cold condition, generalized effervescence under HCl
Dolomite : In cold condition, little or non effervescence under HCL
Four categories from 0 to 3 indicating effervescence under HCL
0 : No detectable reaction
1 : Weak, a few bubbles or murmur of effervescence
2 : Medium, bubbles in continuous layer
3 : Vivid, several superimposed layers of bubbles
Munsell soil colour :
hue: basic colorChroma: the strength or weakness of a colourValue: the lightness or the darkness of the colourdescription color: name of the color
om: Percentage (%) of organic matter calculated after being in muffle furnace at 550 °C during 4 hours.N: Percentage (%) of nitrogen in a sample weighing ~ 35 mg. CHN analysis.C: Percentage (%) of carbon (organic + inorganic) in a sample weighing ~ 35 mg. CHN analysis.
For the statistical analysis we kept the variables that are presented in the following section.
Data summary of variable used in the statistics
Here we show the summary of the variables that were already averaged by replicates by transect. In brief, in the dataset we have 62 values of each soil variable.
Also we recorded litter, stones,
rock and moss in the field along the
vegetation transect.
## ph bulk_density soil_depth hcl_category
## Min. :6.480 Min. :0.5000 Min. : 5.80 Min. :0.0000
## 1st Qu.:6.822 1st Qu.:0.9000 1st Qu.: 11.70 1st Qu.:0.0000
## Median :7.015 Median :1.0000 Median : 16.50 Median :0.7000
## Mean :7.054 Mean :0.9887 Mean : 23.99 Mean :0.6806
## 3rd Qu.:7.265 3rd Qu.:1.1000 3rd Qu.: 25.45 3rd Qu.:1.0000
## Max. :7.710 Max. :1.6000 Max. :101.00 Max. :3.0000
## value N C om
## Min. :2.000 Min. :0.1930 Min. : 2.383 Min. : 5.470
## 1st Qu.:3.000 1st Qu.:0.3415 1st Qu.: 4.123 1st Qu.: 9.153
## Median :3.000 Median :0.4535 Median : 5.832 Median :11.521
## Mean :3.319 Mean :0.5059 Mean : 6.538 Mean :12.691
## 3rd Qu.:4.000 3rd Qu.:0.7000 3rd Qu.: 8.231 3rd Qu.:17.019
## Max. :5.700 Max. :1.0970 Max. :13.369 Max. :26.191
## v_stones lit ston rock
## Min. : 1.00 Min. : 4.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 7.30 1st Qu.:14.00 1st Qu.:10.25 1st Qu.: 1.000
## Median : 10.85 Median :17.00 Median :14.50 Median : 4.000
## Mean : 24.72 Mean :18.94 Mean :16.11 Mean : 5.258
## 3rd Qu.: 41.83 3rd Qu.:22.75 3rd Qu.:21.00 3rd Qu.: 9.000
## Max. :123.70 Max. :37.00 Max. :42.00 Max. :20.000
## moss
## Min. : 0.000
## 1st Qu.: 1.000
## Median : 3.500
## Mean : 6.129
## 3rd Qu.:10.500
## Max. :24.000Data visualization
Correlation matrix
Spearman correlation
## ph bulk_density soil_depth hcl_category value N C om
## ph 1
## bulk_density 0.42 1
## soil_depth 0.13 -0.04 1
## hcl_category 0.48 0.34 0.01 1
## value 0.27 0.44 0.17 0.1 1
## N -0.26 -0.49 -0.37 -0.01 -0.7 1
## C 0.18 -0.2 -0.25 0.34 -0.26 0.63 1
## om -0.27 -0.53 -0.33 -0.06 -0.71 0.98 0.59 1
## v_stones -0.03 -0.18 -0.32 -0.06 -0.03 0.2 0.21 0.16
## lit -0.04 -0.07 -0.09 -0.21 -0.02 -0.05 -0.01 -0.07
## ston 0.26 0.17 -0.25 0.37 0.02 0.18 0.15 0.17
## rock -0.3 -0.38 0.02 -0.43 -0.02 0.11 -0.07 0.12
## moss -0.32 -0.44 -0.04 -0.39 -0.01 0.04 -0.08 0.08
## v_stones lit ston rock moss
## ph
## bulk_density
## soil_depth
## hcl_category
## value
## N
## C
## om
## v_stones 1
## lit 0.03 1
## ston 0.43 -0.34 1
## rock 0.24 0.05 -0.14 1
## moss 0.2 0.07 -0.3 0.26 1Following criterion of |r| > 0.7 for avoid collinearity (Dormann et al. 2013), organic matter is highly correlated to Value and Nitrogen so we removed this variable for the multivariate analysis.
PCA of soil variables
# do not subset db to keep rownames
soil_pca_1 <- rda(db_soil_22_24_q_tp_st, scale = TRUE) #scale=TRUE calls for a standardization of the variables
sum = summary(soil_pca_1) # Default scaling 2
sum$cont## $importance
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Eigenvalue 3.0426 2.2154 1.2884 1.12591 1.06890 0.86364 0.8064
## Proportion Explained 0.2536 0.1846 0.1074 0.09383 0.08908 0.07197 0.0672
## Cumulative Proportion 0.2536 0.4382 0.5455 0.63937 0.72844 0.80041 0.8676
## PC8 PC9 PC10 PC11 PC12
## Eigenvalue 0.51260 0.46479 0.26795 0.24024 0.103044
## Proportion Explained 0.04272 0.03873 0.02233 0.02002 0.008587
## Cumulative Proportion 0.91033 0.94906 0.97139 0.99141 1.000000Principal component one explains 25.4%, component two explains 18.4%, and component three explains 10.7% of the variance.
library(tibble)
inv_scores = data.frame(soil_pca_1$CA$u)
inv_scores1 <- right_join(tibble::rownames_to_column(db_soil_22_24_q_tp_st), rownames_to_column(data.frame(inv_scores)), by = "rowname")
# add categories like common instead of df_grazing_ind_v2 and this code has sense.
var_scores = data.frame(soil_pca_1$CA$v)
Variables and principal components 1-2
Transects and principal Components 1-2
distance-based Redundancy Analysis (db-RDA): Modelling of soil variables and vegetation data
# similar of grazing_indicator rmd
# capscale() with raw (site by species) data (Borcard et al. 2018)
rda_22_24_soil <- capscale(community_data_density_22_23.72_sin_cus_filt ~ ph+ bulk_density+ soil_depth+ hcl_category+ value+ N+ C+ v_stones+ lit+ ston+ rock+ moss + Condition(scores(as.matrix(coord_22_23))), data = db_soil_22_24_q_tp_st, distance = "bray",add = "lingoes")
#rda_22_24_soil$pCCA$tot.chi #inertia of condition
#rda_22_24_soil$CCA$tot.chi #Constrained inertia
# Total variance explained by the model
Tot.var <- rda_22_24_soil$tot.chi
# Constrained and unconstrained eigenvalues
eig.val <- c(rda_22_24_soil$CCA$eig, rda_22_24_soil$CA$eig) ## sum(eig.val)+1.133 (cond.) = 20.099 (tot.chi)
# Relative eigenvalues of Y-hat
eig.val.rel <- eig.val / Tot.var
# Variability explained by the 1,2 and 3 of constrained RDA axes
100*eig.val.rel[1:3] ## other way 100*rda_22_24_soil$CCA$eig[1:3]/Tot.var## CAP1 CAP2 CAP3
## 6.212631 4.685372 3.220668## scores(as.matrix(coord_22_23))x scores(as.matrix(coord_22_23))y
## 2.260562 2.466362
## ph bulk_density
## 2.871942 2.500640
## soil_depth hcl_category
## 1.661522 2.191023
## value N
## 3.181044 5.550705
## C v_stones
## 3.240280 1.541630
## lit ston
## 1.420053 2.242196
## rock moss
## 1.648604 1.572866#Test the significance of the model
anova(rda_22_24_soil, by = "axis",permutations = how(nperm = 999)) ## Permutation test for capscale under reduced model
## Forward tests for axes
## Permutation: free
## Number of permutations: 999
##
## Model: capscale(formula = community_data_density_22_23.72_sin_cus_filt ~ ph + bulk_density + soil_depth + hcl_category + value + N + C + v_stones + lit + ston + rock + moss + Condition(scores(as.matrix(coord_22_23))), data = db_soil_22_24_q_tp_st, distance = "bray", add = "lingoes")
## Df SumOfSqs F Pr(>F)
## CAP1 1 1.2487 4.2776 0.001 ***
## CAP2 1 0.9417 3.2260 0.009 **
## CAP3 1 0.6473 2.2175 0.194
## CAP4 1 0.4555 1.5604 0.895
## CAP5 1 0.3658 1.2532 0.997
## CAP6 1 0.3440 1.1783 0.997
## CAP7 1 0.3118 1.0682 0.997
## CAP8 1 0.2658 0.9107 1.000
## CAP9 1 0.1939 0.6644 1.000
## CAP10 1 0.1712 0.5866 1.000
## CAP11 1 0.1594 0.5459 1.000
## CAP12 1 0.1406 0.4817 1.000
## Residual 47 13.7198
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Figure: Species and varaibles
##
## -----------------------------------------------------------------------
## Site constraints (lc) selected. To obtain site scores that are weighted
## sums of species scores (default in vegan), argument site.sc must be set
## to wa.
## -----------------------------------------------------------------------
Figure: Soil variables and vegetation transects. Angles between variables reflect their correlation
CCA
Using the same dataset of the RDA but now doing a CCA.
# use raw data (Borcard et al. 2018)
# limits of cca https://uw.pressbooks.pub/appliedmultivariatestatistics/chapter/ca-dca-and-cca/
spe.cca <- cca(community_data_density_22_23.72_sin_cus_filt ~ ., db_soil_22_24_q_tp_st)
spe_cca_sum = summary(spe.cca) # Scaling 2 (default)
# Variability explained by axes 1, 2 and 3.
spe_cca_sum$cont$importance[,c(1:4)] ## CCA1 CCA2 CCA3 CCA4
## Eigenvalue 0.2033229 0.14373978 0.12674846 0.10380807
## Proportion Explained 0.0575909 0.04071407 0.03590131 0.02940348
## Cumulative Proportion 0.0575909 0.09830497 0.13420628 0.16360976## $r.squared
## [1] 0.2686791
##
## $adj.r.squared
## [1] 0.09015359# ANOVA like permutation test for CCA to assess the significance of constraints.
anova(spe.cca, by = "axis",permutations = how(nperm = 999)) ## Permutation test for cca under reduced model
## Forward tests for axes
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = community_data_density_22_23.72_sin_cus_filt ~ ph + bulk_density + soil_depth + hcl_category + value + N + C + v_stones + lit + ston + rock + moss, data = db_soil_22_24_q_tp_st)
## Df ChiSquare F Pr(>F)
## CCA1 1 0.20332 3.8587 0.003 **
## CCA2 1 0.14374 2.7279 0.119
## CCA3 1 0.12675 2.4055 0.225
## CCA4 1 0.10381 1.9701 0.473
## CCA5 1 0.07563 1.4354 0.955
## CCA6 1 0.06828 1.2958 0.976
## CCA7 1 0.05497 1.0432 0.999
## CCA8 1 0.04868 0.9238 1.000
## CCA9 1 0.03843 0.7294 1.000
## CCA10 1 0.03421 0.6493 1.000
## CCA11 1 0.03005 0.5703 1.000
## CCA12 1 0.02069 0.3927 1.000
## Residual 49 2.58191
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sites and soil variables
Species and soil variables
CCA uses chi-square distances which are particularly sensitive to or affected by rare species (Borcard et al. 2018). Note that we already removed species present in only one transect yet an option could be to remove also species present in very few transects.