I've done a CCA analysis with the R package vegan on some macrofaunal data and environmental variables, trying to figure out which variables affect the macrofauna and how much. My CCA output is as follows:
Call: cca(formula = abun_df ~ NH4_inv_PW + C_1cm + PLI + season_year, data = env_PLI)
Inertia Proportion Rank
Total 1.2647 1.0000
Constrained 0.4077 0.3224 4
Unconstrained 0.8570 0.6776 20
Inertia is scaled Chi-square
Eigenvalues, and their contribution to the scaled Chi-square
Importance of components:
CCA1 CCA2 CCA3 CCA4 CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 CA9 CA10
Eigenvalue 0.2137 0.1369 0.04801 0.009139 0.1727 0.1386 0.07814 0.07174 0.06194 0.05172 0.04864 0.04413 0.03307 0.02865
Proportion Explained 0.1689 0.1082 0.03796 0.007226 0.1366 0.1096 0.06178 0.05672 0.04897 0.04089 0.03846 0.03489 0.02614 0.02265
Cumulative Proportion 0.1689 0.2772 0.31512 0.322350 0.4589 0.5685 0.63029 0.68702 0.73599 0.77688 0.81534 0.85023 0.87638 0.89903
CA11 CA12 CA13 CA14 CA15 CA16 CA17 CA18 CA19 CA20
Eigenvalue 0.02083 0.01980 0.01885 0.01825 0.01540 0.01308 0.009518 0.005976 0.003381 0.002617
Proportion Explained 0.01647 0.01566 0.01490 0.01443 0.01218 0.01034 0.007526 0.004725 0.002673 0.002069
Cumulative Proportion 0.91550 0.93116 0.94606 0.96049 0.97266 0.98301 0.990533 0.995258 0.997931 1.000000
Accumulated constrained eigenvalues
Importance of components:
CCA1 CCA2 CCA3 CCA4
Eigenvalue 0.2137 0.1369 0.04801 0.009139
Proportion Explained 0.5241 0.3358 0.11776 0.022417
Cumulative Proportion 0.5241 0.8598 0.97758 1.000000
Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
And some significance tests:
> #is CCA significant?
> anova(Koverhar_CCA)
Permutation test for cca under reduced model
Permutation: free
Number of permutations: 999
Model: cca(formula = abun_df ~ NH4_inv_PW + C_1cm + PLI + season_year, data = env_PLI)
Df ChiSquare F Pr(>F)
Model 4 0.40769 5.3515 0.001 ***
Residual 45 0.85705
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #are axes significant?
> anova(Koverhar_CCA, by = "axis")
Permutation test for cca under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 999
Model: cca(formula = abun_df ~ NH4_inv_PW + C_1cm + PLI + season_year, data = env_PLI)
Df ChiSquare F Pr(>F)
CCA1 1 0.21365 11.2181 0.001 ***
CCA2 1 0.13689 7.1873 0.001 ***
CCA3 1 0.04801 2.5207 0.017 *
CCA4 1 0.00914 0.4799 0.931
Residual 45 0.85705
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #are vectors significant?
> anova(Koverhar_CCA, by = "term", permutations = 999)
Permutation test for cca under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999
Model: cca(formula = abun_df ~ NH4_inv_PW + C_1cm + PLI + season_year, data = env_PLI)
Df ChiSquare F Pr(>F)
NH4_inv_PW 1 0.10039 5.2713 0.001 ***
C_1cm 1 0.07373 3.8715 0.003 **
PLI 1 0.08864 4.6540 0.001 ***
season_year 1 0.14492 7.6092 0.001 ***
Residual 45 0.85705
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Am I correct when I interpret this to mean that:
1) the model explains ~32% of the observed variation
2) the first two axis of CCA are significant, and explain ~52% and ~34% of the variation in the model, respectively
3) all four environmental variables (NH4_inv_PW + C_1cm + PLI + season_year) included in the model are significant
Also, is there any way to find out how much of the variation in the macrofaunal data is explained by each environmental variable? I'm new to statistical analysis, and my supervisors haven't used R (or, apparently, CCA), so I'm slightly lost on how to use it and interpret the results.
