Q1: Do inherent and farmer-modified attributes of coffee agroecosystems appear to have an effect on properties associated with soil health?

Method of Analysis

To explore the covariance of within the groups of variables (independent and dependent variables), below we use: /n - Correlation matrices of continuous variables

Factors of Soil Health (Independent Variables)

Correlation matrices show relationships at p <0.01 Key: Green = positive relationship, Red = negative relationship

Factors of Soil Health (Independent Variables)

Probability of observing erosion based on the other factors

Here we use a multinomial logistic regression to understand the influence of the other factors on the probability of observing erosion within a study block.

Since not all dependent variables were collected at each site, below there are correlation matrices that relate to differently-sized datasets depending on the completeness of the data set. The n for these datasets is described in the table below.

Core Soil Dependent Variables

Correlation matrices show relationships at p <0.01

Core Soil Dependent Variables Plus Bulk Density and Aggregate Stability

Correlation matrices show relationships at p <0.01

Core Soil Dependent Variables Plus Bulk Density, Aggregate Stability and Macrofauna

Correlation matrices show relationships at p <0.05

Simple correlations between continuous IVs and DVs

Showing results significant at p-value <0.01

Q1: To what extent do attributes of soil health correspond to yields within coffee plots when controling for other factors?

Descriptives

Yield by Community

Understanding the Relationship between Agroecosystem Attributes on Soil Health Indicators

“Redundancy analysis is a type of asymmetric canonical analysis, that is, a method that analyses two or more data frames simultaneously by combining ordination and regression. Simple ordination via principal components analysis (PCA) is likely familiar to most readers as a method for characterizing the main axes of variance in a matrix (Y) into uncorrelated (orthogonal) synthetic composite variables (the PC axes). For example, PCA of a genetic data matrix (i.e. n individuals or populations genotyped at p loci) can be used to infer similarities and differences among sampled individuals/populations based on their multilocus genotypes. By comparison, multiple regression is used to model a single response variable (y) using a set of multiple predictor variables (X). If we extend multiple regression to the multivariate response matrix used in PCA (Y), we are conducting an RDA. RDA therefore identifies linear combinations of the explanatory variables (X) that maximize the variance explained in linear combinations of the response (Y).”

n
43

Above shows the n for the subset of data analyzed

Proportion of Variation Explained by Factors 0.61
Proportion of Variation Unexplained by Factors 0.39

The rows above indicate the proportion of variation explained by the included agroecosystem variables.

A forward selection can help us select variables that are statistically important. In the forward selection the following variables are retained:

## rda_1_DV ~ coop + slopePerc + altFinal + sandPerc_lab

The following provide the R^2 and Adjusted R^2 for the selected variables (shown above) as well as the significance.

## $r.squared
## [1] 0.2802593
## 
## $adj.r.squared
## [1] 0.2044971
## Permutation test for rda under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: rda(formula = rda_1_DV ~ coop + slopePerc + altFinal + sandPerc_lab, data = rda_1_IV)
##          Df Variance      F Pr(>F)    
## Model     4   4.4841 3.6992  0.001 ***
## Residual 38  11.5159                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation test for rda under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
## 
## Model: rda(formula = rda_1_DV ~ coop + slopePerc + altFinal + sandPerc_lab, data = rda_1_IV)
##              Df Variance      F Pr(>F)    
## coop          1   1.8970 6.2597  0.001 ***
## slopePerc     1   1.2426 4.1004  0.001 ***
## altFinal      1   0.6479 2.1378  0.027 *  
## sandPerc_lab  1   0.6967 2.2989  0.014 *  
## Residual     38  11.5159                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The following shows an RDA plot for the selected variables:

Partial Redundancy Analysis

We can also run a partial RDA “in which the response variables (Y) are related to explanatory variables (X) in the presence of additional explanatory variables (W), called covariates (or covariables). In this case, we can treat our explanatory variables of interest (Y) as those that can be changed through management while unchangeable agroecosystem variables as the covariates (W).

Proportion of Variation Explained by Inherent Factors 0.41
Proportion of Variation Explained by Management Factors 0.19
Proportion of Variation Unexplained by Any Included Factors 0.39 
## $r.squared
## [1] 0.1948699
## 
## $adj.r.squared
## [1] 0.05408979
## Permutation test for rda under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: rda(X = rda_1_DV, Y = rda_IV2, Z = rda_IV1)
##          Df Variance      F Pr(>F)
## Model     9   3.1179 1.2682  0.101
## Residual 23   6.2829

Variation Partitioning

## No. of explanatory tables: 2 
## Total variation (SS): 672 
##             Variance: 16 
## No. of observations: 43 
## 
## Partition table:
##                      Df R.squared Adj.R.squared Testable
## [a+c] = X1           11   0.37933       0.15909     TRUE
## [b+c] = X2           10   0.41245       0.22884     TRUE
## [a+b+c] = X1+X2      19   0.60732       0.28293     TRUE
## Individual fractions                                    
## [a] = X1|X2           9                 0.05409     TRUE
## [b] = X2|X1           8                 0.12383     TRUE
## [c]                   0                 0.10500    FALSE
## [d] = Residuals                         0.71707    FALSE
## ---
## Use function 'rda' to test significance of fractions of interest

…Removing bulk density and aggregates to increase n

n
68

Above shows the n for the subset of data analyzed

Proportion of Variation Explained by Factors 0.44
Proportion of Variation Unexplained by Factors 0.56 
## rda_1_DV ~ coop + aspectQuad
## $r.squared
## [1] 0.1671153
## 
## $adj.r.squared
## [1] 0.1142337
## Permutation test for rda under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: rda(formula = rda_1_DV ~ coop + aspectQuad, data = rda_1_IV)
##          Df Variance      F Pr(>F)    
## Model     4   2.1725 3.1602  0.001 ***
## Residual 63  10.8275                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation test for rda under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
## 
## Model: rda(formula = rda_1_DV ~ coop + aspectQuad, data = rda_1_IV)
##            Df Variance      F Pr(>F)    
## coop        1   1.1610 6.7555  0.001 ***
## aspectQuad  3   1.0115 1.9617  0.005 ** 
## Residual   63  10.8275                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1