Table 1 Linear mixed-effects model for the relationships between multiple biotic (BNPP, plant species richness, and the soil microbial diversity index) and abiotic (aridity, soil pH, and clay content) factors and soil multifunctionality with considering soil and vegetation types as random terms.

From: Aridity-driven shift in biodiversity–soil multifunctionality relationships

Term

df

ddf

MS

F

P

Estimate

VIF

Random terms are soil and vegetation types; Conditional R2 0.69; Marginal R2 0.59

Year

1

37.5

3.30

9.22

0.004

−0.11

2.09

Plant species richness

1

8.9

10.03

28.01

<0.001

0.03

2.12

Soil microbial diversity index

1

103.1

0

0

0.996

0.21

2.45

Aridity

1

18.7

7.45

20.83

0.001

−0.36

2.04

BNPP

1

49.1

1.88

5.25

0.026

0.05

1.10

Soil pH

1

112.6

3.50

9.77

0.002

−0.26

1.65

Soil clay content

1

115.6

5.39

15.07

<0.001

0.18

2.10

Elevation

1

109.5

1.24

3.45

0.066

0.23

2.27

Latitude

1

114.1

4.79

13.38

<0.001

0.35

4.14

Longitude

1

114.6

0.99

2.77

0.098

−0.19

1.72

Plant species richness × Soil microbial diversity index

1

109.1

0

0

0.994

0.20

4.47

Aridity × Plant species richness

1

104.2

1.36

3.79

0.054

−0.13

1.76

Aridity × Soil microbial diversity index

1

115.2

2.03

5.67

0.019

0.26

4.10

  1. df numerator degrees of freedom, ddf denominator degrees of freedom, MS mean squares, F variance ratio, P probability of type-I error (two-sided), VIF variance inflation factor.
  2. Fixed terms are fitted sequentially (type-I sum of squares) as indicated in Eq. 2, and × denotes an interaction term. Marginal (variance explained by fixed terms) and conditional (variance explained by fixed and random terms) R2 values are given. The term “Year” is first introduced into the model to eliminate the variation due to different sampling years. Latitude, longitude, and elevation of the field sites are included to account for the spatial structure of our dataset.