Effects of an invasive root hemiparasite ((Rhinanthus alectorolophus)) on experimental grassland systems of different diversit

Joshi, J., Matthies, D.& Schmid, B. (2000) Root hemiparasites and plant diversity in experimental grassland communities 88, 634-644. Appendix 2 Skeleton analysis of variance/deviance for the measured parameters in the experiment. The treatment model consisted of the effects of the number of species (species richness), the number of functional groups, the presence of legumes and the effect of the Rhinanthus treatment and its interactions with the previously listed factors. The final model was found by backward elimination of factors of minor interest. These were defined as factors that did not reach an F-value > 2 . Because the different species assemblages within each diversity level were randomly selected from the species pool , their mean square was used as the appropriate error term to test the effects of the diversity treatments (number of species and number of functional groups). The interaction term Rhinanthus x assemblage served as error term to test the interaction between the effects of Rhinanthus and the diversity treatments. Because the different aspects of diversity, number of species (A) and number of functional groups (B), were partly confounded we fitted these terms in alternative sequences (in generalised linear modelling terminology the sequence A + B corresponds to "A ignoring B" and "B eliminating A" and the sequence B + A corresponds to "B ignoring A" and "A eliminating B"; the interaction AxB was always omitted from the analyses because of its low F-values). If the combinations of the partial factorial A crossed with B are considered as a major factor "diversity treatment", the above approach is equivalent to forming different sets of orthogonal contrasts within this major factor . Incidentally, this approach is similar to the type-IV sum-of-squares approach in the statistical package SAS where contrasts within a partial factorial design are chosen arbitrarily (SAS, 1990). The preferred sequence of contrasts was in most cases B + A. Thus, for the sake of clarity we only present the results of the analyses in which the number of functional groups (B) preceded the number of species (A). The main effect of the Rhinanthus treatment was tested against the residual variation among the two quadrats within individual plots. The block and subblock effects were used to eliminate spatial variation within the experimental site.

 

 

 

d.f.

Mean square

Variance-ratio

 

Source of variation

[d.f.

[Deviance

[approx. F ]

 

 

change]

change]

 

 

Block (b)

1

MSb

MSb/MSsb

 

Subblock (sb) within b

14

MSsb

MSsb/MSp

Overall

Diversity treatments (d)

6 (9)1

MSd

MSd/MSa

diversity

Number of Functional groups (f)

2

MSf

MSf/MSa

effects

Functional groups (linear)

1

MSfl

MSfl/MSa

 

Functional groups (Deviation from linearity)

1

MSfq

MSfq/MSa

(between -

Species richness (s)

4

MSs

MSs/MSa

plot

Species richness (log-linear)

1

MSsl

MSsl/MSa

analysis)

Species richness (Deviation from log-linearity)

3

MSsd

MSsd/MSa

 

(Functional groups x Species richness

(3)1

MSfs

MSfs/MSa)1

 

Assemblage (a)

25 (22)1

MSa

MSa/MSp

 

Legume contrast (l)

1

MSl

MSl/MSar

 

Remainder (all other species contrasts)

24 (21)1

MSar

MSar/MSp

 

Plot (p) within b

14

MSp

MSp/MSq

 

Parasite treatment (r)

1

MSR

MSR/MSq

Diversity

Diversity treatments x Parasite

6 (9)1

MSdR

MSdR/MSaR

effects

Number Functional groups x Parasite

2

MSfR

MSfR/ MSaR

depending

Functional groups (linear) x Parasite

1

MSflR

MSflR/ MSaR

on

Functional groups (Deviation) x Parasite

1

MSfdR

MSfdR/ MSaR

parasite

Species richness x Parasite

4

MSsR

MSsR/ MSaR

presence

Species richness (log-linear) x Parasite

1

MSslR

MSslR/ MSaR

 

Species richness (Deviation) x Parasite

3

MSsdR

MSsdR/ MSaR

(within-

(Functional groups x Species richness x Parasite

(3)1

MSfsR

MSfsR/ MSaR)1

plot

Assemblage x Parasite

25 (22)1

MSaR

MSaR/MSq

analysis)

Legume contrast x Parasite

1

MSlR

MSlR/MSaR

 

Remainder x Parasite

24 (21)1

MSrR

MSrR/MSq

 

Quadrat (q) within p = Residual

29

MSq

 

 

Total

120

 

 

Notes: random effects (error model) in italic letters, fixed effects (treatment model) in roman letters; effects are always adjusted for effects that precede them.

1 Lines and values in parentheses refer to a full analysis including the interaction "functional groups x species richness". Because these interactions were never significant they were pooled with the random effect below them.