Appendix F: Statistical models

Buffer zones for biodiversity of plants and arthropods: is there a compromise on width?

A number of different models have been applied and a list of these is given in the following table:


No	Type of data	Where used
1	Continuous normally distributed measurements
2		Shannons index and species for transect data Shannons index and species from pitfalls Shannons index and species from sweep nets
3		Bird feed from sweep nets
4		Bird feed in hedgerow
5		Shannons index for plants
6	Counts	Plants in hedge
7	Counts	Arthropods in hedgerow
8	Counts	Plants in field
8a^*	Counts	Arthropods in pitfalls Arthropods from sweep nets
9	Relative counts	Percentage of flowering plants
10	Counts	Arthropods in transects
11	Counts	Arthropods in transects
12	Counts	Plants in field
13	Continuous normally distributed measurements	Accumulated number of plant species Accumulated number of bugs in transects Accumulated number of ground beetles in pitfalls Accumulated number of butterflies in transects Percent flowering plants in hedge-bottom
14		Shannons index and species for plants
15		Accumulated number of species
16	Counts	Relation between number of species of arthropods and plants

^*) The model does not include residual effect as the data are aggregated within each plot

Many of the analyses were carried out for different groups, such as sampling period, Type/class, order, family and specie. However, in order to be able to trust the analyses groups with very sparse occurrence were not analysed. Generally it was required that at least one plant/arthropod should be present in at least 25% of the replicates (when including each replicate in the analyses) or that at least one plant/arthropod should be present in at least 50% of the plots (when using sum of replicates in the analyses). In addition a few groups that fulfilled those requirements were left out because the occurrence of the plants/arthropods made it impossible to do the analyses properly.

All models were either linear mixed models, generalised linear mixed models or non-linear mixed model. The theory of linear mixed models and generalised linear mixed models may be found in books such as McCulloch and Searle (2001) and West et al. (2007). All statistical analyses were performed using the procedures MIXED, GLIMMIX and NLMIXED of SAS (SAS, 2008). Some of the data were visualised using the graphical procedures of SAS (SAS, 2009a and SAS, 2009b)

In all models it was assumed that the fields could be regarded blocks in the same experiment. Therefore analyses that included effects of both buffer width and distance to hedge were analyses at split-block design. Each combination of buffer width and distance from hedge is in the following called a plot.

In all analyses the denummerator degree of freedom were calculated using an extension of the Satterthwaites principle as described by Kenward and Roger (1997).

Pair wise comparisons of buffer widths and distances from hedge were carried out using the method of Tukey and Kramer, which were set up to control the comparison wise error rate at each level of buffer width when comparing distances from hedge and the comparison wise error rate at each level of distance from hedge when comparing buffer width. The method is based on the distribution of Studentized range (for more details see e.g. Miller, 1981).

Click here to see: Model 1

Click here to see: Model 2

Click here to see: Model 3

Click here to see: Model 4

Click here to see: Model 5

Click here to see: Model 6

Click here to see: Model 7

Click here to see: Model 8

Click here to see: Model 8a

Click here to see: Model 9

Click here to see: Model 10

Click here to see: Model 11

Click here to see: Model 12

Click here to see: Model 13

Click here to see: Model 14

Click here to see: Model 15

Click here to see: Model 16