Statistical analysis
We used a mixed effect-modelling approach to address our research
questions. In all models, study was included as a random intercept to
account for the hierarchical structure of the data with field measures
nested within study. To assess whether flower strips and hedgerows
enhanced pollination and pest control services in adjacent crops
(research question 1) linear mixed-effect models with planting (field
with or without planting) were separately fitted for flower strips and
hedgerows for the response variables pollination service and pest
control service. To test how the effects on service provisioning change
with distance (continuous variable; meters) from plantings (question 2)
and with landscape simplification (question 4) these explanatory
variables and their interactions with the fixed effects described above
were included in the models. Exploratory analyses showed that neither
distance nor landscape simplification effects differed between flower
strips and hedgerows; i.e., no significant interactive effects of
planting type with any of the tested fixed effects. We therefore pooled
flower strip and hedgerow data in the final models, excluding planting
type and its two or three-way interactions as fixed effects. In addition
to linear relationships we tested for an exponential decline of measured
response variables from the border of the field by fitting
log10(distance) in the linear mixed-effect models described above. In
this case, field nested within study was included as a random effect. To
test the intermediate landscape complexity hypothesis, we tested for
linear as well as hump-shaped relationships between landscape context,
and its interaction with local floral plantings by fitting landscape
variables as a quadratic fixed predictor in the models described above
(second degree polynomial functions). To present the ranges covered by
the agricultural landscape gradients, we did not standardize measures of
landscape simplification within studies (e.g., Martin et al.2019). To examine how pollination and pest control service provisioning
relates to flower strip plant diversity and time since establishment
(question 3) plant species richness and log10(number of months since
establishment) were included as fixed effects in models with study as a
random effect. Using log(months since establishment) predicted the data
better than establishment time as linear predictor. Plant species
richness and time since establishment of flower strips were not
correlated (r = 0.22). Only 10 studies measured services in several
years since establishment (Table S1), and we included only data from the
last sampling year. To assess how the presence of plantings affected the
agronomic yield of adjacent crops (question 5), we fitted a linear
mixed-effect model with the same fixed and random structure as described
for question 1, but with crop yield as the response variable.
Statistical analyses for different models and response variables
differed in sample sizes as not all studies measured crop yield in
addition to pollination or pest control services (Tables 1, S1). In all
models we initially included planting area as a co-variate in an
explorative analysis, but removed it in the final models, as it did not
explain variation in any of the models and did not improve model fit
(not shown).
Effect sizes provided in the text and figures are model estimates of
z-transformed response variables. For statistical inference of fixed
effects we used log-likelihood ratio tests (LRT) recommended for testing
significant effects of a priori selected parameters relevant to
the hypotheses (Bolker et al. 2009). For all models, assumptions
were checked according to the graphical validation procedures
recommended by Zuur et al. (2009). All statistical analyses were
performed in R version 3.5.2 (R Core Team 2017) using theR -package lme4 (Bates et al. 2015).