Trond Reitan Centre for Ecological and Evolutionary Synthesis, Department of Biosciences, University of Oslo, Norway

We count pollination events on a set of flowers to estimate visitation frequency. Counts of a given frequency* has a given observational noise. The more flowers, better. The counts vary more => frequency varies. Want to know why, because: 1.Scientific curiosity. 2.Extra variation => extra uncertainty in analysis. If we know the nature, maybe we can fix this? Will more flowers make the situation better? * Given temperature and other weather- related variables we control for.

Spatial Large scale – Soil diff., distance to hives Medium scale, individual bushes – Phenotypic variation Small scale, portion of each bush - average light/shadow Individual flowers –State of each flower. Per-measurement variation – multiple counts of the same pollinator. Odor fluctuations. Light/shadow fluctuations. Fluctuations in weather- related variables. TemporalSpatiotemporal Unmeasured weather related changes. Changes in hive states. Whole field odors. PS: For a single measurement day (5-8 hours)

Usual measurement situation: One measurement per farm per time point. Measurement distributed over plots: Farm area divided into sections, max one bush per area.  All extra variation will be per measurement, except medium/large scale spatial variations persisting over a long time or slow temporal variations (per day). Previous year: No plot variation found. Linear time trend. This year: In addition to variation due to temperature, plot and slow temporal variation found. */2.6 from plot variation, */1.6 from per day variation. Plot variation: Large scale, bush variation or even bush portion variation?

Spatial scales: Large: One observer in each section. Switch bushes. Medium: One observer per bush, all in a given section. Vary bush portion. Small: One observer per portion of bush, all at the same bush(!). Sub-portions used as a stand-in for individual flowers. Instead of varying the sub-portion over the measurements, all sub-portions are counted in parallel. Observer as random effect Unexplained variation Sub-portion as random effect Large scale variation Bush variation Bush portion variation Smaller scale or spatio- temporal Spatio- temporal (per measurement) Flower or sub-portion variation Four observers, one day. Spatial + temporal variations not as chaotic as spatiotemporal variations. => Can disentangle temporal variations from spatial.

 No temporal variation found! (We know it’s there, but not detectable here.)  No temporal variation found on small scale: No detectable spatiotemporal variation with spatial scale > bush.  No large scale variation found, but unexplained variation.  Slight evidence for medium scale variation; */2.0. Unexplained variation found.  No evidence for bush portion variation.  Good evidence for sub-portion/flower variation; */2.0. No unexplained variation found.  39% reduction of visits when having 4 people around a bush rather than one. Observations change the outcome. The state of each flower matters quite a bit. Larger scale variations not reliably found, though evidence from medium scale plus normal situation data suggests per bush variation matters also. Also consistent with normal data!

For our particular results:  Try counting on as many flowers as possible. (Both from Poisson and for averaging over flower states).  Switch the flowers you count on often. (Averaging over flower states.) Switch from one bush to the next and you also average out over bush variation!  No need trod all over the field. Large scale variation not found. In general:  Even though unexplained variation is a nuisance, it is a nuisance that will affect the uncertainty of your results and whether or not you are able to detect an effect.  There will always be unexplained variation. Knowing the nature means you might be able to alter your sampling protocol and get more out of your data.

RCN project number: / E50 8