The nature of unexplained variation in flower visitation data

The nature of unexplained variation in flower visitation data

Trond ReitanCentre for Ecological and Evolutionary Synthesis, Department of Biosciences, University of Oslo, Norwaytrond.reitan@ibv.uio.no

Count data and unexplained variationWe 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:Scientific curiosity.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.

The possible nature of the variations

SpatialLarge scale Soil diff., distance to hivesMedium scale, individual bushes Phenotypic variationSmall scale, portion of each bush - average light/shadowIndividual flowers State of each flower.Per-measurement variation multiple counts of the same pollinator.Odor fluctuations.Light/shadow fluctuations.Fluctuations in weather-related variables.

Temporal

SpatiotemporalUnmeasured weather related changes. Changes in hive states.Whole field odors.PS: For a single measurement day (5-8 hours)Normal situationUsual 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?

Disentangling variation Solution: Do parallel measurementsSpatial 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 effectUnexplained variationSub-portion as random effectLarge scale variationBush variationBush portion variationSmaller scale or spatio-temporalSmaller scale or spatio-temporalSpatio-temporal(per measurement)Flower or sub-portion variationFour observers, one day.Spatial + temporal variations not as chaotic as spatiotemporal variations. =>Can disentangle temporal variations from spatial.

ResultsNo temporal variation found! (We know its 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!

What do we get from this?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.

AcknowledgementsRCN project number: 230279 / E50

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