Limited Cross Plant Movement and Non-Crop Preferences Reduce the Efficiency of Honey Bees as Pollinators of Hybrid Carrot Seed Crops

Pollination rates in hybrid carrot crops remain limited after introduction of honey bee hives. In this study, honey bee foraging behaviour was observed in commercial hybrid carrot seed crops. Significantly more visits were made to male-fertile (MF) rather than cytoplasmically male-sterile (CMS) flowers. Pollen was collected from bees returning to a hive, to determine daily variation in pollen loads collected and to what level the bees were foraging for carrot pollen. Honey bees visited a wide range of alternative pollen sources and made relatively few visits to carrot plants throughout the period of flowering. Visitation rates to other individual floral sources fluctuated but visitation to carrot was consistently low. The underlying rate of carrot pollen visits among collecting trips was modelled and estimated to be as low as 1.4%, a likely cause of the limited success implementing honey bee hives in carrot crops.


Field site descriptions
All sites were within 30 km of Hobart and within 15 km of each other ( Figure ). Insect trapping and observations were conducted and umbel trimming was used at some sites to promote lateral flower stem development so that pollinator activity could be observed over an extended carrot growing season. The crop area of these sites and the activities conducted for each trial are detailed in Table S1. Traps were placed in trimming trials to take advantage of the extended carrot flowering time and thus the longer carrot and insect monitoring season. Hives were present adjacent to the carrot crop in all trials. Further details of these trials follow Table S1.

Carrot Cultivars
The carrot cultivars used in all field trials are listed in Table S2. Each cultivar has been given a unique experimental identification number. ) was marked out and divided lengththwise into two blocks. Each of these blocks was then divided into six plots which were 5 m x 4.8 m each. Six different trimming treatments were randomly allocated to the plots within each of the two blocks. Each treatment plot was 1.8 m x 5 m ( Figure S2). All of the carrot trimming treatments were conducted using a line trimmer. The very early, early and mid treatments were trimmed so that all vegetation 50 cm above ground level was removed. The first trimming treatment was conducted when 50 % of the carrots were at an extension of 30 cm or more. Trimming of the late trimming treatments were conducted at the same time, just prior to the opening of primary umbels. Carrot plants in the late-severe treatment were trimmed to 60 cm above ground level and carrot plants in the late-light treatment were trimmed to 75 cm above ground level. Trimming treatments and dates are listed in Table S1. This trial was a randomised block design. Eight blocks were divided into two plots of 2.4 x 5 m. Each plot was planted with one bed of an MF carrot (MX1) and then two beds of either carrot cultivar PF1 or PBF1. Each block contained a plot of PF1 and a plot of PBF1 ( Figure  S3).

Field Trial 4 -December 2003/January 2004 -University Farm (240 m 2 )
The planting layout and carrot cultivar in this trial, MY1 and PN6, were the same as those used in Trial 1. Only treatments control, early and mid, late-severe and late-light were used. Twenty different treatment plots 2.4 m x 5 m were randomly allocated to a 50 m x 4.8 m block of CMS cultivar PN6. Each treatment plot was 2.4 m x 5 m ( Figure S4). Trimming treatments and dates are listed in Table S4.  Over the course of the last decade the accessibility and use of MCMC tools has increased substantially. The original BUGS (Bayesian analysis using the Gibbs Sampler) software has diversified into a family of tools which now includes WinBUGS (Lunn et al., 2000), OpenBUGS (Thomas et al.,2006), and JAGS (Just Another Gibbs Sampler) (Plummer, 2003); CODA (Plummer et al., 2009)  We used R as an interface to JAGS to estimate the rate at which carrot pollen was being collected, given the sampling process used to make observations of carrot pollen counts. That is, the most likely rate of carrot pollen collection given the observed counts of carrot pollen during each sampling period, adjusted for the estimated total number of pollen balls collected during that period and the sub-sample of 60 balls used to determine the carrot pollen count. We begin by making the assumption that there is a "true" underlying rate of preference for carrot pollen µ, and that the sampling periods i = 1; 2; : : : ;N from which observations were obtained are in some sense representative of the larger set of hypothetical sampling periods from which we could potentially collect data. The individual probability of observing carrot pollen pi in the ith sample period is related to the underlying mean as.  (mu)) mu ~ dnorm(0.0,1.0E-6) sigma < -1 / sqrt(tau) tau ~ dgamma(0.001,0.001) }, from which we can see that the process relies on a nested pair of binomial distributions. For each sampling period i = 1; 2; : : : ;N, the observed carrot pollen count ri is used to generate a simulated count qi which adjusts for the sub-sample of size 60. We then use qi to estimate the probability pi of observing carrot pollen in a sample of size n̂i, the total estimated pollen ball count for period i. The quantity pi is related to the underlying population mean by equation (1), where µ is a measure expressed on the logit scale. For convenience we convert this back to the probability scale using θ = exp μ 1 + exp μ Where Ɵ̂ is the estimated underlying mean probability of observing carrot pollen in the population of sampling periods for which those considered here form a representative sample.

Results
Results from the model are provided in Table S6. Results from simulation model, where individual estimates for each sampling period i = 1; 2; : : : ; 21 are shown along with the estimates of the underlying mean, expressed as the log-odds µ and a probability. An indication of the precision of these estimates are provided by the posterior quantiles, of which interpretation is straightforward. The estimated mean probability of observing carrot pollen in sample period 1 p1 (first day's sampling in morning, p2 afternoon of first day's sampling and so on) was 0.01488, or nearly 1.5 %, the median was 0.014, and 95 % of the samples generated against p1 lay in the interval [0:004503; 0:03052].

Discussion
The estimates of the individual sampling periods display the "shrinkage" characteristic of mixed-effects models (G. Lee pers, comm.). The estimates for the extreme observations are pulled in towards the overall mean. In the current scenario this is useful, because of the large number of zeroes in the data. However, the model also shows signs of instability due to the paucity of carrot pollen observations. If the core research question was to identify the underlying rate of pollen collection in the carrot crop by examination of the observed proportion of carrot pollen in the samples, it would have been useful to set the subsample count at a threshold which allowed a minimum carrot pollen count (in the range 5-10, say) for the majority of (and preferably all) sampling periods. This is recommended for any future study which aims to estimate this quantity with accuracy.