Plant species and pollinators
Medicago sativa L. (Fabaceae), also called alfalfa or lucerne, is a perennial legume with flowers arranged in a cluster or raceme. It is a self-compatible plant with fairly high outcrossing rate (5.3–30%)46, and it requires insect visits for seed production47. No plant material was collected for this study. Honey bees, Apis mellifera, and alfalfa leafcutting bees, Megachile rotundata, are used as managed pollinators in alfalfa seed-production fields in the USA while bumble bees are commonly used in alfalfa breeding47.
Experimental design and pollinator observations
Five 11 m × 11 m patches of M. sativa plants were set up in an east–west linear arrangement at the West Madison Agricultural Research Station in Madison, Wisconsin, USA. Within each patch, we transplanted 169 young plants grown from seeds in the greenhouse, each placed 90 cm apart. These plants grew and, at flowering, a plant had an average of 30.65 ± 16.4 stems per plant, with 4.93 ± 3.41 racemes per stem, and 7.53 ± 2.44 open flowers per raceme.
A honey bee hive was placed approximately 100 m from the patches and a bumble bee hive was set up at the center of the southern edge of the patches. For leafcutting bees, a 60 × 30 × 7.6 cm bee board was set up in each of two boxes placed 1/3 and 2/3 along the southern edge of the patches and a half gallon of bees was released at periodic intervals throughout the alfalfa flowering season.
Over two consecutive summers, observers followed bees foraging in the alfalfa patches, marked each raceme visited in succession within a foraging bout with a numbered clip, and recorded the number of flowers visited per raceme. After a bee had left a patch, observers went back to the marked racemes and measured the distance and direction traveled between consecutive racemes. Directions were recorded as one of the cardinal directions: North (N), South (S), East (E) or West (W), or inter-cardinal directions: Northeast (NE), Southeast (SE), Northwest (NW) and Southwest (SW). The frequency distributions of distances and directions traveled between two successive racemes are presented for each bee species each year in Figs. 1 (distances) and 2 (directions). The low pollinator abundance permitted observers to follow individual bees foraging in a patch. Little interference among bee species was observed in the patches.
Frequency distributions for distances traveled between consecutive racemes (cm) for each bee species each year.
Frequency distributions of directions traveled between consecutive racemes for each bee species each year.
Model for the distance traveled between consecutive racemes
We first determined whether a statistical model best described the distance traveled between consecutive racemes (Modeled Distance), and examined whether the model differed among bee species. We used mixed effect linear models (proc Mixed in SAS 9.3)48 to identify the model that best described the distance traveled by pollinators between consecutive racemes. The model included loge distance as a linear function of loge flower number and bee species as fixed effects. The distance traveled between consecutive racemes and the number of flowers visited per raceme were log transformed prior to analyses in order to improve the models’ residuals. In addition, we included patch and foraging bout as random effects in the model. A foraging bout includes the racemes visited in succession from the time a bee is spotted in a patch to the time it leaves that patch. We used foraging bout instead of individual bee as the random effect because bees were not individually marked in this study. Moreover, to take into consideration the potential correlation between successive observations within a foraging bout, we added clip to the model. Clip 1 represents the first and second racemes visited in the foraging bout; clip 2, the second and third, and so on. Clip was added to the model either as a random effect or as a repeated measure with an AR(1) structure. The combination of random clip and random foraging bout creates a model that is sometimes called the “compound symmetry” model. The AR(1) structure represents correlations that decline exponentially as the gap between measurements increases such that measurements closer together in time are more strongly correlated than measurements further apart. Because we expected bees to visit flowers at close proximity when resources are abundant, we chose this correlation structure as a good potential descriptor of the way distances might be correlated within foraging bouts. We started with a full model which included loge flower number, bee species, patch, foraging bout, and clip either as a random effect or as a repeated measure with an AR(1) structure. We then removed variables and compared models by inspecting AIC values and the p values for each term in the model. We considered both low AIC and statistically significant (p < 0.05) terms for model selection. We examined each year separately, and within each year, determined whether bee species affected the model and, thus, whether we needed a separate model for each bee species.
Transition matrix or vector for directions traveled between consecutive racemes
We computed matrices of transition probabilities based on field-collected data for bumble bees and honey bees because these two bee species exhibited directionality of movement within foraging bouts1. These matrices represent the probability that a bee moved from one direction to the next when visiting two consecutive pairs of racemes (Modeled Direction). We recorded eight potential directions in the field which lead to a transition matrix with 64 cells. For a given bee species, each year, the transition probability for a cell in the matrix was calculated by dividing the number of transitions (counts) within a cell in a particular row by the total number of transitions for that row such that each row’s total frequency was equal to 1.0. Because leafcutting bees do not exhibit directionality of movement within foraging bouts1, given the eight possible directions, we assigned an equal probability of 0.125 of moving from one direction to the next for all cells of the matrix.
Because a matrix of transition probabilities contained 64 cells, and therefore 64 probabilities to estimate, we alternatively calculated transition vectors which reduced the number of transitions to estimate. The eight cells in the transition vector represented, respectively, the probability that a bee remained in the same direction (0), turned left 45°, 90°, 135°, 180°, 225°, 270° or 315° angles. For example, if a bee moved south, north, northeast and then northwest during its foraging bout, this represented, respectively, a 180° (south to north), 315° (north to northeast), and 90° (northeast to northwest) left angles. To obtain the probability for each of the eight cells of the transition vector, we summed the number of times a bee moved a given angle and divided that number for each angle by the total number of transitions for that bee species. This frequency table was used as an approximation of the transition vector for bumble bees and honey bees. For leafcutting bees, we assigned a probability of 0.125 to each cell of the vector. Because, for each bee species, the transition probability matrices or the transition vectors were very similar between years, we combined data from both years to calculate them, which increased sample sizes.
Modeling pollinator movement
We examined models simulating a path along which a bee traveled for each foraging bout (Supplementary Fig. S2). A foraging bout included all racemes visited by a bee during one visit to the patch. Bee movement was modeled by the distance traveled and the direction of movement between consecutive racemes. Starting from the origin (0, 0), the first move was simulated by randomly selecting a direction amongst the eight possible directions, N, NE, E, SE, S, SW, W, NW, which corresponds to a bee showing no overall preference for a direction. Following the first move, a distance and a direction traveled between consecutive racemes were chosen each time a bee moved between consecutive racemes.
Four distinct models of bee movement were tested for each bee species. These models are referred to as the Random Distance-Random Direction model; the Random Distance-Modeled Direction model; the Modeled Distance-Random Direction model; and the Modeled Distance-Modeled Direction model (Table 1). For the Random Distance or Random Direction part of a model, the distances or directions traveled between consecutive racemes were selected randomly from the respective distribution of empirical distances (Fig. 1) or directions (Fig. 2) traveled for that bee species that year (Table 1). For Modeled Distance, distances were predicted as a function of the number of flowers visited in the previous raceme (statistical model for the distance traveled between consecutive racemes) plus a prediction error. This error was generated from a normal distribution whose spread was based on the residuals’ standard deviation. A separate equation was used for each bee species. For Modeled Direction, we used the transition matrix or transition vector for the bee species. When using the transition vector, directions were simulated using the frequency distribution of potential transitions. The length of a foraging bout was selected randomly from the empirical distribution of foraging bout lengths obtained for a bee species in a given year without replacement.
Selecting the best movement model for each bee species
To select the best movement model, we contrasted the empirical mean or median net distance traveled by a bee species in a given year, against the distribution of mean or median net distances generated for each of the four models for that bee species that year. The net distance is the straight-line distance between the first- and the last- visited raceme of the foraging bout and this measure relates well to pollen dispersal and gene flow. While many movement models have used mean-square displacements49,50, which describes an average distance traveled per unit of time, we used the average (or median) net distance traveled. No one- or two-dimensional measure necessarily captures all features of a movement model and the mean and/or median permitted us to distinguish among some of the models. We tabulated the mean and median empirical net distances traveled, over all observed foraging bouts, for a bee species each year. This approach generated six observed means and six observed medians, one for each of three bee species and two years.
For simulated net distances, we followed a similar approach but here distances and directions were generated differently depending on which of the four models was being tested (Table 1). For each bee species each year, and for each of the four models, we simulated 2000 mean and median net distances traveled, and thus, 24 sets of 2000 mean and median net distances traveled (4 models × 3 bee species × 2 years). In addition, we obtained 500 mean and median net distances traveled for combined years for each bee species.
A randomization approach was used to identify the model that best fitted the observed data. The p value was determined by counting the percentage of time, out of 2000, the simulated mean or median net distance was greater or smaller than the observed mean or median distance traveled for the bee species that year. With three bee species, 2 years, and four models, we performed 24 randomization tests. When testing the observed mean to the simulated distribution of means, a low probability value indicates rejection of the model. To determine the robustness of our findings, we repeated each randomization test using five different starting points, i.e. random number seeds. This was done using the set.seed random number generator function in R 3.5.1.
Our ability to reject or accept a given model was similar whether we used the median or the mean distance traveled between consecutive racemes. Because the mean may better reflect the skewness of the distributions of distances traveled, we present the results obtained using the mean net distance traveled. Moreover, few differences existed between the results of the simulation models based on transition matrices or transition vectors, and fewer parameters needed to be estimated for transition vectors, therefore parameter estimates of the transition vectors were more stable for a given sample size, and we present the results of the simulation models obtained using transition vectors.
Source: Ecology - nature.com
