The potential and realized foraging movements of bees are differentially determined by body size and sociality

Abstract Reversing biodiversity declines requires a better understanding of organismal mobility, as movement processes dictate the scale at which species interact with the environment. Previous studies have demonstrated that species foraging ranges, and therefore, habitat use increases with body size. Yet, foraging ranges are also affected by other life‐history traits, such as sociality, which influence the need of and ability to detect resources. We evaluated the effect of body size and sociality on potential and realized foraging ranges using a compiled dataset of 383 measurements for 81 bee species. Potential ranges were larger than realized ranges and increased more steeply with body size. Highly eusocial species had larger realized foraging ranges than primitively eusocial or solitary taxa. We contend that potential ranges describe species movement capabilities, whereas realized ranges depict how foraging movements result from interactions between species traits and environmental conditions. Furthermore, the complex communication strategies and large colony sizes in highly eusocial species may facilitate foraging over wider areas in response to resource depletion. Our findings should contribute to a greater understanding of landscape ecology and conservation, as traits that influence movement mediate species vulnerability to habitat loss and fragmentation.

To demonstrate and test the predictive performance of our most-predictive model (see results), we explore how model predictions differ depending on the random structure (which can be chosen by users of the R function foraging.range within the pollimetry package (Kendall et al. 2019): iii) fixed effects only (random effects set to zero) These three scenarios correspond to predictions of species present in the original database, species not present but for which you can leverage the information encoded in their phylogeny, and completely unrepresented species respectively.
We then compared these formulations with pre-existing models of foraging range by calculating the mean absolute error (MAE) between predicted values and actual values in our dataset. Specifically, we compared our model against predicted estimates from Greenleaf et al.
(2007)'s maximum and typical homing range models. We calculated the MAE independently for potential and realized measurements. We acknowledge the bias introduced from assessing predictive accuracy between actual and predicted values, where all actual values were used in model creation. However, the aim of this exercise is to compare the performance among models, and show their usability, and not to test their true (out-of-sample) predictive power.
Furthermore, the complex data structure (91 publications, seven measurement types, 81 species) made splitting the dataset into training and testing sets unrepresentative. Note that Greenleaf et al. (2007) models were parameterized using a subset of the total dataset used herein, so exhibit some of the same bias.

Predictive performance and accuracy
Across all types of foraging range, we found that the model incorporating measurement type and sociality had considerably greater predictive accuracy relative to pre-existing models. We found that improved predictive accuracy was most notable for realized estimates ( Figure S1).
The mean absolute error of potential estimates was reduced by up to 15% for typical range (130 m) and, up to 29% for maximum foraging range (488 m). For realized estimates, predictive error was reduced by 65% -74% for typical range (910 m -1.04 km) and reduced by 69% -76% for maximum range (3.35 km -3.68 km). Predictions for all species in our dataset, based on each of the three model formulations, are provided in Figure S2. Figure S1. Pairwise comparison of marginal absolute error (Δ MAE) in kilometers for typical and maximum foraging ranges of bees (potential and realized) between new foraging range models and pre-existing models (Greenleaf et al. 2007). Blue values denote marginal or null differences between models in terms of precision, whereas white and red values indicate lower model error in models in the columns relative to the rows. Predictions come from either Greenleaf et al. (2007)'s homing range model for maximum or typical foraging range, or our most-predictive model: ~ body mass * sociality * measurement type, with differing random effect structures: Phylo + species: ~1|phylogeny + 1|species, Phylo: ~1|phylogeny, and FE only: fixed effects only (random effects set to zero).

A demonstrative example
To demonstrate the use of the developed models, we used a bee of the same size (body mass: 23 mg) from each social group, such as Apis mellifera (highly eusocial), a small Bombus bifarius worker (primitively eusocial) and Osmia cornifrons (solitary), to generate predictions of typical and maximum foraging ranges, using three different model parameterizations ( Figure   S3).
Model predictions from each formulation were highly similar for primitively eusocial and solitary species, irrespective of the random effect structure. For highly eusocial species, predictions that considered phylogeny, and especially both phylogeny and the species effect for Apis mellifera, increased both the median estimate of foraging range by as much as 123% (3.14 km) and its associated uncertainty (by as much as 7.24 km). Potential typical foraging ranges were, on average, 47%, 53%, and 66% larger than realized ranges for highly eusocial, solitary and primitively eusocial bee species, respectively. In contrast, potential maximum foraging ranges were, on average, 65% and 36% larger than realized ranges for the primitively eusocial bee and solitary species, and 29% shorter for the highly eusocial species.
Foraging ranges for the highly eusocial species were considerably larger than the ranges of primitively eusocial and solitary species. Maximum foraging ranges (potential and realized) of the highly eusocial species were between 23% -147% and 356 % -800% larger than the primitively eusocial species, and between 96% -343% and 294% -793% larger than the solitary species. Maximum foraging ranges of the primitively eusocial species were between 59% -80% larger (potential) and between 1% -14% shorter (realized) than the solitary species.