# How much nectar can wild bees carry? Allometric equations of nectar crop capacities for investigating bee nutrition and foraging ecology

Sarah Bourdon, Léo Mouillard-Lample, Taïna Lemoine, Maxime Lewin, Laurent Guilbaud, Léna Barascou, Bertrand Schatz, Mickaël Henry

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## To cite this version:

Sarah Bourdon, Léo Mouillard-Lample, Taïna Lemoine, Maxime Lewin, Laurent Guilbaud, et al. How much nectar can wild bees carry? Allometric equations of nectar crop capacities for investigating bee nutrition and foraging ecology. Journal of Insect Physiology, 2025, 164, pp.104840. 10.1016/j.jinsphys.2025.104840. hal-05133543

HAL Id: hal-05133543

https://hal.inrae.fr/hal-05133543v1

Submitted on 27 Jun 2025

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# How much nectar can wild bees carry? Allometric equations of nectar crop capacities for investigating bee nutrition and foraging ecology☆

Sarah Bourdon<sup>a,1</sup>, Léo Mouillard-Lample<sup>a,b,1</sup>, Taïna Lemoine<sup>c</sup>, Maxime Lewin<sup>a</sup>, Laurent Guilbaud<sup>a</sup>, Léna Barascou<sup>a,d</sup>, Bertrand Schatz<sup>e</sup>, Mickaël Henry<sup>a,∗</sup> ◐

## ARTICLE INFO

Keywords:

Allometry

Anthophila

Body length

Bumblebees

Floral resource limitation

Nectar load

Solitary bees

## ABSTRACT

The decline in bee populations is influenced by the scarcity of floral resources, mainly nectar and pollen, resulting from the loss of natural habitats and climate change. In this context, it is essential to understand the foraging success and nutritional status of wild bees, particularly as research on honeybees has overshadowed that of wild species. This study aims to establish allometric functions for the nectar crop capacities of wild bees, which may be used as predictive tools in research related to bee nutrition and foraging ecology. Allometric scaling models, which typically relate body size to morphological or ecological traits, are proposed as a method of estimating crop capacity in wild bees. The crop load was measured in 2358 free-ranging foragers of different sizes (body length 5–29 mm) belonging to 25 different genera, in southern France. Overall, we established consistent allometric functions for predicting crop load capacities from the body length of wild bees, with a satisfactory degree of confidence. Sex is an important determinant of crop capacity, with females carrying maximal nectar loads around three times greater than males of similar size. We also found evidence that taxonomic affiliation influences allometric properties of crop capacities. Further studies are however needed to refine the predictions by taxonomic group, and in particular for the eusocial bumblebees. Field validation involving complementary data on floral nectar availability indicated that an allometric framework can be used to address research questions related to foraging success and competition for nectar in large wild bees (body length similar or greater than that of honeybees). Future studies should aim at refining the taxonomic resolution of allometric functions to family or genus level, which would provide a better understanding of the ecological particularities of certain groups of bees, such as eusocial species whose foragers store nectar for the entire colony or, conversely, cleptoparasitic (cuckoo) female bees that do not supply their broods.

## 1. Introduction

The overarching objective of this study is to provide a set of allometric functions of wild bee nectar crop capacities, which may be used as a baseline predictive tool in studies of bee nutrition, ecophysiology or foraging ecology. Floral resource scarcity arising from natural habitat loss and climate change is one of the key threats driving bee declines, both in diversity and abundance (Byrne and delBarco-Trillo, 2019; Kerr

et al., 2015; Roulston and Goodell, 2011) and has been increasingly studied over the past decade (Decourtye et al., 2019). Floral resources are essential food for bees and their offspring. Nectar, a source of carbohydrates, fuels energetic needs, while pollen provide essential aminoacids, lipids and vitamins for growth and the maintenance of keystone physiological functions. Therefore, a deficiency in pollen or nectar intake can have cascading effects on wild bee health and population sustainability (Leroy et al., 2023; Parreño et al., 2022).

<footnote><sup>a</sup> INRAE, UR 406 Abeilles et Environnement, 84914 Avignon, France</footnote>

<footnote><sup>b</sup> INRAE, UMR DYNAFOR, Université de Toulouse, 31326 Castanet-Tolosan, France</footnote>

<footnote><sup>c</sup> Université Grenoble Alpes, INRAE, LESSEM, 38402 St-Martin-d'Hères, France</footnote>

<footnote><sup>d</sup> Entomology and Nematology Department, University of Florida, Gainesville, FL, USA</footnote>

<footnote><sup>e</sup> CEFE, CNRS, Université de Montpellier, EPHE, IRD, 34293 Montpellier, France</footnote>

<footnote>* This article is part of a special issue entitled: 'Non-eusocial Bees and Pollination' published in Journal of Insect Physiology.</footnote>

<footnote>∗ Corresponding author at: UR 406 Abeilles et Environnement, Domaine Saint Paul - Site Agroparc, 228, route de l'Aérodrome - CS 40 509, 84914 AVIGNON Cedex 09, France.</footnote>

<footnote>E-mail address: mickael.henry@inrae.fr (M. Henry).</footnote>

<footnote n="1">¹ Equally contributing authors.</footnote>
To assess individual bee foraging success and nutritional status in the field, specific tools need to be developed. Such tools may include baseline references on resource requirements in pollen and nectar at the individual or population scale. Nutrition and foraging ecology have been extensively studied in the honeybee *Apis mellifera*, owing to the ease with which it can be reared. Detailed honeybee individual-based and demographic models have now been developed to predict foraging patterns and population dynamics (Becher et al., 2016, 2014). In wild bees, on the contrary, species are so numerous and with extremely varied body sizes, dietary habits and life history traits that our ability to document their foraging needs are limited by the lack of suitable methods.

One way to address this issue is to rely on allometric scaling models, i.e. the empiric or theoretic predictive functions that typically link morphological, physiological and ecological traits with body size. Unlike isometric relationships, in which two related variables increase proportionally, allometric relationships involve different increasing scales, and therefore use models where a variable is expressed as a power function of another variable. Allometric scaling relationships have acceptably predicted a range of morphological (Cariveau et al., 2016; Kendall et al., 2019) or even ecological (Greenleaf et al., 2007; Kendall et al., 2022) traits as a power function of body size across the diversified bee fauna. For instance, allometric functions have already been studied to predict pollen-carrying capacities in wild bees (Everaars and Dormann, 2014; Ramalho et al., 1998). Pollen is most often carried externally by female bees in their scopa (hind legs or ventral surface of the abdomen) or corbiculae (tibia external surface in some Apinae species like honeybees and bumblebees). Pollen foraging is therefore easy to sample and quantify at the individual scale.

Nectar, on the contrary, is carried internally by males and females, and thus inconspicuous and difficult to sample and quantify from foraging bees. Nectar is stored in the bee's crop, or honey sac, which is the collecting organ preceding the midgut, and in which no absorption takes place (Snodgrass, 1956). The crop load may be regurgitated by females to provision their nest or transferred towards the midgut through the proventriculus, for digestion (Crailsheim, 1988a, 1988b). The nectar crop load may be collected either through dissection (Huang and Seeley, 2003), or in a non-invasive way by narcotizing the bees and gently squeezing their abdomen to cause them to regurgitate (e.g. Couvillon et al., 2014).

The bee nectar crop load has mainly been documented for the well-studied honeybee. Maximal loads in satiated workers returning at their colony have been estimated to range typically between 36 µl and 54 µl, and up to 60 µl (Huang and Seeley, 2003). In addition, crop size in males appears to be much smaller than that of workers (Snodgrass, 1956). A better understanding of the morphological properties may help to investigate fundamental and applied questions in the fields of ecophysiology and energetics (Schmid-Hempel, 1987), toxicology and pesticide oral exposure assessment (Fournier et al., 2014; Henry et al., 2015; Rodney and Purdy, 2020). For instance, assessing bee oral exposure to systemic insecticides found at trace levels in nectar requires to elucidate the residual insecticide concentration in floral nectar, the amount of nectar ingested by foraging bees in their crop during foraging trips, as well as the nectar assimilation rate required to cover the energetic cost of flight (e.g. Rortais et al., 2005). Those parameters are well-known in the honeybees but still poorly documented in wild bees. In that respect, Fournier et al. (2014) stresses the importance of properly quantifying the nectar crop emptying rates in captive bees when setting the design of oral exposure experiments for pesticide risk assessment. The crop load capacity and crop emptying rate in wild bees seem to follow allometric properties (Fournier et al., 2014), but their mathematical relationships with body size have yet to be formalised.

The nectar crop load also appears to be a critical parameter in theoretical and applied ecology. In the context of the floral resource competition between wild bees and the managed honeybee, Sørensen et al. (2020) used individuals' honeybee crop load capacity to set a

theoretical basis for predicting an area's carrying capacity for beekeeping. In a more empirical way, Henry and Rodet (2018) computed an index of nectar foraging success based on a crop load allometric function of bee body length. Although this index delivered valuable insights on wild bee ecology, this approach was restricted to female bees only, and with no attempt to control for possible variations among taxonomic groups.

Consistent information on nectar crop load is overall scarce for wild bees, because laboratory feeding methods are currently only known and being developed for a handful of species other than the honeybee (e.g. Azpiazu et al., 2023). Similarly, little is known about actual crop loads in wild bee individuals that do not provision any nest but solely forage for their own energetic needs – namely males and cleptoparasitic species, also called cuckoo bees. Facing the tremendous diversity of their ecological traits and body sizes, allometric modelling may offer a promising approach for filling this knowledge gap in free-ranging wild bees (Fournier et al., 2014; Henry and Rodet, 2018).

The overall objective of this study is to establish reference allometric functions of maximal field crop load as a function of body length in wild bees. The maximal field crop load, hereafter $V_{max}$, may also be termed “realized” crop load, in that it represents maximal loads that are actually encountered in real field conditions, independently from “potential” loads that would represent the physiological upper limits (see Kendall et al., 2022 for a similar terminology in movement ecology). Our specific objectives were (i) to provide the first assessment of these morphological properties in wild bees, which are considerably less studied than the honeybee, (ii) to further assess the role of sex and taxonomic affiliation of individual bees as a determinant of $V_{max}$, and (iii) to test the ability of $V_{max}$ allometric functions to reveal ecological patterns of nectar foraging success, by means of a field validation trial. We will finally provide guidelines to use these reference functions as benchmarks in foraging ecology and discuss possible improvements and future perspectives.

## 2. Materials and methods

### 2.1. Study areas and sampled floral resources

Bee nectar crop data collated for this study proceed from two different surveys based on the same methodology, both aimed at studying ecological interactions between wild bees and honeybees and targeting the locally most common flowering plants visited by bees. The original study (Henry and Rodet 2018) was carried out in 2015–16 in the Côte Bleue area, a 55-km² Mediterranean scrubland (Natura 2000 Special Area of Conservation) dominated by rosemary *Salvia rosmarinus* (Lamiaceae) and held by the French Coastal Protection Agency, in southeast France (43.34°N, 5.22°E). Besides rosemary, the main floral resources sampled in this area were thyme *Thymus vulgaris* (Lamiaceae), and several species from the Cistaceae family (*Cistus albidus*, *C. salviifolius*, *Helianthemum marifolium*, *H. nummularium*). The dataset from this study was supplemented with the corresponding data for males.

In this study, the Henry and Rodet (2018) sampling design was replicated at a larger and more heterogeneous area, the core protection zone of the Cévennes National Park, in southern France. The National Park covers 938 km² with an altitude varying from 117 m to 1699 m. More specifically, after extensive interviews with local beekeepers on their practices (Mouillard-Lample et al., 2023), we targeted three different zones recognized for the abundance and diversity of floral resources: (i) the Cévennes schistose valleys (44.22°N, 3.68°E) dominated by oak and chestnut forests, (ii) Mont Lozère (44.42°N, 3.77°E), a granite massif predominantly covered with grazing areas and *Calluna vulgaris* heathlands maintained by pastoral grazing (Lehébel-Péron et al., 2016) and (iii) Mont Bougès (44.32°N, 3.71°E), a transitory area between the schistose valleys and granite part of the massif. The main floral resources sampled in these areas were clover species (*Trifolium*
dubium, T. incarnatum, T. nigrescens, T. repens, Fabaceae) in grasslands in May 2021, brambles (Rubus sp, Rosaceae), Erica heathlands (E. cinerea, Ericaceae) in June and July 2020–21, and Calluna heathlands (C. vulgaris, Ericaceae) in August 2020–21. Several additional floral resource species were sampled opportunistically in grasslands to obtain as many individual bee samples as possible. In total, 509 sites have been sampled (121 in the Côte Bleue area and 388 in the Cévennes area), representing 18 different flowering plant genera (Suppl. Table 1).

## 2.2. Individual bee capture and field crop load measurement

As in the original study (Henry and Rodet, 2018), we favored a spatially extensive sampling design in the Cévennes National Park, in which we reduced capturing effort at each sampling site in order to increase the number of sites and cover a broad variety of sampling contexts. At a given site, bees were sampled with nets while foraging on flowers, during 10-minute capture sessions involving two observers, typically between 9:00 and 17:00. No sampling was performed during rainy, windy or cold (<12 °C) weather.

As their crop load is expected to be gradually absorbed after capture (Fournier et al. 2014), bees were stored in coolers at 4 °C to slow down their metabolism and then processed immediately in situ after capture.

The field crop load refers to the nectar volume V stored in the bee's crop at the time of capture. Bees were first narcotized for a few seconds with CO₂ (ProFlora U500 Cylinder, JBL GmbH & co, Neuhofen, Germany) injected into the capture container (Suppl. Fig. 1) and measured (to the nearest mm) from the front of the head to the end of the abdomen, for later allometric modelling of nectar crop volume V as a function of body length L. Then, a gentle dorso-ventral pressure was applied on their abdomen until their crop load was regurgitated. The extracted nectar was capillary-collected (1-µl or 10-µl micropipettes Ringcaps, Hirshmann Laborgeräte GmbH & co, Eberstadt, Germany) for volume measurement, with an estimated ± 0.05 µl resolution. We were concerned that some individuals would actually carry water in their crop (as would do honeybee water foragers), with unknown consequences on our estimates of nectar crop allometric properties. We then performed confirmatory sucrose measurements using a hand-held refractometer (REF108, Index Instruments Ltd., Cambridgeshire, England) to ascertain the presence of measurable concentrations of sugar when the volume of collected nectar permitted (typically > 0.2 µl).

Finally, individuals were carefully examined for sex determination and taxonomic identification to family, genus, or species, whenever possible. The taxonomic validation to genus or species levels often requires invasive individual sampling. Instead, we favoured a morphotype approach, whereby individuals collected at a given capture site and sharing the same appearance and morphological characteristics were presumed to be of the same species. For each sex and morphotype, only a few individuals were collected within a given site or over several neighbouring sites, while all other individuals were released immediately after processing. Collected specimens were frozen, and subsequently pinned and dried before identification with the help of a network of expert taxonomists recognized by the French Inventaire National du Patrimoine Naturel (INPN).

## 2.3. Statistical analyses

*General principles of allometric modelling.* The goal of the study was to establish reference allometric functions of maximal field crop load $Vmax$ (µl) as a function of bee body length L (mm). $Vmax$ may be used, for instance, to correct the actual nectar volumes V found in bee crops, relative to the size of sampled individuals. To do so, we expanded on the general allometric framework described in Henry and Rodet (2018, Suppl. Fig. S4), using the regular allometric function of the form:

$$Vmax = aL^b \qquad (1)$$

indicating that $Vmax$ scales as a power function of L, with a and b as scaling constants. This allometric relation may be linearized as:

$$\ln(Vmax) = \ln(a) + b \times \ln(L) \qquad (2)$$

Linearization (eq. (2)) opens the way to more advanced modelling approaches, for example, implementing or testing the effect of additional covariates, such as sex, family or any other morphological characteristic, within a generalized linear model (GLM) framework. In this study, we used GLMs to further assess the role of sex and family, either as simple covariates or in interaction with body length, in shaping the allometric laws underlying maximal field crop load $Vmax$.

Under the circumstances, scaling constants $\ln(a)$ and $b$ correspond to parameters returned by the GLM, respectively the intercept and the slope estimate. One should back-transform the intercept with an e-exponentiation, and use the slope estimate as power coefficient of body length in order to recover the original allometric function (eq. (1)).

To assess the overall goodness of fit of the allometric models, we computed the adjusted R² of models, which adjust the regular R² for the number of predictors. We also ensured the residual normality requirements were fulfilled using the residual diagnostic facilities provided by the testResiduals function of the DHARMA R package (Hartig, 2022).

*Generic field crop load allometric model.* In a first step (model #1), all observed crop load values V were pooled in the same analysis, regardless of sex, and assigned to the body length class of the corresponding individual, from 5 mm to 29 mm. Given the rather limited number of large bees (body length > 19 mm, mostly from the Bombus genus) in our samples, we redefined body length classes using a 2-mm resolution instead of 1-mm. Large (>19 mm) individuals were therefore pooled by 2-mm body size classes, and assigned the median value for subsequent modelling – e.g. L = 19.5 mm for the pooled 19- and 20-mm body size classes.

Then, the maximal observed volume in each body length class $L_i$ was selected and considered as the virtual maximal crop load $Vmax_i$ for that body length class $L_i$. We finally modelled $Vmax$ as a function of L using GLMs, with a prior natural logarithm (ln) transformation of both variables. $Vmax_i$ will be arguably all the more accurate given that the body length class $L_i$ includes more data. To account for variable sample size among body length classes, we followed two principles. First, we ignored under-sampled body length classes, with n < 5 crop load measurements. Second, we used the weighting argument in the GLM to assign greater weight to each $Vmax_i$ value in proportion to the initial sample size in the corresponding body length class $L_i$. This approach reflects the fact that our confidence in approaching the true maximum within a size class increases with the number of raw observations in that class—a consideration directly incorporated through the GLM weighting argument.

*Sex-specific allometric models.* In a second step, we further introduced the sex component into GLMs, either as a simple covariate (model #2) or in interaction with body length (model #3). This involved re-assigning raw crop load values V into body length classes separately for males and females, before identifying a new set of $Vmax_i$ values specific for each sex. Models #2 and #3 were computed with respect to the same sample size control previously described for model #1 (minimum sample size and weighting argument). The relevance of sex as a simple or interacting covariate was assessed by comparing models #2 and #3, regarding a trade-off between model fit and complexity using the Akaike information criterion corrected for small samples, AICc, and the corresponding AICc weight, indicating the relative likelihood of each competing model.

*Improving the robustness of reference allometric functions.* The above-mentioned modelling procedure is based on a single $Vmax$ value per body length class, and may therefore return inaccurate estimates when including poorly sampled size classes. To further improve allometric model stability and robustness, we considered a second approach
whereby the highest 10 % of values in each body length class were used, i.e. all of the V values spanning from the 90 % upper quantile to the maximal value Vmax. Those data will therefore on average approximate the 95 % upper boundary in each body length class. This approach was expected to base the allometric models on larger datasets, though it entails the substitution of the notion of “maximal” field crop load Vmax for a less concrete notion of “95 % upper range” of field crop load, hereafter abbreviated as V95%. Models #4 to #6 were computed for V95% analogously to previous Models #1 to #3, respectively. This analysis could not handle poorly sampled body length classes with less than 10 crop load measurements.

Dealing with Bombus species and other taxonomic levels. We noticed (see results) that Vmax or V95% values of small Bombus species were higher compared to other bees with similar body lengths. We therefore decided to treat them separately so as to obtain allometric candidate models independent from those of all other bee groups. Models #7 to #12 were computed for Bombus species only, analogous to those computed for all other bees, Models #1 to #6, respectively. As with the other large bees, due to the limited sample size, consecutive body length classes were merged into broader 2-mm classes whenever necessary to achieve the minimum number of bees per size class.

We also investigated how Vmax or V95% would further vary among taxonomic groups (Bombus species set apart), and whether taking into account the taxonomic information would improve the allometric model fit to data. Introducing the taxonomic affiliation into models requires recomputing Vmax and V95% after re-assigning individuals into distinct taxonomic groups within each body length class. Given that all the corresponding combinations could not be properly covered, this analysis could only be supported at the broadest taxonomic level, i.e. the family level, and only considering females bees of the most common families. In this restricted taxonomic framework, we computed family-specific Vmax models by introducing the family identity into GLMs, either as a simple covariate (model #13) or in interaction with body length (model #14). Analogous models were computed for V95% (models #15 and #16, respectively). The relevance of family-specific models was assessed following the AICc-based model selection procedure similar to that for sex-specific models.

Field validation of the crop load allometric functions. As a reminder, the ultimate objective of the study was to test the ability of Vmax allometric functions to reveal patterns of nectar foraging success in female wild bees. In this field validation part, Vmax is used as a reference baseline in order to appraise to what extent a bee's nectar crop is filled given its loading capacity expected from body length, sex or even taxonomic affiliation. In case of slight nectar limitation, individual bees may increase the duration of their foraging trip to meet their nectar requirement or to optimise the quantity of nectar transported per foraging trip. In this circumstance, average nectar crop loads measured at a given moment in foraging bees may not be different from average loads measured in non-limiting conditions. Conversely, in case of severe nectar limitation, bees may not be able to compensate by adapting their time budget, which would translate into lower average nectar crop loads. If such a critical tipping point exists, we predict that the relative bee nectar crop load would, on average, decrease significantly as nectar becomes scarcer.

We tested this assertion using the nectar availability data originating from the Côte Bleue dataset. On top of the crop loads measured on bees foraging in rosemary, Henry and Rodet (2018, 2020) recorded the nectar availability from nearby rosemary flowers at the time of capture in 63 different capture sites. Nectar availability was expressed in nectar volume (µl) per 100 flowers. We selected from the database all female nectar crop loads originating from these capture sites (n = 104 females from 56 capture sites, after excluding cuckoo bees owing to their peculiar biology – here Nomada spp. and Coelioxys spp.). We then computed (i) their expected Vmax following the corresponding best candidate allometric functions regarding each bee body length and group (Bombus spp. vs. other bees) and (ii) their relative crop load Vrel,

expressed as a ratio of the observed crop load V at the time of capture to the expected maximal load Vmax:

$$Vrel = V \times 100/Vmax \quad (3)$$

Importantly, although Vrel may be expressed as a percentage of Vmax (or of V95%), it was handled as a continuous variable hereafter, not as a proportional variable, because it is not strictly bounded by 100 %. Indeed, Vmax in eq. (3) is given by a regression of maximal crop loads as a function of body length. As such, some crop load data points V are slightly above and others slightly below the regression line. This translates into Vrel values either higher or lower, respectively, than 100 % for those data points. There are even more values above 100 % when expressing Vrel as a function of V95%, because by definition, about 5 % of observed crop loads V lay above the V95% predicted line.

As a final step, we assessed whether Vrel was significantly related to actual nectar availability in flowers at the time of capture. To do so, we computed generalized linear mixed models (GLMM) with Vrel as the response variable and nectar availability as a fixed effect variable, while taking into account the random effect of capture sites. Indeed, several measurements of bee crop load are recorded per site and therefore associated with a single value of nectar availability. Moreover, we took into account the family as an additional random effect variable, given its potential effect on crop loads (see results).

The GLMM was computed using the glmmTMB function of the glmmTMB R package (Brooks et al., 2017). We used a gaussian error distribution and specified a zero-inflated probability distribution in the model due to the crop load data that seemingly have an excess of zeros. Zero-inflated models handle data with excess zeros by combining two submodels: a binary logistic part that determines the probability of a zero versus a non-zero observation, and a continuous part that models the outcome for non-zero observations. This dual structure allows differentiation between “true zeros” and zeros arising from a separate process. We finally applied a log(value + 1) transformation of Vrel data in order to reduce data dispersion and to meet the residual normality requirements, as assessed by the DHARMA residual diagnostics. The “+1” allows to keep zeros in the analysis in spite of the log-transformation. Zeros are important to denote low or hardly detectable crop loads whenever flower nectar availability is low.

## 3. Results and discussion

Overall, we captured and processed 2358 specimens (1492 females and 866 males) from six bee families: Andrenidae (n = 558 individuals), Apidae (966), Colletidae (76), Halictidae (540), Megachilidae (217) and Melittidae (1). Individuals were further assigned into 25 distinct genera (see Suppl. Table 2 for details). Body length ranged from 5 to 29 mm. Tiny individuals with body lengths of less than 5 mm were not processed in this study. Bumblebees (Apidae) totaled 531 specimens (263 females and 268 males) and had a body length typically ranging from 13 to 25 mm, though a handful of individuals were slightly smaller.

### 3.1. Practicability of crop load measurement in wild bees

As an important first result, we successfully collected nectar by crop regurgitation from a broad range of wild bee specimens representing various families and both sexes, including cleptoparasitic bees (Suppl. Table 2). Sucrose contents provided by the refractometer confirmed that the collected oral fluids had measurable sugar concentrations (44.1 ± 11.1 % [sd] in weight/weight) which matches expectations for floral nectar. No water forager, i.e. with low or undetectable sucrose in crop content, was encountered in the course of this study.

Still, we found a substantial proportion of individuals with empty crops, namely 24.7 % of females, and up to 69.9 % of males (Suppl. Table 2). The absence of nectar stored in the crop (V = 0) theoretically indicates that the individual was at the very beginning of its foraging trip
<caption>**Table 1**</caption>

Summary of allometric model selection of maximal (Vmax) and upper range (V95%) crop loads in wild bees. Generic models (#1, #4, #7, #10) express crop loads as a function of body length L only. Sex-specific models further include sex S, either as a simple (“+”) or interacting (“×”) covariate. Bumblebees (models #7–12) were treated separately from other wild bees. Family-specific models (#13 to #16) focus on females only (bumblebees excluded) and include family F either as simple (“+”) or interacting (“×”) covariate. The best candidate sex-specific models and family-specific models (lowest AICc and AICc Weight of evidence ≫50 %) are indicated in bold. AICc and weights of less supported models are not shown (i.e. null models and one-way models including only sex or body length alone). The adjusted R² is provided as an indicator of model's goodness of fit.

<table><thead><tr><th>Response variable</th><th>Model id.</th><th>Candidate models</th><th>Adjusted R<sup>2</sup> (%)</th><th>AICc</th><th>Weights (%)</th></tr></thead><tbody><tr><td rowspan="3">Vmax</td><td>#1</td><td>ln(Vmax) ~ ln(L)</td><td>93.71</td><td>-</td><td>-</td></tr><tr><td>#2</td><td>ln(Vmax) ~ ln(L) + S</td><td><strong>89.58</strong></td><td><strong>59.5</strong></td><td><strong>70</strong></td></tr><tr><td>#3</td><td>ln(Vmax) ~ ln(L) × S</td><td>89.57</td><td>61.2</td><td>30</td></tr><tr><td rowspan="3">V95%</td><td>#4</td><td>ln(V95%) ~ ln(L)</td><td>87.66</td><td>-</td><td>-</td></tr><tr><td>#5</td><td>ln(V95%) ~ ln(L) + S</td><td>88.34</td><td>295.2</td><td>13</td></tr><tr><td>#6</td><td>ln(V95%) ~ ln(L) × S</td><td><strong>88.64</strong></td><td><strong>291.4</strong></td><td><strong>87</strong></td></tr><tr><td rowspan="3">Vmax<br>(Bumblebees only)</td><td>#7</td><td>ln(Vmax) ~ ln(L)</td><td>25.94</td><td>-</td><td>-</td></tr><tr><td>#8</td><td>ln(Vmax) ~ ln(L) + S</td><td>17.35</td><td>40.4</td><td>18.2</td></tr><tr><td>#9</td><td>ln(Vmax) ~ ln(L) × S</td><td>13.03</td><td>43.9</td><td>3.3</td></tr><tr><td rowspan="3">V95%<br>(Bumblebees only)</td><td>#10</td><td>ln(V95%) ~ ln(L)</td><td>28.81</td><td>-</td><td>-</td></tr><tr><td>#11</td><td>ln(V95%) ~ ln(L) + S</td><td><strong>28.59</strong></td><td><strong>82.00</strong></td><td><strong>76.0</strong></td></tr><tr><td>#12</td><td>ln(V95%) ~ ln(L) × S</td><td>27.29</td><td>84.4</td><td>23.2</td></tr><tr><td rowspan="2">Vmax (Females only, bumblebees excluded)</td><td>#13</td><td>ln(Vmax) ~ ln(L) + F</td><td><strong>87.71</strong></td><td><strong>99.6</strong></td><td><strong>77.0</strong></td></tr><tr><td>#14</td><td>ln(Vmax) ~ ln(L) × F</td><td>88.79</td><td>102.5</td><td>17.8</td></tr><tr><td rowspan="2">V95% (Females only, bumblebees excluded)</td><td>#15</td><td>ln(V95%) ~ ln(L) + F</td><td>91.24</td><td>150.6</td><td>0.3</td></tr><tr><td>#16</td><td>ln(V95%) ~ ln(L) × F</td><td><strong>92.32</strong></td><td><strong>138.9</strong></td><td><strong>99.7</strong></td></tr></tbody></table>

at the time of capture, or that it failed to encounter nectar-rewarding flowers. Such a pattern has already been reported in honeybees using the same regurgitation method (Couvillon et al., 2014), with about 50 to 60 % of nectar foragers returning to their colonies with empty crops, and up to 90 % during periods of floral scarcity. For the sake of comparison, only 11.1 % of the honeybees sampled and processed in our study areas had empty crops (unpublished data). In practice, empty crops may also arise from an imperfect measurement method, i.e. incomplete regurgitation. Previous standardized feeding experiments in honeybees (Fournier et al., 2014) reported a slight underestimation of about 2.5 µl out of 20 µl (i.e. −13 %) in crop volume assessment. Such an underestimation may explain a portion of the virtually empty crops found in the field. However, this did not compromise our attempt to investigate maximal field load capacities of bee crops.

Altogether, the generic allometric models (Fig. 1) successfully captured a significant body size-dependent pattern in maximal crop loads for wild bees (models #1 and #4 in Table 1 and Suppl. Table 3), and to a lesser extent for the particular case of bumblebees that were treated separately (models #7 and #10 in Table 1 and Suppl. Tables 4). When considering all individuals regardless of sex (and bumblebees set apart), maximal crop load values Vmax and upper range values V95% could be satisfactorily predicted from bee body length with a R²

reaching about 94 % and 88 % of explained variance, respectively (Table 1). The corresponding allometric equations expressed in their usual form of a power function (Table 2) also appear consistent with theory. Indeed, the power coefficients b (3.27 and 3.89 for Vmax and V95%, respectively) both fall within the expected order of magnitude for such scaling properties, i.e. around 3 (Henry and Rodet, 2018). Given that body length L is a one-dimensional metric and volumes Vmax and V95% are three-dimensional, volumes that are expected to increase roughly as a cubic function of L, i.e. with a scaling constant b approaching 3 in eq. (1). This property appeared to be respected here, although with slightly higher coefficients than the previously reported value of b = 3.062 for Vmax (Henry and Rodet, 2018). It should be noted that the crop is an organ that can stretch according to the bee's needs, pushing other organs aside. It may therefore expand proportionally more than what would be predicted from usual scaling laws.

For bumblebees, maximal crop load was also significantly, or nearly so, linked with body length (p = 0.0629 and p < 0.001 for Vmax and V95%, respectively, Suppl. Table 4). However, explained variance was much lower (R² = 26 % and 29 %, respectively, for models #7 and #10 in Table 1), indicating that allometric predictability of maximal crop loads was overall weaker for bumblebees compared to other wild bees. In addition, maximal nectar crop loads were rather high for small

<caption>**Table 2**</caption>

Allometric equations of the maximal (Vmax) and upper range (V95%) crop loads in wild bees, as returned by the best candidate models. Equations stand for crop loads in µl and body length L in mm. Sex-specific models display distinct exponentiations for males and females when an interacting effect of sex is included, and identical ones, otherwise (see Table 1). The adjusted R² is provided as an indicator of model's goodness of fit. Sex-specific models for bumblebees' Vmax were not statistically supported by the AICc-based model selection.

<table><thead><tr><th>Response variable</th><th>Model id.</th><th>Sex</th><th>Formula</th><th>Adjusted R<sup>2</sup> (%)</th></tr></thead><tbody><tr><td rowspan="3">Vmax</td><td>#1</td><td>All</td><td>Vmax = 0.00306 × L<sup>3.2702</sup></td><td>93.71</td></tr><tr><td>#2</td><td>Female</td><td>Vmax = 0.00274 × L<sup>3.3155</sup></td><td>89.58</td></tr><tr><td></td><td>Male</td><td>Vmax = 0.00091 × L<sup>3.3155</sup></td><td></td></tr><tr><td rowspan="3">V95%</td><td>#4</td><td>All</td><td>V95% = 0.00038 × L<sup>3.8857</sup></td><td>87.66</td></tr><tr><td>#6</td><td>Female</td><td>V95% = 0.00072 × L<sup>3.7035</sup></td><td>88.64</td></tr><tr><td></td><td>Male</td><td>V95% = 0.00101 × L<sup>2.9175</sup></td><td></td></tr><tr><td rowspan="3">Vmax<br>(Bumblebees only)</td><td>#7</td><td>All</td><td>Vmax = 0.85676 × L<sup>1.4736</sup></td><td>25.94</td></tr><tr><td>-</td><td>Female</td><td>-</td><td>-</td></tr><tr><td></td><td>Male</td><td>-</td><td></td></tr><tr><td rowspan="3">V95%<br>(Bumblebees only)</td><td>#10</td><td>All</td><td>V95% = 0.23148 × L<sup>1.7984</sup></td><td>28.81</td></tr><tr><td>#11</td><td>Female</td><td>V95% = 0.16271 × L<sup>1.9654</sup></td><td>28.59</td></tr><tr><td></td><td>Male</td><td>V95% = 0.10562 × L<sup>1.9654</sup></td><td></td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Generic field crop load allometric models for wild bees (except bumblebees) and for bumblebees taken separately. All individuals are included, regardless of sex.</figcaption></figure>

bumblebees compared to other bee species similar in size (Fig. 1). This
difference may reflect a sociality effect. Bumblebees are eusocial species
and workers collect nectar for the entire colony. Larger crop sizes may
have been naturally selected in bumblebee species to meet their eusocial
needs.

Conversely, the corresponding scaling coefficient *b* in bumblebees (1.47 and 1.79 for *Vmax* and *V95%*, respectively, *Table 2*) was much lower than in other bees, and deviated substantially from the theoretical expectation of 3. This means that maximal crop loads do not increase as their body sizes increase as steeply as in other bees. It is not clear why larger bumblebees would have lower crop loads than expected from the allometric properties observed in other bee species. The same trend was also observed to a lesser extent in large-bodied (>20 mm) individuals from other bee genera. We tentatively suggest two mutually non-exclusive hypotheses. First, from an energetic perspective, it may become prohibitively costly for larger bees, in terms of foraging time or flight sustainability, to acquire and store nectar loads beyond a certain critical threshold. Second, from an ecological perspective, larger bumblebees, with greater nectar intake requirements and crop capacities, may be more nectar-limited in our study areas due to foraging competition with the super-abundant honeybee (Henry and Rodet, 2018; Mouillard-Lample et al., 2023). These results call for complementary studies focused on bumblebees, or more generally, at a finer taxonomic resolution, in line with the family-specific analyses reported hereafter.

3.2. *Sex as a determinant of crop load*

Allometric properties of crop loads are markedly different between sexes (Table 1), with significantly different scaling properties for males compared to females (Suppl. Tables 5 and 6), in turn leading to distinct allometric equations (Table 2).

For all bees except bumblebees, Vmax was best explained by an allometric model with sex as a simple additional term, i.e. not interacting with body length (model #2 in Table 1), which translates into equations with distinct intercepts for males and females, but identical scaling in relation to body length (see power coefficients in Table 2). In other words, linearized allometric models of Vmax (Fig. 2a) predict the same slopes for males and females, with Vmax values being about 3

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Sex-specific field crop load allometric models for wild bees (except bumblebees). Allometric models are given for *Vmax* (A) and *V95%* (B). See Suppl. Fig. 2 for bumblebees.</figcaption></figure>
times greater in females compared to males. V95% values, on the contrary, were best explained by an interacting effect of sex with body length (model #6 in Table 1), resulting in different scaling coefficients between sexes (Table 2) and therefore different intercepts and slopes (Fig. 2b). Under these circumstances, the relative difference in crop capacity between sexes is predicted to increase as the bee body gets larger; for example, V95% values are about 2.5 and 9 times greater in females than their male counterparts for 5 and 25 mm-sized bees, respectively. This is in line with the observation that foraging males were more frequently found with empty crops than females. In all cases, sex-specific models preserved a fairly high predictability of Vmax and V95% values (about 90% and 89% of variance explained, respectively, Table 2) as well as scaling coefficients close to the theoretical expectation of 3 (from 2.92 to 3.70, Table 2).

Sex-specific allometric patterns in bumblebees were consistent overall with the aforementioned models, but less supported from a statistical viewpoint. First, Vmax could not be satisfactorily modelled as a function of sex, as sex-specific models showed fairly low (≪50 %) AICc weight of evidence for being the best candidate models compared to a simple generic model ignoring sex (AICc weights = 18.2 % and 3.3 % for models #8 and #9, respectively, Table1). Still, V95% values were satisfactorily modelled using a simple non-interacting effect of sex (AICc weight = 76 %, model #11 in Table 1), which was deemed highly significant (p < 0.001, Suppl. Table 6). Although consistent with previous findings for other bees, the V95% models for bumblebees (Suppl. Fig. 2) had a rather low predictability (29 % of explained variance, Table 2).

Male and female bees differ in many ways regarding their foraging behavior (Bohart and Nye, 1956), which may further explain morphological adaptations like larger crop capacities in females, as documented herein. At the adult stage, both sexes consume floral nectar for their own energetic needs. However, only females collect pollen and nectar to feed their progeny (or conspecifics in the case of eusocial species), and therefore forage at higher rates. This implies different floral resource selection patterns between sexes (Cullen et al., 2021; Roswell et al., 2019; Smith et al., 2019), but also greater temporal constraints and energetic costs for females. Therefore, females may have been naturally selected for larger crops, relative to their size, to meet their energetic needs. More importantly, as females also offload nectar to provision the nest, larger crop sizes are critical for optimizing foraging trips. Few studies have contrasted crop contents between males and females. In the honeybee, males (also called drones) display different crop content patterns compared to worker honeybees. In particular they carry nectar with greater sugar concentration in their crop when they leave their colony for mating flights, but also appear to have a faster assimilation rate of nectar from crop to midgut in order to fuel their flight after feeding (Hayashi et al., 2016). Those observations are in line with the fact that they do not offload nectar when they get back to the colony.

Nectar offload and storage in “honeypot” cells is well-known in eusocial species like bumblebees (Pattrick et al., 2020) and honeybees (Huang and Seeley, 2003). Although less documented, solitary female bees also provision nectar for larvae, in the form of packed nectar and pollen mixtures (Batra, 1984). Regurgitated nectar is used by nesting females to moisten and agglomerate the pollen grains, further supplementing the overall energetic value of the larval diet. The required nectar quantity for larval diet is not trivial. In the alfalfa leaf-cutting bee *Megachile rotundata*, nectar may account for up to twice the weight of pollen (Cane et al., 2011), which in turn represents about a quarter or a third of the total foraging effort. The eusocial honeybee and bumblebee workers also resort to nectar (or honey) regurgitation in order to pack pollen pellets in their corbiculae while foraging (e.g. Vaissière et al., 1996). Altogether, these various additional demands for nectar could have contributed to the natural selection of solitary females and eusocial worker bees with greater crop capacities than those required for their own energetic needs alone.

### 3.3. Family influences crop load but more data are needed to refine allometric equations

As illustrated by the distinctive allometric properties of maximal crop load in bumblebees compared to other bees, taxonomic affiliation is certainly influential. This assertion was further confirmed by the family-specific models. When considering only female bees from the most common families (*Bombus* species excluded), we found that taking into account a family effect substantially improves the fit of allometric models to data (Table 1 and Suppl. Table 7), either as a simple covariate (for Vmax), or in interaction with body length (for V95%).

However, we have identified some signals that call for caution when using the resulting allometric equations. First, the *a posteriori* Tukey tests reported few actually significant pairwise contrasts between families – considering an average body length (Suppl. Table 8, see also the overlapping confidence intervals among curves on Suppl. Fig. 3). These differences essentially concerned the Andrenidae and Halictidae families which both tended to express Vmax or V95% values significantly (or nearly so) higher than those of the Apidae. Second, the resulting allometric equations return poorly realistic power coefficients for some families, far above the expected value of 3 (e.g. up to 5.78 for Megachilidae, Suppl. Table 9). This casts doubt on the reliability of crop load predictions on a per-family basis, at least for extreme body length classes. More data would be needed over a broader range of bee species and body length classes to establish consistent crop load allometric equations with higher taxonomic resolution.

Likewise, it appears important to keep in mind that the best allometric models selected in this study (Table 2) may not be readily applied to some bee species or functional groups with peculiar biologies or foraging patterns. For instance, the highly eusocial honeybee was not considered in this study due to its extreme adaptation to maximize nectar collection and storage at the colony level. Our model predicts a Vmax of 13.3 µl for female bees of similar body length (12–13 mm), while honeybee maximal field crop loads in Henry and Rodet (2018) were three times larger (41.1 µl, out of n = 1709 processed individuals). Studies even report an average crop load of 45.9 ± 8.7 µl (n = 50) in satiated honeybees, and maximal physiological capacities of up to about 60 µl (Huang and Seeley, 2003). Conversely, we expect the cuckoo bees (e.g. *Nomada* spp.) to present lower crop capacities than allometric predictions. Indeed, cuckoo bees only forage for their own energetic needs, and do not provision their brood as females of other solitary bee species do. Although we found here measurable nectar crop contents in cuckoo bees, our data are currently too limited to test this hypothesis.

### 3.4. Field validation of the crop load allometric functions

The reference maximal crop load equations established herein (Table 2) seem to return realistic predictions. Unfortunately, analogous values in the literature are too scarce to perform any formal, independent validation. Still, among solitary bee species, we found our predictions to be quite congruent with the literature for *Anthophora plumipes* and *Andrena agilissima*. In Stone (1995), females *A. plumipes* returning to their nest after foraging had mean crop loads of 30.1 ± 1.1 µl, and males had 2.8 ± 5.2 µl (after conversion from mg, considering an average nectar volumetric mass of 1.1 g/cm³), which gives a maximal range (mean ± sd) of about 31.2 µl and 8.0 µl, respectively. For comparison, individuals from that species (body length about 15–17 mm) should theoretically have Vmax values of 21.7–32.9 µl for females and 7.2–10.9 µl for males (using sex-specific model #2 in Table 2). These observed and predicted values appear to overlap quite well for both sexes. Likewise, in Giovanetti and Lasso (2005), *A. agilissima* (body length about 14 mm) displayed a maximal crop load of 17.3 µl (after conversion from mg), which matches the Vmax value predicted by our model.

For the eusocial *Bombus terrestris*, we found our predictions to be relatively low compared to individual foragers fed in captivity with sucrose solutions. Captive foragers drank on average 105 ± 17 µl at
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Field validation of relative crop load *Vrel* as a function of available nectar in flowers, for larger (A: body length ≥ 12 mm) and smaller (B: <12 mm) wild bees. The analyses presented herein were performed using the *Vmax* allometric body-length standardization. The 95 % confidence interval of predictions is shown as a shaded area for significant effects, and as dashed lines otherwise. Analogous results using the V95% standardization may be found in *Suppl. Table 10* and *Suppl. Fig. 4*.</figcaption></figure>

artificial feeders, and up to 163 µl (Pattrick et al., 2020), while our best model predicted a field *Vmax* of 70.8 to 98.3 µl for the largest bumblebees at 20–25 mm in body length (generic bumblebee model #7 in Table 2). These observed and predicted values barely overlap. Nevertheless, the captive conditions in Pattrick et al. (2020), with ad-libitum diet and contiguity of feeders to the nest, are quite different from our field conditions where nectar availability is arguably limited for large bees. In other words, the notion of maximal “physiological” crop load, potentially observable in captivity, is to be distinguished from our maximal “field” crop load measured in free-ranging individuals. Other studies report crop loads in large bumblebee individuals that exceed our maximal observations, e.g. about 109 µl and 127 µl (converted from mg), respectively in *B. terrestris* (Goulson et al., 2002) and *B. vosnesenskii* (Kerr et al., 2019). However, comparisons with our models are not straightforward because authors report morphological metrics (thorax width or intertegular span) other than body length.

Still, the consistency and usefulness of crop load allometric functions were further supported by significant links established between the

relative crop load *Vrel* of foraging female bees on the one hand, and nectar resource availability in flowers on the other hand (Table 3, Fig. 3). First, as would be logically expected, we found that (i) raw nectar crop loads *V* were significantly and positively correlated with female bee body length (Spearman rank correlation *r*<sub>s</sub> = 0.314, *n* = 104, *p* = 0.0012) and that (ii) the standardization of raw *V* values into *Vrel*, relative to *Vmax* or V95% (eq. (3)) successfully negated that correlation (*r*<sub>s</sub> = 0.002, *p* = 0.986 and *r*<sub>s</sub> = -0.053, *p* = 0.595, respectively), which allowed us to consider relative crop loads *Vrel* as independent from body length. Second, we found that the standardised volumes *Vrel* were significantly and positively influenced by available nectar in flowers (Table 3). However, this pattern held true for the largest bees only (of size similar or larger than the honeybee, ≥12 mm, Iwasaki and Hogendoorn, 2022), while smaller bees (5 to 11 mm) had a relative crop load *Vrel* unaffected by nectar availability in flowers. Results and conclusions are identical, whether we compute *Vrel* relative to *Vmax* (Table 3, Fig. 3) or to V95% (Suppl. Table 10, *Suppl. Fig. 4*). Thus, when flower nectar is scarce, larger bees appear to struggle to fill their crops,

<caption>**Table 3**</caption>

Detailed field validation statistics of relative crop load *Vrel* as a function of available nectar in flowers, for Larger (body length ≥ 12 mm) and Smaller (<12 mm) wild bees. The analyses presented herein were performed using the *Vmax* allometric body-length standardization. Analogous results using the V95% standardization may be found in *Suppl. Table 10*. Significant terms are indicated by bold *P*-values. Larger bees' relative crop loads were significantly driven by nectar availability in flowers. See Fig. 3 for graphical representation of the models.

<table><thead><tr><th></th><th>Covariates</th><th>Estimate</th><th>Std. error</th><th>Z-value</th><th>P-value</th></tr></thead><tbody><tr><td rowspan="3">Larger bees<br>(n = 70 females, nb. of site: 41)</td><td>Intercept</td><td>1.1203</td><td>0.1380</td><td>8.12</td><td><strong>&lt;0.001</strong></td></tr><tr><td>Nectar availability</td><td>0.5511</td><td>0.2034</td><td>2.71</td><td><strong>0.0067</strong></td></tr><tr><td>(Zero-inflation factor)</td><td>-0.5885</td><td>0.2496</td><td>-2.36</td><td><strong>0.0184</strong></td></tr><tr><td rowspan="3">Smaller bees<br>(n = 34 females, nb. of sites: 26)</td><td>Intercept</td><td>1.6240</td><td>0.1889</td><td>8.60</td><td><strong>&lt;0.001</strong></td></tr><tr><td>Nectar availability</td><td>-0.2929</td><td>0.3160</td><td>-0.93</td><td>0.354</td></tr><tr><td>(Zero-inflation factor)</td><td>-0.4796</td><td>0.3529</td><td>-1.36</td><td>0.174</td></tr></tbody></table>
while smaller bees seem to respond by increasing their foraging activity, resulting in unchanged average crop loads. This result illustrates the higher sensitivity of large-bodied bees to competition for floral resource exploitation, compared to smaller ones, due to higher nectar intake needs (Henry and Rodet, 2018; Iwasaki and Hogendoorn, 2022). It also supports the consistency and usefulness of allometric functions of crop capacities (Table 2) as a reference baseline for investigating wild bee nutrition and foraging ecology.

Unfortunately, this validation analysis could not be performed based on the family-specific allometric models, due to potentially biased maximal crop load predictions for large-bodied individuals in some families, as discussed previously. Alternatively, we accounted for the taxonomic affiliation of individuals by incorporating their family identity as a random effect variable. This significantly improved the model's fit to the data, yielding gains of 2.4 and 2.8 AICc units for the models in Table 3 compared to analogous models without taxonomic information. These findings also underscore the importance of future studies aimed at refining and validating the tentative family-specific allometric equations established here (Suppl. Table 9).

## 4. Conclusions and perspectives

Overall, this study established consistent allometric functions to predict field crop load capacities from wild bee body length, with a satisfactorily high degree of confidence (adjusted R² > 87 %). The most relevant and supported functions are summarized in Table 4 and in Fig. 4 on a non-transformed scale. Further studies are however required to refine predictions for larger bees, especially for the eusocial Bombus species, but also other large solitary species such as Xylocopa spp. The Vmax and V95% allometric models performed equally well at characterizing crop capacities in wild bees. However, the V95% approach appeared more robust owing to the larger, underlying datasets. Sex was an important determinant of crop capacities, as females carried maximal loads about three times larger than did males with a similar body length. The field validation involving complementary data on flower nectar availability indicated that larger bees are more subject to deficient crop load than smaller ones, as their relative crop load Vrel significantly decreases when nectar becomes scarcer in flowers. This illustrates the

<figure><img src="image_7.png" /><figcaption>Fig. 4. Graphical summary of the most relevant and supported allometric functions of field crop load capacity in wild bees (sex-specific models #2, #6 and #11).</figcaption></figure>

### Table 4

Field crop load capacity in wild bees (µl) as a function of body length, as predicted by the most relevant and supported allometric functions (sex-specific models #2, #6 and #11). Vmax values are not shown for bumblebees due to model uncertainty. Predictions are not applicable to the honeybee, and are only shown for the wild bee body length ranges actually covered by analyses. Likewise, these predictions might not be suited for cuckoo bee species, whose females only forage for their own energetic needs.

<table><thead><tr><th rowspan="2">Body length<br>(mm)</th><th colspan="2">Vmax<br>(Bumblebees excluded)</th><th colspan="2">V95%<br>(Bumblebees excluded)</th><th colspan="2">V95%<br>(Bumblebees only)</th></tr><tr><th>Females</th><th>Males</th><th>Females</th><th>Males</th><th>Females</th><th>Males</th></tr></thead><tbody><tr><td>5</td><td>0.6</td><td>0.2</td><td>0.3</td><td>0.1</td><td>-</td><td>-</td></tr><tr><td>6</td><td>1.0</td><td>0.3</td><td>0.5</td><td>0.2</td><td>-</td><td>-</td></tr><tr><td>7</td><td>1.7</td><td>0.6</td><td>1.0</td><td>0.3</td><td>-</td><td>-</td></tr><tr><td>8</td><td>2.7</td><td>0.9</td><td>1.6</td><td>0.4</td><td>-</td><td>-</td></tr><tr><td>9</td><td>4.0</td><td>1.3</td><td>2.5</td><td>0.6</td><td>-</td><td>-</td></tr><tr><td>10</td><td>5.7</td><td>1.9</td><td>3.6</td><td>0.8</td><td>-</td><td>-</td></tr><tr><td>11</td><td>7.8</td><td>2.6</td><td>5.2</td><td>1.1</td><td>-</td><td>-</td></tr><tr><td>12</td><td>10.4</td><td>3.4</td><td>7.1</td><td>1.4</td><td>-</td><td>-</td></tr><tr><td>13</td><td>13.5</td><td>4.5</td><td>9.6</td><td>1.8</td><td>-</td><td>-</td></tr><tr><td>14</td><td>17.3</td><td>5.7</td><td>12.6</td><td>2.2</td><td>29.1</td><td>18.9</td></tr><tr><td>15</td><td>21.7</td><td>7.2</td><td>16.3</td><td>2.7</td><td>33.3</td><td>21.6</td></tr><tr><td>16</td><td>26.9</td><td>8.9</td><td>20.7</td><td>3.3</td><td>37.8</td><td>24.6</td></tr><tr><td>17</td><td>32.9</td><td>10.9</td><td>25.9</td><td>3.9</td><td>42.6</td><td>27.7</td></tr><tr><td>18</td><td>39.8</td><td>13.2</td><td>32.0</td><td>4.6</td><td>47.7</td><td>31.0</td></tr><tr><td>19</td><td>47.6</td><td>15.8</td><td>39.1</td><td>5.4</td><td>53.0</td><td>34.4</td></tr><tr><td>20</td><td>56.4</td><td>18.7</td><td>47.3</td><td>6.3</td><td>58.7</td><td>38.1</td></tr><tr><td>21</td><td>66.3</td><td>22.0</td><td>56.7</td><td>7.3</td><td>64.6</td><td>41.9</td></tr><tr><td>22</td><td>77.4</td><td>25.7</td><td>67.4</td><td>8.3</td><td>70.8</td><td>45.9</td></tr><tr><td>23</td><td>89.7</td><td>29.7</td><td>79.4</td><td>9.5</td><td>77.2</td><td>50.1</td></tr><tr><td>24</td><td>103.2</td><td>34.2</td><td>93.0</td><td>10.7</td><td>84.0</td><td>54.5</td></tr><tr><td>25</td><td>118.2</td><td>39.2</td><td>108.1</td><td>12.1</td><td>91.0</td><td>59.1</td></tr></tbody></table>
utility of crop capacity allometric function in revealing ecological patterns of nectar foraging success in free-ranging bees.

Future challenges will be to fine-tune the taxonomic resolution so as to provide consistent family- or even genus-specific allometric reference functions. Indeed, bees with a peculiar biology, such as the cuckoo bees whose females only forage for their own energetic needs, may display distinctive allometric patterns. Model predictions may also be improved by incorporating a phylogenetic relatedness component among species (Kendall et al., 2019), which is unfortunately not yet affordable given current sample sizes, but may be considered after more data are accumulated. In that respect, nectar intake experiments in controlled conditions with artificial feeders may have a role to play. They are, to date, only feasible with a fairly limited number of wild bee species due to the difficulty in feeding them in captivity, but solutions may emerge on a species-specific basis (Azpiazu et al., 2023).

## CRediT authorship contribution statement

**Sarah Bourdon:** Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Data curation, Conceptualization. **Léo Mouillard-Lample:** Writing – review & editing, Writing – original draft, Validation, Methodology, Formal analysis, Data curation, Conceptualization. **Taïna Lemoine:** Writing – review & editing, Data curation. **Maxime Lewin:** Writing – review & editing, Data curation. **Laurent Guilbaud:** Writing – review & editing, Data curation. **Léna Barascou:** Writing – review & editing, Data curation. **Bertrand Schatz:** Writing – review & editing, Data curation. **Mickaël Henry:** Writing – review & editing, Writing – original draft, Validation, Project administration, Methodology, Formal analysis, Data curation, Conceptualization.

## Funding

This work was supported by the Conservatoire du Littoral, the Lune de Miel Foundation, the Sojufel company and the French agency of ecological transition (ADEME) through the CO3 (CO-COstruction de CONnaissances) program (agreement #00147459 / PR-170024).

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

We are grateful to the Conservatoire du Littoral and the Cévennes National Park for granting sampling authorizations and for providing logistical support. In particular the authors would like to thank Jocelyn Fonderflick, Tifenn Pedron and Viviane de Montaigne for their help in setting up the study design and field assistance, as well as Morgane for pinning collected specimens. We are grateful to all those who participated in the sampling sessions: Guy Rodet, Axel Decourtye, Cécile Férus, Pierre Le Bivic, Zoé Le Marchand, Julien Vallon. Special thanks also go to D. Genoud, M. Aubert, A. Pauly, H. Dathe, E. Dufrêne, M. Kuhlmann, J. Litman, D. Michez and S. Risch for bee identifications, J. Cane for providing useful references, C. McDonnell for help in revising the text, as well as two anonymous reviewers for helpful comments on earlier versions of the manuscript.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jinsphys.2025.104840.

## Data availability

Data will be made available on request.

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