We showed that the evolution of food load manipulation ability, which has occurred independently twice in the present set of species, is associated with a decrease of FMR and an increase in WL across species. Moreover, a high FMR was associated with a low WL, indicating coevolution of morphological traits related to foraging.
Within, as well as across, wasp species, the dependence of the maximum theoretical load that could be carried (Loadmax) on body mass allows larger individuals/species to potentially carry large prey, even though there is no relationship between FMR and body mass (Table 2). Empirical studies of individual wasp species indeed showed that larger individuals carry larger prey compared to smaller ones [20, 25, 26]. Moreover, larger species appear to be able to carry heavier loads (Pearson correlation test, r = 0.95, P < 0.001, data from 12 species reviewed by ). However, the degree to which individuals and species maximize their food load is highly variable, suggesting that other factors, such as prey specialization , prey availability  and intra-specific competition  may affect the food load mass. For example, females of Bembix troglodytes, a solitary wasp of about 0.01 g, hunt for flies weighing only half the theoretical maximum they can carry . This may be a strategy to limit the attack of conspecific kleptoparasitic females, since carrying small prey may allow entering nest holes more rapidly and avoiding harassment . On the other hand, the species-specialist cicada-hunting wasp Sphecius convallis carries prey loads approaching the theoretical maximum value of Loadmax, possibly because the strong specialization on a single prey species has allowed selection to adjust the morphology of females to an almost ideal size .
As re-calculated from data provided in a recent review , UtM-species carry on average loads weighing 89 ± 14% of body mass (data from 11 species of Sphecidae, Crabronidae and Vespidae), similar to the predicted % Loadmax/Mb average value of 118% on the entire set of species considered in this study (89.3% with data for the shared UtM-species in our study and , n = 7 species). Moreover, among UtM species, there was no correlation between prey size and FMR (Pearson correlation test, r = 0.43, P = 0.19, data from 11 species reviewed by ). It is believed that the first apoid wasps were specialized in hunting large orthopterans, and the prey spectrum would have then become broader to include smaller arthropods as diverse as flies, bees, beetles and spiders . Thus, the evolution of flight morphology adapted to carry large items possibly preceded, during evolution, prey diversification, and did not change too much thereafter in apoid wasps. A change in flight morphology may have appeared when bees (sensu stricto, i.e. pollen/nectar foragers) separated from apoid wasps about 140 to 110 m.y.a. . A similar pattern may have occurred among Vespidae, where solitary species (subfamily Eumeninae), unable to manipulate food load size, are basal to the social species , which are able to manipulate food. In Eumeninae, prey diversification was less pronounced, with only lepidopteran or coleopteran larvae used as prey, and a change in flight morphology may have appeared when eusociality, together with its associated foraging mode (e.g. direct liquid-feeding from adult foragers to larvae, made possible because of food manipulation ability) evolved .
The maintenance of higher FMR in UtM-species could also depend on the fact that the position of load during carrying may affect the center of gravity, unbalancing the wasp while flying. A recently developed model shows that, among species carrying prey impaled on the sting (i.e. well posterior to the wasp center of gravity), the Loadmax can be severely reduced compared to the expected value . Wasps can limit to some extent this problem by increasing the angle which the straight line connecting the wasp with the load center of mass makes with the horizontal line , but, evolutionarily speaking, any increase in FMR, positively affecting Loadmax, would help in carrying larger prey in such an unbalanced flight mode.
On the other hand, AtM species are far from approaching the average values of relative load size observed among UtM species, as they appear carrying loads weighing only 31 ± 6% (calculated from data of 17 species provided in [20, 34–36]). This value is much lower than the average % Loadmax estimated for our set of AtM-species (86%).
Actually, females of UtM-species were sometimes observed to return to the nests with a prey weighing more than Loadmax, implying an unsuccessful take-off . With very large prey items, UtM wasps can potentially shift to an alternative strategy, such as carrying the prey to the nest by dragging it on the ground. Such behaviour has been described in some (but not all) species, though flight transportation was the preferred option if prey size is adequate . For example, Ammophila spp. typically drag large caterpillar prey over the ground, but shift to flight transportation in case of smaller prey (reviewed in ). Indeed, dragging a prey on the ground may make it much more vulnerable to kleptoparasites and predators. The cicada-hunting wasp Sphecius speciosus can drag very large cicadas over a distance sometimes full of obstacles (e.g. dense and high grass) which makes prey prone to be abandoned and exploited by ants . Dragging a prey over such complex substrates may also increase the duration of the hunting trip compared to flying across the same distance. Despite hunting site-nest distances are not provided and conclusions cannot be really drawn, data from the literature reported very short hunting trips (≤ 2 minutes) apparently only for flight-carrying wasps (e.g. [38–41]). Thus, although in specific cases wasps can use the alternative strategy of dragging very large prey, we expect a fitness advantage in term of foraging efficiency (e.g. number of prey hunted per day) when the prey is carried in flight. Clearly, a robust and direct comparison of the actual fitness costs and benefits of prey carrying in flight vs. prey dragging would be needed to confirm this speculation.
An interesting consequence of load-lifting/manoeuvrability constraints concerns diet composition and resource specialization. In bees, any individual could have access to its preferred resource (assuming these are available in the foraging environment) because food collection is only limited by the number of pollen grains it can carry and by the nectar volume it can ingest, i.e. by volumetric, not mass, constraints. In wasps that are able to manipulate food load the situation is similar: Coelho and Hoagland  studied the foraging behaviour of Vespula germanica on dead honeybees, and found that foragers too small to carry entire honeybees simply chopped body parts and took off with a smaller portion , without the need to discard the food item and search for a new, smaller one. Food manipulation ability would thus help to exploit the target food in a highly efficient way. At the same time, AtM-wasps can have access to a wider range of prey types, since also large prey, once chopped, can be readily exploited. Such increased efficiency in foraging may have even been important in promoting the evolution of eusociality, since social behaviour is unstable unless it provides important economic benefits and fitness gains to the individuals . As a matter of fact, eusociality arose at least five times independently within AtM-lineages, while apparently only once within UtM-lineages (see also [43, 44] for theoretical predictions on the link between food resource and social evolution in Hymenoptera).
On the other side, wasp species unable to manipulate food load will face a more adverse situation if the prey item is too large to be carried, and the wasp has to spend additional time and energy to search for a different, smaller, profitable prey . In a simple model, Polidori et al.  predicted that wasp species hunting for hemimetabolous prey can be so affected by the body growth of their preferred prey during the course of the breeding season that they may be forced to shift to different prey species at a certain point. Later, a study on the orthopteran-hunting wasp, Stizus continuus, confirmed this prediction . Furthermore, this shift to smaller prey species is confined in such wasps to only few other species, given their phylogenetic constraint in prey selection (typically prey species belong to one single order ), so that overall prey spectrum cannot be wide as in AtM-wasps.
As an additional advantage, higher FMR would enhance the escape ability of UtM-species, given that FMR is correlated with linear acceleration and the ability to accelerate vertically against gravity  and with flight speed . Low WL is expected to confer similar advantages. In UtM-wasps, which are also those limited to hunt for living prey, lower WL could increase manoeuvrability during prey transportation, but could also increase efficiency while pursuing a living prey (e.g. via reduced minimum flight-speed requirement and turning radius), including fast-flying insects . A similar example involves bats, in which species with greater WL forage in areas where there are fewer obstacles to detect and avoid . On the other side, increased WL consistently decreased escape performance in a bird .
Despite higher WL requires higher wing-beat frequency and increases flight cost , flight speed generally increases with WL [11, 52], so that higher WL could be positively selected in specific contexts. For example, males of perching butterfly species (which sit and wait on prominent landmarks and rapidly take off to intercept females) had higher WL than patrolling closely-related species . AtM-species may thus fly faster while sacrificing manoeuvrability (an important factor while carrying loads) than UtM-species. These considerations, together with the observed negative covariation of FMR and WL across species, suggest that the selection pressures related to foraging (load-lifting/manoeuvrability) constitute the main determinants of flight morphology in central-place foraging Hymenoptera.
Moreover, among AtM species, investment in flight muscles and wing size, which would be of limited adaptive value during foraging, may further be counteracted by contrasting selection acting on other life-history traits, such as reproductive investment. In butterflies, for example, palatable species have higher FMR because of higher predation risk and stronger escape demands, but also smaller ovaries than unpalatable species, suggesting that investment in the flight apparatus and predator avoidance trades off with investment in reproduction . Intriguingly, a preliminary analysis based on literature data suggests that this could be the case also among the Apoidea. In fact, the number of ovarioles per ovary was significantly higher in bees (3.6 ± 0.09, n = 32 species) than in apoid wasps (2.9 ± 0.03, n = 75 species) (t39 = 6.8, P < 0.0001) (data from [54, 55]; highly eusocial bee species (queens), parasitoid apoid wasps and brood-parasitic apoid wasps were not considered because of their peculiar life-style). Though it might be speculated that eusocial bee species represent an exception to this pattern, we note that honeybee workers can have from 1 to 12 ovarioles per ovary (with an average of about 4) , thus roughly agreeing with the rest of bees. In addition, workers of one species of Bombus (the primitively eusocial B. morio) have the same number of ovarioles per ovary as related solitary species (4) . This hypothesis, however, needs a robust, phylogenetically controlled, test, using species for which both flight morphology and measurements of fecundity are available.