Interindividual variation of eye optics and single object resolution in bumblebees

The ability of animals to detect a single target depends on the optical quality of the eye (Exner,1891; Burtt and Catton,1962; Kirschfeld,1984; Land, 1999; Warrant and McIntyre, 1993) as well as intrinsic properties of the target such as size, shape and colour(Srinivasan and Lehrer, 1988; Giurfa et al., 1996; Lehrer and Bischof, 1995; Dafni et al., 1997; Ne'eman and Kevan, 2001; Spaethe et al., 2001). Eye optics are limited by eye size, which in turn is constrained by body size(Kirschfeld, 1976; Nilsson, 1990; Rutowski, 2000; Wehner, 1981). However, eye optics only set the upper limit to visual resolution; they do not determine it directly. This is because there can be significant convergence in the neuronal processing of signals from the visual periphery. In honeybees (Apis mellifera), for example, the resolving power of the ommatidial array is about 1° (Hecht and Wolf,1929; Dafni and Kevan,1995; Land, 1999). However, behavioural experiments reveal that in single object detection tasks,such as perceiving a coloured flower against its green foliage background, a minimum angle of 5° must be subtended by the target on the bee's eye,corresponding to an excitation of seven ommatidia(Giurfa et al., 1996; Giurfa and Lehrer, 2001; Vorobyev et al., 1997). Furthermore, the extent of neuronal pooling in the visual neuropils might depend on the environmental luminance level(Dvorak et al., 1980; Srinivasan and Dvorak,1980).

Thus, behavioural tests must be combined with quantifications of eye optics to determine how target detection ability varies with body size. Here, we employ a size-polymorphic insect species, the bumblebee Bombus terrestris, to determine this relationship quantitatively. There are numerous studies to show that the optical properties of complex eyes are scaled with body size (Land,1981; Snyder and Menzel,1975) both within (Zollikofer et al., 1995) and across species(Jander and Jander, 2002). Larger animals tend to have more ommatidia per eye, larger facets (and hence higher overall sensitivity) and smaller interommatidial angles, resulting in higher visual resolution (Jander and Jander, 2002; Wehner,1981; Zollikofer et al.,1995). But can we extrapolate directly from eye optics to behavioural ability at target detection? There are behavioural studies to determine the minimal detectable size of visual targets or, alternatively, the minimum grating resolution across a range of insects(Baumgärtner, 1928; Gould, 1988; Lehrer and Bischof, 1995; Macuda et al., 2001; Rutowski et al., 2001; Vallet and Coles, 1991). But the experimental conditions and behavioural contexts are too heterogeneous across studies to reveal a consistent picture.

Bumblebees are an ideal species to quantify the relationship between body size, eye optics and behavioural ability at visual stimulus detection. They exhibit a pronounced size polymorphism: workers of a single colony can differ in body mass by a factor of 10, which is unique in the social bees(Michener, 1974). We quantify the optics of the eyes of Bombus terrestris workers over a wide range of sizes, and their relationship with the ability to detect artificial flowers.

We bought bumblebee (Bombus terrestris L.) colonies from a commercial breeder (Koppert, Berkel en Rodenrijs, The Netherlands). For morphometrical measurements, bumblebee workers were selected according to their size and killed by cooling in a freezer at -20°C. The head and thorax of each bee were mounted on a table with a micrometer screw. Size measurements were carried out using a stereomicroscope (Wild TM M3Z;Heerbrugg, Switzerland) at 20× magnification. We determined thorax width(intertegula span) and the length of the left eye (distance of the longest surface perimeter through the centre; see inset of Fig. 1B) from each worker.

For estimating ommatidial number and diameter, we removed the left eyes of freshly killed bees with a razor blade and glued them with their inner side on an SEM table. Eyes were air-dried, gold-palladium coated (Balzers sputter coater SCD 005; Bal-Tec, Balzers, Switzerland) and viewed with a scanning electron microscope (Zeiss DSM 962; Jena, Germany). On the SEM photos, we marked a 1 mm² area in the centre of each eye and counted all ommatidia inside this area. Of 15 randomly selected ommatidia, we measured facet diameter (tip-to-tip distance of the hexagonal lens). We scanned the photos of each eye into a computer and measured eye surface area using an imaging program (Scion image; Scion corporation, Frederick, MA, USA). The number of ommatidia per eye was calculated by counting ommatidia per 1 mm² multiplied by eye surface area. Note that this provides an underestimate of total ommatidial number because, in bees, the largest lenses are found in the centre of the eye, where we performed our measurements. Ommatidial size decreases systematically as one moves to the periphery(Jander and Jander, 2002). However, the ratio of facet diameters between the centre and the (dorsal)margin of the eye appears to be nearly constant over a wide range of diurnal bee species with different sized individuals(Jander and Jander, 2002). Therefore, it is unlikely that our estimates bias the qualitative relationship between eye size and facet number.

The green contrast between target and background in our set-up was 0.11,where maximum green contrast is 0.5(Spaethe et al., 2001). This is because, by definition, for the adaptation background E equals 0.5 in each photoreceptor. Green contrast, then, is the degree to which any given stimulus generates an excitation value different from 0.5 in the green receptor. Because excitation can range from 0 to 1, the maximum green contrast is 0.5.

This means that, in our target, green contrast is strong and is well above detection threshold (Giurfa et al.,1996). This is important because the green receptor channel limits spatial resolving power in bees(Srinivasan and Lehrer, 1988)- if a target differs from its background only in the UV or blue receptor signals, spatial resolution is substantially worse. This is because bees will then resort to using colour contrast, which requires that a target subtends 15° (Giurfa et al., 1996; Giurfa and Lehrer, 2001). Colour contrast between target and background was 0.301; brightness contrast,given as the difference in sum of the three photoreceptor type signals, is 0.912.

We found not only a strong correlation of eye size with body size(Fig. 1B) but also a highly significant increase of ommatidial number and diameter of facet lenses with body size (Fig. 4A,B). Workers with double thorax width have about 50% more ommatidia and also have facets that are about 50% larger in diameter. But increases in facet diameter can only help to generate a more fine-grained image if interommatidial angles are decreased at the same time(Hocking, 1964).

We found that interommatidial angles in the medial-frontal part of the eye decrease with increasing body size (Fig. 5), both in the vertical (from 0.6° to 1.4°; Spearman's rank correlation r_s=-0.52, P=0.041, N=16) and the horizontal (from 1.8° to 3.3°; r_s=-0.69, P=0.003, N=16) dimension. An increase in body size (thorax width) by a factor of 1.5 is accompanied by a 32% reduction of the divergence angles in the vertical dimension and a 19%reduction in the horizontal dimension. In conclusion, large bees combine the advantage of larger facet diameters (lower diffraction, higher overall sensitivity) with the benefit of lower interommatidial angles (more fine-grained picture). They should therefore have higher visual resolving power.

Our results show that the gains associated with an increase in body size(and the predicted improvement in visuo-spatial resolving power) are significant. We found a significant negative correlation between the minimum visual angle at which a stimulus can be detected and the size of the bumblebee(r_s=-0.73, P=0.01, N=11). For example, a large bee (4.7 mm thorax width) can detect objects of half the size that a small bee (3.5 mm thorax width) can from the same distance(Fig. 2B). Large bumblebee workers also exhibit much better visual resolution than honeybees (minimum visual angle of 3.5° vs 5°), whereas small bumblebees perform worse (7° minimum visual angle). Qualitatively, the observed correlation is unsurprising, but can behavioural detection ability be quantitatively predicted from eye optics alone? To answer this question, we must calculate the number of ommatidia actually involved in detection for workers of different sizes.

The number of ommatidia involved in object detection varies between individuals and correlates with worker size(Fig. 6). In small bees (thorax width <3.5 mm), excitation of seven ommatidia is required for stimulus detection; the same number that was determined in the honeybee(Giurfa et al., 1996). Over a range of intermediate sizes (3.5-4.3 mm), the number of ommatidia that need to be excited for target detection is three. In large workers (>4.3 mm), only a single ommatidium is necessary for reliable detection of a coloured object.(Note that there are no body sizes for which we predict a minimal ommatidia number of 2, 4 or 6, because the minimal area expands in the horizontal and vertical directions symmetrically as a function of body size.)

We determined quantitatively the relationship between eye optical quality and behavioural ability at target detection over a range of sizes of insects of the same species, the bumblebee Bombus terrestris. We show that large individuals outperform small ones as a result of an improved optical setting (larger facets combined with smaller interommatidial angles). Additionally, in large bees, a lower number of ommatidia needs to be stimulated for target detection. In small B. terrestris workers, as in honeybee workers (Giurfa et al.,1996), seven ommatidia must be subtended by a reflecting target. In large workers, conversely, stimulation of a single ommatidium appears to be sufficient.

These estimates are based on the acceptance angle from honeybee ommatidia,as quantified by Laughlin and Horridge(1971). The lens diameter in the frontal eye is similar between honeybees (21.6 μm; Barlow, 1952) and our smallest worker (19.5 μm). It is likely that larger bumblebees have ommatidia with smaller acceptance angles due to larger lens diameters(Warrant and McIntyre, 1993). Taking this into account, the superscript in equation 9 would be additionally reduced in larger bees, which might result in an even stronger reduction of the ommatidial array stimulated as shown in Fig. 6 for large workers. Thus,our estimate is conservative.

There are two possible interpretations for our findings. One possibility is that receptive field sizes of visual interneurons involved in target detection differ between small and large workers, so that each cell receives input from seven ommatidia in small workers and from only a single ommatidium in large workers. This would be reasonable since smaller ommatidia will suffer more strongly from signal-to-noise problems. Small bees possess ommatidia with smaller diameters with lower rates of photon capture over time and thus provide a worse signal-to-noise ratio than do large ommatidia(Snyder, 1979; Land, 1981). The excitation of only one ommatidium by a small object might not be sufficient for reliable detection. A summation of signals from several ommatidia at a higher neural level, as is realised in neural superposition eyes(Land, 1999), increases the signal-to-noise ratio and might also improve reliable detection by small bees. Conversely, large bees with about 50% larger ommatidial diameter benefit from a better signal-to-noise ratio and might be able to waive a subsequent neural summation. Their visuo-spatial resolution might be directly limited by the ommatidial array.

The other possible interpretation is that the degree of neuronal convergence is identical in small and large workers and that workers of all sizes pool the responses from seven ommatidia. In this case, we would have to assume that a single ommatidium is seven times more sensitive in a large worker than in a small worker. An increase in lens diameter of about 50% would result in an increase of aperture of ∼2.3-fold. But bees with larger eyes also have longer and wider rhabdoms and thus more membrane surface with a higher number of visual pigments to increase photon capture(Kirschfeld, 1976; Warrant and McIntyre, 1993). Therefore, it is indeed conceivable that larger lenses combined with larger rhabdoms might cause the 7-fold increase in sensitivity.

Two unambiguous ways to quantify receptive field size would be to use sinusoidal gratings of varied spatial frequency(Wehner, 1981; Srinivasan and Lehrer, 1988)or to measure the minimum separable distance between two points. Here, we were concerned with performance of bees at a biologically realistic task, that of flower detection. In future experiments, it will be especially interesting to see if the extent of pooling in a given sized worker is hard-wired or whether it changes with the intensity of the illumination. There is evidence for this in movement-detecting neurons of flies(Dvorak et al., 1980; Srinivasan and Dvorak, 1980)and in grating resolution in honeybees(Warrant et al., 1996).

Behavioural ecologists have long been interested in the importance of eye design for navigation (Land,1999; Wehner,1981), foraging efficiency(Dafni and Kevan, 1995; Macuda et al., 2001; Spaethe et al., 2001) and mate search (Rutowski, 2000; Vallet and Coles, 1991). Our results allow quantitative predictions of how visually constrained behavioural ability changes with compound eye optics. Data on the optical system alone are not sufficient to determine single object resolution capability. Information about subsequent neuronal processing, gained from behavioural experiments, is indispensable.

Polymorphism of eye optics is not uncommon in arthropods. Many species exhibit a sexual dimorphism of the eyes: males often have acute zones with increased facets and reduced interommatidial angles. These zones are used in rapid pursuit of flying females (Land,1999; Menzel et al.,1991). As an example of polymorphism within a sex, eye optics of Cataglyphis ant workers are also scaled with body size(Zollikofer et al., 1995). But all of these studies have stopped short of actually measuring the behavioural performance in target detection and its correlation with eye optics. We show here that, if eye optics alone are quantified, one might even underestimate the differences in behavioural ability at target detection that exist between members of the same species or between different species.

Large bumblebees might be the `acute vision specialists' of the bee colony,whose workforce might be most efficiently employed in tasks such as searching for flowers. Indeed, large bees contribute disproportionately to colony foraging intake: they harvest significantly more nectar per unit foraging time than do small bees (Spaethe and Weidenmüller, 2002). Also in line with our prediction, large bees exhibit a higher propensity to forage rather than to perform household duties such as brood care and nest cleaning(Cumber, 1949). We also conjecture that large bees might be less constrained by low light intensities than are small bees and might thus start foraging earlier in the morning and stop later in the evening. We conclude that our understanding of task specialization in social insects might greatly benefit from considering sensory and cognitive differences between individual animals(Thomson and Chittka, 2001; Chittka et al., 2003).

We thank W. Kaiser and H. Vogt for suggestions and equipment and two anonymous referees for their most helpful comments. This work was supported by grants SFB554 and Ch147-3/1 from the German Research Foundation DFG and a grant from the Central Research Fund of the University of London to L.C.