Optical Scaling in Conspecific Cataglyphis Ants

Even though the worker castes of most ant genera, including the Old World desert ants of the genus Cataglyphis, are monomorphic (Hölldobler and Wilson, 1990; Wehner, 1983), individual workers of a given species come in various sizes. In Cataglyphis, they may vary by a factor of 2 in linear dimensions (e.g. head width; C. albicans, 0.8–1.7 mm; C. bicolor, 1.5–3.2 mm; Wehner, 1983). Furthermore, the workers of all Cataglyphis species are highly visually guided navigators, not relying on pheromone trails while foraging, so how do differently sized workers compare in their visual performances? First and foremost, how do the optics of the ants’ compound eyes (e.g. optical parameters such as the size of the visual field, the angular distance between adjacent ommatidia, the radius of curvature of the eye, etc.) scale with the size of the animal?

There are likely to be trade-offs between particular optical functions. For example, take the simple observation that, within conspecific individuals, eye size decreases with decreasing body size. Small ants have fewer and smaller ommatidia than large ants. Does this mean that small ants exhibit lower visual acuities or smaller fields of view than larger ants? In other words, is field size functionally more important than acuity, or vice versa? Answers to such questions might reveal some important functional aspects of the ant’s visually guided behaviour. They might also shed some light on the developmental constraints of compound eye design, because the size and the shape of the eye are governed by some basic developmental rules. As shown by Franks and Norris (1987) for the ant genera Atta, Eciton and Pheidole, allometric relationships of varying pairs of body measurements are linked over the entire body.

In the latter context, one should recall that ants, like all hymenopterans, are holometabolous insects, which pass through a complete metamorphosis. Consequently, theirpostembryonic life cycle consists of several larval stages, a pupal stage and one final stage, the imago. As only the imago (in this case the worker ant) possesses compound eyes and as the imago does not grow, body size and, hence, eye size remain constant during the life span of an individual ant. However, the shape of the size-frequency distribution of the workers can be controlled by the colony (most probably by differential larval feeding). It varies according to season and/or the amount of forage available in the habitat (R. Wehner, unpublished observations obtained from several Cataglyphis species). As a consequence, the relative number of workers belonging to a particular size class and, hence, exhibiting particular optical properties of their eyes varies during the course of the year. This observation might add further interest to our study.

Live individuals of Cataglyphis bicolor Fabr. (workers, reproductive females, and males; for species rank, see Wehner et al. 1994) and live workers of C. albicans Santschi and C. fortis Forel were taken from colonies in Maharès (Tunisia: 34.58 ° N, 10.50 ° E) and reared in the laboratory. Linear size varied by a factor of 2 within conspecific workers.

The spatial directions of the optical axes of ommatidia were determined by examining corneal as well as deep pseudopupils under antidromic illumination conditions (Franceschini, 1975; Via, 1977). The head of an ant was glued onto the tip of a light guide (diameter 1 mm) and mounted in the centre of a goniometer (Fig. 1). The outer axis (β) of the goniometer was adjusted along a plane perpendicular to the optical axis of the microscope. Then, under the microscope, the head of the ant was adjusted so that its sagittal plane was parallel to the equatorial plane of the goniometer. Assuming this position, the poles of the spherical coordinate system of the goniometer were aligned with the laterally looking ommatidia of the left and right compound eyes. By rotating the goniometer about its poles (Fig. 1, axis λ), the head was rotated on its transversal axis and adjusted according to the position assumed during free walking. This position was defined by an angle of 45 ° between the horizon and the rear margin of the compound eye. Using this experimental arrangement, two different types of measurement were performed; first, the spatial direction of the optical axis of single ommatidia in a spherical coordinate system was determined [(λβ); for definitions and conventions see Table 1] and, second, individual ommatidia oriented in a pre-defined direction (λβ) in space were identified. In the latter case, it was necessary to locate the position of the respective ommatidia on the surface of the compound eye. To this end, minute quantities of optical grinding powder (silicon carbide particles) were dispersed over the compound eyes to serve as landmarks. During optical measurements, the position of any given ommatidium was defined relative to several conspicuous landmarks in its neighbourhood. Since the particles maintained their original position during scanning electron microscopy, they could be used for subsequent identification of the absolute position of ommatidia on the compound eye.

A compound eye system of coordinates was defined on the basis of the ommatidial rows: After counting the x-, y- and z-rows, the respective median rows were marked. The ommatidium nearest to the intersection point of the three rows defined the origin of the coordinate system. Ommatidial positions could then be expressed in (x,y,z)-coordinates of the hexagonal raster grid by counting rows from the origin. The x-axis of this system of coordinates is equivalent to the vertical axis (V) of the HV-system proposed by Stavenga (1979). In order to facilitate comparisons among eyes of different sizes, coordinates (x,y,z) were normalised to a range between −1.0 and +1.0 [(x′,y′,z′), see Fig. 4].

The boundaries of the visual field of compound eyes were determined by measuring the spatial directions of the optical axes of the marginal ommatidia. To this end, the goniometer was rotated about the axis λ (corresponding to a rotation about the transversal axis of the ant’s head) at fixed intervals of 10 ° (Fig. 1, angle λ). At each position of λ the goniometer was tilted about its outer axis (Fig. 1, angle β) until the pseudopupil of a marginal ommatidium was centred. This position indicated the alignment of the optical axis of an individual ommatidium with that of the microscope. The angular deviation β from the sagittal plane (β=0 °) was then read to the nearest 0.5 °.

Subsequently, the distribution of the optical axes across the compound eye of worker ants was analysed. At each position of a spherical coordinate grid (λ=0 ° 15 °,…, 270 °; β=-15 °, 0 °, 15 °,…, 90 °), the ommatidium whose optical axis was aligned with the microscope axis was identified. Using landmarks on the eye surface, as described above, every grid point (λ β) could be identified on scanning electron micrographs of the compound eye and transformed to (x′,y′,z′)-coordinates.

For the sake of clarity, measurements performed in the spherical coordinate system of the goniometer (λ βwere transformed to geographical coordinates corresponding to the natural position of the head during walking (azimuth α and elevation ϵ frontal direction α=0 ° ϵ=0 °lateral: α=±90 °, ϵ=0 ° zenith: ϵ=90 ° see Fig. 3A).

The spatial orientation of individual ommatidial axes was determined in the frontal (α=0 ° ϵ=0 °), lateral (α=90°ϵ=0 °) and caudal (α=150 °ϵ=0 °) regions of the eye. In each region, optical axes were determined according to the following protocols: the ommatidium with its optical axis closest to one of the directions mentioned above was selected as a centre point. Tracking along the x-, y- and z-rows outwards from the centre yielded a starlike pattern of 12 ommatidial axis positions (Fig. 2). Divergence angles (Δ φ) between any two ommatidial axes (α₁,ϵ₁) and (α₂,ϵ₂) were calculated using the following formula:

Preliminary studies showed that all marginal ommatidia of one compound eye lie close to one plane, whose orientation is defined by a normal vector where α=±65 °ϵ=60 ° for the left and right eyes, respectively. Scanning electron micrographs of both compound eyes of 24 C. bicolor workers were taken from this position and used to measure the area (A_c′), height (H_c) and width (W_c) of the eyes. A_c′ represents a two-dimensional estimate of the convex corneal surface area (A_c).

Since every corneal facet is individually convex, the cornea of the compound eye as a whole does not appear as a smooth surface, which would be a prerequisite for determination of the radius of curvature. However, an accurate description of the corneal surface of the compound eye can be provided in the form of a grid, consisting of the midpoints of all ommatidial corneal facets and the normals to the surface at each point of the grid. Using optical methods, it was possible to determine the midpoint of the corneal facets as well as the normal to the surface of each midpoint (referred to as the ommatidial surface normal).

The spatial extent of the visual field of the compound eyes was determined in workers, reproductive females and males of Cataglyphis bicolor and in workers of C. fortis and C. albicans (Fig. 3). As a general feature, visual fields exhibit a region of binocular overlap with frontal/dorsal orientation and attaining maximum lateral extent near the zenith (Fig. 3A,B). Posteriorly as well as below the horizon, there is an optically inaccessible area (blind region). When projected onto a unit sphere, the spatial extent of the visual field approximates that of a laterally oriented hemisphere which is slightly inclined towards the contralateral side in the region of the zenith.

To study the influence of head size on the properties of the visual field, data were sampled from workers with head widths varying by a factor of 2 in each of the species mentioned above. Data from individual C. bicolor workers (Fig. 3B,C) show that neither the overall size nor the shape of the visual field varies with increasing head width. Analogous observations could be made in C. fortis and C. albicans, indicating that the form (size and shape) of the visual field as a whole is held constant among conspecific workers. In each species, however, the form of the visual field exhibits characteristic traits, notably with respect to lateral extent and the proportions of the binocular and blind regions. For example, C. fortis exhibits a marked zenithal constriction of the binocular region, whereas C. albicans shows an extended blind region.

In a further step, sex-related differences were studied in C. bicolor. Measurements performed on reproductive females indicate that the dimensions of the visual field do not differ from those found in workers of the same species (Fig. 3B). In males, pseudopupil measurements were hampered by intense internal pigmentation of the compound eye. Nevertheless, data from two individuals clearly indicate that males differ from females with respect to the size and shape of the region of binocular overlap (Fig. 3B). We can thus state that the overall form of the visual field exhibits species-specific as well as sex-specific features, but does not vary with varying head size.

Further analyses of the properties of the visual field were carried out on workers of Cataglyphis bicolor. To record the overall distribution of the spatial orientation of the optical ommatidial axes, a 30 ° ×30 ° azimuth/elevation grid of spatial directions (β1, ϵ) was back-projected onto the compound eye. This was achieved by identifying the ommatidia whose optical axes were oriented in the directions of the grid points. To facilitate comparisons among individuals, ommatidial positions on the compound eye were expressed in normalised hexagonal coordinates [(x′,y′,z′); see Materials and methods]. Projection of a given spatial direction (α ϵ) onto the surface of the compound eye always yielded the same surface position (′,y′z′), irrespective of the head width of the individual under examination. It was thus possible to pool the data obtained from 10 workers and to compute average values.

The spatial distribution of the ommatidial axes on the surface of the compound eye exhibits regional as well as directional asymmetries (Fig. 4A). The distances between the horizontal grid lines (which are at equal vertical angular distances of Δϵ=30 °) indicate that the regions above and below the horizon (between ϵ=±30 °) are over-represented and appear to be vertically expanded compared with adjacent regions (from ϵ=+30 °to +60 °, and from E=−30 ° to −60 °). Further, it is evident that the spacing of the vertical grid lines (with horizontal angular distance Δα=30 °) is consistently smaller than that of the horizontal grid lines. This means that the compound eye exhibits a pronounced horizontal/vertical astigmatism. Examination of the distribution of the divergence angles Δ φ_x (measured along the vertically oriented ommatidial x-rows) reveals a foveal belt of elevated vertical resolution, especially in the frontal and caudal regions of the compound eye (Fig. 4B).

It emerges as an overall result from the above analyses that, for conspecific workers of different sizes, the extent of the visual field is constant and corresponding regions on the compound eye point to corresponding spatial directions in space. At the same time, however, morphometric features of the compound eye, for example the number of ommatidia, are known to increase with increasing head width (Menzel and Wehner, 1970). Consequently, one might expect that interommatidial angles would decrease with increasing head dimensions. To confirm this, divergence angles (c.) were measured in individuals of different sizes. Data sampling was confined to three areas positioned along the horizon (i.e. in the region of highest vertical resolution), at α=0 ° (frontal), α=90 ° (lateral) and α=150 ° (caudal). Despite considerable variation within and between individuals, it is obvious that divergence angles decrease with increasing head width (Fig. 5A). With respect to spatial direction, Δ φ_x is consistently smaller than Δ φ_y and Δ φ_z, providing direct evidence for the foveal belt along the horizon (Fig. 4B). In order to obtain direction-independent data and to reduce the individual variation, mean values of ommatidial divergence areas (A_φ., see Materials and methods and Fig. 2) were calculated for the frontal, lateral and dorsal sampling areas (Fig. 5B). As with c., divergence areas A_φ. (sr) decrease with increasing head width. Log–linear regression equations (Table 2) show that, with increasing head width, both A_φ. (average exponent −0.70) and Δ φ (average exponent −0.39) decrease significantly.

Now that the optical parameters of the compound eye have been related to head size, it is necessary to complete the analysis by examining the scaling properties of the underlying morphological features of the eye. The surface area (A_c ′), height (H_c) and width (W_c) of compound eyes were measured on scanning electron micrographs. In relation to head width (W_h), A_c ′ scales with an exponent less than 2, and the exponents of height and of width of the compound eye differ from each other (Table 2). This signifies that compound eyes change their relative size and form as head size varies. The radius of curvature (R_c) of the surface of the compound eye was measured along an optical cross section taken through the lateral meridian (α=90 °; see Materials and methods). Data from four worker ants with different head widths show consistent fluctuations of R_c along the section (Fig. 6A). Peaks of R_c near the horizon (E=0 °) as well as at medium elevation (ϵ=45 °) indicate flattening of the surface in these regions. The conspicuous interindividual similarity of the data can be expressed in quantitative terms. Both the mean radius of curvature along the section (R_c, Table 2) and the length of the surface segment under examination (D₇₅, Table 2) scale with head width with an exponent near 1. Accordingly, reconstructions of the cross sections that had been rescaled to the same relative size (Fig. 6C), show geometric similarity between individuals of different sizes.

The variability of body size in conspecific workers of Cataglyphis ants is of considerable significance with respect to the ecological consequences for the species as a whole (Wehner et al. 1972) as well as for the behaviour of individual ants (Zollikofer, 1994). Since workers of Cataglyphis species are individual foragers that rely mainly on visual cues for homing (see review by Wehner, 1992), a comparative examination of the visual system in small and large ants is of special interest. Scaling properties of the visual system similar to those described in this study reflect developmental constraints imposed on the morphological design of the compound eye and determine its optical performance. These intraspecific data can then be compared with the interspecific scaling properties of the compound eyes of insects in general. Since the latter have been shown to reflect adaptation to optical performance constraints (see Wehner, 1981), it is of special interest to compare intra- and interspecific variation with respect to different constraints acting on the morphogenesis and phylogenesis of the compound eye.

Among conspecific Cataglyphis workers, the visual field of compound eyes is shown to be independent of head size. This is a unique feature, especially if one bears in mind that virtually every other dimension of the compound eye depends on head size, which itself varies by a factor of 2. With the evidence presented in this study, for Cataglyphis bicolor workers, it is possible to demonstrate that visual field constancy is an effect of the exact tuning of morphological and optical scaling rules governing eye growth.

What are the optical implications of a constant-sized visual field? Among conspecific worker ants, a constant visual field and a decreasing number of ommatidia lead to poorer visual acuity (i.e. increased values of Δ φ) in smaller individuals.

In our sample of conspecific workers, head widths vary by a factor of 2, and visual acuity (which is inversely proportional to both Δ φ and A_φ.) varies by a factor of 2^0.70=1.62. How do smaller ants cope with this apparent loss of visual acuity, since one might expect that errors made in reading the points of the celestial compass will increase correspondingly? From behavioural studies, we know that in comparing C. albicans and C. bicolor, foraging distance is roughly proportional to the size of the forager (Wehner, 1987). Hence, we may conclude that, in small individuals, orientation errors are compensated for by shorter foraging distances. However, the compound eye of ants is a multifunctional visual organ with regionally distinct morphological and physiological properties and functions (Fent, 1985; Wehner, 1991).

If we consider the inhomogeneous spacing of the optical axes (Fig. 4), it appears that the resulting acuity gradients may be more significant than absolute visual acuity. This view is supported by the fact that gradients and astigmatism of Δ φ similar to those described here have already been reported in a variety of flying insects (see review by Land, 1989). For example, foveal belts along the horizon representing a vertical acuity gradient have been reported in bees (Baumgärtner, 1928; Horridge, 1978), wasps (Horridge, 1978), butterflies (del Portillo, 1936) and locusts (Autrum and Wiedemann, 1962;

Land, 1981, p. 555) and may be involved in functions such as maintaining horizontal head position or tracking distant landmarks on the horizon. Taking into account that the species reported are of different sizes, one is led to the conclusion that, in performing such tasks, gradient information is more important than absolute resolving power. Further, the fact that Cataglyphis ants walking on the ground exhibit optical gradient patterns almost identical to those found in flying insects may lead to a more general conclusion. Fast-walking insects appear to be confronted with optical requirements that are similar to those of many flying insects, whose optical environment is dominated by fast optic flow parallel to the longitudinal axis of the body and slow optic flow in the vertical direction (hence the horizontal extension and vertical compression of Δ φ; Land, 1989).

There remains the question of how the overall shape of the compound eye changes with increasing head width and how these changes are related to the optical spacing of the ommatidial axes. First, it appears that, in workers of different sizes, the directions of the optical axes of the ommatidia (expressed in spherical coordinates) map onto corresponding positions on the compound eye (expressed in ommatidial row coordinates; Fig. 4A). This signifies that not only the boundaries of the visual field but also the spatial distribution of the optical axes as a whole remain constant. Thus, one might expect that the shape of the surface of the compound eye would be similar in individuals of different sizes. Surface data sampled along a line leading from the upper to the lower margin of the compound eye (Fig. 6) show that the radius of curvature exhibits a characteristic pattern of zonal variation that is identical for small and large individuals. Moreover, the total length of the curved segment (D₇₅) as well as the mean radius of curvature (R_c) scale nearly linearly with head width (Table 2). The straight-line distance between the upper and lower margins of the compound eye (H_c, eye height) also scales linearly with head width. This suggests that the overall shape of the compound eye surface remains constant, which may be an important morphological prerequisite for the optical mapping properties described above.