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First published online August 9, 2007
Journal of Experimental Biology 210, 2819-2828 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.004697

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Behavioral evidence for within-eyelet resolution in twisted-winged insects (Strepsiptera)

Srdjan Maksimovic, John E. Layne and Elke K. Buschbeck^*

Department of Biological Sciences, University of Cincinnati, Cincinnati, OH 45221-0006, USA

View larger version (132K): [in this window] [in a new window]   Fig. 1. Comparison of eye anatomy of Drosophila melanogaster (A) and Xenos peckii (B). The retina of D. melanogaster is composed of hundreds of long, narrow ommatidia, each containing eight receptor cells. In X. peckii an extended, cup-shaped retina lies beneath each of the large lenses. (C) Two principal sample bases () are hypothesized: a smaller based on comparisons within eyelets (right), and a larger based on comparisons between photoreceptors in neighboring eyelets (left). Scale bars, 50 µm.

View larger version (16K): [in this window] [in a new window]   Fig. 2. Schematic of experimental setup. A computer generated stimulus was projected into a white cylinder, at the center of which an insect was mounted. Behavioral responses were recorded with a video camera for frame-by-frame analysis (inset). The animal's head deflection was measured as the angle between a line through the centers of both eyes [transverse axis of the head (c) and the transverse axis of the body (b)]. Longitudinal body axis (a) was used to determine the transverse axis of the body (b).

View larger version (18K): [in this window] [in a new window]   Fig. 3. Drosophila optomotor behavior. (A) Average response of eight (except for 5°, where N=4) individuals to six different spatial wavelengths. Positive values indicate head deflections with the direction of the pattern, and negative values indicate deflections in the reverse direction. (B) For each wavelength the cumulative, normalized, mean of the last 3 s is indicated by a circle ± s.e.m. bars. The solid line is the best-fitting EMD model, with mean sampling bases of 4.8° and 4.9° with s.d. of 0.1° for both, acceptance angle of 7°, and a bias B of 1.02 towards the smaller sampling base. Numbers indicate sample sizes for each spatial wavelength.

View larger version (28K): [in this window] [in a new window]   Fig. 4. Xenos peckii optomotor behavior. (A) Average responses of all tested individuals to 12 different spatial wavelengths. As in Fig. 3, positive values indicate head movements following the direction of the pattern, and negative values indicate head movements in reverse direction. (B) Examples of three normalized, average responses of the last 3 s to each wavelength. Although details of the curves vary, each of them is characterized by a local maximum between 18° and 24° (arrow). (C) For each wavelength the cumulative normalized response of the last 3 s of all individuals is indicated by a circle ± s.e.m. The number of individuals that were tested for each of the points are indicated.

View larger version (47K): [in this window] [in a new window]   Fig. 5. The EMD model for Xenos peckii. (A) Nine small sample bases were calculated and summed into a single curve (B), which would be the response curve if only the smaller principal sample base and its variation were present. (C) Similarly nine larger sample bases were calculated and summed into the curve in (D). Numbers enclosed in parentheses in A and C indicate weights for respective sampling bases. (E) For the final model output the two curves illustrated in B and D were summed after multiplying the smaller sampling base response by the bias value (2.1). (F) The normalized version of the model response (solid line) is used to illustrate the close fit of experimental data (circles).

View larger version (27K): [in this window] [in a new window]   Fig. 6. The EMD model for Xenos peckii is relatively insensitive to the acceptance angle () and independent of the time constant (). (A) Response curves between 10° and 60° result in similar fits of the experimental data, except for the degree of aliasing, which is strongest for the smallest values. (B) Eqn 1 is used to illustrate that the time constant () affects only the amplitude of the calculated response. Three different time constants result in curves with different amplitudes. However, results are independent of , as curves are normalized to the maximum response (C).

View larger version (20K): [in this window] [in a new window]   Fig. 7. Sampling bases resulting from 1000 optimizations. Initial states were drawn from uniform random distributions between , and =3–25° for X. peckii (A,B), and between , and =0.1–10° for Drosophila (C,D). In both cases s.d.1 and s.d.2 were one-half the initial sampling bases. Gray scale is proportional to f, the sum of the absolute difference between empirical data and model, darkest bars indicating best fit (see key in A).

View larger version (74K): [in this window] [in a new window]   Fig. 8. Geometrical interpretations of sample bases. (A) Geometry of standing and lying hexagonal arrays. (B) Hypothetical organization of sampling units in three neighboring eyelets. The retina of one eyelet has up to four sampling units in the horizontal plane, subsuming a total of about 30–35°. The smaller sampling base around 10° occurs within an eyelet, for instance between units 1–2, 2–3, 3–4 in the middle eyelet. One possibility for the larger sample base around 20° is that neighboring eyelets span, for instance between units 1–1, 2–2, etc. (C) Irregularities in the organization of eyelets indicated by the number of nearest neighbors for several specific eyelets. (D) A horizontal section of X. peckii illustrates an alternative explanation for the larger sample base, connecting only nearest optical neighbors. The angles of two such connections are indicated. Variation results because some eyelets lie in the same horizontal plane as their neighbors, such as those in which the same number of sampling units are visible (their optical axes in 2D indicated with straight lines), while other neighbors lie outside the horizontal plane, such as those in which different numbers of units are visible. Scale bars, 50 µm.