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Provided by Elsevier - Publisher Connector Current Biology 20, 1679–1684, September 28, 2010 ª2010 Elsevier Ltd All rights reserved DOI 10.1016/j.cub.2010.08.033 Report Great Create Theaters with Forced Perspective When Seen by Their Audience

John A. Endler,1,2,* Lorna C. Endler,1 and Natalie R. Doerr2,3 An observer’s eye receives a two-dimensional projection of 1Centre for Integrative Ecology, School of Life & Environmental the objects in the scene [12, 13], making a mosaic of patches Sciences, Deakin University at Waurn Ponds, Pigdons Road, on the retina. Retinal patch size is proportional to the angle Geelong VIC 3217, Australia subtended on the viewer’s eye (f) by the object, which is jointly 2School of Marine and Tropical Ecology, James Cook dependent upon the object size and distance to the viewer University, PO Box 6811, Smithfield QLD 4870, Australia (Figures 1C and 1D; Figures S1–S3). Visible width (w) is the 3Department of Ecology, Evolution and Marine Biology, width of an object measured horizontally perpendicular to University of California Santa Barbara, Santa Barbara, the viewer’s line of sight, and visible depth (d) is measured CA 93106, USA parallel to the line of sight; w and d result in visual width and

depth angles fw and fd, respectively, corresponding to lateral and vertical directions on the retina. Summary In natural scenes, the angles (f) subtended on the viewer’s eye by objects of similar size decline with distance in the infraorder Corvida [1] (ravens, jays, bowerbirds) (Figure 1C), and this is used by the brain to estimate object are renowned for their cognitive abilities [2–4], which size and distance [12, 14, 15]. Retaining this relationship in include advanced problem solving with spatial inference constructed scenes and images makes them look more [4–8], tool use and complex constructions [7–10], and natural [12–14]. Altering the natural relationship between f cognitive ability is associated with mating and distance is called forced perspective, and it can make success [11]. Great bowerbird males construct bowers some objects, and entire scenes, appear larger or smaller with a long avenue from within which females view the than they are [12, 14–18]. In scenes where object size declines male displaying over his bower court [10]. This predictable with distance, the more rapidly decreasing f appear to corre- audience viewpoint is a prerequisite for forced (altered) spond to larger scenes or objects [15–18]. This is used in visual perspective [12–14]. Males make courts with gray gardens, buildings, theaters, movie sets, and amusement and white objects that increase in size with distance from parks to give the illusion of greater size [16–18]. When object the avenue entrance. This gradient creates forced visual size increases with distance, the f decrease more slowly perspective for the audience; court object visual angles than normal, or remain constant (Figure 1D) and the visual subtended on the female viewer’s eye are more uniform pattern (f distribution) is more regular than random. The scene than if the objects were placed at random. Forced perspec- may appear smaller, depending upon the gradient. To avoid tive can yield false perception of size and distance [12, 15]. the variable meanings of perspective in different sets of litera- After experimental reversal of their size-distance gradient, ture, we define forced perspective simply from geometric males recovered their gradients within 3 days, and there optics [14] as a geometric pattern projected to a predeter- was little difference from the original after 2 wks. Variation mined viewpoint with abnormal relationships between object among males in their forced-perspective quality as seen by size and object visual angles. Forced perspective works only their female audience indicates that visual perspective is from the appropriate viewpoint. available for use in mate choice, perhaps as an indicator of Great bowerbird courts consist of gray to whitish objects cognitive ability. Regardless of function, the creation and (pebbles, bones, shells, etc.; Figures 1A and 1B, Figure 2B, maintenance of forced visual perspective is clearly impor- Figure S6) on which are placed colored objects, some of which tant to great bowerbirds and suggests the possibility of are used by displaying males [10]. We will collectively call a previously unknown dimension of cognition. these gray and white objects the gesso, because, as in painting, males place colored objects upon gesso. In two Results and Discussion Queensland populations separated by 700 km (Mary Valley: 15.04S, 143.77E; Dreghorn: 20.25S, 147.73E), the gesso Male bowerbirds in the avenue species group build structures objects are arranged in order of increasing size with distance in the form of an avenue defined by two parallel walls of sticks from the avenue (Figures 2A and 2B); regressions of object [10](Figures 1A and 1B; Figure S1 available online). During visible width (w) on distance from the avenue center (x, courtship, a female stands within the avenue and watches the Figure S4) were positive for all bowers at both sites and were male display over the court [10](Figure 1A and Movie S1). Great significantly (p < 0.05) positive in 79% of Mary Valley bowers bowerbird females (Ptilinorhynchus [=] nuchalis) (14 bowers, 7 to 66 degrees of freedom [df]) and 95% of Dreg- have a small field of view (46 6 6, 19 bowers; Figure S1) horn bowers (19 bowers, 185 to 405 df; Figure 3A), with very because they view males through a long channel (Figure 2A) similar results for visual depth (d). Bowers vary in their slopes, within a long avenue [10] (our data: 61 6 11cm; Figure 1B). suggesting individual variation in the ability to create This predefined viewpoint makes the creation of forced visual geometric patterns. Photographs of bowers throughout the perspective by great bowerbird males, for female viewers, species range suggest that this pattern is widespread and vari- possible and practical because forced perspective requires able within and among locations. a predefined (forced) field of view [12–14]. From the female’s viewpoint within the avenue, the increasing gesso object size with distance is an example of forced perspective (Figure 1D). The consequence is a more *Correspondence: [email protected] uniform distribution of visual angles (f) than random or than Current Biology Vol 20 No 18 1680

Figure 1. Great Bowerbird Bower and Viewing Geometry A B (A) From inside the bower avenue a female watches a male displaying his nuchal crest toward her and holding an ornament within her field of view (see Movie S1). She may be able to see only his head and neck from his normal display position at the edge of the court by the avenue entrance. The black object is an infrared motion sensor camera trigger. (B) A typical bower found remote from sources of manmade objects. Note the court with gray and white gesso objects in front of the avenue entrance, a second court visible through the other entrance, and the depression in the center of the avenue filled with objects. Females usually watch the male while standing on the avenue floor on the edge of the central depression opposite the displaying male (Figure S1). (C) Normal perspective: if the court consisted of objects of the same size (bars), then the angles of the objects subtended on the viewer’s eye (f) would decrease with the distance between the

viewer and the object (only fd shown here; see Figures S1–S3). C (D) Forced perspective: if the objects increase in size with distance, then they may all subtend the same angle (f) on the viewer’s eye. This will yield a more regular pattern for the viewer (Figure 2A) than if the objects were placed at random. It may make the court seem smaller than it is, with the φ possible result that the male seems larger than he is. Still more rapid size-distance gradients will cause increased f variation.

D Dreghorn are shown in Figure 4A and show the variation in the degree of forced perspective among bowers. A very similar result was obtained for permutations of x and d. Results were the same when the φ north and south courts of each bower were tested separately. Almost all males constructed female views of their courts with forced perspective; visual angles fw and fd have much lower standard deviations than if the objects were placed at random on the court. normal perspective (Figure 2A). If bowerbirds were to create To test for maintenance and repair of the forced perspective, forced perspective with no variation in f, they would place we reversed the size-distance gradient (Figures 2C and 2D) of objects with visible width w and depth d at viewing distance all objects on the courts in 15 Dreghorn bowers and recorded x according to w =2O(h2+x2) tan (f /2) and d=f (h2+x2)/ subsequent changes after 3 days and 2 wks (Figure 3, Figure 4, (h-xf), where h is the female’s eye height (Figures S2 and Table 1, Figure S6). Three days after the reversal, most bower- S3). This, plus errors in placement of objects, predicts the birds returned their courts to positive slopes (Figure 3C) and positive regressions of w and d on x that we observed. The positive effect sizes ds (Figure 4C). The bowers were back to result of this male behavior is a female view of the gesso their original perspective after 2 wks (Figure 3D, Figure 4D, with low variation in f: a significantly even visual background visits 1 and 4 in Table 1). Control bowers did not change pattern. sign, but the slopes changed slightly (shaded bars in Figure 3 The critical test for forced perspective is whether s, the and Figure 4; repeat measurement error is less than one histo- standard deviation of f, is smaller than random expectation gram bar width), most likely because the birds continually shift (the same objects placed at random). Permutations of x and object positions (Figure S6). Individual bowers were consistent w within each bower (Figure S5) show that all bowers at in the quality of their forced perspective over 2 wks. The corre- Mary Valley and 95% of the bowers at Dreghorn showed lation between visits 1 and 4 for mean f was highly significant some variance reduction (p < 0.50 or better). 64% of the (fw r = 0.82, p < 0.0001; fd r = 0.76, p = 0.0002, 17 df), indicating bowers at Mary Valley and 95% of the bowers at Dreghorn consistency in the scale (patch size) of the forced perspective. showed significantly (p < 0.05) less variation in f than if the The visit 1–4 correlations for s were significant only for width gesso objects were placed at random. Effect sizes (ds) for (fw r = 0.77, p = 0.0001; fd r = 0.36, p = 0.13), indicating that Bowerbirds Create Forced Perspective 1681

Figure 2. Normal and Experimentally Altered Undisturbed Inverted Courts at Dreghorn (A) The court as seen by a female; camera placed in a female head position above the central avenue floor depression. Note the fairly uniform visual angles (size in photo) of the gesso. (B) Top view of the court in (A). The upper and lower dowels define the maximum female field of view from the avenue center. The cross bar with screw marks the avenue entrance, and its ‘‘tail’’ extends along the avenue axis and defines the view axis. Sticks are marked at 1 cm intervals, allowing calibration for scale and camera angle. (C) The court as seen by the female after experi- mental reversal of the size-distance gradient. Note how the visual angles of the court objects rapidly decline with distance and produce a more irregular pattern than the undisturbed court shown in (A). (D) Top view of the reversed court.

gradient repair, rY should be low or zero, because Y direction is irrelevant. The results reject object replacement A C (Table 2, Figure S7). X correlations are moderate and either remain the same Female Views or decrease with time. Y correlations

are significantly smaller than rX, not B D significantly different from zero in the experimentals, and one is significant in the controls, owing to objects not touched by the birds during the sampling period. All rY decrease with time, because males continually move the gesso objects on their bowers (Figure S6) and random movement yields decreasing position correlation unless corrected by males. This is consistent with gradient-specific behavior in the X direction, but random placement and movement in Y, and Top Views (1cm marks on dowels) inconsistent with location replacement. Like humans, bowerbird art varies; there is among-individual variation in males consistently differed in the quality of their forced both mean and standard deviation of f, and individual styles perspective (degree of patch regularity) with respect to visible remain stable over two weeks. This could arise from variation width (horizontal size) but not visible depth. in males’ abilities or variation in local gesso availability, or To test the possibility that the repair of the gradients was both. If a bowerbird placed his bower in an area where there incidental to males putting each gesso object back in its was a small range (variance) in potential gesso object sizes, original location, we compared the locations of unequivocally then he would not be able to produce size gradients as steep recognizable objects at visit 1 (V1, original) with visits V3 or V4. as another male in an area with a greater available size range. X is the distance from the avenue along the avenue axis, and Y We do not have availability data, but a simple test would be to is the distance perpendicular to the X axis. If objects were regress the slope of the gradient against the variance of object replaced at their original locations, then the correlation size on the assumption that the observed size variance on between V1 and either V3 or V4 would be high (r = 0.9 for a bower represents local availability. However, this results in 5 cm location error, 0.7 for 9 cm) and roughly equal for X a classical artifact [19], because the size data appear in both and Y directions (rX z rY). If relocation were imperfect, then the gradient and the variance. As when using the opportunity rY R rX because the courts are longer than they are wide, for sexual selection (Is) as a measure of the intensity of sexual making maximum random errors smaller in Y. If males gradu- selection [20], the variance in object size can give only an ally transfer the objects to their original locations, then both upper limit to the gradient and is not a good predictor. Another rX and rY should increase with time. Alternatively, if males approach is to examine the bowers and their neighbors by simply repair the gradient, then rX should be high but not as using spatial autocorrelation; local availability differences high as in object relocation, because exact location of each may result in near neighbors having more similar variances object is unimportant; only size and distance matter. For than distant neighbors. Tests of the Dreghorn bowers at visit Current Biology Vol 20 No 18 1682

A original A 6 6 original 4 4

2 2

0 0 B B reversed reversed 6 6

4 4

2 2

0 0 3 days C C 6 6 3 days 4 4 2 Number of bowers 2 Number of bowers 0 0 D D 2 weeks 6 6 4 2 weeks 4

2 2

0 0 -0.2 -0.1 0 0.1 0.2 -5 0 5 slope Effect size s

d f Figure 3. Slopes of the Size-Distance Gradients of Dreghorn Bowers before Figure 4. Effect Size s of the Observed Visual Width Angles, w, Before and and during the Experiment; Data from Both Courts Pooled within Bowers During the Experiment f Positive slopes indicate that objects increase in size with distance. Zero Results were qualitatively the same for d. Effect size measures the degree slopes indicate random size-distance relationships, and negative slopes of evenness of f. A positive value indicates that s (the standard deviation indicate that objects decrease in size with distance. Experimental bowers of f) is smaller than that resulting from permutations of the observed object are shown as open bars; control bars are shaded. A shift of about one bar distances and sizes; the more positive, the more even the pattern. A nega- width in time is not significant, and the mean absolute difference between tive value indicates a higher s than random and a more irregular pattern. slopes of a court measured twice (0.006) is smaller than a bar width. (A–D) Conventions as in Figure 3. (A) Original bower (visit 1 [V1]). (B) Reversed gradient (V2); note lack of change in controls, as well as one experimental bower where the reversal was not sufficient to produce a quality attributes, unless one assumes that some males select negative slope. bower sites with more variation in object size when they first (C) Three days after the reversal (V3). establish their bowers. (D) Two weeks after the reversal (V4). It is not clear how much cognition is needed to create the size-distance gradients. Males might explicitly place small objects close to the avenue entrances and larger objects 1 using Moran’s I [21] indicate the highest similarity among farther away. This could result from complex cognition, be groups of 4–6 bowers and significant similarity (Z-scores > created through a simple inherited decision rule, or be the 1.96) within groups of 9–11 bowers. The peak at 4–6 bowers result of trial and error. Video recordings show that males is suggestive because the bowers are spaced evenly, males spend 78% 6 15% of their time at their bowers on bower frequently steal objects from neighbors, and object availability ‘‘maintenance,’’ which involves moving gesso and other is a function of what is present at several neighboring bowers objects on their courts and avenue. They frequently show and what is found in the environment [22]. The 9–11 bower a cycle of looking at the court from the female’s avenue view- similarity scale may correspond to local differences in funda- point and then moving court objects, and this is repeated mental availability: half the bowers are found in the riparian throughout the day. Forced perspective could therefore be region of the Burdekin river and the other half in the riparian created by trial and error, in which the male moves the objects region along a small tributary of the Burdekin; differences on this scale could arise from local geology and drainage (stone Table 1. Friedman Test Probabilities for Differences in Slopes among size), local density of snail populations (shells), and other local Visits within Experimental Bowers habitat differences. There are therefore four possible nonex- clusive causes of consistent variation among bowers: (1) vari- Visit V1 and V2 V2 and V3 V3 and V4 V1 and V4 ation in ability to construct the gradient, (2) variation in the w (n = 15) 0.0001 0.0001 0.20 0.80 ability to steal ornaments [22] with high variation, (3) variation d (n = 15) 0.0001 0.0001 0.20 0.20 in the ability to resist theft of ornaments [23] leaving high vari- Visits are abbreviated as follows: V1, original bower; V2, immediately after ance, and (4) local variation in availability of objects unrelated reversal; V3, 3 days after reversal; V4, 2 wks after reversal. p < 0.05 indicates to behavior. Only the last possibility does not involve male a significant change in the slopes of w or d on x between visits. Bowerbirds Create Forced Perspective 1683

Table 2. Correlations between Object Locations between Visits signal geometry would repay further study. Whatever the perceptual effects in bowerbirds, the geometry is clearly very Experimental Bowers (n = 59) Control Bowers (n = 32) important to them, because they repair defects in their designs

rx ry Zrx ry Z within a few days and the regular pattern has to be viewed from V1 and V3 0.501*** 0.164 11.12**** 0.884**** 0.713*** 7.23**** a particular place to be seen (Figure 2). V1 and V4 0.526** 0.079 14.15**** 0.777**** 0.326 10.13**** The regularity of the pattern itself (small variance in f, larger Z 0.61 2.42* 5.16**** 8.05**** ds) is available to be used as a male quality indicator [30]. As for the among-individual variation in style, there are six Shown are rX, correlations between X values (measured along avenue axis from avenue entrance) at visits 1 and 3 (V1 and V3) or visits 1 and 4 (V1 possible sources of variation: (1) cognitive ability needed to and V4) and rY, correlations between Y vales (measured perpendicular to construct forced perspective directly (other cognitive behavior the avenue axis; positive is left from inside avenue). increases mating success in satin bowerbirds [11]), (2) ability Z are test values and significance levels for differences between pairs (rows to create forced perspective by trial and error, possibly by or columns) of correlation coefficients. Sample sizes are much lower than regular pattern template matching or a sensory bias [31], (3) the gradient data because objects are continually moved within courts, moved to the other court, and/or stolen by other birds (up to 50% turnover experience and age needed to learn to construct the bower per court in 2 wks); we included only objects that were easily identifiable in [10] and gradient, (4) ability to steal ornaments with a high all visits. size variance, permitting better gradients, (5) ability to prevent *p < 0.05, **p < 0.01, ***p < 0.001, ****p < 0.0001. theft of larger and smaller objects to retain high size variance, and (6) ability to choose bower sites with higher object vari- ance. Some or all of these could affect the quality of a male’s until the court looks ‘‘good’’ from the avenue. Trial and error forced perspective, but this requires further research. For could reinforce a preexisting decision rule or formulate the whatever reason, the behavior of bowerbirds leads to their rule. These possibilities require a value judgment by the male audience viewing a scene with forced perspective, which about the regularity of the view, which is essential in an depends upon viewing the pattern from a predetermined angle aesthetic sense [24], but if constructed only by trial and error and distance, something unknown aside from humans. or a spatial rule (small objects close), this might not require a direct sense of perspective. It is noteworthy, however, that Experimental Procedures standard (linear) perspective was not invented by humans until the 15th century; before that it appears to have resulted from Nineteen active bowers were found and measured at Dreghorn (V1). Measurement was performed by computer-assisted analysis of scaled trial and error [14, 25]. Was there a significant evolutionary photographs. Fifteen had their size-distance gradients (both courts) transition in humans (which also allowed the Renaissance) reversed by moving existing gesso objects such that larger ones were [25] and bowerbirds that allowed the evolution of perspective? closer and smaller ones farther away from the avenue, with random left-right Assuming that bower building occurred in bowerbirds before movements. The inverted gradients were measured (V2). All courts the 15th century, why did perspective evolve in bowerbirds were measured again 3 days (V3) and 2 wks (V4) later. See Supplemental before it did in humans? Information for details. Great bowerbird courts produce forced perspective when Supplemental Information the female views them from within the avenue; the image of the court projected on her retina, when viewed from within Supplemental Information includes bower viewing geometry; definition of the avenue, has a more regular pattern than expected by the variables; the relationships between visual angle, height of eye, distance chance. We do not yet know the consequences. The regular to object, and object size; sample calculations; example photographs of an visual background (Figure 2A) may make the displaying male experimental and control bower court over time; plots of the positions of more conspicuous than if he was seen against an irregular objects tracked among visits; tests for left or right position replacement; a movie of a male displaying to a female; detailed Supplemental Experi- background (Figure 2C). We do not know if this forced mental Procedures; and a Supplemental Discussion. These can be found perspective produces the same illusions as it produces in with this article online at doi:10.1016/j.cub.2010.08.033. humans, but pigeons perceive at least three illusions that are well known in humans: the Ponzo [26], Ebbinghaus-Titchener Acknowledgments [27], and Mu¨ller-Lyer [28] illusions. If similar to humans, the regular pattern would make the court look smaller than it is We thank the National Geographic Society for financial support, Kirk and and less deep, perhaps making the visible parts of the display- Bron Smith for access and hospitality at Dreghorn Station, Michael Dalla Costa for access and hospitality at Mary Valley Station, and Andy Bennett, ing male and his colored ornaments appear larger. The regular Bill Buttemer, Marcel Klaassen, Joah Madden, and four anonymous reviews pattern created by the gesso might generate Ebbinghaus- for excellent and useful comments on the manuscript. The field research Titchener effects when combined with colored objects or was done with an EPA-Queensland Parks and Wildlife Service permit the male’s nuchal crest, which are displayed on or over the (WISP01994004) and James Cook University Ethics approval (A1318). gesso and have the required similar sizes. Females use a fixed position within the avenue during the male’s display, restrict- Received: June 2, 2010 ing their head motion to mostly side-to side and rotational Revised: July 22, 2010 movements (see Movie S1), yielding predictable motion Accepted: August 16, 2010 Published online: September 9, 2010 parallax. Depth and size cues given falsely by the forced visual perspective will conflict with motion parallax cues; this may References yield perceptive or illusion effects similar to the reversed perspective effect in humans [29]. The forced perspective of 1. Barker, F.K., Barrowclough, G.F., and Groth, J.G. (2002). 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