The effect of building ability and object availability on the construction of bower courts in great bowerbirds

Animal-built structures that function in mate attraction can be constrained in signal expression by the availability of building materials in the environment and the male's ability to ﬁ nd them as well as the ability to construct the structure itself. As part of their courtship display, male great bowerbirds, Ptilo-norhynchus nuchalis , use hundreds of grey-white objects to create a bower court. Males arrange these objects to create a positive size e distance gradient, the evenness of which generates a forced perspective visual illusion that is associated with mating success. However, a range of differently sized objects are required to build a high-quality gradient

Some animals build structures that function in mate attraction, such as weaverbird (Ploceidae) nests and cichlid (Cichlidae) bowers (Kelley & Endler, 2012a;Quader, 2006;Young et al., 2010).Compared to bearing bodily ornaments, such extended phenotypes may be advantageous for signalling quality for several reasons, such as flexibility in signal form and continuity in signalling during the signaller's absence (Coleman et al., 2004;Schaedelin & Taborsky, 2009;€ Ostlund-Nilsson & Holmlund, 2003).However, extended phenotypes may be less suitable for signalling when a stochastic environment imposes limits on the availability of building materials.Modelling work suggests that receivers' ability to accurately assess signallers that use external display objects is increased when display resources are plentiful and signallers can reliably produce display signals to the best of their ability (Leighton, 2014).Therefore, stochasticity in the availability of building materials in the environment may affect the reliability of built structures as indicators of quality.Investigating how the environment affects the construction of extended phenotypes allows us to determine whether such structures can be used as reliable signals.
Polygynous bowerbirds (Ptilonorhynchidae) are well known for using an extended phenotype in courtship, where males of most species build and maintain an elaborate bower structure that females assess during mate choice (Frith et al., 2004).A bower consists of multiple components, typically including a structure made of grass or sticks and a collection of coloured decorations (Frith et al., 2004).Bower components such as the number and type of coloured decorations, as well as the symmetry, stick density and size of the bower affect mating success in various species (Borgia, 1985;Kelley & Endler, 2012a;Madden, 2003;Patricelli et al., 2003;Uy & Borgia, 2000), suggesting that the bower structure is a target of female mate choice, and potentially a reflection of male quality.However, the effects of the availability of materials used to construct the bower display are seldom considered (but see Doerr & Endler, 2015;Hunter & Dwyer, 1997;Madden & Balmford, 2004).
Male great bowerbirds, Ptilonorhynchus nuchalis, also known as Chlamydera nuchalis, construct an avenue-type bower consisting of two parallel stick walls that open onto a display court at each end.The court is a cleared area of ground covered in a large collection (tens to hundreds) of grey and white objects such as stones, shells and bones.During courtship, the female stands in the bower avenue and looks onto one of the courts, which serves as a background to the male's behavioural display of coloured decorations (Frith et al., 2004).Objects on the court are arranged with smaller objects closer to the bower and larger objects further away, forming a positive sizeedistance gradient (hereafter referred to as a 'gradient', Endler et al., 2010).When this arrangement of court objects is observed from the female's perspective in the avenue, a more even visual scene is formed than if objects were arranged randomly.This creates a forced perspective illusion that may alter the female's perception of size and the salience of the male's behavioural display (Kelley & Endler, 2012a).The evenness of the gradient (i.e. the quality of the forced perspective illusion) varies among males but is consistent within males, and is associated with mating success (Endler et al., 2010;Kelley & Endler, 2012a, 2012b).However, it is unclear whether differences in court gradients among males are primarily due to differences in the objects available to males or to differences in their ability to organize them into a pattern (Doerr & Endler, 2015;Kelley & Endler, 2012a).
To create a high-quality gradient, males must select objects of an appropriate size for their location on the court.Selecting the right object is encumbered by the irregularity of object shapes found in the environment.Most objects are noncircular, which affects the depth and width component of the visual illusion to different extents, creating a trade-off between prioritizing visual width or depth, although males appear to prioritize visual depth (Endler et al., 2010).Orienting court objects to create the appropriate visual angle, in addition to selecting the appropriate object size and shape, are likely to be major factors that increase the gradient quality of the court.Proficiency in these actions can be considered as an individual's building ability and may reflect prior experience and/or some aspect of cognitive ability.As a result, building ability may vary among males, which could explain the high repeatability of gradient quality within individuals while showing improvement over subsequent years (Kelley & Endler, 2012b).
Alternatively, variation and repeatability in gradient quality among males may be explained by the availability of objects in the environment, the male's ability to find them, the male's ability to establish and hold a bower in an area with access to a wide variety of objects, or a combination of these factors.Males that can find a wide variety of objects to build with have more opportunities to select the appropriate object to create a high-quality gradient (Doerr & Endler, 2015;Endler et al., 2010).A previous study investigating the effect of object availability on gradient quality switched court objects between pairs of bowers (Doerr & Endler, 2015).The newly built gradient was more similar to the donor bower than the recipient male's original gradient, demonstrating that gradient quality was affected by the availability of objects.However, this effect was most pronounced in pairings that involved object collections of predominantly similarly sized snail shells, which prevented donor and recipient males from building highquality gradients.Therefore, the extent to which object availability constrains gradient construction remains unclear.If individual differences in gradient quality are consistent when the constraint of object availability is removed, then building ability may be a stable trait that is targeted during female mate choice.Alternatively, if object availability largely predicts individual differences in gradient quality, then gradient quality may signal the ability to secure those objects.
We disentangled the effect that building ability and object availability have on gradient quality by removing each male's natural court objects and providing them with a set of objects with the same standardized array of sizes to rebuild their courts, thereby homogenizing the availability of objects and the ability to find them among males.We measured gradient quality before removal and 3 days after supplying the standardized objects.If male building ability drives gradient quality, we predicted that natural gradient quality would be positively correlated with the quality of the rebuilt court, that is, males with naturally high-quality gradients would rebuild high-quality gradients, and vice versa.Alternatively, if object availability drives gradient quality, we expected that all males would construct gradients of similar quality to each other when given the same objects for construction, irrespective of their original gradient quality.In this case, we would also expect bowers that are closer together to have more similar natural gradient values due to similarities in local object availability.Finally, we removed the standardized objects and returned the original court objects to quantify male motivation for reconstructing courts within 3 days, and to determine whether male gradients are individually consistent as previously reported (Kelley & Endler, 2012b).

Species and Study Site
We monitored the bowers of 29 male great bowerbirds on Dreghorn cattle station in Queensland, Australia (20.25 S, 147.73 E), which has been the site of previous studies (e.g.Doerr & Endler, 2015;Endler et al., 2010;Kelley & Endler, 2012b).Data were collected between August and December 2019, in accordance with a Scientific Purposes Permit from the Queensland Department of Environmental Science (WA0016886).

Ethical Note
Data were collected in line with ASAB/ABS guidelines for the Treatment of Animals in Behavioural Research.Ethical approval was granted by James Cook University (A2630) and the University of Exeter (eCORN001983).To prevent disruption to natural display behaviour on courts, we left the secondary court undisturbed and limited experimental manipulation of the main court to 6 days, after which we returned each male's natural objects onto his court, to facilitate an expedient recovery of the natural court state.

Experimental Manipulation
All manipulations took place between September and October 2019.To determine the gradient quality of each male's 'natural' court, top-down photographs were taken of the primary court (identified as the court with the most coloured decorations present; Fig. 1a).We then removed all grey and white objects from the main court and the areas adjacent to the avenue and repositioned the coloured decorations at the side of the court.We then placed a standardized set of grey and white objects in a pile approximately 2 m from the bower (Fig. 1c).The standardized set consisted of 70 white and 70 grey stones of six size categories (15e45 mm in 5 mm increments).Stones were measured by their longest dimension and selected to be roughly oval.These objects were sourced from a local garden centre but resembled objects that were naturally found on bower courts.Males were then left undisturbed for 3 days to reconstruct the court, as in previous experiments (Endler et al., 2010;Kelley & Endler, 2012b, 2017).
Three days after we supplied the standardized objects, we returned and photographed the primary court again (the 'standardized' court).We then removed all supplied objects and placed the previously removed original set of objects approximately 2 m from the bower.Males were again left undisturbed for 3 days to rebuild their court, and we returned 3 days later and photographed the primary court once more (the 'restored' court).At the end of the experiment, any remaining original court objects that had not been moved from the pile near the bower were placed back onto the court.

Quantifying Courts
To quantify gradient quality (detailed below), we took photographs from a height of 1 m directly above the court.The female's field of view was demarcated by two wooden dowels that had markings at 1 cm increments to allow for size calibration (Fig. 1a).
Photographs were taken with a Sony a7 camera with a 28e70 mm lens, using an umbrella to exclude shadows.Photographs were analysed using a custom MATLAB program (Endler et al., 2010), which has been used to quantify courts previously (Endler et al., 2010;Kelley & Endler, 2012a, 2012b, 2017).
First, photographs were calibrated for size using the 1 cm dowel markings.Second, the visible depth and width of every visible object on the court was measured alongside the distance of the object from the female (Fig. 1b).This included objects that were foraged from the environment during the experiment because they form part of the reconstructed court.These measurements were then used to calculate gradient evenness and gradient steepness, which are used as measures of gradient quality.Gradient steepness (b) describes how the court appears from above, and a positive slope confirms that males place objects by size, with smaller objects closer to the bower avenue and larger objects further away.Gradient steepness (b) was calculated by regressing the depth or width of objects against their distance from the female's location for the depth (b d ) and width (b w ) of objects, where higher steepness values signify higher gradient quality.
Gradient evenness describes how the gradient appears to the female viewing the court from inside the avenue, as it takes her viewing angle and distance from the objects into account.Evenness was calculated from the visual angles (f) subtended by the court objects on the viewing female's eye, in both depth (f d ) and width (f w ).The standard deviation (SD) of visual angles for the entire court was calculated for depth (SDf d ) and width (SDf w ) and used as a measure of their respective evenness.Lower evenness values signify higher gradient quality due to a more even pattern (and therefore a higher quality forced perspective illusion) and have previously been associated with higher mating success (Kelley & Endler, 2012a).

Analysis
All data were analysed and visualized in R4.1.0(RCoreTeam, 2021), using the 'dplyr' package for data frame manipulation (Wickham et al., 2021) and 'ggplot2' for data visualization (Villanueva & Chen, 2019).The evenness (for depth and width) and steepness (for depth and width) of the sizeedistance gradient are four measurements of quality.From these measures, we used a principal components analysis (PCA) to represent an overall measure of gradient quality that we used in our analysis (Pearson, 1901).Gradient quality (PC1) for the natural, standardized and restored court was centred around the mean of natural gradient quality, which allowed us to interpret the gradient quality of rebuilt courts relative to each male's original court.
We investigated whether the quality of a male's standardized and restored court ('rebuilt gradient quality') was predicted by the quality of his natural court ('natural gradient quality').We also investigated whether there was an interaction between natural gradient quality and whether the rebuilt court was built with standardized or original objects ('court type').This allowed the slopes of the regression between the natural and both types of rebuilt courts to vary, to test whether natural gradient quality was associated differently with the standardized than the restored court.The inclusion of 'court type' as an interaction term was justified with a likelihood ratio test to determine whether it improved the model's fit compared to a simpler model where court was included as a main effect.Finally, variance caused by individual differences was taken into account as a random effect ('1jID') in the resulting linear mixed model: 'rebuilt gradient quality ~natural gradient quality)court typeþ (1jID)'.Linear models were tested using the 'lme4' package in R (Bates et al., 2014).
We also tested whether gradient quality was predicted by individual motivation, using the number of objects placed on each type of court ('natural', 'standardized' and 'restored') as a proxy.We explored an interaction between the number of objects placed and whether the court was natural, standardized or restored ('court type'), to determine whether motivation was associated with gradient quality.The inclusion of 'court type' as an interaction term was justified with a likelihood ratio test to determine whether it improved the model's fit compared to a simpler model where court was included as a main effect.Again, variance caused by individual differences was taken into account as a random effect in the resulting linear mixed model: 'gradient quality ~number of objects placed)court type þ (1jID)'.For all linear mixed models, influential observations were identified by a Cook's distance greater than three times the mean Cook's distance.Removing influential points had no qualitative effect on the results and were therefore included in the analysis.Finally, we examined the relationship that object availability has on gradient quality by determining whether close neighbours build similar gradients due to access to similar building materials.We compared the bowers of different males and their gradient quality and calculated Moran's I, a measure of autocorrelation ranging between À1 (perfect negative correlation) and 1 (perfect positive correlation; Getis & Ord, 1992).We tested for correlations at distance intervals of 2 km, 3 km, 5 km and 10 km, using the 'ape' for spatial autocorrelation (Paradis & Schliep, 2019).
Previous studies on gradient quality in this species have analysed measures of gradient evenness (depth and width) and steepness (depth and width) as four separate aspects of gradient quality, rather than using a PCA as we have here.To facilitate direct comparison to the literature, we additionally provide the results of our analyses for each of these measures in the Appendix.

RESULTS
Of all males (N ¼ 29), 27 engaged with the experiment and placed an average of 33 ± 15 (mean ± SD) objects on the manipulated court within 3 days (Fig. 2).Two males placed fewer than eight objects on the court and were excluded from subsequent analysis as the bower owner was deemed to have insufficient engagement with the task (one standardized court and one restored court).All analyses were also done without the exclusion of these two males, but these showed no difference in the significance of results and are therefore not reported.

Principal Component Construction
We constructed a principal component (PC1) that accounted for 62.0% of the variation between the four measures of gradient quality: evennessedepth (loading: 0.49), evennessewidth (loading: 0.54), steepnessedepth (loading: 0.50) and steepnessewidth (loading: 0.46) (Pearson, 1901).The next largest principal component (PC2) accounted for 26.3% of the variation.We included PC1 in our analyses as the most predictive measure of gradient quality and use it synonymously with gradient quality henceforth.We also analysed the four separate measures of bower gradient quality separately and obtained similar results (see Appendix).

Court Comparison: Population Level
When males reconstructed their court from a standardized set of objects, they generally built courts with positive gradients (depth: 74% of males; width: 59% of males), and there was large variation in gradient quality among bowers (Fig. 3).At a population level, the gradient quality of the natural court was significantly higher than that of standardized courts, but not significantly different from restored courts (Fig. 3, Table 1).The gradient quality of standardized courts was also found to be significantly lower than that of restored courts (Fig. 3, Table 1).Similar results were found when comparing each court type's gradient quality, measured as gradient evenness (depth and width) and steepness (depth and width; see Appendix, Fig. A1, Table A1).

Court Comparison: Individual Level
Natural gradient quality predicted the gradient quality of rebuilt courts, but only when they were built with natural objects (restored courts) and not when built with supplied objects (standardized court; Fig. 4, Table 1).Our model containing this interaction was a better fit compared to one with only main effects included (Dc 2 2 ¼ 14.176, P < 0.001).Results for the four separate measures of gradient quality can be found in the Appendix (Fig. A2, Table A2).

Effect of Motivation: Number of Objects Used
Males used significantly fewer objects when rebuilding courts with both standardized objects (33 ± 15; t 26 ¼ À9.343, P < 0.001) and natural objects (41 ± 22; t 26 ¼ À8.197, P < 0.001), compared to their natural court (128 ± 51 objects).The number of objects had no effect on the gradient quality (PC1) for the natural court (Table 2).Compared to this coefficient, the number of objects used positively affected the gradient quality of the restored court and negatively affected the standardized court, but these interactions were nonsignificant (Table 2).However, when these effects were compared to each other, we found a significant interaction.In other words, when a male rebuilds his court with more standardized objects, gradient quality does not improve as much as it would when using natural objects (Table 2).Our model containing this interaction was a better fit compared to one with only main effects included (Dc 2 2 ¼ 6.44, P ¼ 0.04).Identical analyses were performed for the four separate measures of gradient quality, the results of which can be found in the Appendix (Table A3).

Spatial Autocorrelation
Gradient quality (PC1) showed significant spatial autocorrelation, where neighbouring bowers within 1 km were most similar (Table 3).This effect deteriorated with distance and disappeared between 5 km and 10 km (Table 3, Fig. A3).Significant spatial autocorrelation between bowers was also found for each separate measure of gradient quality (Table A4, Fig. A4).

Objects Foraged from the Environment During the Experiment
When building standardized courts, males incorporated a number of objects sourced from the environment or their secondary court (25.8 ± 16.0%).For our analyses, we pooled supplied and sourced objects to accurately quantify the entire reconstructed court.A small percentage of all used objects (4.6 ± 6.6%) were smaller or larger than the range of objects in the standardized set, which could have allowed males to build higher quality gradients.Exclusion of the individuals (N ¼ 5) that used more than 10% of objects outside the standardized size range did not affect the significance of our results and they were therefore included in the analysis.

DISCUSSION
When males were provided with either a standardized set of objects or the return of their own objects, almost all males constructed courts that had a positive sizeedistance gradient.This is consistent with previous studies where males actively create positive sizeedistance gradients, demonstrating that males have the flexibility to use unfamiliar objects during court construction   (Doerr & Endler, 2015;Endler et al., 2010;Kelley & Endler, 2012a, 2012b).However, contrary to our predictions, males that built highquality gradients on their natural court did not build high-quality gradients when given a standardized set of objects.Our findings build upon those of Doerr and Endler (2015), who swapped objects between bowers with high and low object size variance, by providing the same objects to all males and thus removing the effects of differential access to objects.We observed a moderate amount of variance among males in the gradient quality of the court that was built with a standardized set of objects.Those individual differences can be assumed to reflect building ability as the availability of objects and the ability to find them were equalized; they are predominantly the result of the behaviour governing object placement.Drivers of the variation in standardized courts may be explained by underlying cognitive aspects that could affect engagement with unfamiliar objects, such as object neophobia and behavioural flexibility.In the closely related satin bowerbird, Ptilonorhynchus violaceus, a composite measure of bower symmetry, stick geometry and decoration colour can be estimated from cognitive ability (Keagy et al., 2012), so we cannot rule out the effects of underlying cognitive aspects when constructing a gradient with novel objects.Size and/or body condition of males could also drive variation in building ability, although a study on the closely related spotted bowerbird, Chlamydera maculata, failed to find a link between morphological measures (such as mass and tarsus length) and bower-owning status, suggesting that male morphology is unlikely to affect bower attributes (Madden, Endler, et al., 2004).
As quality of the standardized court gradient was not predicted by the quality of the natural court gradient, it seems unlikely that gradient quality itself signals male building ability to potential mates.It is unclear why gradient quality then correlated with mating success in a previous study (Kelley & Endler, 2012a), but there are several possible explanations.First, gradient quality may affect mating success by signalling something other than building ability, such as the ability to forage for suitable court objects or resource-holding potential.If object availability is primarily responsible for the differences in gradient quality among males, then object foraging ability, or the ability to secure a high-quality territory with suitable objects, could be reflected in gradient quality.Second, fluctuating female preference for male traits (Chaine & Lyon, 2008;Coleman et al., 2004) may cause males to prioritize other bower features in different years.
Third, the relationship between gradient quality and mating success may be more complex.For example, females may judge the court on an absolute threshold level, above which variation in quality is irrelevant (Valone et al., 1996), as seen in red jungle fowl, Gallus gallus (Zuk et al., 1990), female decorated cricket, Gryllodes sigillatus (Ivy & Sakaluk, 2007) and zebra finch, Taeniopygia castanotis (Caves et al., 2018).If much of the variation in natural gradient quality falls above such a threshold level or if females have variable thresholds, then the lack of correlation between natural and standardized gradients may not exclude building ability being assessed during mate choice (Peniston et al., 2020).
Furthermore, little is known about how females assess the various components of male displays.The reported relationship with mating success may not be causal if an unobserved trait affected gradient quality and mating success simultaneously.For example, proficiency in object manipulation may have manifested not only in a higher quality court but also in a higher quality avenue, which is associated with mating success in satin bowerbirds (Borgia, 1985).Similarly, ability may still be signalled through gradient quality and affect mating success if this trait is assessed in conjunction with other display components.Gradient quality may be a signal that is uninformative in isolation but informative in conjunction with other bower component signals.
We may have been unable to detect an effect of building ability due to the unfamiliarity of the objects we provided and/or constraints on building time.We provided males with a standardized set of objects of varying sizes so that a near-perfect gradient could theoretically be built, and we expected that males would build generally high-quality gradients using these objects.Males built gradients of significantly lower quality compared to their original gradients, which may be due to unfamiliarity with the novel objects given that males reuse approximately 30% of their court objects from the previous year (Doerr, 2009a).Our results on the effect of the number of objects placed reflects this, as gradient quality of rebuilt courts only improved with more objects when they were natural.Our standardized set of objects was also lacking in long thin bones that are placed at the far edge of the court, which may have affected gradient quality as there was lower variance in object size and shape, compared with natural court objects.We assumed that object placement is solely governed by the visual angle that is subtended on the female's eye, which is a product of the object's size, shape and orientation.However, other characteristics such as colour or texture may also be used.For example, bones may be placed at the edge of the court based on texture or their low density.All objects in the standardized set were grey and white stones, which may have provided males with limited information for successful object placement.Constraints on building time may have prevented us from estimating a male's building ability accurately as the courts they rebuilt were incomplete.However, previous studies where court objects were moved around the court or fully removed from the court showed that males reconstructed their gradients (with natural objects) to a level similar to their original quality within a similar timeframe.Quality measures at 3 or 4 days postmanipulation did not significantly change over the following 7e10  days (Doerr & Endler, 2015;Endler et al., 2010;Kelley & Endler, 2012b).It would be useful to determine whether time constraints or object familiarity may have affected observed gradient quality by extending the building duration until the rate of object placement/ movement plateaued, indicating that court reconstruction was complete.
Males also used fewer objects to rebuild their courts both with standardized objects and when they had their own objects returned.This is unsurprising given that males had only 3 days to rebuild their courts and had to trade construction time against foraging, courtship and maintaining other bower components.Males may also have replaced fewer objects if they favoured other aspects of their multicomponent signal; in satin bowerbirds, males compensated for the removal of their decorations by enhancing other display components, rather than focusing on replacing the lost signal component (Bravery & Goldizen, 2007).In previous studies, males have successfully recovered their original court gradients within a similar timeframe after objects were experimentally shuffled on their court (Doerr & Endler, 2015;Endler et al., 2010;Kelley & Endler, 2012b).Although court objects were removed and not shuffled in the current experiment, males were similarly able to rebuild their gradient to a quality representative of their original gradient within 3 days when their original objects were returned.Individual differences in gradient quality were maintained and restored courts were of similar quality, suggesting that the short 3-day duration of the task has no limiting effect.Males have demonstrated that they can restore their gradients to individual levels, even when having to construct entirely new gradients and while using fewer objects.However, the combination of using unfamiliar objects to rebuild within a limited timeframe may have prevented males from rebuilding their court to representative levels when using standardized objects.
Our finding that males do not build gradients of different quality using standardized objects suggests that object availability may explain individual repeatability in previous studies (Kelley & Endler, 2012b) and interindividual differences in gradient quality.In this case, we would expect close neighbours to have similar courts due to similar local object availability.We found that interbower distance and gradient quality were moderately correlated with each other, suggesting that object availability is likely to explain some (although not all) amongmale variation in gradient quality.Endler et al. (2010) reported a similar spatial autocorrelation but stipulated that the greatest differences in quality were between bowers in two different habitats: along the Burdekin River where differently sized cattle bones are abundant, and along a tributary of the river where homogeneously sized snail shells are abundant.Therefore, variable availability in object sizes can affect gradient quality between and within habitat types.
It is also possible that the observed spatial autocorrelation may be attributed at least in part to social learning, as neighbouring bower owners tend to engage in more social interactions such as stealing events than distant ones (Doerr, 2009a(Doerr, , 2009b(Doerr, , 2010)), which could result in court similarities.In spotted bowerbirds, finescale similarities in decoration use of neighbouring bowers were not explained by environmental factors and may be the product of localized traditions arising from rivals inspecting each other's bower, or of localized female preference (Madden, Lowe, et al., 2004).However, the effects of social learning on bower and gradient construction requires further study in great bowerbirds.
Our behavioural experiment and spatial analysis both suggest that local object availability explains a moderate amount of the variation in gradient quality among males.We suspect that a stronger relationship between object availability and gradient quality was not observed due to mediating factors that are likely to exist, such as the ability to forage for suitable objects and the (social) learning of correct object placement.The high levels of participation in our behavioural experiment and the successful adoption of novel objects into the court gradient adds further evidence that the presence of courts and their associated gradients appear to be important to male great bowerbirds.While our work has focused on a single court attribute (the gradient) to identify its significance, more research effort is needed to determine how the court interacts with the male's wider courtship display to identify trade-offs within court construction.Our study demonstrates that extended phenotypes can be restricted by the availability of building materials in the environment.The stochasticity of the environment should therefore be taken into account when considering whether animal architects can signal their building ability through an extended phenotype.

Figure 1 .
Figure 1.Top-down photographs of the court where dowel rods indicate the female's field of view.Black lines on dowels represent 10 cm intervals and red lines represent 1 cm.(a) The court in a natural state before removal.(b) The natural court where the width (w) and depth (d) of objects is measured from the female's point of view.Using distance (x), the visual angle (f) of width and depth can be calculated.The height of the female is also included in calculations of the visual angle of depth.(c) The standardized set of 70 grey and 70 white court objects (15e45 mm) laid out in size order; these were presented in a large pile during the experiment.

Figure 2 .
Figure 2.An overview of (a) the natural court, (b) the standardized court (built in 3 days with standardized objects) and (c) the restored court (built in 3 days with natural objects).The horizontal dowel denotes the entrance of the avenue at the bottom of the photos, and the two vertical dowels denote the limits of the female's field of view from inside the bower avenue.

Figure 4 .Figure 3 .
Figure4.The relationship between the gradient quality (PC1 measured in standard deviations) of the natural court and the two rebuilt courts (N ¼ 27).All data are centred on the mean of the natural court, so that the Y-intercept relates to a male with an average natural court.Grey shaded regions show 95% confidence intervals.

Figure A1 .Figure A2 .Figure A3 .Figure A4 .
Figure A1.The distribution of gradient quality for each court type (N ¼ 27).Four measures of gradient quality are shown: (a) evennessedepth and (b) evennessewidth, measured as the standard deviation of visual angles (f); (c) steepnessedepth and (d) steepnessewidth, measured as the slope (b) at which objects increase in size with distance.The box plots show the median and 25th and 75th percentiles; the whiskers indicate the values within 1.5 times the interquartile range and the circles are outliers.Between court types, P values are shown to indicate significance and are from a comparison between the intercepts of a linear mixed model (a difference in means).

Table 1
Output of a linear mixed model investigating the relationships between court types Data are mean centred to natural gradient quality.Significant P values are in bold.

Table 2
Output of a linear mixed model investigating the relationship between the number of objects used and the gradient quality of the natural, restored and standardized courts Gradient quality ~number of objects placed)court type þ (1jID) Observed values are compared to the expected value occurring at no correlation.Autocorrelation for bowers within specific distances of each other is measured to show clustering effects.Significant P values are in bold.

Table A1
The difference in means between the gradient quality of the natural, standardized and restored courts Models are fitted to four measures of gradient quality: evennessedepth; evennessewidth; steepnessedepth; steepnessewidth.Significant P values are in bold.Output of a linear mixed model investigating the relationships between a male's natural gradient quality and the two types of rebuilt courts (restored and standardized)The table shows the difference in how natural gradient quality affects restored and standardized gradient quality (interaction).Models are fitted to four types of gradient quality: evennessedepth; evennessewidth; steepnessedepth; steepnessewidth.Significant P values are in bold.
Observed values are compared to the expected value occurring at no correlation.Autocorrelation for bowers within specific distances of each other is measured to show clustering effects.Significant P values are in bold.