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17 February 2010 Assessing fluctuating asymmetry of white-tailed deer antlers in a three-dimensional context
Stephen S. Ditchkoff, Rachel L. deFreese
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Fluctuating asymmetry, random departure from perfect symmetry in bilateral traits, has been proposed as an indirect indicator of individual quality. Sexually selected traits, such as deer antlers, are hypothesized to demonstrate decreasing level of fluctuating asymmetry with increasing trait size and decreasing level of fluctuating asymmetry with increasing age. These hypotheses have been previously tested for antlers using linear measurements to quantify fluctuating asymmetry. However, antlers are complex, 3-dimensional traits making it difficult to quantify all forms of visual asymmetry using traditional, linear measurements. It is this visual asymmetry that would be assessed by potential mates and rivals. Therefore, we created 3-dimensional computer models of white-tailed deer (Odocoileus virginianus) antlers to measure visual fluctuating asymmetry. Asymmetry measures of various antler traits were computed using the models by measuring distances from the trait to a vertical and horizontal plane created using coordinate points generated within the model. We found no association between degree of fluctuating asymmetry and trait size, nor was any association found between degree of fluctuating asymmetry and age using either the 3-dimensional measures of asymmetry or traditional, linear measures of asymmetry. Examination of these data suggests that fluctuating asymmetry of white-tailed deer antlers is not a reliable indicator of quality.

Fluctuating asymmetry is random deviation from perfect symmetry in traits that are normally bilaterally symmetrical. Because these traits arise from the same genome, their optimal condition is assumed to be perfect symmetry (Polak and Trivers 1994). Therefore, a departure from symmetry indicates disruption of normal development, most likely due to genetic or environmental stresses (Parsons 1992). Homozygosity, inbreeding, and mutation are some of the genetic stresses that have been associated with increased fluctuating asymmetry (Møller 1998). Most studies have focused on the relationship between environmental stressors and fluctuating asymmetry, and numerous studies have found a positive relationship between parasitism and fluctuating asymmetry (reviewed in Møller 1996). Other environmental stresses that have been studied include nutritional stress, temperature extremes, high population density, and pollutants (reviewed in Møller 1998).

One reason for interest in asymmetry is the proposed association between fluctuating asymmetry and individual quality (Palmer 1996). Variation in the level of fluctuating asymmetry exhibited by different individuals in the same environment allows for an indirect measure of developmental stability (Møller 1998), which is defined as the ability of an individual to buffer detrimental effects of stress during development (Palmer 1996). This measure may in turn reflect the quality or fitness of an individual (Møller 1998). Although it is assumed that fluctuating asymmetry itself is not heritable (Polak 2008), it also is assumed that the ability to overcome developmental stress is at least partially heritable (Palmer 1996).

This proposed relationship between fluctuating asymmetry and quality has been studied for a variety of different traits. However, not every trait shows an increase in fluctuating asymmetry with increased stress; different traits appear to be under different levels of stabilizing selection. Many morphological traits, especially those used in functions related to survival, are highly canalized and therefore are less susceptible to developmental disturbance (Polak 1993). Other traits seem to be much more susceptible to stress. These include characters that are under directional selection, such as ornamental traits (Møller and Pomiankowski 1993).

Ornamental traits and secondary sexual characters are important factors influencing mate choice and intrasexual competition in many species (Andersson 1982; Mateos and Carranza 1997; Møller 1988; Pärt and Qvarnström 1997). Also, several studies have documented that females prefer more symmetrical males (López et al. 2002; Schlüter et al. 1998; Sheridan and Pomiankowski 1997). Therefore, it is hypothesized that the symmetry of these ornamental traits may play an important role in mate choice, and hence, have important implications for sexual selection.

If ornamental traits are used in sexual selection they are expected to provide reliable information about the condition of the bearer (Berglund et al. 1996; Zahavi 1975), and several studies have reported cases of ornamental characters signaling honest information about condition (David et al. 2000; Malo et al. 2005; Møller 1991; Velando et al. 2001). Because ornamental traits are costly to produce and maintain (Kodric-Brown and Brown 1984) only high-quality males should be able to produce large, symmetrical ornaments. This leads to the hypothesis that fluctuating asymmetry and sexual selection are related as follows: low levels of fluctuating asymmetry in a male may indicate a male's heritable ability to cope with stress, so a female should choose to mate with a more symmetrical male to increase her offspring's viability and, in turn, her fitness. An alternative hypothesis, for the case of disease- or parasite-induced fluctuating asymmetry, is that a female should choose to mate with a more symmetrical male to gain the direct benefit of avoiding parasite or disease transmission (Polak 1993). These ideas lead to predicted patterns of fluctuating asymmetry in ornamental traits. It has been hypothesized that level of fluctuating asymmetry will decrease with increasing trait size because only high-quality males will be capable of producing large ornaments (Møller 1992). This is a contrast to the predicted pattern for nonornamental traits. For these characters a flat or U-shaped pattern is expected for the relationship between fluctuating asymmetry and trait size (Møller 1992).

Antlers of cervids seem to be well suited to studies of fluctuating asymmetry. Not only are these secondary sexual characters important in intrasexual competition (Clutton-Brock 1982; Goss 1983; Lincoln 1992), dominance (Bowyer 1986; Lincoln 1972), and possibly mate choice (Bartoš and Bahbouh 2006; Ditchkoff et al. 2001a; Kruuk et al. 2002; Lincoln 1992), but also rapid development of antlers (Goss 1983) should make them particularly sensitive to stress (Watson and Thornhill 1994). Swaddle and Witter (1997) suggested that rapid growth might prohibit compensational growth feedback between sides of a bilateral trait, thereby making it even more difficult for an individual to produce symmetrical traits. In addition, the deciduous nature of antlers in most species of cervids can provide an annual record of the level of stress experienced during antler development. This highlights the potential value of using fluctuating asymmetry of antlers as a relatively easy way to monitor environmental quality.

Previous studies of antler asymmetry have found positive relationships between fluctuating asymmetry and parasitism (Folstad et al. 1996; Lagesen and Folstad 1998), and several studies (Bowyer et al. 2001; Ditchkoff et al. 2001b; Mateos et al. 2008; Putman and Sullivan 2000) have reported support for Møller's (1992) hypothesized negative relationship between fluctuating asymmetry and trait size. Solberg and Sæther (1993) further hypothesized a decrease in fluctuating asymmetry with increasing age because only higher quality males will survive to older ages.

Although previous studies have examined fluctuating asymmetry of antlers, the most common way of measuring asymmetry was through simple measures of length, width, and circumferences of various parts of the antlers. Although these measures may provide information on level of asymmetry, they do not allow for the measurement of all forms of spatial, visual asymmetry. Antlers are complex 3-dimensional traits, which makes it difficult to quantify fluctuating asymmetry using traditional methods. For example, it is possible for 2 antler tines of equal length to appear asymmetrical based on the way that they are curved or oriented in space. Two corresponding tines of equal length could appear very different if, for example, 1 tine was oriented 90° from the ground plane and the other 45° from the ground plane. However, traditional linear measures would consider those 2 tines to be symmetrical because they have the same length. Visual asymmetry is the type of asymmetry that most likely would be assessed by potential mates or rivals. We used 3-dimensional computer models of white-tailed deer (Odocoileus virginianus) antlers to evaluate patterns of both 2- and 3-dimensional fluctuating asymmetry, thereby considering an additional aspect of asymmetry that may have been neglected in earlier studies. Specifically, we tested for the hypothesized negative relationships between level of fluctuating asymmetry with antler size and individual age. In addition, we compared detected levels of asymmetry between traditional (2-dimensional) and our 3-dimensional measures of fluctuating asymmetry.

Materials and Methods

Data were collected from hunter-harvested deer from Tallapoosa and Bullock counties in Alabama during the 2002 and 2003 hunting seasons. In addition, to increase sample size, antler measurements were obtained from various sets of antlers collected in previous hunting seasons. These antlers were still attached to the skull plate. Antlers were measured following guidelines for the Boone and Crockett trophy scoring system (Nesbitt and Reneau 1988). Measurements taken included greatest inside spread of main beams, tine lengths, main beam lengths, and main beam circumferences at the antler bases and between antler tines (not to exceed 4 circumferences measured per antler). The official Boone and Crockett scoring system includes deductions based on antler asymmetry. However, these deductions were not used in this study. Total gross score was calculated for each antler set by adding together tine lengths, main beam lengths, inside spread, and circumference measures. An individual gross score also was calculated for each antler side by omitting the inside spread measure. When possible, we also measured chest girth, body length, body weight, skull length, and tail length on deer collected during the 2002–2003 hunting seasons. Measurements were made using a flexible measuring tape and were recorded to the nearest millimeter. In addition, deer were aged using tooth wear and replacement patterns (Severinghaus 1949).

To create the 3-dimensional computer models, approximately 12 digital photographs were taken around the circumference of each antler set and from above. The antlers were 1st marked with approximately 3-mm dots using paint or stickers or both to provide landmark points for use in modeling. These photographs then were entered into the program PhotoModeler (Eos Systems Inc., Vancouver, British Columbia, Canada). Using between 9 and 12 pictures for each antler set, we marked the landmark points and tips of tines and main beams and cross-referenced them between all photographs resulting in a 3-dimensional “stick” model of each antler set. The scale of the model was calibrated using a manual measure of distance between the tips of the right and left G2 tines (2nd tine erupting vertically from the main beam; Fig. 1). The PhotoModeler program assigned each scaled model point a 3-dimensional (x, y, z) coordinate point, resulting in approximately 40–60 modeled points per antler set depending on the complexity of a given set of antlers. These coordinate point values were labeled to correspond to important antler features (Table 1) to allow for comparison among individuals. Coordinate points were exported to SAS (SAS Institute, Inc. 1990) for all analyses.

Fig. 1

Diagram showing vertical and horizontal planes used to measure 3-dimensional asymmetry of white-tailed antler traits. The main beam (MB), brow tine (G1), and G2 and G3 tines are labeled on the left antler.


Table 1

Abbreviations and descriptions of antler variables (features).


By using the base points of the antlers and a center point (marked between the deer's eyes), a vertical plane between the antlers and horizontal plane at the base of the antlers was calculated. Base points were marked for both the right (aR) and left (aL) antlers along the outside of the main beam and at the base where the antler erupts from the skull. A midpoint (m) calculated using these 2 base points is the origin of the coordinate system:

The y-axis runs between the 2 antler bases. The x-axis runs from the origin toward the nose, and the z-axis runs from the origin up between the 2 antlers perpendicular to the x-axis. Therefore, the x–y plane is the horizontal plane, and the x–z plane is the vertical plane. The unit vector in the y direction (ŷ) was calculated using the following equation:
To approximate viewing angle of antlers by other deer, x- and z-axes were shifted up by a correction angle (θ). For this study the correction angle used was 15° based upon a subjective determination by the authors that this approximated the angle that a prospective mate or rival would view the antlers in a normal heads-up display relative to the x-axis as used in these calculations. The unit vector in the uncorrected z-direction (zˆUNC) was calculated by the following equation:
where b was the center point marked between the deer's eyes. The unit vector in the uncorrected x-direction (x̂UNC) was calculated using the following equation:
The equation for the horizontal plane (NH) with the angle correction (θ) is as follows:
The vertical plane (NV) was calculated as follows:
Given modeled point (p) on a set of antlers, the distance from that point to the horizontal plane (dH) is:
The distance from a modeled point (p) to the vertical plane (dV) is:
Perpendicular distances were calculated from the horizontal and vertical planes to selected antler features, and distances of tines were calculated. In addition, the angle between the main beam and the G2 tine was calculated.

We calculated absolute asymmetry as the absolute difference between right- and left-side antler measurements. From the data generated by the 3-dimensional computer models, absolute asymmetry was calculated for many variables: distance from the horizontal plane to the G1, G2, and tips of the main beam; distance from the vertical plane to the G1, G2, and main beam tips; and angle between the G2 tine and the main beam. In addition, absolute asymmetry was calculated for the manual measurements of basal circumference, score, main beam length, and lengths of G1 and G2 tines.

To assess the precision of the measurement technique that used the computer models we used the same photographs to model a subset of 10 antler sets twice. Differences in lengths of corresponding tines were divided by the average trait size to obtain a percent difference between the 2 models, thereby allowing us to evaluate repeatability. Accuracy of computer models was evaluated by comparing manually measured tine lengths with the computer-modeled tine lengths. This was evaluated using t-tests on nontransformed data (Zar 1984).

Broken or worn antler points were not included in analyses of asymmetry. Because the data were not normally distributed, asymmetry measures were log transformed. To test for relationships between asymmetry measures a Pearson correlation test was used (Zar 1984). Pearson correlations also were used to test for relationships between levels of asymmetry of the manual measurements and asymmetry measures generated with the computer model. In addition, we compared relationships between asymmetry measures and measures of trait size (basal circumference, antler score, and main beam length) and age using Pearson correlation. To test for differences in level of asymmetry between age classes a 1-way analysis of variance (ANOVA) was conducted (Zar 1984). Because of small sample sizes, deer aged 4.5 years and older were grouped in a single age class. In addition, within each age class antlers were objectively divided into 3 size classes (low, medium, and high) of approximate equal sample size based on score, and an ANOVA was conducted to test for differences in level of fluctuating asymmetry based on antler size.


The percent differences between corresponding measures of repeated models ranged from <0.01% to 4.75%, and absolute differences ranged from <0.01 to 3.86 mm (Table 2). Mean percent differences were <1% for all but 4 variables measured and were <2% for all variables measured. All comparisons of tine lengths measured via the computer models versus the corresponding manually measured lengths were different (P > 0.001; Table 3). Mean measurements for computer model lengths were greater than manual lengths, and mean differences ranged from 8.28 to 32.40 mm.

Table 2

Absolute and percent differences between measures from repeated computer models for selected antler traits.


Table 3

Mean differences (mm) between manual and computer-generated measurements of antler dimensions and corresponding statistical tests for difference from parity.


Overall, no consistent patterns in correlations among asymmetry measures emerged (Table 4), and correlation coefficients were generally weak, where r ≤ 0.33. We found no consistent correlations between asymmetry measures and variables used to estimate trait size, that is, mean score, mean main beam length, and mean basal circumference. Age was not significantly correlated (P ≥ 0.083) with any of the asymmetry measures.

Table 4

Correlation matrix of relationships between measures of fluctuating asymmetry of antler traits, trait size, and age.a


No age affect (P ≥ 0.153) on any measures of asymmetry (Table 5) was apparent, and also no consistent directional trends in mean measures of asymmetry among ages (Table 6) or antler score classes (Table 7) were found. Between the 3 score classes only 2 asymmetry variables (labsymbv and labsymsc) were different (Table 5). The log of the absolute asymmetry of the distance from the tip of the main beam to the vertical plane (labsymbv; P  =  0.024) and the log of the absolute asymmetry of score (labsymsc; P  =  0.004) were different among score classes.

Table 5

Results from ANOVA comparing degree of fluctuating asymmetry in selected traits of white-tailed deer antlers among age and score classes.


Table 6

Absolute asymmetry of selected antler traits among 4 age classes (1.5, 2.5, 3.5, and ≥4.5 years of age).


Table 7

Absolute asymmetry measures of selected antler traits of white-tailed deer among 3 antler score classes (low, medium, and high).



Antlers are a prominent secondary sexual character in male deer, and fluctuating asymmetry of this trait is hypothesized to provide a reliable signal of individual quality to potential mates (Kodric-Brown and Brown 1984; Zahavi 1975). Assessment of the symmetry of this complex trait by potential mates would be based on visual differences in the conformational shape of a set of antlers, which may or may not correspond to differences in linear measurements of antler traits. Specific trends exist in levels of fluctuating asymmetry predicted for sexually selected traits (Møller and Pomiankowski 1993; Solberg and Sæther 1993). However, we found no support for these hypotheses using the 3-dimensional measures of fluctuating asymmetry. Specifically, no consistent relationship between antler asymmetry measures and trait size was apparent. Secondary sexual characters, like antlers, are costly to produce, and the relative cost to produce equal-sized traits is greater for low-quality individuals (Grafen 1990; Zahavi 1977). Thus, only high-quality individuals are expected to produce large antlers, and because fluctuating asymmetry is an indirect measurement of individual quality (Møller 1998), these high-quality individuals are expected to produce symmetrical traits. We also found no evidence to support the hypothesized decrease in level of fluctuating asymmetry with increasing age. Antlers tend to increase in size with increasing age until a point when the cost of producing larger antlers outweighs the benefits of a larger trait, or until the individual reaches an age of senescence (Clutton-Brock 1982). Individuals that have reached a mature age are expected to be high-quality individuals because low-quality individuals cannot survive into old age (Solberg and Sæther 1993). Consequently, males of prime age should exhibit lower levels of fluctuating asymmetry than immature males. We found no evidence that 3-dimensional asymmetry of antlers as measured in this study honestly signals male quality.

The traditional linear measures of fluctuating asymmetry also failed to reveal relationships between level of fluctuating asymmetry and trait size, and no relationship between level of fluctuating asymmetry and age was detected using manual measurements. The expected patterns of decreasing asymmetry with increasing trait size and increasing age were not supported by data from this study using either measurement technique. Although many previous studies have found positive relationships between fluctuating asymmetry and antler size (Bowyer et al. 2001; Ditchkoff et al. 2001b; Putman and Sullivan 2000), other studies have failed to find this hypothesized relationship. Kruuk et al. (2003) found no association between level of antler asymmetry of red deer (Cervus elaphus) and trait size or environmental stress. Bartoš and Bahbouh (2006) found that fluctuating asymmetry in red deer decreased with increasing trait size in some measured antler traits, but results were not consistent across all traits measured, thereby violating 1 of the expected patterns of fluctuating asymmetry as an indicator of quality.

Manual measures of asymmetry were not correlated consistently with 3-dimensional measures of asymmetry. If the levels of asymmetry found with both methods were similar it would have implied that manual measurements were adequate to quantify visual antler asymmetry. However, the lack of consistent trends in the data makes it difficult to draw conclusions about the efficacy of our measurements at quantifying visual asymmetry. Our measures of visual asymmetry may document different components of spatial asymmetry than the linear asymmetry measures. Additionally, it is possible that our measures did not address 3-dimensional asymmetry adequately, or 3-dimensional asymmetry does not follow the same predicted patterns as traditional measures. Regardless of the possible reasons for the lack of associations between asymmetry measures, our data fail to support the hypothesis that 3-dimensional fluctuating asymmetry can be used to assess individual quality reliably, as has been predicted for traditional measures of fluctuating asymmetry.

Asymmetry measures of the different antler components were not correlated consistently with each other using either measurement method. This is contrary to expected findings, because fluctuating asymmetry researchers have predicted that multiple components of a trait are integrated developmentally and would experience the same stressors during development causing them to exhibit similar patterns of symmetry (Leamy 1993; Palmer and Strobeck 2003; Whitlock 1996); features within a trait would be expected to have the same developmental stability properties and level of stabilizing selection. Variations present in precursor stages of a trait can be expected to perpetuate into later growth stages that arise from it.

The computer models were highly repeatable. Mean differences between the repeated model measurements were well below asymmetry values measured and generally <1 mm (ranging from 0.11 mm to 1.74 mm); these values are generally below 1% difference between replicates. Therefore, we applied no correction for measurement error in this study. These are similar or lower than levels of measurement error that have been found acceptable in other studies of fluctuating asymmetry of antlers (Bartoš and Bahbouh 2006; Ditchkoff et al. 2001b; Kruuk et al. 2003).

Differences between the manually measured and computer-measured tine lengths can be explained by the disparity in measurement landmarks for the 2 techniques. For the manual Boone and Crockett–type measurements (Nesbitt and Reneau 1988) tines were measured from the tip of the tine to where the tine intersected the top edge of the main beam. However, to facilitate the construction of the 3-dimensional stick model, tine lengths were measured from the tip of the tine to where the tine intersected the middle of the main beam. Therefore, it was expected that computer-generated tine lengths would be greater than manual measurements by approximately one-half the width of the main beam. In addition, tine lengths calculated from computer models were measured as a straight-line distance from tip of the tine to the base of the tine, but manual measurements followed the outside curve of tines. The purpose of comparing corresponding measurements from the 2 techniques was to determine if measurements were similar and differed by approximately one-half the width of the main beam. Measurements differed by approximately 10–20 mm, which is consistent with one-half the width of the main beam. Therefore, computer models were scaled and representative of actual size and proportion of antler sets.

Antler sets that were very simple, such as spikes or forked antlers, were unable to be modeled using PhotoModeler because not enough data points for the computer program were available to generate a 3-dimensional model. Therefore, this limitation, at least for this computer program, may in part determine the types of traits for which this technique is well suited; complex 3-dimensional traits such as antlers and skulls seem appropriate. Conversely, to provide enough data to model, simpler traits, such as horns, could be marked with numerous landmark points, more than necessary to depict the shape of a trait.

Although analysis of our data did not support the hypothesis that 3-dimensional asymmetry of antlers could be used as a reliable signal of quality, further study of 3-dimensional measures of asymmetry is warranted as this type of visual asymmetry is likely to be assessed by potential mates or rivals. Several authors (Jennions and Møller 2003; Palmer 1999, 2000) have suggested that bias exists in the literature toward only positive or expected results in publications relating to fluctuating asymmetry, and others (Houle 1998; Simmons et al. 1999) suggest caution when generalizing conclusions about the relationship between fluctuating asymmetry and sexual selection. Early enthusiasm for fluctuating asymmetry as an indicator of individual quality may have been overstated due to unbalanced reporting of studies with positive results. It is possible that, for this study, environmental conditions were not severe enough to produce distinguishable patterns of asymmetry. Alternatively, if patterns did exist and we were unable to detect them, this type of research may require more sophisticated methods of analyzing and measuring 3-dimensional shape; these methods may provide more-sensitive detection of patterns of asymmetry. Laser grids, computed tomography scans, and magnetic resonance imaging have been used to measure asymmetry, although these methods are very costly and generally not applicable for fieldwork.


Support for this project was provided by the School of Forestry and Wildlife Sciences and the Center for Forest Sustainability at Auburn University. We thank G E. Hill and T. S. Denney for earlier reviews of the manuscript.

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Received: 13 April 2009; Accepted: 2 June 2009; Published: 17 February 2010

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