Linking human male vocal parameters to perceptions, body morphology, strength and hormonal profiles in contexts of sexual selection

Sexual selection appears to have shaped the acoustic signals of diverse species, including humans. Deep, resonant vocalizations in particular may function in attracting mates and/or intimidating same-sex competitors. Evidence for these adaptive functions in human males derives predominantly from perception studies in which vocal acoustic parameters were manipulated using specialist software. This approach affords tight experimental control but provides little ecological validity, especially when the target acoustic parameters vary naturally with other parameters. Furthermore, such experimental studies provide no information about what acoustic variables indicate about the speaker—that is, why attention to vocal cues may be favored in intrasexual and intersexual contexts. Using voice recordings with high ecological validity from 160 male speakers and biomarkers of condition, including baseline cortisol and testosterone levels, body morphology and strength, we tested a series of pre-registered hypotheses relating to both perceptions and underlying condition of the speaker. We found negative curvilinear and negative linear relationships between male fundamental frequency (fo) and female perceptions of attractiveness and male perceptions of dominance. In addition, cortisol and testosterone negatively interacted in predicting fo, and strength and measures of body size negatively predicted formant frequencies (Pf). Meta-analyses of the present results and those from two previous samples confirmed that fonegatively predicted testosterone only among men with lower cortisol levels. This research offers empirical evidence of possible evolutionary functions for attention to men’s vocal characteristics in contexts of sexual selection.

Acoustic signals comprise a fundamental component of mating competition [1][2][3][4] and are highly sexually dimorphic in many species, including many anthropoid primates. Humans in particular exhibit strong sexual dimorphism in acoustic signals 5 , such that the distributions of male and female vocal parameters related to pitch and timbre barely overlap 6 .
From hearing the voice alone, humans can assess diverse salient social characteristics of a speaker, such biological sex, age and physical strength [7][8][9] . Many of these evaluations rely on inter-individual variation in specific sets of vocal parameters, including fundamental frequency and formant frequencies 5,10 . Fundamental frequency (f o ) is the rate of vocal fold vibration during phonation and influences perceptions of pitch. Formant frequencies are resonant frequencies determined by the length and shape of the vocal tract and influence perceptions of vocal timbre.
Perceptions of attractiveness and dominance. Because deep male voices may display social power 29 , threat potential 11 , and predict greater anticipated 42,86,87 and actual 42,88 sexual infidelity, there may be costs as well as benefits to mating with males with masculine voices 11 . Further, some studies suggest that the link between mean f o and attractiveness is weaker and rather curvilinear: Very low-pitched voices are not seen as more attractive and sometimes even less attractive as low-pitched voices 11,64 . In line with the context-dependent nature of costs and benefits and reports from previous literature, we therefore predicted negative linear 5 and negative quadratic 11 relationships between attractiveness ratings and both mean f o (H1) and formant position (P f ) (H2). P f is a measure of formant structure, calculated as the average standardized formant value for the first n (usually four) formants 6 .
Masculine voices (i.e. low f o and P f ) have been found to be preferred by females to a greater extent in shortterm compared to long-term relationship contexts 14,89 . This might reflect an adaptive trade-off strategy in which a mate's genetic fitness, putatively indicated by masculine traits, is granted greater value in short-term contexts, whereas his expected investment and fidelity are valued more in long-term contexts 89,90 . Consequently, we predicted stronger relationships between short-term, compared to long-term, attractiveness ratings and both mean f o (H3) and P f (H4).
It has been hypothesized that deep voices display threat potential 6 ; hence, we predicted negative relationships between dominance ratings and both mean f o (H5) and P f (H6). According to the source-filter theory, f o and P f are theoretically distinct 91 . They are also only weakly correlated 10 and seem to convey different information about a male speaker 6 . Accordingly, we predicted f o and P f to be independent predictors of both attractiveness (H7) and dominance (H8) ratings.  45 135 61 Size Size + 6 Rendall et al. 46 163 68 Size Size + 7 Rosenfield et al. 15 84 4 Att; Pres; Dom MS + 8 Šebesta et al. 47 62 93 Att Size + 9 Šebesta et al. 48 63 40 Dom Size + 10 Simmons et al. 49 30 44 Att; Mas Semen + 11 Valentova et al. 50  circulating testosterone levels, and more recently this relationship was found to be stronger in men with lower cortisol levels 5 , a result seemingly consistent with the stress-linked immunocompetence handicap hypothesis that f o honestly signals a speaker's physical condition 36 . We therefore predicted a negative relationship between mean f o and testosterone (H9) and predicted that this relationship would be attenuated by high baseline cortisol (H10). Formants have been shown to relate moderately to body height, a phenotype that is relevant in both intra-and intersexual selective contexts 92 . We therefore predicted a negative relationship between P f and body height (H11).

Exploratory analyses.
In addition to these preregistered predictions, we conducted the following exploratory analyses. First, we examined how vocal parameters related to physical strength and body morphology. Second, we compared whether distinct parameters are used as cues for ratings on social dominance (i.e. being respected) and physical dominance (i.e. fighting ability), as they describe separate aspects of social evaluation 93 . Third, we explored whether jitter and shimmer influence attractiveness and dominance perceptions, as these acoustic parameters seem to provide information on male body shape. Jitter and shimmer quantify cycle-tocycle variation in f o and amplitude, respectively, and influence perceptions of voice roughness. Fourth, we conducted three mediation analyses: (1) a moderated mediation model to test whether f o mediates the relationship between vocalizers' testosterone levels (condition) and dominance ratings (perception), and whether this mediation is further moderated by cortisol, (2) a mediation model to test whether f o and P f , mediate the relationship between vocalizers' height and dominance ratings, and 3) a mediation model to test whether f o and P f , mediate the relationship between vocalizers' composite measure of size (extracted via factor analysis with varimax rotation) and dominance ratings. We conducted a separate mediation model for height, in addition to its inclusion in the factor analysis, as height has been shown to reflect good nutrition and low stress during development, as well as genetic predictors of immune function 94 . Additionally, a recent study 31 reported that f o mediated the relationship between height and physical dominance ratings in two separate samples. Finally, we conducted three meta-analyses to test: (1) the mediating effect of f o between height and dominance ratings, (2) whether cortisol and testosterone negatively interact to predict male f o , and 3) whether f o negatively predicts testosterone levels, especially among men with lower cortisol levels.

Design and methods
Participants. One hundred sixty-five heterosexual males participated in a study on testosterone reactivity and personality state changes, which was conducted at the University of Goettingen, Germany (for details, see 95 ). Each participant provided a standardized video recording, saliva samples, body morphology measurements, and handgrip as well as upper-body strength. Data from five individuals could not be used due to technical issues during video recording or because consent for further use of the video material was not given, resulting in a final sample of 160 males (mean age = 24.28, SD = 3.25 years). All participants were at least 18 years old. In a sensitivity power analysis using G*Power 96 this sample had sufficient power (> 0.80) to detect an effect size of r = + / − 0.20, assuming one-tailed alpha = 0.05. All procedures were in accordance with relevant guidelines and regulations, and received ethics approval from the local Ethics Committees at the University of Goettingen and the Pennsylvania State University. Informed consent was obtained from all subjects.
Voice recordings. Standardized video recordings were obtained using a Full-HD camera and Line6 Modell XD-V75 microphones. The participants were instructed to describe what is great about themselves, choosing three domains such as "friendship" or "success in studies/job" from a list of overall eight domains (for details, see 95 ). The video clips were cut to a length of 5 s, beginning 5 s after participants had begun to speak, and voice clips were extracted. Five seconds were chosen because vocal parameters usually show strong correlations across different recordings, independent of length and content 88,97 , and both attractiveness and dominance ratings are stable and highly correlated across different recordings 6,97 . Further, the use of relatively brief voice clips allowed us to avoid rater fatigue. The voice clips were analyzed using PRAAT software 98 (Version 6.0.36). The measures obtained were mean f o , the first four formant frequencies (F 1 -F 4 ), four measures of jitter and five measures of shimmer. Because both jitter (all rs > 0.83, ps < 0.001) and shimmer measures (all rs > 0.56, ps < 0.001) were highly intercorrelated, a standardized mean was calculated for each perturbation measure 10 . Additionally, P f was computed for the first four formants 6 . Formants were measured at each glottal pulse using automated detection in PRAAT. Formant measurement across standardized speech samples produces highly similar results to measurement of individual vowels and averaging across these measurements 6 .
It should be noted that different methods of measuring formant structure are used across studies. Formant dispersion (D f ), for example, describes the distance between the highest (e.g., F 4 ) and lowest formants (e.g., F 1 ) measured 39 . While D f is commonly used, it has also been criticized especially for not using information about the middle formants (e.g., F 2 and F 3 ). Further, although D f is theoretically dependent on body height, other measures of formant structure have shown stronger relations with body height 6,33 . One of these measures is formant position (P f ) which describes the average standardized formant value for the first n formants (e.g., F 1 -F 4 ) and thus utilizes information of all formants measured 6 . Given these advantages of P f over D f , P f was chosen as the relevant measure for formant structure in this study. For further discussion, see 6 . Saliva samples. Based on previous studies 99,100 , we controlled for circadian variation in participants' hormonal reactivity by collecting saliva samples only between 2 and 6 pm. Approximately 12-15 min after each participant arrived at the lab, he rinsed his mouth with water and provided at least 2 ml of saliva via passive drool through a straw, just prior to the video recording. The collected samples were immediately transported Scientific Reports | (2020) 10:21296 | https://doi.org/10.1038/s41598-020-77940-z www.nature.com/scientificreports/ to an ultra-low temperature freezer (− 80 °C), where salivary testosterone is expected to be stable for at least 36 months 101 . At the end of the data collection period (see 95 for details), saliva samples were shipped on dry ice to the Technical University of Dresden and analyzed using chemiluminescence-immuno-assays with high sensitivity (IBL International, Hamburg, Germany). The intra-and inter-assay coefficients (CVs) for cortisol are below 8% and for testosterone below 11%. Basal cortisol and testosterone outliers were identified and winsorized to 3 SDs 102 . To correct for skewness, we log10-transformed both variables.
Body morphology and strength measurements. As this procedure was also reported in 103 , procedural and methodological descriptions overlap. Participants were scanned three times using a Vitus Smart XXL 3D body scanner, running AnthroScan software (both Human Solutions GmbH, Kaiserslautern, Germany). Participants wore standardized tight underwear and were instructed to stand upright with legs hip-width apart, arms extended and held slightly away from the body, making a fist with thumbs showing forward, the head positioned in accordance with the Frankfort Horizontal, and to breathe normally during the scanning process. Using AnthroScan's automatic measures (according to ISO 20685), we extracted muscularity-relevant body dimensions from the body scan: body volume, bust-chest girth, buttock girth, chest-to-hip ratio (CHR), forearm girth, lower limb ("leg") length-to-height ratio (LHR), shoulder-to-hip ratio (SHR), thigh girth, upper arm girth, waist girth, waist-to-chest ratio (WCR), and waist-to-hip ratio (WHR Attractiveness and dominance ratings. In exchange for course credit, 120 men (mean age = 19.82, SD = 2.71 years) and 120 women (mean age = 19.90, SD = 3.80 years) participated in a rating study on short-and long-term attractiveness as well as social and physical dominance at the Pennsylvania State University. All raters were at least 18 years old. Raters were equipped with Sennheiser HD 280 Professional Headphones and seated at private workstations. Raters provided demographic data on age, gender, sexual orientation, and relationship status. To control for the influence of semantic content, we also asked raters to indicate their German language comprehension ("How well do you understand German?") on a 7-point Likert scale from 0 ("Not at All") to 6 ("Fluent"). Below, we report results with all participants, but excluding raters score 2 or higher (n = 26) does not change results. Raters were then randomly assigned to one of four rating experiments, each asking for perceptions of either short-term attractiveness, long-term attractiveness, social dominance, or physical dominance of 160 randomly assigned voice files (for specific items see Appendix A). The voice file pool contained 320 voice samples that were taken from the 160 former targets before and after the competitive setting 95 . Raters always rated both files of a target, but both recordings of the same individual were separated by at least ten other voice samples. However, only ratings of the recordings before the competition were used in the present study. To ensure that each file was rated 15 times by each sex, a file was removed from the pool of remaining files to be rated once this criterion was met. The only exception was long-term attractiveness, where one male rater dropped out because of technical issues. Because correlations between male and female ratings were high (all rs > 0.70, ps < 0.001), and intraclass correlations within each rating condition were at least satisfactory (all ICCs > 0.76, ps < 0.001), mean scores were calculated.

Results
For tests of directed hypothesis one-tailed tests were used, and for exploratory tests two-tailed tests were used. Analyses were conducted using R 106 .

Perceptions of Attractiveness and Dominance. Attractiveness H1) Predictions on negative linear and
negative quadratic relationships between attractiveness ratings and mean f o were supported. We found that f o negatively linearly predicted both short-term and long-term attractiveness. Furthermore, we found significant negatively quadratic (inverted U-shaped) relationships between f o and both short-term (Fig. 1a) and long-term attractiveness (Fig. 1b). Comparisons of linear and curvilinear models showed that the relationship between f o and short-term attractiveness was significantly better described by the curvilinear model (F 2,157 = 4.38, p = 0.038), while there was no significant difference between models for long-term attractiveness (F 2,157 = 3.76, p = 0.054). H2) Predictions of negative linear and negative quadratic relationships between attractiveness ratings and P f were only partially supported. We found no significant linear relationships between P f and either short-term or long-term attractiveness. While the non-linear relationship of P f and short-term attractiveness was not significant (Fig. 2a), a significant negative quadratic relationship between P f and long-term attractiveness emerged (Fig. 2b).
H3) The prediction of a stronger relationship between mean f o and short-term, compared to long-term attractiveness ratings was supported. Although both attractiveness ratings were highly correlated (r = 0.82, p < 0.001), the relationship between f o and short-term attractiveness was significantly stronger (z = − 2.06, p = 0.020) when comparing dependent correlation coefficients 108 .
Dominance H5) The prediction of a negative relationship between dominance ratings and mean f o was partially supported: f o negatively predicted physical dominance (Fig. 1c), but not social dominance ratings (Fig. 1d). H6) The prediction of a negative relationship between dominance ratings and P f was supported. P f negatively predicted perceptions of both physical (Fig. 2c) and social (Fig. 2d) dominance ratings.
Independent Predictors H7) The prediction that mean f o and P f are independent predictors of attractiveness ratings was partially supported. When f o and P f were included in a multiple regression (F 2,157 = 16.78, p < 0.001, R 2 = 0.17), f o negatively predicted short-term attractiveness (β = − 0.40, p < 0.001), but P f did not (β = − 0.08, p = 0.132). Similarly, f o negatively predicted long-term attractiveness (β = − 0.32, p < 0.001) in a multiple regression (F 2,157 = 8.94, p < 0.001, R 2 = 0.09), but P f did not (β = 0.01, p = 0.471). Because the curvilinear relationship between long-term attractiveness and P f was significant, we investigated whether the linear term of f o and the quadratic term of P f were independent predictors of long-term attractiveness. Indeed, adding the quadratic term of P f explained significantly more variance in long-term attractiveness ratings (  (Fig. 3a). While these results do not support H9) a negative relationship between mean f o and testosterone, they supported H10) a negative relationship between mean f o and testosterone, which is attenuated by high baseline cortisol.
Body Morphology and P f A significant relationship between P f and body height was found (r = − 0.13, p = 0.046), supporting H11).  (Table 2). Perturbation measures, vocal perception and target parameters Pearson correlations showed significant negative relationships between shimmer and both social (r = − 0.31, p < 0.001) and physical dominance (r = − 0.31, p < 0.001). No significant relationships were found between shimmer and short-term (r = − 0.14, p = 0.076) or long-term attractiveness (r = − 0.12, p = 0.122). Jitter showed no significant relationship to any of the four ratings (all rs < + / − 0.11, ps > 0.16). Moreover, the only significant relationship between perturbation measures and any of the target parameters was a significant negative correlation between shimmer and baseline cortisol (r = − 0.21, p = 0.006). Multiple regressions with f o , P f , jitter and shimmer as predictors and all ratings as outcomes can be found in Tables S1-S4.
We ran two additional mediation models: (1) f o and P f were entered as mediators between height and physical dominance ratings, (2) f o and P f were entered as mediators between physical strength and dominance ratings. A composite measure of physical size was extracted from a factor analysis (Fig. 4d) on the following body morphology measures that significantly correlated with P f (Table 2): height, weight, body volume, bust-chest girth, buttock girth, forearm girth, physical strength, thigh girth, upper body size, upper arm girth, and waist girth. In model 1, f o and P f were entered as mediators between height and physical dominance ratings (Fig. 4a). Neither f o nor P f was a significant mediator. In model 2, we found evidence that P f mediated the relationship between physical strength condition and physical dominance ratings (Fig. 4b).

Meta-analyses
We combined results of the present study with prior results 31 in a meta-analysis to assess the strength of the mediating effect of f o on the relationship between height and perceptions of physical dominance. We found a significant overall mediating effect of f o, independent of P f (Fig. 4c); f o mediated about 44% the relationship between height and physical dominance ratings.
We also conducted a meta-analysis of the interaction of testosterone and cortisol in predicting f o . For this analysis, the t-value and degrees of freedom (df) of the overall interaction effect were transformed into a correlation 114 . The effect of the testosterone and cortisol interaction on male f o (k = 3, n = 279) was significant: r = 0.23, p = 0.001, 95% CI [0.12, 0.34] (Fig. 3b). In follow-up analyses, the relationship between testosterone and f o was significant in men with low cortisol levels (Fig. 3c), but not in those with high cortisol levels (Fig. 3d).
Finally, Fig. 5 provides a lens model 115 overview of the key relations between perceptions, vocal cues and target parameters found in this study.

Discussion
We investigated the role of vocal parameters in perceptions of male attractiveness and found that f o was the strongest predictor of short-and long-term attractiveness among the vocal parameters measured (P f , shimmer, and jitter). Consistent with previous studies 11,64 , the relationship between f o and male vocal attractiveness was both negatively linear and negatively curvilinear, the latter suggesting that women's voice preferences may reflect a tradeoff between the potential genetic or other benefits versus the potential costs of mating with masculine males 6 . Such costs may include lower investment and perhaps risk of interpersonal violence. Low male f o has previously been linked to sexual infidelity 42,88,89,116 , and several lines of evidence suggest that phenotypic masculinity-and vocal masculinity in particular-indicate threat potential not only to same-sex competitors but also to potential mates. For example, images of male-on-female violence disrupted U.S. women's preferences for both masculine voices and faces 117 , and Colombian women with perceptions of greater local domestic violence (c) Although f o was not found to be a significant mediator between height and physical dominance ratings in the present study, a meta-analysis using a random-effects model indicated a significant mediating effect, with f o mediating 44% of the relationship between height and physical dominance. Proportion mediated lower than 0 indicates the suppression effect of a mediating variable. In addition, the current study used mean dominance ratings as the primary unit of analyses for calculating proportion mediated, whereas Aung et al., Study 1 (n = 8,103 observations) and Study 2 (n = 6,586 observations) used individual ratings. (d) Using the "nFactors" package 112 and rotated factors with Varimax method using the "psych" package 113 , we reduced the set of size related measures into one dimensional factor (n = 1), which we labelled "composite size", via principal axis factoring analysis. ***p < .001.

Scientific Reports
| (2020) 10:21296 | https://doi.org/10.1038/s41598-020-77940-z www.nature.com/scientificreports/ preferred less masculine male faces 118 . In another study, Filipino women who were younger and rated themselves as less attractive tended to prefer feminized male f o , again suggesting that women's f o preferences may in part reflect their own perceived vulnerability 62 . In our data, f o was a stronger predictor of short-term than long-term attractiveness, once again supporting the notion of a mate choice trade-off in which putative indicators of genetic fitness are prioritized in short-term contexts, and expected investment and fidelity are prioritized in long-term contexts 90 .
Although P f predicted strength and body morphology in our study and predicted ratings of attractiveness in some prior studies 13,21 , it did not predict attractiveness in another large sample 5 and was unrelated to shortterm attractiveness and only weakly negatively curvilinearly linked to long-term attractiveness in the present study. These lines of evidence suggest that the information provided by formant frequencies may be less relevant to mate quality than that provided by f o . By contrast, shimmer negatively predicted both short-and long-term attractiveness ratings. Shimmer is utilized to assess vocal quality in clinical contexts, such that pathological voices show higher shimmer levels than those of healthy individuals [119][120][121] ; however, a composite of shimmer and harmonics-to-noise ratio (which were highly correlated) showed no relationship to dominance or attractiveness perception in a recent study 5 . These divergent findings may be explained by the fact that the latter study used voice samples in which male individuals read a standardized voice passage, while our study used more natural but less standardized stimuli that might have been influenced more strongly by the speaker's affective state.
Importantly, a Fisherian mate choice model via runaway sexual selection has also been suggested as a possible driver favoring low male f o 14,122 . A Fisherian model would suggest that female choice primarily drives and exaggerates the evolution of male traits; hence, the model predicts that females prefer males with the lowest f o . However, evidence from the current study and previous studies 15,62,65 (suggests a general preference for lower f o by women, but also a relatively stronger negative linear relationship between f o and dominance perceptions by men across studies 29 .
While f o predicted both short-and long-term attractiveness, it predicted physical dominance but not social dominance, in line with previous studies 13,123 . P f and shimmer were linked to both social and physical dominance ratings. A possible explanation for this pattern of results is that social dominance is influenced less by threat potential and more by other qualities, such as competence, communication and cooperation skills, or leadership qualities. These attributes might be more strongly associated with P f and shimmer than with f o .
The other aim of this study was to explore whether attention to vocal cues is adaptive by investigating the information content of acoustic parameters. We replicated a negative relationship between P f and height 33 and found that P f negatively predicted strength and several body morphology measures. Men with lower P f were taller, stronger, and had larger bodies in general. Further, our mediation analysis indicated that P f , independently of f o , mediated the relationship between a composite measure of body size and physical dominance ratings.
Importantly, baseline cortisol and testosterone levels interacted in predicting f o , such that testosterone levels more strongly negatively predicted f o as cortisol levels decreased across participants. When we entered the interaction term between testosterone and median-split cortisol levels into our exploratory moderated mediation analyses, the interaction effect became non-significant, likely due to reduced statistical power 124 from dichotomizing a continuous variable (cortisol). Nevertheless, the overall interaction between testosterone and cortisol in predicting male f o was confirmed in a meta-analysis (Fig. 3b). Male f o was negatively correlated with www.nature.com/scientificreports/ testosterone when cortisol was low, whereas no significant relationship was observed between male f o and testosterone when cortisol was high (Fig. 3c). These patterns of relationships may help clarify why dose-dependent effects of androgen levels on the intensity of elaborate male traits are sometimes undetected 125 , and why f o is only weakly correlated with testosterone when cortisol is not considered. Across a variety of species, testosterone and cortisol are linked to measures of physical condition, including disease, stress, and diet 126 . The interaction between testosterone and cortisol, in particular, has been tied to immune function in birds 127 , but the functional and behavioral correlates of this hormonal interaction in humans are not yet clear 36,128 , and most studies are arguably underpowered. Further, a recent meta-analysis found only modest support for an interactive relationship between testosterone and cortisol in predicting status-relevant behavior (e.g., dominance & risk taking) and suggested that this association could be driven by publication bias and flexibility in data analysis 129,130 . Although only one paper 5 besides the current one has reported the specific interaction effect of testosterone and cortisol on male f o , the meta-analysis reported here suggests that the interaction is robust. There is widespread agreement 5,11,27,40,46 that low male f o evolved to exaggerate apparent size by leveraging a predisposition to perceive low frequencies as emanating from large sound sources. Phylogenetic reconstruction suggests that relatively male f o evolved in the common ancestor of the catarrhine primates after their divergence from platyrrhines approximately 43.5mya 5 . Given the weak correspondence between f o and body size, some have argued that f o is purely deceptive and is not an honest indicator of physical dominance 27,28,131 . Others have suggested that f o may reliably correlate with other salient speaker characteristics such as status, threat, and dominance, and that these dimensions may overlap with, and hence intrude onto impressions of, size 46 . Our results better comport with the latter possibility. Indeed, relatively low male f o tends to be lost in primate species in which male-male mating competition is reduced, suggesting that there are costs associated with low f o that cause this trait to be selected against when compensatory benefits are absent.
Deference to males with low f o is demonstrably costly in humans in terms of social status, mates, and reproduction, and thus attention to f o would seemingly be selected against if f o did not provide valid information about male condition 30 . However, this does not mean that f o is cheat-proof, or that the assessment of condition or formidability from f o is largely accurate. Honest signals are often corrupted into conventional signals where cheating is common because the assessment of the signal itself is costly to the receiver 132 . Although we did not find support for the cortisol-moderated mediation role of f o between testosterone levels and physical dominance ratings in the present sample, this may be explained by reduced statistical power due to dichotomized cortisol levels and reduced sample sizes for testing two separate indirect effects. Indeed, we found a strong meta-analytic support for an overall interaction between testosterone and cortisol in predicting male f o , suggesting that f o conveys underlying endocrine state, if imprecisely, and lower male f o has consistently been shown to predict perceptions of physical dominance across multiple studies. Likewise, a recent study 31 reported that f o mediated the relationship between developmental condition (measured via height) and physical dominance ratings in two separate samples with different types of vocal stimuli. Although we did not find that f o significantly mediated the relationship between height and physical dominance ratings in our data, our meta-analysis suggests that f o mediates about 44% of the relationship between height and physical dominance ratings. Collectively, our findings support the hypothesis that, while the correlation between f o and underlying quality is imperfect, f o might be utilized as one of many cues for assessing competitors and potential mates 29 because it communicates the quality of the signaler significantly better than chance 132,133 .
Shimmer also negatively predicted social and physical dominance ratings, as well as lower cortisol levels. The latter finding is consistent with prior evidence that shimmer is reduced when stress is induced experimentally or when the speaker is under high tension 134 . However, the other perturbation measure, jitter, showed no such associations. Future research should continue to explore the relevance of jitter and shimmer to human sexual selection (see also), as they have been shown to be associated with pathological voice quality 120 and body shape in men 41 and might therefore be relevant in contexts of sexual selection.
One limitation with our study is that we tested only hypotheses associated with receiver-independent costs and did not consider receiver-dependent costs associated with attention to male f o . Some 135,136 have suggested that additional mechanisms that incorporate receiver-dependent costs are required to ensure signal honesty. For example, under a mating-motive priming condition, male voices with low f o enhanced recognition for men with high threat potential 135 and elicited aggressive cognitions and intent in men who perceived themselves to be more dominant and stronger 136 . Future studies should investigate the extent to which receiver-dependent and independent costs are needed in ensuring the signal honesty of low f o in cross-cultural contexts.
Following suggestions by Lakens 137 , we used one-sided significance tests for preregistered directional hypotheses. The only result influenced by this decision is the relation between P f and height, which would be nonsignificant using a two-sided test. However, we note that meta-analytic findings 33 suggest a robust link between P f and height, and the lack of a significant relation in this particular study is likely due to a lack of statistical power. Thus, also our conclusions remain highly similar when two-sided tests are used.

Conclusion
Vocal parameters were linked to hormone levels, as well as body morphology and physical strength, and appear to be used for judgements relevant to intrasexual competition and intersexual mate choice. The present study thus provides evidence that natural interindividual variation in men's vocal parameters influences judgements of attractiveness and dominance because these parameters provide valid information about speakers' underlying condition.