Does greater variation reside in the larger sex?

Abstract

The question of whether males or females are the more variable sex is long-standing, and yet to be fully answered. We investigate the relationships between body mass and variation across species using a phylogenetically informed analysis of the body mass of 337 species representing six mammalian orders. Within each order, we found that the larger sex is typically the more variable sex, whether male or female, and the variation–size relationship is arguably often close to unity. Thus, size may be the main or even sole driver of variability in at least some orders. Deviations from the expected 1 : 1 relationship emerged, however, in regressions of male : female mass variance against male : female mean mass, for Chiroptera and Rodentia, which both presented hyperallometric relationships suggesting that drivers over and above size influence differences in variation between the sexes. In Chiroptera, most species have larger females. The y-intercept value for Artiodactyla and Primates were significantly greater than 0 suggesting greater male variation in species where the sexes are of commensurable size. Historic belief of exclusively greater male variability may have resulted from a focus on species with intense male–male competition and, thus, larger male body sizes. Our results suggest that it is often size, not sex per se, that influences within-sex variability, although additional sex-specific factors might be present in at least some orders.

1. Introduction

Perhaps Charles Darwin was the first to claim that, when it comes to gross morphology, males of a species are more variable than females [1,2]. That is, a randomly selected sample of males is believed to exhibit more variability amongst themselves in terms of, for example, their weight than is a similarly sized sample of females. This phenomenon is termed greater male variance (GMV), but the extent to which it applies across traits and taxa is far from clear [3–6], with many studies underpowered [7]. Moreover, rather than showing GMV, some traits show the reverse pattern of greater female variance (GFV) [3,6,8,9].

Arguably, the most straightforward hypothesis to explain GMV and GFV is that the larger sex will be more varied because of a simple 1 : 1 mathematical coupling between the size of the measures taken and their spread. This would predict a unitary relationship across species between mean body mass and the standard deviation of body mass—where proportional changes in the standard deviation follow from proportional changes in the mean—and, therefore, a flat relationship between mean body mass and the coefficient of variance of body mass.

Larger traits (and more elaborate traits) are not only bigger, however, but tend to be more vulnerable (more sensitive to disruption by stressors) than smaller ones [10,11]. Larger traits often take longer to develop and require more energy and more nutritional resources for full expression and thus are more sensitive to disruption by stressors. We see this play out in the condition-dependent expression of male sexually selected traits, such as large body size or elaborate plumage, whereby stressor exposure (e.g. nutritional shortfalls, parasitism) compromises these traits in less fit males [12–14]. The result is more male than female variation in these traits. These observations have led to the development of male-specific models of vulnerability, such as androgen-dependent immunosuppression [15,16]. There is some supportive evidence [15], but immunosuppression is not the full explanation. Moore & Wilson [17] found that males were more prone to parasitism than females but only when they were the larger sex. Critically, females were more prone to parasitism when they were the larger sex, suggesting that trait size, independent of sex, might increase vulnerability and intrasexual variability.

Larger traits being more vulnerable reasonably predicts a relationship between the variability and mean of body mass having a value greater than one because that relationship is driven by both the mathematical 1 : 1 coupling of size and spread and the greater vulnerability of larger size.

It is possible, then, that Darwin and others commonly observed GMV because, in most of the species they studied, males are physically larger or have more elaborate traits (e.g. plumage), that is, sexual size dimorphism in favour of males. In mammals at least, a well studied order, males are typically the larger sex. However, recently, Tombak et al. [18] collated data from the literature indicating that in fact many mammalian species have negligible sexual size dimorphism and for a substantial number of them (about one in six), females are larger than males. Along with mean body masses per sex, Tombak et al. [18] reported the associated standard deviations, apparently to detect potential bias in the means due to data collected from pregnant females. We took advantage of this dataset on the means and variances of body mass in species of multiple orders within the class Mammalia, along with additional data on Primates, to investigate sex differences in the relationships between size and variation across species.

2. Methods

This study is based on the dataset provided by Tombak et al. [18]. To explore relationships between GMV and sexual size dimorphism across species, our data comprised the mean and standard deviation of adult mass for both sexes of each species, along with taxonomic order. From these data, we calculated sexual size dimorphism, as the log₁₀ ratio of mean male mass to mean female mass. We also calculated greater male variance as the log₁₀ ratio of the standard deviation of male mass to the standard deviation of female mass. Negative values of sexual size dimorphism indicate that females are larger than males, whereas negative values of greater male variance indicate that females are more variable in body mass than males. The variable log₁₀(sexual size dimorphism) was centred prior to analysis, such that the significance of the main effects would still be estimated at the average values in the presence of significant interactions in the model [19].

The main analysis presented in [18] included 429 unique species. We edited this dataset prior to our own analyses. First, when more than one sample was available for a species, we retained only the largest sample. Due to the sensitivity of analyses of GMV to sample size [7], species with less than 10 individuals of either sex were excluded and taxonomic orders with less than 15 species were removed. We also removed the data point for northern elephant seals (Mirounga angustirostris), which was a strong outlier in graphical plots. We then added data from the literature for further primate species [20]. Preliminary plots of outliers and examination of associated studies indicated a few errors in the calculations of standard errors reported by Tombak et al. [18] and these were corrected by inspecting the original papers (see electronic supplementary material). The consequent dataset included six orders: Artiodactyla, Carnivora, Chiroptera, Eulipotyphla, Primates and Rodentia.

These data were analysed using the phylogenetic generalized least squares (PGLS) method applying a phylogeny generated from the Open Tree of Life [21] using the rotl() package in R. A small number of species (n = 7) were not recognized by the Open Tree of Life and thus were not included in the phylogenetic analyses, which included 336 species (Artiodactyla, n = 26; Carnivora, n = 17; Chiroptera, n = 96; Eulipotyphla, n = 18; Primates, n = 47; Rodentia, n = 132).

We analysed the data to assess the possible presence of relationships between size and variation across species in several ways. First, for both sexes separately, log₁₀(standard deviation of mass) was the outcome variable in phylogenetically informed linear models composed of first simply log₁₀(mean mass) and then also taxonomic order and the interaction between mean mass and order. Model residuals were checked for normality and homogeneity of variance. Model parameters were considered statistically significant below α = 0.05. Slope estimates were considered statistically different from unity if the associated 95% confidence interval did not encompass 1. The slope estimates for males and females within each order were considered significantly different if the associated 95% confidence intervals of the male slope did not encompass the estimated value of the female slope. Second, the models were rerun with the coefficient of variance (s.d./mean) as the outcome variable. Slope estimates were considered statistically significantly different from zero if the associated 95% confidence interval did not encompass 0.

Third, to directly test for relationships between GMV or GFV and sexual size dimorphism, we placed log₁₀(s.d. mass male/s.d. mass female) as the outcome variable in a phylogenetically informed linear model composed of first simply log₁₀(mean mass male/mean mass female) and then also taxonomic order, and the interaction between dimorphism and order. Model residuals were checked for normality and homogeneity of variance. Model parameters were compared to 0 and also 1 where appropriate and were considered statistically significant below α = 0.05.

3. Results

PGLS analysis of the dataset testing for a relationship between the logs of standard deviation of mass and mean mass was significant for males (R² = 0.93; F_1,333= 4334, p < 0.001) and females (R² = 0.91; F_1,333 = 3578, p < 0.001). In both cases, the slope value was not significantly different from 1 (males: 1.03 [95% CI: 0.04]; females: 1.02 [95% CI: 0.04]). For both sexes, neither taxonomic order as a main effect nor as an interaction was significant (males: F₅ = 0.255, p = 0.937 and F₅ = 1.752, p = 0.122; females: F₅ = 0.313, p = 0.905 and F₅ = 1.396, p = 0.226; figure 1a,b). For males, one order had a slope value significantly different from 1 (Eulipotyphla: 1.23 [95% CI: 0.19]), and in females, no orders were significantly different from 1. Excluding Eulipotyphla, all slope estimates were close to 1, ranging from 0.961 to 1.087 (table 1). For both sexes in all orders, the slopes of the coefficient of variance against mass were not significantly different from 0 (figure 1c,d).

Figure 1.

Standard deviation (s.d.; log₁₀ transformed) of body mass or the coefficient of variance of body mass against mean body mass (log₁₀ transformed) for six mammalian orders by sex (a and c, male; b and d, female). Each data point represents values for a unique species. Linear lines of best fit are applied to each taxonomic order and account for phylogenetic relatedness between species. In a and b, the line of unity is presented (grey dash).

Table 1.

Slope values and 95% confidence intervals (CI) for each mammalian order, obtained from a phylogenetic least squares analysis of standard deviation in body mass against mean body mass, separately for males and females.

	males			females
	parameter estimate	upper 95% CI	lower 95% CI	parameter estimate	upper 95% CI	lower 95% CI
Artiodactyla	0.982	1.098	0.866	0.993	1.117	0.869
Carnivora	1.057	1.267	0.847	1.087	1.311	0.863
Chiroptera	1.002	1.165	0.841	0.982	1.158	0.806
Eulipotyphla	1.235a	1.429	1.041	1.194	1.404	0.984
Primates	1.004	1.132	0.876	1.003	1.139	0.867
Rodentia	1.031	1.169	0.893	0.961	1.109	0.813

^a Statistically significantly different from a slope value of 1.

For all six orders, the slope value of the relationship between the logs of standard deviation of mass and mean mass did not differ between males and females within each order (table 1).

In five of the taxonomic orders, males are generally the larger and more variable sex, while in Chiroptera the females are generally larger and more variable (figure 3). PGLS analyses testing for a relationship between GMV or GFV and sexual size dimorphism was significant (R² = 0.34; F_1,334 = 168.4, p < 0.001), indicating a positive relationship and a slope value significantly greater than 0, and also than 1 (slope: 1.464 ± 0.113 s.e., p < 0.001 in both cases). The model intercept represents the ratio of male to female variability when the sexes are the same size (i.e. x = 0). The intercept value was not significantly different from 0 (0.045 ± 0.027 s.e., p = 0.091). When including taxonomic order (figure 3), the main effect was significant (F₅ = 2.735, p = 0.019) and the slopes of all six taxonomic orders were significantly greater than 0, with the slopes of two orders also being significantly greater than 1 (table 2). The interaction term was not significant (F₅ = 1.771, p = 0.119). Analysis of the intercepts indicated that for the Artiodactyla and Primates, the y value was greater than 0 (table 2), while in the other orders, the intercept was not statistically different from 0.

Table 2.

Phylogenetic least squares analyses of greater male variance or greater female variance (s.d. mass males/s.d. mass females) against sexual size dimorphism (mean mass males/mean mass females) disaggregated by taxonomic order. s.e. = standard error.

				baseline: 0		baseline: 1
		parameter est.	estimate s.e.	t-value	p‐value	t-value	p‐value
Artiodactyla	intercept	0.272	0.071	3.855	<0.001a
	slope	0.894	0.326	2.746	0.006a	0.325	0.745
Carnivora	intercept	0.155	0.103	1.496	0.136
	slope	1.259	0.314	4.016	<0.001a	0.825	0.410
Chiroptera	intercept	0.092	0.053	1.747	0.082
	slope	1.747	0.345	5.059	<0.001a	2.165	0.031a
Eulipotyphla	intercept	−0.086	0.083	−1.033	0.303
	slope	1.594	0.636	2.508	0.013a	0.934	0.351
Primates	intercept	0.135	0.053	2.523	0.012a
	slope	0.948	0.232	4.081	<0.001a	0.224	0.823
Rodentia	intercept	−0.007	0.029	−0.256	0.798
	slope	1.705	0.222	7.687	<0.001a	3.176	0.002a

^a Statistically significantly different from either 0 or 1

4. Discussion

Across orders, we found a positive and mainly consistent relation between standard deviation in body mass and mean body mass—as would be expected, larger species tend to vary more inter-individually in absolute terms. Moreover, we did not find evidence in these regressions to suggest that the relationship between standard deviation and mean body mass statistically differs from unity within either sex in any of the orders, except for one case—the slope estimate for Eulipotyphla was substantially greater in both males and females than for the other orders; however, it was statistically greater than 1 in the males only (figures 1a,b and 2). At least for the other orders, then, arguably the parsimonious interpretation is that the scaling of variation to size is close to unity for both sexes. This is further clarified in a plot of the coefficient of variance (CV; calculated as s.d./mean) against body mass, where all best fit lines are statistically flat (figure 1c,d).

Figure 2.

Standard deviation (s.d.) of body mass (log₁₀ transformed) against mean body mass (log₁₀ transformed) separately for six mammalian orders. The data are disaggregated by sex (blue, male; red, female). Each data point represents values for a unique species. Linear lines of best fit are applied to each taxonomic order and account for phylogenetic relatedness between species. The line of unity is presented (grey dash).

In five of those orders, most species exhibit GMV and sexual size dimorphism favouring males. In one order (Chiroptera—the bats), GFV predominates, alongside larger females. Historically, there has been a focus on mammalian species where males engage in physical competition and thus are typically larger than females [1,2]. As Tombak et al. [18] show, however, males are not always the larger sex. Our data suggest that, rather than body size variability being related to sex per se it is more consistently related to sex differences in body size. We urge that arguments about GMV reflecting intrinsic sex differences should be made cautiously, as GMV could reflect simply size differences for the trait in question. Of course, sexual selection often results in larger or more elaborate traits in males and thus produces GMV, but here GMV could be parsimoniously explained by trait size.

However, the body mass range of mammals, even within orders, is considerable and could serve to mask differences between those orders in terms of variability–mass relationships. Analysing regressions of the ratio of standard deviation in body mass of males and females (GMV and GFV) against the ratio of mean body mass of males and females (sexual size dimorphism) removes the effect of differing body mass between species. In this analysis, not only did we find a positive overall relation between sex differences in body size variability and sex differences in body size, but also an overall slope value statistically greater than 1. At the order level, two groups—Chiroptera and Rodentia—had slope values that were statistically greater than 1 (figure 3). These hyperallometric slopes suggest that GMV and GFV are sometimes driven by other factors alongside sexual size dimorphism in favour of males and females, respectively.

Figure 3.

Greater female variance (negative y-axis values) and greater male variance (positive y-axis values) against sexual size dimorphism in body mass (negative x-axis values represent sexual size dimorphism in favour of females while positive values represent sexual size dimorphism in favour of males). Each data point represents a log₁₀ transformed raw value for a unique species. Linear lines of best fit are applied to each taxonomic order and are estimates from a model that accounts for phylogenetic relatedness between species and includes sexual size dimorphism centred at 0. The line of unity is presented (grey dash).

What factor(s) could these be? For example, larger-bodied species may be under greater directional selection, and greater directional selection is expected to be associated with greater additive genetic variation [22]. Alternatively, [23] suggested that stabilizing selection in smaller species for key organs (e.g. heart) that are a substantial proportion of overall body size would result in lower body mass variation. For larger species, these organs are proportionately smaller and thus other body components (e.g. fat, muscle, skeleton) that are more independent of overall body size contribute to higher variation in these species. A third possibility is that the investment of resources in the development and maintenance of larger size could result in trade-offs whereby larger size compromises other systems such as those that support immunocompetence, which could affect size development (e.g. skeletal) that in turn would more strongly influence variation in larger than smaller species. Indeed, in most mammals, the larger sex has higher parasite loads than the smaller sex [17].

The slope intercept values for the regressions of GMV or GFV against sexual size dimorphism are also worth interrogating. In four of the orders studied—Carnivora, Chiroptera, Eulipotyphla and Rodentia—the y-intercept of the relationship between GMV and sexual size dimorphism is not significantly different from 0 (table 1). That is, there is a lack of evidence that for the theoretical scenario of the two sexes being the same size, body size variability between the two sexes differs. In contrast, for the Primates and especially the Artiodactyla, the model predicts that males will be more variable in body size than females when the sexes are the same size. This is apparent upon inspection of figure 2 for Artiodactyla, where the best-fit line for males is above that for females at all body masses on a logged y-axis scale. This suggests that variation in males is greater than in females for the same body size and therefore that there is an additional factor over and above body size difference influencing male physical development in these species. Monogamy is common in mammals where males and females are similar in size, but males often have larger ranges (e.g. related to mate search) that could increase energy demands and parasite exposure, especially for the comparatively large Artiodactyla and Primate orders, perhaps resulting in GMV. In some cases, males and females are similar in size (e.g. Damaliscus pygargus phillipsi) but males, especially in Artiodactyla, may still engage in rigorous male–male competition that would result in GMV due to the health costs of this competition.

From heterogamety [9] and the oestrus cycle [6] to sexual selection [24] and amplification of genetic effects [25], a plethora of theories abound to explain GMV and GFV. We find evidence in all the mammalian orders we studied for the most parsimonious explanation, that bigger individuals exhibit more variation among each other, and this can be explained by the mathematical proportional relationship between size and variation. GMV and GFV appear to be more consistently related to sex differences in trait size than to sex per se. Nonetheless, our analyses hint that other biological processes sometimes also cause differing variation between the sexes. Valuable future work would explore the level of consistency of relationships between variance and a range of aspects of gross morphology, and beyond the class Mammalia.

Ethics

This work did not require ethical approval from a human subject or animal welfare committee.

Data accessibility

Data available from the Dryad Digital Repository [26].

Declaration of AI use

We have not used AI-assisted technologies in creating this article.

Authors’ contributions

L.G.H.: conceptualization, data curation, formal analysis, investigation, methodology, project administration, validation, visualization, writing—original draft, writing—review and editing; D.G.: data curation, formal analysis, writing—review and editing; D.C.G.: conceptualization, methodology, writing—original draft, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

No funding has been received for this article.