Open Access

Sexual size dimorphism in ground squirrels (Rodentia: Sciuridae: Marmotini) does not correlate with body size and sociality

Contributed equally
Frontiers in Zoology201310:27

https://doi.org/10.1186/1742-9994-10-27

Received: 11 March 2012

Accepted: 7 May 2013

Published: 14 May 2013

Abstract

Introduction

Sexual size dimorphism (SSD) is a widespread phenomenon in animals including mammals. It has been demonstrated that across species, the direction and magnitude of sexual dimorphism in body size often corresponds to social systems. Moreover, many animal lineages conform to “Rensch’s rule”, which states that male-biased SSD increases with body size. We tested whether considerable differences in sociality and large variation in body size were connected with the evolution of SSD in the structural body size of ground squirrels, an otherwise ecologically relatively homogenous group of terrestrial rodents.

Results

We found the general trend of male-biased SSD in ground squirrels, however, male size increases nearly perfectly isometrically with female size among species and sociality does not explain departures from this relationship. Species with different sociality grades significantly differ in body size, with the most social species tending to be the largest.

Conclusions

We suggest that lack of conformity with Rensch´s rule in ground squirrels may be attributed to their low variation in SSD, and briefly discuss three potential causes of small magnitude of SSD in the structural size in rodents: low selection on SSD in structural dimensions, ontogenetic and genetic constraints and the existence of ecological/selection factors preventing the evolution of extensive SSD.

Keywords

AllometryConstraints Cynomys Marmota Phylogenetic comparative studySocial system Spermophilus

Introduction

Sexual size dimorphism - a difference in size between males and females, is a widespread phenomenon in animals [1]; recently reviewed in [2]. The evolution of sexual size dimorphism (SSD) is usually ascribed to different selection pressures (natural or sexual selection) operating in males and females. Male-biased SSD is predominantly attributed to intense intrasexual competition in males [1, 3], as is supported by the correlation between SSD and social or mating systems in several mammalian lineages, e.g. [46], as well as in mammals in general [3]. Nevertheless, the extent of SSD does not depend exclusively on male size, but it is a function of both male and female size and SSD often scales with body size. An allometric relationship between SSD and body size has been documented in a wide array of animals at various taxonomical levels, and is described by the so-called “Rensch´s rule”. This empirical rule states that male-biased SSD tends to increase with increasing body size among related species [7]. Consequently, male size increases positively allometrically with female size and males are more evolutionary plastic in body size than females [2] and references therein, [810]. This rule holds across the whole mammalian clade, and is followed by some, but not all, mammalian orders [3].

Although male-biased SSD generally predominates among mammals, the review of sexual dimorphism among rodents indicates that monomorphism, male-biased and female-biased SSD is typical for particular rodent lineages [11]. It is of particular interest that rodents do not conform to Rensch´s rule, although they possess a wide range of body sizes and extensive variability in social systems. The recent analysis was based on data covering nearly 300 species, and thus the lack of conformity with Rensch´s rule could certainly not be attributed to small sample size [3]. However, it was speculated that these results may have been biased by the more extensive coverage of larger species in the dataset [3]. Moreover, the inclusion of species with different morphology, ecology and phylogenetic position into a single comparison may contribute to this pattern. Therefore, we decided to perform an analysis of SSD scaling on a new original dataset restricted to ground squirrels forming a rodent tribe that displays a wide range of body size and large diversity in social systems, yet are still similar in other aspects of their general biology.

Ground squirrels (tribe Marmotini Pocock, 1923; see [12]) are a monophyletic group within the family Sciuridae [13, 14]. Ground squirrels occupy mostly open habitats of North America and Eurasia [15], are diurnal, omnivorous, reproduce usually once a year and all are semi-fossorial [15, 16]. Members of the tribe display diverse social systems, from polygyny (a single male monopolizes multiple females), to promiscuity, where male success largely depends on scramble competition [17, 18]. We can thus expect that the strength of sexual selection on male body size is different among particular species.

Specifically, we tested whether the allometry of SSD among ground squirrels corresponds to Rensch´s rule and whether different levels of sociality, taken as a presumable correlate of the magnitude of sexual selection on male body size, correlates with SSD and the body size pattern.

Results

The two expressions of structural body size (condylo-basal length of the skull, CBL, and hind foot length, HFL) were highly correlated with each other across species (Pearson’s product–moment correlation of species means, r > 0.975, p < 0.0001, n = 63 for both males and females), but due to differences in body proportions among species, they exhibited somewhat different distributions (cf. Figure 1a, b). Although ground squirrels exhibit large variation in body size (Figure 1) and sociality, our comparison of male and female body size measurements revealed only limited variation in SSD. A significant presence of SSD among ground squirrels was found in 38% of included species based on CBL and in only 24% based on HFL (Table 1). Wherever significant, SSD proved to be male-biased, males being maximally around 8% larger in CBL and 14% larger in HFL. Estimations of SSD expressed as ratios of male to female mean CBL and HFL were correlated among species (Pearson’s product–moment correlation, r = 0.44, p < 0.001, n = 63). Both these estimations do not significantly depart from normal distribution (Kolmogorov-Smirnov tests not significant) with means 1.026 ± 0.003 (S.E.) for CBL ratio and 1.037 ± 0.005 for HFL ratio. The linear regression of log-transformed species means of male CBL on log-transformed species means of female CBL accounted for a large proportion of the variation (r2 = 0.997, F = 20296.75, p < 0.0001, n = 63) and showed a nearly perfectly isometric increase between male and female size across species (slope 1.008 ± 0.007 (means ± S.E. are given), 95%-CI 0.994 - 1.022; intercept n.s.; Figure 1a). Nearly identical results were found for log-transformed maximal CBL (proportion of explained variation by linear regression r2 = 0.994, F = 10241.77, p < 0.0001, n = 63; slope 1.014 ± 0.010, 95%-CI 0.994 - 1.034) and log-transformed mean HFL (r2 = 0.992, F = 7268.03, p < 0.0001, n = 63; slope 1.026 ± 0.012, 95%-CI 0.999 - 1.050; Figure 1b). In the case of log-transformed maximal HFL, linear regression (r2 = 0.986, F = 2105.32, p < 0.0001, n = 63) revealed a slight but significant departure from isometry (slope 1.058 ± 0.023 (S.E.), 95%-CI 1.012 - 1.105) caused by the single influential outlier, Marmota vancouverensis, one of the largest species. The high value of maximal HFL for males of this species was caused by a single individual with unusually long feet. We suggest that mean species values are less sensitive to such outlying individuals with extreme measurements, and we use them henceforth as more reliable expressions of size.
Figure 1

Mean male body size increases isometrically with mean female body size among species of ground squirrels. a) condylobasal length, b) hind foot length. Ordinary least-square regression (solid lines) and 1:1 relationship (dashed lines) are shown.

Table 1

Sociality and body size, measured as hind foot length (HFL) and condylobasal length (CBL) in males and females of 63 species of ground squirrels and the tests of sexual size dimorphism within species

Species

Sociality

HFL

CBL

References to sociality grade

  

n(M,F)

M/F ratio

F

p

n(M,F)

M/F ratio

F

p

 

Ammospermophilus harrisii

1

6,6

1.044

2.500

0.145

6,6

0.990

0.678

0.429

[19]

Ammospermophilus insularis

1

6,4

0.985

0.419

0.535

6,4

1.048

4.852

0.059

[20]

Ammospermophilus interpres

1

6,6

1.007

0.117

0.740

6,6

1.000

0.002

0.969

[21]

Ammospermophilus leucurus

1

6,6

1.020

0.636

0.444

6,6

1.023

2.183

0.170

[22]

Ammospermophilus nelsoni

 

6,6

1.042

4.032

0.072

6,6

1.012

1.556

0.241

 

Callospermophilus lateralis

1

15,15

0.982

1.013

0.323

15,15

0.995

0.251

0.620

[18]

Callospermophilus madrensis

1

3,5

1.010

0.346

0.578

3,5

0.990

0.136

0.725

[23]

Callospermophilus saturatus

1

15,15

1.027

3.944

0.057

15,15

1.037

11.526

0.002**

[23]

Cynomys gunnisoni

4

16,14

1.024

3.416

0.075

16,14

1.036

13.928

0.001**

[18]

Cynomys leucurus

2

14,15

1.011

0.118

0.734

15,15

1.038

22.521

<0.001***

[18]

Cynomys ludovicianus

5

15,15

1.038

7.591

0.010*

15,15

1.024

7.640

0.010*

[18]

Cynomys mexicanus

5

5,7

0.979

0.117

0.740

5,7

1.020

2.591

0.139

[24]

Cynomys parvidens

4

15,10

1.064

4.136

0.054

15,10

1.064

44.093

<0.001***

[25, 26]

Ictidomys mexicanus

 

9,11

1.041

2.958

0.103

9,11

1.012

0.203

0.658

 

Ictidomys parvidens

 

7,7

1.048

2.101

0.173

7,7

1.036

5.986

0.031*

 

Ictidomys tridecemlineatus

2

15,15

1.055

9.068

0.005**

15,15

1.013

1.074

0.309

[18]

Marmota baibacina

5

9,4

1.089

2.595

0.136

10,5

1.020

0.691

0.421

[27]

Marmota bobac

5

15,9

1.093

15.947

0.001**

15,11

1.033

4.604

0.042*

[27]

Marmota broweri

5

1,2

1.080

16.333

0.154

5,6

1.020

0.557

0.475

[27]

Marmota caligata

5

14,14

1.039

3.032

0.093

15,15

1.024

2.168

0.152

[27]

Marmota camtschatica

5

7,9

1.084

5.059

0.041*

15,17

1.024

2.018

0.166

[27]

Marmota caudata

5

12,8

0.978

4.136

0.054

15,15

1.023

0.974

0.332

[27]

Marmota flaviventris

4

22,23

1.066

10.125

0.003**

24,24

1.065

21.606

<0.001***

[17]

Marmota himalayana

5

4,3

1.140

5.560

0.065

14,10

1.029

2.236

0.149

[27]

Marmota marmota

5

12,6

0.978

0.644

0.434

17,10

1.007

0.240

0.628

[27]

Marmota menzbieri

5

1,2

1.028

0.870

0.522

3,3

1.023

2.638

0.180

[27]

Marmota monax

1

15,15

1.029

1.551

0.223

15,15

1.004

0.091

0.765

[17, 27]

Marmota olympus

5

3,5

1.120

4.903

0.069

7,6

1.061

14.770

0.003**

[17, 18, 27]

Marmota sibirica

5

5,5

1.107

3.974

0.081

16,16

1.060

18.914

<0.001***

[27]

Marmota vancouverensis

5

3,4

1.081

0.358

0.576

5,4

1.002

0.008

0.931

[27]

Notocitellus adocetus

 

9,7

1.026

1.553

0.233

9,7

1.014

0.581

0.459

 

Notocitellus annulatus

 

14,13

1.018

4.136

0.054

14,13

1.004

0.091

0.766

 

Otospermophilus beecheyi

2

15,15

1.074

17.659

<0.001***

15,15

1.064

12.426

0.001*

[17]

Otospermophilus atricapillus

 

8,10

1.028

1.897

0.187

8,10

1.021

1.021

0.327

 

Otospermophilus variegatus

3

14,15

1.028

2.446

0.129

14,15

1.022

3.951

0.057

[28]

Poliocitellus franklinii

1

15,15

1.056

7.736

0.010*

15,15

1.016

2.081

0.160

[18]

Spermophilus alashanicus

 

1,5

1.038

0.340

0.591

2,5

1.059

3.545

0.118

 

Spermophilus citellus

2

15,15

1.010

0.126

0.725

17,16

1.028

3.492

0.071

J. Matějů, own data

Spermophilus dauricus

 

16,15

1.051

5.067

0.032*

16,15

1.022

2.421

0.131

 

Spermophilus erythrogenys

 

15,15

1.044

5.067

0.032*

16,15

1.073

32.773

<0.001***

 

Spermophilus fulvus

3

5,9

1.029

0.336

0.573

17,15

1.032

5.431

0.027*

[29, 30]

Spermophilus major

 

15,16

1.073

4.785

0.037*

15,16

1.053

9.868

0.004**

 

Spermophilus musicus

 

16,14

1.045

2.729

0.110

16,15

1.042

9.784

0.004**

 

Spermophilus pygmaeus

2

16,15

1.073

12.634

0.001**

16,15

1.035

8.442

0.007**

[31], A.V. Tchabovsky pers. comm

Spermophilus relictus

 

6,13

0.982

0.273

0.608

6,13

0.995

0.052

0.822

 

Spermophilus suslicus

2

16,15

1.060

7.928

0.009**

16,15

1.015

0.661

0.423

A.V. Tchabovsky pers. comm.

Spermophilus xanthoprymnus

2

11,11

1.061

3.615

0.072

11,11

1.046

5.715

0.027*

[32, 33], V. Vohralík pers. comm.

Urocitellus washingtoni

 

15,15

1.038

4.395

0.045*

15,15

1.039

13.177

0.001**

 

Urocitellus armatus

2

15,15

1.014

1.101

0.303

15,15

1.021

1.868

0.183

[18]

Urocitellus beldingi

2

15,15

1.011

0.527

0.474

15,15

1.015

2.501

0.125

[18]

Urocitellus brunneus

 

7,3

1.044

1.434

0.265

7,3

1.065

11.068

0.010*

 

Urocitellus cannus

2

15,15

1.015

0.429

0.518

15,15

1.011

0.794

0.381

[17, 18]

Urocitellus columbianus

3

15,15

1.008

0.208

0.652

15,15

1.029

3.526

0.071

[18]

Urocitellus elegans

2

15,15

1.029

2.454

0.128

15,15

1.033

7.597

0.010*

[18]

Urocitellus mollis

2

15,15

1.028

1.620

0.214

15,15

1.008

0.304

0.586

[17, 18]

Urocitellus parryii

3

15,15

1.000

0.000

1.000

15,15

1.037

14.354

0.001**

[18]

Urocitellus richardsonii

2

15,15

1.073

20.956

<0.001***

15,15

1.036

7.284

0.012*

[18]

Urocitellus townsendii

2

15,12

0.993

0.629

0.472

15,12

0.986

1.658

0.210

[17, 18]

Urocitellus undulatus

 

15,18

1.040

5.592

0.024*

15,18

1.038

13.657

0.001**

 

Xerospermophilus mohavensis

1

4,2

1.036

0.629

0.472

5,6

1.008

0.757

0.407

[34]

Xerospermophilus perotensis

 

8,5

1.012

0.939

0.353

8,5

1.019

3.831

0.076

 

Xerospermophilus spilosoma

 

15,15

1.030

3.811

0.061

15,15

1.027

6.995

0.013*

 

Xerospermophilus tereticaudus

2

15,15

0.995

0.137

0.714

16,18

1.009

1.316

0.260

[18]

* p < 0.05, ** p < 0.01, *** p < 0.001.

Sociality does not significantly explain departures of mean male CBL from the common relationship with mean female CBL across species, and generally explains only a minor proportion of the total variability (ANCOVA: mean male CBL as continuous dependent variable; mean female CBL as a continuous independent variable: F1,40 = 5304.68, p < 0.0001, sociality coded as five grades as categorical independent variable: F4,40 = 2.05, p = 0.11). The results of the ANCOVA model for mean HFL as a proxy of body size were congruent with this conclusion (mean male HFL as dependent continuous variable, mean female HFL: F1,40 = 828.28, p < 0.0001, sociality: F4,40 = 0.37, p = 0.83).

Nevertheless, species with different sociality grades significantly differ in body size, with the most social species tending to be the largest (one-way ANOVA of mean male CBL, factor sociality: F4,41 = 29.03, p < 0.0001; Figure 2; the results for female mean CBL and male and female mean HFL are practically identical). The results do not differ when sociality is coded as 0–1 dummy variable (not shown).
Figure 2

Body size tends to increase with sociality among species of ground squirrels. Results of one-way ANOVA of male condylobasal length results are shown as means and 95-% confidence intervals.

Phylogenetically-informed analyses confirmed that the results and their interpretations cannot be explained by a bias caused by shared ancestry. Pagel´s λ estimated in the phylogenetic generalized least squares (PGLS) regression of log-transformed mean male CBL on log-transformed mean female CBL is very low (0.07) and close to 0.0, which indicates that the effect of phylogeny on the allometry of SSD expressed in CBL is minimal. This conclusion is supported by the result of the likelihood ratio (LR) test showing that the PGLS models with λ restricted to 0.0 (equivalent to the ordinary least squares regression based on raw data) and with λ = 0.07 are statistically indistinguishable (LR1 = 0.32, p = 0.57). The analyses of independent contrasts, although not supported by the PGLS regression as adequate, also support the isometric increase of log-transformed male CBL with log-transformed mean female CBL (not shown). On the other hand, the effect of phylogeny is significant in the allometry of SSD based on HFL measurements, where λ estimated by maximum likelihood in the PGLS model is 0.67. The LH test confirmed significant differences between the fits of the PGLS models with λ = 0.67 and λ = 0.0 (LR1 = 4.06, p = 0.044). The fits of the PGLS models with λ = 0.67 and λ = 1.0, equivalent to phylogenetic independent contrasts, are not statistically different (LR1 = 1.68, p = 0.19). Independent contrasts in log-transformed mean male HFL and log-transformed mean female HFL scales isometrically (r2 = 0.960, slope 0.965 ± 0.050 is not different from 1.0 expected under isometry, n = 62 contrasts), which proves isometric scaling of male and female size in HFL as well.

Comparisons of the fits of the nested PGLS models with and without sociality as a predictor confirmed that addition of sociality into the models does not increase their explanatory power. The fit of the multivariate PGLS model of log-transformed mean male CBL on log-transformed mean female CBL and sociality coded as the five grades is not statistically different from the model after dropping of the predictor sociality (LH1 = 0.44, p = 0.51). The same is true for sociality coded as the 0-1dummy variable (LH1 = 1.44, p = 0.23). The situation for the models based on log-transformed HFL measurements is equivalent (sociality coded as five grades: LH1 = 0.14, p= 0.71; sociality coded as 0–1: LH1 = 0.02 p = 0.89). Non-significance of the factor sociality was found also in the multiple regression of independent contrasts (not shown). Estimates of Pagel´s λ were large (between 0.78 and 1.0) in all PGLS models describing association of log-transformed CBL and HFL with sociality coded either as five grades or a 0–1 dummy variable for males and females, respectively, showing a significant influence of phylogenetic relationships on the correlation between body size and sociality. The LH tests confirmed that these PGLS models are not significantly different from the respective models with λ restricted to 1.0 equivalent to phylogenetic independent contrasts (all p > 0.15). The analyses of phylogenetic contrasts confirmed significant correlations between log-transformed mean CBL and mean HFL in males and females and sociality coded as five grades and 0–1, respectively (all r > 0.39, p < 0.05, n = 45 contrasts).

Exclusion of seven species (Ammospermophilus insularis, Callospermophilus madrensis, Marmota menzbieri, Marmota vancouverensis, Urocitellus brunneus and Spermophilus alashanicus) with sample size less than five individuals for at least one sex in CBL does not change significance of any results and the major interpretations are thus robust with respect to inclusion of these species with small sample size.

Discussion

Our results revealed only limited variation in SSD in two measurements representing different aspects of structural body size among ground squirrels, although we stress that the lack of significant SSD in some species can be attributed to small sample size. This variability in SSD cannot be explained by either of the two commonly reported correlates of SSD, i.e. body size and social system. Ground squirrels thus do not conform to Rensch’s rule, in contrast to the general trend in mammals [3]. Our results, based on an original morphometric dataset covering most species in a monophyletic group with similar general biology, are thus in line with a previous report showing similar results in rodents [3]. Rensch´s rule is usually not followed in groups with female-biased SSD [3537]. Here, we report that it is not followed in a mammalian group with predominantly male-biased SSD.

We suggest that the limited extent of SSD in structural body size and the lack of the support for Rensch´s rule in ground squirrels could be generally explained by three possible scenarios: i) low selection on SSD in structural dimensions, ii) ontogenetic and genetic constraints or iii) the existence of ecological/selection factors preventing the evolution of extensive SSD.

Male-biased SSD, typical for mammals, is usually associated with sexual selection on body size enlargement that correlates with success in female monopolization. Reiss [38] argued that the relationship between body size and SSD found in some mammalian lineages can be largely explained by the co-variation of mating systems with body size: larger species have a larger opportunity for polygyny and thus stronger selection for male size increases leading to male-biased SSD. The pattern consistent with Rensch´s rule driven probably by sexual selection in males has also been found in other animal groups, i.e. shorebirds [39]. In ground squirrels, social organization changes with body size. Small species are typically less social and hence presumably more promiscuous [18], while the more social larger species probably exhibit larger selective pressure on female monopolization and hence body size enlargement in males. This is also evident in marmots, the largest species of ground squirrels, where polygyny or facultative monogamy is based on active female-defence [18]. A correspondence between social grade and sexual selection on male size enlargement in ground squirrels is supported by single-species studies. For instance, success in male-male combat over females is positively related to male body size in Urocitellus parryii[40], where territorial males are associated with female kin clusters (social grade 3; [18]). Similarly, larger males of most Cynomys species (grades 3–5) are more successful in securing breeding territories and sire more offspring [41]. On the other hand, selection pressure towards smaller male body size was observed in the low social (grade 2) promiscuous Ictidomys tridecemlineatus, where males are selected for maneuverability and early sexual maturation [42].

In summary, selection for male body size enlargement should increase with increased sociality and body size in ground squirrels, which should lead to a pattern consistent with Rench’s rule. We can thus tentatively conclude that differences in sexual selection among ground squirrels, although associated with body size variation, do not lead to conformity with Rensch´s rule. The support for Rensch´s rule across breeds of domestic mammals suggests that the allometry for SSD could be a more general consequence of body size evolution caused by different selective agents [43, 44]. Nevertheless, ground squirrels do not follow the rule although they have large variation in body size. We suggest that this state can be explained by the limited extent of SSD in this rodent group.

Limited SSD could reflect ontogenetic or genetic constraints, an idea going back to Charles R. Darwin [1], see also e.g. [45, 46]. It is notable that a generally low degree of SSD in structural body size has been reported for rodents [11], although they inhabit a wide variety of habitats and possess various social systems. Nevertheless, it is not clear why rodents should have, for instance, a stronger intersexual genetic correlation in body size than other animal groups. Moreover, the existence of SSD (although with limited magnitude) in some species of ground squirrels suggest that there is sufficient genetic variation for SSD and that this trait should thus be subject to evolution.

Alternatively, selection may operate on male and female structural size independently, males being shaped by sexual selection and females by fecundity selection, but the optimal size for both sexes can be similar. In most ground squirrel species, female reproductive success (litter size, progeny survival) is positively related to body size [41, 4749]. Selection pressure towards larger female body size may contribute to low SSD in ground squirrels; however, it is not clear why male and females of species differing in body size and thus the energetics of growth and reproduction, and also having different mating or social systems, should always have a similar optimal body size.

It is also possible that there is selection for an increase of SSD in structural size, but that this pressure is counterbalanced by other selective pressures constraining its extent and resulting in both sexes having a similar, optimal structural body size. One potential limiting factor for large differences in such SSD is the subterranean environment. Both male and female ground squirrels occupy underground burrows, which they often share for mating, shelter e.g. [50, 51] and even hibernation in some marmot species [16, 50]. The disadvantage of significant male and female body size differences in this case is apparent – large animals can suffer locomotion difficulties in tunnels made by smaller individuals. This hypothesis makes a straightforward prediction that SSD should be larger in species where both sexes do not share common underground tunnels, which could be tested in future comparative analyses.

It is necessary to stress that the limited extent of SSD in ground squirrels may only be restricted to structural size measurements. Sexual differences in ground squirrel body mass are often more pronounced (for reviews see [11, 52]). For example, seasonally variable sexual body mass dimorphism was found in Utah prairie dogs (Cynomys parvidens) where the M:F ratio varies across seasons between 0.99 and even 1.53 [41]. Part of this large range in body mass SSD can be attributed to the fact that body mass increases approximately with the third power of length measurements. Nevertheless, the SSD index for mean CBL in this species is only around 1.06, which predicts that males should be only 20% heavier than females. It is evident that SSD in body mass reflects not only differences in structural body size, but also different allocations of males and females to fat reserves or musculature and different energetic consequences of reproduction.

Although SSD in structural body size is not associated with body size and sociality, sociality and body size proved to be highly correlated (Figure 2). Solitary and gregarious species (grades 1 and 2) tend to be small, while especially polygynous and/or monogamous species living in stable family groups (grade 5) are large. The ultimate explanations of the evolution of social living in ground squirrels may be anti-predator behaviour and the male protection of offspring against infanticide [18]. Correlation between sociality and body size in ground squirrels can be proximately explained by longer postnatal growth and development in large species, which leads to the longer retention of offspring within the maternal home range [17] and a large coincidence of above-ground activity between adult and immature cohorts [18], hence allowing a longer time for the building of social contacts.

Conclusions

The analyses of our original dataset confirmed low SSD in the structural dimensions of ground squirrels, a group with variable social systems and large variation in body size. We also found that male and female body structural sizes increase nearly perfectly isometrically, and that the group does not follow the otherwise widely applicable Rensch´s rule. Negative results are more difficult to explain than positive findings; however, we suggest that the lack of conformity with Rensch´s rule in ground squirrels may be attributed to the generally low variation of SSD in structural size in rodents, a phenomenon that deserves further comparative work.

Material and methods

We measured CBL in 1527 specimens from museum collections. Our material covers 63 out of 68 species of ground squirrels recently recognized in the tribe Marmotini sensu [12]; for the number of species see [53]. Only adult, undamaged and located specimens (modus 15 per sex-species category) were examined. Adults were identified according to the degree of teeth abrasion or stage (adult/juvenile) was obtained directly from specimen tags. Our dataset can be biased by geographic intraspecific variability in body size documented in ground squirrels [54]. Nevertheless, taking into account the large variability in body size across species of the studied group, we expect that intraspecific variability does not largely influence the interspecific pattern. Moreover, only individuals determined as a same subspecies and/or collected within a restricted geographic area were measured in most species. Four Spermophilus species (S. ralli, S. pallidicauda, S. taurensis and S. brevicauda) and Marmota kastschenkoi were not included into our study, as we were not able to obtain enough specimens. All CBL measurements were taken by a single person (JM). Data on HFL for adult males and females of each species were taken from museum tags (in total available in 1392 specimens, Table 1).

Body mass is often used as a measure of body size in the SSD literature, including [3]. Nevertheless, body mass is not a good expression of body size in ground squirrels [54], because many species considerably fluctuate in body mass throughout the year. For instance, data on body mass before and after hibernation are highly different e.g. [55] and are not comparable to body mass in less seasonal species. Our measurements, CBL and HFL, represent the structural component of size that is less dependent on body conditions. Moreover, it is known that HFL in rodents is among those external measurements that reach their final size very early during postnatal ontogeny e.g. [56, 57]. There is not a single perfect measurement expressing general body size (see e.g. [58]) and most body measurements use to be highly intercorrelated in morphometric analyses. For example, skull measurements are highly correlated with each other in ground squirrels [54]. To avoid this problem, we selected CBL and HFL, because they reflect size of very different body parts, although due to large variability in body size among ground squirrels, we can a priori expect that these measures will be highly correlated across all species included (we tested the correlation by Pearson test for males and females separately).

The data on social organization were obtained in two ways. Most of information was taken from literature concerning ground squirrel sociality [17, 18, 27]. Second, the level of sociality was classified using publications on general biology (see Table 1 for particular references) or our personal knowledge of the species biology (S. citellus). In this way, sociality was particularly assessed for the genus Ammospermophilus, species Callospermophilus madrensis, C. saturatus, Cynomys mexicanus, C. parvidens, Otospermophilus variegatus, Spermophilus citellus, S. suslicus, S. pygmaeus, S. fulvus, S. xanthoprymnus and Xerospermophilus mohavensis. Moreover, in the case of mentioned Palaearctic species, the social grades assignment was consulted with A. V. Tchabovski (N. A. Severtsov Institute of Ecology and Evolution, Russian Academy of Sciences) and V. Vohralík (Faculty of Science, Charles University in Prague). In classifying the species social grades, we especially consider descriptions of inter-individual contacts, age of first reproduction, age of dispersal, character of dispersal and density of individuals (see [17] documenting correlation of sociality and the mentioned variables).

Species were classified into five categories representing different levels of sociality defined by [18]: 1 – asocial, 2 – single-family female kin clusters, 3 – female kin clusters with a territorial male, 4 – polygynous harems with male dominance, 5 – egalitarian polygynous harems. Facultative monogamy, known in some marmots, was included in the last category, as it is usually interpreted as an extreme case of polygyny where males are unable to monopolize more than one female under harsh environmental conditions ([59] and references therein). In cases of transient classification (i.e. level 1 – 2 in Urocitellus townsendii, Ictidomys tridecemlineatus, and 2 – 3 in Otospermophilus beecheyii) of species sociality in [18], we adopted the social grades of [17]. Despite extensive literature search we were not able to obtain or estimate data about sociality in 17 species from our morphological dataset. These species are thus not included into the analyses concerning effects of sociality. The sociality scale in ground squirrels forms a continuum from the least social (grade 1) to the most social (grade 5) organization; species placed into same category have similar but not always identical social system [18]. Throughout this work, we assume that these social grades reflect the strength of sexual selection on males. However, we are aware that social systems are not always necessary surrogates for mating systems, e.g. [60]. We summarized information about species mating systems as well, but primary data for the group are scarce and frequently in contradiction, for a review see [59]. Moreover, the definition of the polygynous mating system is disputable in rodents [59].

The significance of SSD in a given species was tested by one-way ANOVAs. We expressed SSD as ratios of male to female mean CBL and HFL and tested whether the SSD estimation from CBL and HFL are correlated across species by Pearson´s product–moment correlation. We also tested whether these SSD indexes follow normal distribution across species by Kolmogorov-Smirnov test. Ordinary least square regression of log-transformed mean or maximal size measurements in males on log-transformed mean or maximal size measurements in females was used for testing the allometry of SSD and hence Rensch´s rule. Slope 1.0 was expected under isometric increase of male size with female size. The ANCOVA models with size measurements in males as the dependent continuous variable, size measurements in females as the continuous independent variable and degree of sociality as the independent categorical variable were used to test the relationship between SSD and sociality among species. We tested the effect of sociality on species body size by one-way ANOVAs with male, respectively female body size measurements as dependent variable and sociality as factor.

Because species data are not independent, we performed analyses that take the phylogenetic relationship among species into account as well, specifically, the analyses of phylogenetic independent contrasts and PGLS [6163]. We used the topology of the tribe published recently by [14]. Three species (U. cannus, U. mollis and A. nelsoni) are missing in their tree. We took the position of U. cannus and U. mollis from [13]. A. nelsoni is considered to diverged from A. leucurus, following [64], we took it as sister to this species. See the Additional file 1 for the whole composite tree. The branch length estimations for our tree are not available. Nevertheless, simulated studies showed that the independent contrasts method is sufficiently robust to errors in branch lengths [65]. We report results based on arbitrary, equal branch length both in PGLS models and in analyses of phylogenetic independent contrasts. In some cases, the phylogenetic contrasts based on equal branch length did not meet assumptions suggested by [66]. Therefore, in the analyses of independent contrasts, we used Graafen´s branch lengths instead as well, which did not lead to significant correlations between contrasts and branch length [66]. The results of all analyses of phylogenetic independent contrasts computed using either equal or Graafen´s branch lengths were equivalent; therefore, we report only the results for equal branch length.

We used phylogenetic independent contrasts [62] and PGLS models [63, 67] - for recent application, discussion and minute description of the PGLS technique see e.g. [68, 69] - to test for allometry in SSD, association of SSD with sociality and correlation between body size and sociality. In PGLS, the λ parameter is found by maximum likelihood. This parameter potentially varies between 0, indicating no effect of phylogenetic signal, and 1, corresponding to the analysis of independent contrasts where trait variation among species is predicted by phylogeny. Fit of nested PGLS models (models with and without a particular predictor) or PGLS models with and without a parameter restricted to a constant (e.g. λ can be restricted to 0 or 1, estimation of the λ parameter requires 1 degree of freedom) can be compared using a LR test: LRdf = −2 × [Lh (better-fitting model) – Lh (worse-fitting model)], where the best fitting model has the highest log-likelihood (Lh) score. The significance of this difference can be evaluated with a χ2 distribution with degrees of freedom equal to the difference in the number of parameters between the two competing models [63]. We used this approach for comparison of PGLS models with λ estimated by maximum likelihood with the analyses of raw data (λ restricted to 0 in PGLS) or of independent contrasts (λ restricted to 1) to estimate the impact of the phylogenetic signal for a given analysis. Further, we applied this procedure for comparison of PGLS models with and without predictor sociality to test the association of sociality on SSD.

Degree of sociality is an ordered variable. In many cases, an ordered variable represent coarse information about an underlying continuous variable, which is also true in our case [18]. Thus, we used it in PGLS regressions and analysis of independent contrasts as a continuous variable. This approach may lead to increased Type I error largely due to potentially unequal distances between subsequent categories [70]. To control for this potential bias, we also coded sociality as a variable with two levels, that can be used as a dummy variable in regressions. In this approach, we coded sociality grades 1 and 2 as 0, and the grades 3, 4 and 5 as 1. This division is based on the expectation that different social organization should be associated with different potential for female monopolization, which should be connected with the strength of major selective pressure for male body size enlargement. And just the social grades 1–2 and 3–5 differ in the presence of the stable association of males with females.

Because sample size was small for some species, we repeated all analyses after exclusion of species with the sample size in CBL less than 5 for a minority sex.

We used an α level of significance of 0.05.

All analyses were performed in Statistica 10.0 (Stat Soft 2011), the PDAP:PDTREE module [71] within Mesquite 2.75 [72] and Compare vers. 4.6b [73] for independent contrasts and BayesTraits [74] for PGLS models.

Ethical note: The study is based on measurements of museum specimens and does not involve living animals.

Notes

Declarations

Acknowledgement

We are grateful to Linda K. Gordon (National Museum of Natural History, Smithsonian Institution, Washington D.C.), Galina I. Barnova (Zoological Institute of the Russian Academy of Sciences, St. Petersburg), Eileen Westwig (American Museum of Natural History, New York), Barbara Herzig (Museum of Natural History, Vienna), Brandy Jacobsen (Museum of the North, University of Alaska, Fairbanks), Rex Kenner (Cowan Vertebrate Museum, University of British Columbia, Vancouver), Gavin Hanke (Royal British Columbia Museum, Victoria) and Miloš Anděra (National Museum, Prague) for kind help in access to the material. JM thanks to Brian K. Schmidt and Christina A. Gebhard for their hospitality during his stay in Washington D.C. We thank Vladimír Vohralík and Andrey V. Tchabovsky for consultations of species sociality and Vladimír Vohralík, Věra Pavelková-Říčánková and two anonymous reviewers for comments on earlier drafts of the manuscript. JM was supported by the Ministry of Environment of the Czech Republic (project No. SP/2d4/61/08), LK by the Czech Science Foundation (No. 206/09/0895).

Authors’ Affiliations

(1)
Departments of Zoology and Ecology, Faculty of Science, Charles University in Prague
(2)
Karlovy Vary Museum

References

  1. Darwin CR: The descent of man and selection in relation to sex. 1871, London: John MurrayView ArticleGoogle Scholar
  2. Fairbairn DJ, Blanckenhorn WU, Szekely T: Sex, size, and gender roles: evolutionary studies of sexual size dimorphism. 2007, Oxford: Oxford University PressView ArticleGoogle Scholar
  3. Lindenfors P, Gittelman JL, Jones KE: Sexual size dimorphism in mammals. Sex, size, and gender roles: evolutionary studies of sexual size dimorphism. Edited by: Fairbairn DJ, Blanckenhorn WU, Szekely T. 2007, Oxford: Oxford University Press, 16-26.View ArticleGoogle Scholar
  4. Lindenfors P, Tullberg BS: Phylogenetic analyses of primate size evolution: the consequences of sexual selection. Biol J Linn Soc. 1998, 64: 413-447. 10.1111/j.1095-8312.1998.tb00342.x.View ArticleGoogle Scholar
  5. Lindenfors P, Tullberg BS, Biuw M: Phylogenetic analyses of sexual selection and sexual size dimorphism in pinnipeds. Behav Ecol Sociobiol. 2002, 52: 188-193. 10.1007/s00265-002-0507-x.View ArticleGoogle Scholar
  6. Pérez-Barbería FJ, Gordon IJ, Pagel M: The origins of sexual dimorphism in body size in ungulates. Evolution. 2002, 56: 1276-1285.View ArticlePubMedGoogle Scholar
  7. Rensch B: Die Abhängigkeit der relativen Sexualdifferenz von der Körpergrösse. Bonner Zool Beitr. 1950, 1: 58-69.Google Scholar
  8. Fairbairn DJ: Allometry for sexual size dimorphism: pattern and process in the coevolution of body size in males and females. Annu Rev Ecol Syst. 1997, 28: 659-687. 10.1146/annurev.ecolsys.28.1.659.View ArticleGoogle Scholar
  9. Abouheif E, Fairbairn DJ: A comparative analysis of allometry for sexual size dimorphism: assessing Rensch’s rule. Am Nat. 1997, 149: 340-362.View ArticleGoogle Scholar
  10. Starostová Z, Kubička L, Kratochvíl L: Macroevolutionary pattern of sexual size dimorphism in geckos corresponds to intraspecific temperature-induced variation. J Evol Biol. 2010, 23: 670-677. 10.1111/j.1420-9101.2010.01933.x.View ArticlePubMedGoogle Scholar
  11. Shulte-Hostedde AI: Sexual size dimorphism in Rodents. Rodent societies: An ecological and evolutionary perspective. Edited by: Wolff JO, Sherman PW. 2007, Chicago and London: The University of Chicago Press, 115-128.Google Scholar
  12. McKenna MC, Bell SK: Classification of mammals above the species level. 1997, New York: Columbia University PressGoogle Scholar
  13. Herron MD, Castoe TA, Parkinson CL: Sciurid phylogeny and the paraphyly of Holarctic ground squirrels (Spermophilus). Mol Phylogenet Evol. 2004, 31: 1015-1030. 10.1016/j.ympev.2003.09.015.View ArticlePubMedGoogle Scholar
  14. Fabre P-H, Hautier L, Dimitrov D, Douzery EJP: A glimpse on the pattern of rodent diversification: a phylogenetic approach. BMC Evol Biol. 2012, 12: 88-10.1186/1471-2148-12-88.PubMed CentralView ArticlePubMedGoogle Scholar
  15. Nowak RM: Walker’s mammals of the world. 1999, Baltimore and London: The Johns Hopkins University PressGoogle Scholar
  16. Bibikow DI: Die Murmeltiere der Welt. 1996, Heidelberg: Spektrum Akademischer VerlagGoogle Scholar
  17. Armitage KB: Sociality as a life-history tactic of ground squirrels. Oecol. 1981, 48: 36-49. 10.1007/BF00346986.View ArticleGoogle Scholar
  18. Michener GR: Kin identification, matriarchies, and the evolution of sociality in ground-dwelling sciurids. Advances in the Study of Mammalian Behavior. Edited by: Eisenberg JF, Kleiman DG. 1983, Lawrence: American Society of Mammalogists, 528-572. [Special Publication No. 7]Google Scholar
  19. Best TL, Titus AS, Caesar K, Lewis CL:Ammospermophilus harrisii. Mamm Species. 1990, 366: 1-7.Google Scholar
  20. Best TL, Caesar K, Titus AS, Lewis CL:Ammospermophilus insularis. Mamm Species. 1990, 364: 1-4.Google Scholar
  21. Best TL, Lewis CL, Caesar K, Titus AS:Ammospermophilus interpres. Mamm Species. 1990, 365: 1-6.Google Scholar
  22. Belk MC, Smith DH:Ammospermophilus leucurus. Mamm Species. 1991, 368: 1-8.View ArticleGoogle Scholar
  23. Helgen KM, Cole RF, Helgen LE, Wilson DE: Generic revision in the holoarctic ground squirrels genus Spermophilus. J Mamm. 2009, 90: 270-305. 10.1644/07-MAMM-A-309.1.View ArticleGoogle Scholar
  24. Ceballos G, Wilson DE:Cynomys mexicanus. Mamm Species. 1985, 248: 1-3.View ArticleGoogle Scholar
  25. Linzey AV, Rosmarino N, Willson K, Roth E, Hammerson G, Cannings S: Cynomys parvidens. IUCN Red List of Threatened Species. Version 2010.4. 2010, IUCN, [http://www.iucnredlist.org]Google Scholar
  26. Blumstein DT, Armitage KB: Does sociality drive the evolution of communicative complexity? A comparative test with ground-dwelling sciurid alarm calls. Am Nat. 1997, 150: 179-200. 10.1086/286062.View ArticlePubMedGoogle Scholar
  27. Allainé D: Sociality, mating system and reproductive skew in marmots: evidence and hypotheses. Behav Process. 2000, 51: 21-34. 10.1016/S0376-6357(00)00116-9.View ArticleGoogle Scholar
  28. Oaks E, Young PJ, Kirkland GL, Schmidt DF:Spermophilus variegatus. Mamm Species. 1987, 272: 1-8.View ArticleGoogle Scholar
  29. Popov VS: Rol’ social’nyh svjazej v prostranstvennoj strukture poselenija zheltogo suslika. [The role of social relationships in the spatial structure of the colony in the yellow ground squirrel (Spermophilus fulvus Licht. 1823)]. PhD thesis. Moscow State University; 2007Google Scholar
  30. Kucheruk VV, Khlyap LA: Lagomorphs and Rodents of Middle Asia (Zairseobraznye I Gryzuny Sredney Azii). 2005, Moscow: GeosGoogle Scholar
  31. Soldatova AN: Vlijanie plotnosti naselenia na charakter ispolzovanija territorii malym suslikom [Effect of population density on the character of the utilization of home ranges by Citellus pygmaeus Pall.]. Zool Zh. 1962, 41: 913-921.Google Scholar
  32. Kryštufek B, Vohralík V: Mammals of Turkey and Cyprus, Vol. 2, Rodentia I: Sciuridae, Dipodidae, Gliridae, Arvicolinae. 2005, Koper: Science and Research Centre of the Republic of SloveniaGoogle Scholar
  33. Gür MK, Gür H:Spermophilus xanthoprymnus. Mamm Species. 1995, 864: 183-194.Google Scholar
  34. Best TL:Spermophilus mohavensis. Mamm Species. 1995, 509: 1-7.Google Scholar
  35. Webb TJ, Freckleton RP: Only half right: species with female-biased sexual size dimorphism consistently break Rensch's rule. PLoS One. 2007, 2: e897-10.1371/journal.pone.0000897.PubMed CentralView ArticlePubMedGoogle Scholar
  36. Tubaro PL, Bertelli S: Female-biased sexual size dimorphism in tinamous: a comparative test fails to support Rensch's rule. Biol J Linn Soc. 2003, 80: 519-527. 10.1046/j.1095-8312.2003.00252.x.View ArticleGoogle Scholar
  37. Stuart-Fox D: A test of Rensch’s rule in dwarf chameleons (Bradypodion spp.), a group with female-biased sexual size dimorphism. Evol Ecol. 2009, 23: 425-433. 10.1007/s10682-008-9242-8.View ArticleGoogle Scholar
  38. Reiss MJ: Sexual dimorphism in body size: Are larger species more dimorphic?. J Theor Biol. 1986, 121: 163-172. 10.1016/S0022-5193(86)80090-X.View ArticleGoogle Scholar
  39. Székely T, Lislevand T, Figuerola J: Sexual size dimorphism in birds. Sex, size and gender roles. Edited by: Fairbairn D, Székely T, Blackenhorn W. 2007, Oxford: Oxford University Press, 27-37.View ArticleGoogle Scholar
  40. Lacey EA, Wieczorek JR: Territoriality and male reproductive success in arctic ground squirrels. Behav Ecol. 2001, 12: 626-632. 10.1093/beheco/12.5.626.View ArticleGoogle Scholar
  41. Hoogland JL: Sexual dimorphism of prairie dogs. J Mamm. 2003, 84: 1254-1266. 10.1644/BME-008.View ArticleGoogle Scholar
  42. Schwagmeyer PL: Scramble-competition polygyny in an asocial mammal: Male mobility and mating success. Am Nat. 1988, 131: 885-892. 10.1086/284828.View ArticleGoogle Scholar
  43. Polák J, Frynta D: Sexual size dimorphism in domestic goats, sheep, and their wild relatives. Biol J Linn Soc. 2009, 98: 872-883. 10.1111/j.1095-8312.2009.01294.x.View ArticleGoogle Scholar
  44. Frynta D, Baudyšová J, Hradcová P, Faltusová K, Kratochvíl L: Allometry of sexual size dimorphism in domestic dog. PLoS One. 2012, 7: e46125-10.1371/journal.pone.0046125.PubMed CentralView ArticlePubMedGoogle Scholar
  45. Maynard-Smith J: The evolution of sex. 1978, Cambridge: Cambridge University PressGoogle Scholar
  46. Lande R: Sexual dimorphism, sexual selection, and adaptation in polygenic characters. Evolution. 1980, 34: 292-305. 10.2307/2407393.View ArticleGoogle Scholar
  47. Dobson FS, Michener GR: Maternal traits and reproduction in Richardson's ground squirrels. Ecology. 1995, 76: 851-862. 10.2307/1939350.View ArticleGoogle Scholar
  48. Huber S, Millesi E, Walzl M, Dittami J, Arnold W: Reproductive effort and costs of reproduction in female European ground squirrels. Oecologia. 1999, 121: 19-24. 10.1007/s004420050902.View ArticleGoogle Scholar
  49. Sauer JR, Slade NA: Uinta ground squirrel demography: is body mass a better categorical variable than age?. Ecology. 1987, 68: 642-650. 10.2307/1938469.View ArticleGoogle Scholar
  50. Barash D: Marmots: Social behavior and ecology. 1989, Stanford: Stanford University PressGoogle Scholar
  51. Hoogland JL:Cynomys ludovicianus. Mamm Species. 1996, 535: 1-10.View ArticleGoogle Scholar
  52. Hayssen V: Patterns of body and tail length and body mass in Sciuridae. J Mamm. 2008, 89: 852-873. 10.1644/07-MAMM-A-217.1.View ArticleGoogle Scholar
  53. Thorington RW, Koprowski JL, Steele MA, Whatton JF: Squirrels of the World. 2012, Baltimore: The John Hopkins University PressGoogle Scholar
  54. Gür H: Why do Anatolian ground squirrels exhibit a Bergmannian size pattern? A phylogenetic comparative analysis of geographic variation in body size. Biol J Linn Soc. 2010, 100: 695-710. 10.1111/j.1095-8312.2010.01447.x.View ArticleGoogle Scholar
  55. Millesi E, Strijkstra AM, Hoffmann IE, Ditami JP, Daan S: Sex and age differences in mass, morphology, and annual cycle in European ground squirrels, Spermophilus citellus. J Mamm. 1999, 80: 218-231. 10.2307/1383222.View ArticleGoogle Scholar
  56. Zimmerman EG: Growth and age determination in the thirteen-lined ground squirrel, Spermophilus tridecemlineatus. Am Midl Nat. 1972, 87: 314-325. 10.2307/2423564.View ArticleGoogle Scholar
  57. Turner BN, Iverson SL, Severson KL: Postnatal growth and development of captive franklin's ground squirrels (Spermophilus franklinii). Am midl nat. 1976, 95: 93-102. 10.2307/2424236.View ArticleGoogle Scholar
  58. Kratochvíl L, Fokt M, Rehák I, Frynta D: Misinterpretation of character scaling: A tale of sexual dimorphism in body shape of common lizards. Can J Zool. 2003, 81: 1112-1117. 10.1139/z03-078.View ArticleGoogle Scholar
  59. Waterman JM: Male mating strategies in rodents. Rodent Societes: an ecological and evolutionary perspective. Edited by: Wolff JO, Sherman PW. 2007, Chicago and London: The University of Chicago Press, 27-41.Google Scholar
  60. Rowell TE: Beyond the one-male group. Behaviour. 1988, 104: 189-201. 10.1163/156853988X00511.View ArticleGoogle Scholar
  61. Martins EP, Hansen TF: Phylogenies and the comparative method: A general approach to incorporating phylogenetic information into analysis of interspecific data. Am Nat. 1997, 149: 646-667. 10.1086/286013.View ArticleGoogle Scholar
  62. Felsenstein J: Phylogenies and the comparative method. Am Nat. 1985, 125: 1-15. 10.1086/284325.View ArticleGoogle Scholar
  63. Pagel MD: Modelling the evolution of continuously varying characters on phylogenetic trees. Morphology, shape and phylogeny. Edited by: MacLeod N, Foley PL. 2002, London: Taylor & Francis, 269-286.View ArticleGoogle Scholar
  64. Best TL, Titus AS, Lewis CL, Caesar K:Ammospermophilus nelsoni. Mamm Species. 1990, 367: 1-7.Google Scholar
  65. Díaz-Uriarte R, Garland T: Effects of branch length errors on the performance of phylogenetically independent contrasts. Syst Biol. 1998, 47: 654-672. 10.1080/106351598260653.View ArticlePubMedGoogle Scholar
  66. Díaz-Uriarte R, Garland T: Testing hypotheses of correlated evolution using phylogenetically independent contrasts: Sensitivity to deviations from Brownian motion. Syst Biol. 1996, 45: 27-47. 10.1093/sysbio/45.1.27.View ArticleGoogle Scholar
  67. Revell LJ: Phylogenetic signal and linear regression on species data. Meth Ecol Evol. 2010, 1: 319-329. 10.1111/j.2041-210X.2010.00044.x.View ArticleGoogle Scholar
  68. Capellini I, Venditti C, Barton RA: Phylogeny and metabolic scaling in mammals. Ecology. 2010, 91: 2783-2793. 10.1890/09-0817.1.View ArticlePubMedGoogle Scholar
  69. Capellini I, Venditti C, Barton RA: Placentation and maternal investment in mammals. Am Nat. 2011, 177: 86-98. 10.1086/657435.View ArticlePubMedGoogle Scholar
  70. Matthews LJ, Amold C, Machanda Z, Nunn CL: Primate extinction risk and historical patterns of speciation and extinction in relation to body mass. Proc R Soc B. 2011, 278: 1256-1263. 10.1098/rspb.2010.1489.PubMed CentralView ArticlePubMedGoogle Scholar
  71. Midford PET, Garland T, Maddison WP: PDAP Package of Mesquite. Version 1.07. [http://mesquiteproject.org]
  72. Maddison WP, Maddison DR: Mesquite: a modular system for evolutionary analysis. Version 2.75. [http://mesquiteproject.org]
  73. Martins EP: COMPARE, Computer programs for the statistical analysis of comparative data. version 4.6b. [http://compare.bio.indiana.edu/]
  74. Pagel M, Meade A: BayesTraits version 1.0 computer package. [http://www.evolution.rdg.ac.uk]

Copyright

© Matějů and Kratochvíl; licensee BioMed Central Ltd. 2013

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Advertisement