Introduction

Sexual size dimorphism (SSD) occurs when males and females of a species or population differ systematically in body size (Fairbairn et al. 2007). SSD can be explained by several specific hypotheses (Andersson 1994; Dale et al. 2007). More general is empirical Rensch's rule (Abouheif and Fairbairn 1997) claiming that SSD increases with overall body size across species where males are larger the sex and decreases with body size where females are larger. The Rensch's rule is a pervasive macroecological pattern that has been observed in various animal taxa (Colwell 2000; Székely et al. 2004; Dale et al. 2007).

The degree of SSD within species is usually viewed as resulting from sex-specific equilibrium of sexual, fecundity, and natural selections (Colwell 2000; Blanckenhorn 2005) and the correlational selection (Fairbairn 1997). As the most supported hypothesis, sexual selection predicts that intense selection drives the evolution of body size of the selected sex, usually the males, with weaker correlated selection on body size in the other sex (Dale et al. 2007). Moreover, life-history hypothesis predicts that difference in development time (age) and growth between males and females also results in extent of SSD (Monnet and Cherry 2002; Blanckenhorn et al. 2007). Sexual selection is an ultimate cause of the extent of SSD, while growth rate and age are proximate causes.

Studies of Rensch's rule, as far as we are aware, focused mainly on animal populations in the laboratory with the inclusion of insects (Fairbairn et al. 2007), domestic goats and sheep (Polák and Frynta 2009), domestic chickens (Remeš and Székely 2010), and cattle breeds (Polák and Frynta 2010). Recently, researchers are increasingly interested to extend Rensch's rule to vertebrates in their natural environment intraspecific level (Lengkeek et al. 2008; Herczeg et al. 2010). However, intraspecific study of Rensch's rule in frogs is unavailable. In this study, we provided one of the first intraspecific tests of Rensch's rule in frogs, using data on SSD from 27 (Table 1) Chinese Wood frog Rana chensinensis populations differing markedly in their mean body size and covering the known size range of the species. We tested the consistency of allometric relationships between male and female body size with Rensch's rule; we also evaluated the plausibility of the hypothesis that population divergence in SSD was largely a function of age differences between the sexes.

Table 1 Location, altitude, sample size (males/females), mean body size, and age in males and females of 27 populations and references of published papers by Lu et al. (2006); Ma et al. (2009); Chen et al. (2011a, b)
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Materials and methods

Chinese Wood frog R. chensinensis is a medium-sized species with female-biased size dimorphism (Xie et al. 2000). The species is adapted to a wide range of climate regimes and is found over a broad geographical area in terms of both latitude (between 31 ° N and 44 ° N) and elevation (300–3,100 m) (Xie et al. 2000). Life-history characteristics along environmental gradients have been investigated in the species in recent years (Lu et al. 2006; Ma et al. 2009; Chen et al. 2011a, b). From these literatures, we obtained morphological data on mean age and body size from 27 populations with female-biased SSD (Table 1). Each population was not equidistant from the other, and there was no direct gene flow between populations (Fig. 1). All the individuals used in this study were adults, based on direct observation of the secondary sexual characteristics (i.e., the vocal sacs in adult males and the eggs readily visible by the skin of the abdomen in adult females). Each individual body size (the snout–vent length, SVL) was measured using a caliper by holding it in normal posture. Individual age was estimated by skeletochronology because this method has been successfully used in assessing age for most anurans based on lines of arrested growth recorded in cross sections of long bones in phalanges (Liao and Lu 2011). The data from literature were reliable because the same standard measurements were performed as mentioned, and all individuals were deposited in a standard museum for all populations. Following a protocol of Monnet and Cherry (2002), we calculated SSD as log (female mean size)–log (male mean size) ratio and sexual age difference (SAD) as log (female mean age)–log (male mean age) difference for each population.

Fig. 1
figure 1

Topographic map showing the location of the sampling of 27 populations in northern China

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Body size and age were log10-transformed to achieve normality. We applied a general linear model with log10 (SVL) as dependent variable and population and sex as fixed factors to test for sex differences in mean SVL among the 27 populations. The standard ordinary least squares (model I) regression would be statistically incorrect because males' size or females' size measurements are fixed and both are measured with error. To test for Rensch's rule, we fitted major axis regression (model II) of log10 (female size) against log10 (male size) using the population means, and we tested the null hypothesis of β = 1 using 95 % confidence intervals (Fairbairn 1997). Model II regression was done manually following that of Sokal and Rohlf (1981). We performed Pearson correlation to test the effect of SAD on the degree of SSD. All statistical tests were two-tailed and were conducted by using Type III sums of squares in SPSS 17.0 software.

Results

The degree of SSD differed significantly among populations (population: F 23,53 = 68.055, P < 0.001; sex: F 1,53 = 11.055, P < 0.001; and population × sex: F 23,53 = 9.524, P < 0.001). Model I regression showed a significant relationship between male size and female size across populations, and the relationship was significantly different from 1 (F 1,26 = 62.746, R 2 = 0.715, β = 0.716, SE (β) = 0.090, P < 0.001; Fig. 2). Model II regression revealed a close slope and is indicative of a similar relationship (β = 0.846, SE (β) = 0.106), confirming that variation in SSD supported an inverse of Rensch's rule.

Fig. 2
figure 2

Allometry of sexual size dimorphism in Rana chensinensis. Linear (model I) regression line (β = 0.716) with 95 % confidence interval (dotted line) is shown. The thick gray line represents isometry, i.e., β = 1. Each dot represents a single population based on the mean body size of males and females

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As SSD and SAD had a normal distribution (one-sample Kolgomorov–Smirnov two-tailed test: SSD Z = 0.602, P = 0.861; SAD Z = 0.781, P = 0.657), we were able to perform Pearson correlation analysis to test the relationship between SAD and the degree of SSD, which also indicated a highly significant relationship across populations (r = 0.530, P = 0.005, n = 26). Plots of SSD as a function of SAD were shown in Fig. 3.

Fig. 3
figure 3

SSD (log (female mean size)–log (male mean size) ratio) as a function of SAD (log (female mean age)–log (male mean age) difference) in R. chensinensis populations. Each dot represents a single population

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Discussion

Most anuran species exhibit female-biased SSD (Shine 1979). Sexual selection, fecundity selection, and sexual age difference can explain this pattern of size dimorphism (Shine 1979; Monnet and Cherry 2002; Herczeg et al. 2010). For R. chensinensis, the relationship between SSD and body size showed the inverse of Rensch's rule. In other words, female-biased SSD displayed a hyperallometric relationship with the mean body size such that SSD increased with increasing mean body size. Similar results are observed previously in other studies (Abouheif and Fairbairn 1997; Fairbairn 1997; Colwell 2000; Herczeg et al. 2010). The inverse Rensch's rule in R. chensinensis suggested that the most important evolutionary point which fecundity selection acted increases reproductive output in large females, a phenomenon proven both within and among populations (Lu 1994).

Although studies of Rensch's rule is originally framed for interspecific comparisons, its predictions can be also tested among populations within species where the mechanisms behind SSD allometry can be explained by detailed knowledge about the species' biology (Colwell 2000; Székely et al. 2004; Blanckenhorn et al. 2007). For R. chensinensis, body size/SSD trends from the wild can be interesting; phenotypic plasticity may be the cause behind the observed patterns because environmental condition influences markedly the expression of SSD (Lu et al. 2006). Moreover, genetic basis can explain the inverse of Rensch's rule in nine-spined stickleback Pungitius pungitius based on the common garden experiment (Herczeg et al. 2010). Population genetic differentiation might result in the inverse of Rensch's rule because of the data on body size and age in R. chensinensis resulting from over a broad geographical area. Solving the question by common garden experiment in the future is necessary.

For ectothermic indeterminate growers like anurans, it has been shown that body size differences can be explained by age differences between sexes (Monnet and Cherry 2002; Liao and Lu 2010a, b; Liao and Lu 2011; Liao et al. 2010, 2011; Liao 2011; Liao and Lu 2012). Comparisons across populations using standard techniques of correlation showed a highly significant correlation between SSD and SAD. Thus, in the populations we have considered, SAD is one mechanism that most probably contributes to the extent of SSD across populations. Moreover, SSD can result from differences in growth rate and/or time available for growth, and these two factors can act simultaneously.

Some reservations may be propitious to our methodology. First, population mean age and size in this species is unstable because of the small sample in some populations. Second, skeletochronological assessment of an individual's age might be problematic because resorption of the first lines and the presence of double or false lines affect the accuracy in estimating age (Hemelaar 1981). However, Monnet and Cherry (2002) found that if there is systematic bias in estimating individual age, it should affect age for both sexes in the same way, in which case SAD should remove any such bias. In our study, the potential sources of error resulting from natural and experimental constraints are likely to constitute only random noise. Therefore, the error should not affect systematically the results.

In conclusion, our results demonstrate hyperallometry in SSD in a species where the sexes are that females being larger than males. This translates to a pattern following an inverse of Rensch's rule. Fecundity selection plays the important role in the inverse Rensch's rule because large females increase reproductive output than small males within and among populations. The variation of SSD in the species can be explained in terms of differences in age between the sexes for populations.