A review of sexual dimorphism of eye size in Colubroidea snakes

Eye size is interesting in snakes because in most species body length differs between the sexes, while the eye’s performance depends on its absolute size. So, does the smaller sex see less well? We hypothesized that eye sexual mensural dimorphism (SMD) would be smaller than Body SMD. We found among 26 snake populations that body length SMD was female biased in 47.6% and male biased in 38.1% of samples. Often the larger sex’s head was further enlarged but the SMD of absolute eye size was mitigated or annulled by the smaller sex’s eye being enlarged within the head, and the head enlarged relative to the body. Overall generally the SMD of eye size was smaller than body SMD. This accords with a hypothesis that eye size affects the evolution of head size and its SMD, both reflecting and emphasizing that absolute eye size is functionally important. Although Colubridae exceed Viperidae in length, Viperidae have larger eyes in absolute terms. In Colubridae the females have larger eyes and in Viperidae the males have larger eyes. Additionally we examine to what extent SMD in different characters is correlated, and briefly review other aspects of SMD, including some aspects of Rensch’s rule.

Eye size has usually been ignored, despite the interest in eye anatomy with regards to the evolution of the snakes (capRette et al., 2004) and despite the precedent of eyesize SMD in urodeles (MölleR, 1950).But the dependence of the eye's performance (resolution and sensitivity) on its absolute size (Walls, 1942;hoWland, MeRola & basaRab, 2004;nuMMela et al., 2013) raises a question: does the smaller sex see less well?Hypothetically, the smaller sex might (1) maintain isometry and have smaller eyes and poorer eyesight; or (2) its eyes could have the same absolute size as in the larger sex, being larger in percents of rostrum-anus length (PERCRA - Werner, 1971).For this, its head could either (2a) be relatively larger, retaining isometric architecture, or (2b) the eyes could be allometrically larger within the head.
These hypotheses were tested by WeRneR & seiFan (2006) in gekkonoid lizards (han, Zhou & baueR 2004) whose eyelids, too, comprise a transparent spectacle (bellaiRs, 1948;hilleR, RehoReK & WeRneR, 2007), facilitating eye measurement.In four of those species with the male larger, its absolute eye size, too, exceeded the female's (hypothesis 1).In three of these, relative eye size (PERCRA) was equal in the two sexes (still fitting hypothesis 1).However, in Gekko gecko the females' eyes were larger in PERCRA (hypothesis 2); and so was also their eye size relative to head length (HdL) (hypothesis 2b).This was the only species in which eye size relative to HdL showed SMD.
Similarly, in three of the gecko species with males the smaller sex, their absolute eye size, too, appeared smaller than the females' (hypothesis 1).In two of these, eye size in PERCRA lacked sexual dimorphism (again fitting hypothesis 1).Only in Stenodactylus doriae did the males' eyes seem larger in PERCRA than the females'; but eye size relative to HdL was equal in the two sexes (hypothesis 2a).
For snakes the data are heterogeneous.There is no eye-size sexual dimorphism in seven viperid species (dulleMeiJeR, 1969) nor in the colubrid Thelotornis cap ensis (shine et al., 1996b).Among 33 Malaysian species, eye-size sexual dimorphism occurs only in Dendrelaphis pictus in which the male, the smaller sex with smaller head, has larger eyes in absolute terms (MeRtens, 1937;Kopstein, 1941); compatible with hypothesis 2b and "overshooting".Similar is the case of Bothrops moojeni (leloup, 1975).Yet in Crotaphopeltis hotamboeia the smaller male maintains head isometry and has absolutely smaller eyes (hypothesis 1; KeoGh, bRanch & shine, 2000).Extraordinarily, in Mehelya sp.(Colubridae), the female is the larger sex, its head further enlarged, within it the eyes enlarged, significantly surpassing the male's in absolute size (shine et al., 1996a).This deviant situation may still accord with the above hypotheses.Mehelya are nocturnal (shine et al., 1996a) but the small-eyed males might forage at relatively illuminated times.Recently liu et al. (2012) surveyed eye size in colubrids, ignoring sexual dimorphism.
Thus eye-size, despite its function, is insufficiently known in snakes, and under-represented in books on snake life (GReene, 1997;lillyWhite, 2014).Therefore we wished to explore how ophidian evolution maintains optimal eye size while developing major sexual size dimorphism (shine & Wall, 2007).We hypothesized that among snake species, the SMD of eye size would be smaller than the SSD.Following preliminary observations on five species (FaiMan et al., 2005) we examined additional species (RaZZetti, FaiMan & WeRneR, 2007) and literature data.We tested sexual dimorphism of absolute and relative eye size, and of related body proportions.Finally, we explored the relations among these variables, searching for functional and evolutionary trends.

Material and Methods
The abbreviations used throughout the study are also listed in Table 0.
The mensural characters considered were: Sex, male (M) or female (F) (we excluded juveniles, which could not be easily sexed); rostrum-anus length (RA -WeRneR, 1971); head length (HdL), taken axially to behind the angle of the jaw, in our samples using GoRen and WeRneR (1993) calipers (the method varies among sources but not within samples); and spectacle diameter, which here properly represents the size of the eyeball (Walls, 1942;WeRneR, 1969).The eye may show directional asymmetry (WeRneR, Rothenstein & sivan, 1991;WeRneR & seiFan, 2006), which may differ between the sexes (RaZZetti et al., 2007), but herein we use the means of the two sides.
We presented for each individual the HdL also in PERCRA, mean eye size in mm, and relative eye size in PERCRA and in percents of HdL.This enables comparison of single specimens to our data.For all characters we computed the female-to-male ratio (FMR -mean female value as percent of mean male value), matching Fitch's (1981) data.Each FMR value is considered significant if the female and male means from which it originated, differed significantly by T-test (P < 0.05, without bonFeRRoni-type corrections for multiple tests).Ontogenetic allometry is addressed in the Discussion.
We quantified the difference between samples by the simple coefficient of difference (CD).For the difference between samples a and b (b having the larger mean, (M), CD = (Mb -Ma) / (SDa + SDb), where SD is the standard deviation.In classical taxonomy CD ≥ 1.28 characterizes subspecific differences or above (MayR, 1969).Characters were compared between the sexes using the Two-Sample T-test or, for non-normally distributed samples, the Mann-Whitney U-test.We adopted the significance threshold of α = 5%.Linear regression was tested between normally distributed variables to determine the form and strength of their relationship.The interaction between regressions was addressed by ANCOVA after Excluding five small samples (N < 10), few samples failed to show any significant FMR (Table 3, Fig. 1A).For RA, FMR > 100 in 10/21 samples (significant in 4/10 samples), FMR < 100 in 9/21 samples (significant in 3/9 samples) and FMR ≈ 100 in 3/21 samples.The number of samples with significantly FMR ≠ 100 greatly exceeds that statistically expected.The generalization that RA lengths of snake species have FMR ≠ 100 applies to our material.For the hard-to-define character RA (seiFan et al., 2009) Table 3 presents in addition to the FMR derived from means also the FMR derived from the longest male and female of each sample (though sample sizes vary greatly; Table 1).Within the Colubridae these two FMR values are correlated across species (r = 0.681, P = 0.021; Table 5).

Intraspecific observations: eye size and head size.
Absolute eye size (Table 2B) was greater in the larger sex (Table 2A), based on the largest male and female, in 19/26 samples, regardless which sex was larger, and re- 13.4 ± 1.5 11.3 -16.5 97.1 94.8 0.26 3 ± 0.5 1.9 -3.7 3.2 ± 0.4 2.5 -3.9 107 105 0.86 gardless of family (Fig. 2).However, its FMR was rarely significant (Table 3).This remained true in 18/26 samples when based on the sex means.Among the species with eye larger in the larger sex, the FMR of eye size was often more moderate (closer to 100) than that for RA: using FMRs based on sample maxima, this occurred in 10/19 samples but with FMRs based on sample averages, it occurred in 15/18 samples.Among the species deviating from this pattern, there occurred different patterns.In 5/26 samples the male had absolutely larger eyes although the female was the larger sex; e.g., Echis borkini.In three of the remaining samples  eye size was identical in the two sexes although RA differed between them, e.g., E. coloratus terraesanctae.In contrast, Eirenis coronella fennelli females had the larger eyes despite being the smaller sex (Table 2A,B) but sample size was only 3 + 3 (Table 1).Among the five samples in which the eye was bigger in the male, although the smaller sex, this apparently accrued differently in different species.The FMRs were statistically insignificant but in Eirenis c. coronella they derived from 29 males and 34 females; RA FMR = 110.2(or from the maxima, 117), and Eye (mm) FMR = 93.1.This "over-correction" of eye size was achieved through HdL PERCRA being greater in males, FMR = 85.7.Eye size relative to HdL was isometric, FMR = 100.7 (hypothesis 2a).In Coronella austriaca, Cerastes c. cerastes and Echis borkini with RA FMR = 104.2,102 and 123 respectively, and absolute eye size FMR = 95.7,92.3 and 97.4 respectively, the "over-correction" was achieved in two steps.Relative head size seemed only moderately increased in the smaller sex, being FMR = 90.2,96.6 and 95.2 respectively, but FMR for eye size relative to HdL was 96.4,89.4 and 92.1 (hypotheses 2a + 2b).Finally, in Crotalus cerastes, while females were larger than males (see also KlaubeR, 1944), mean FMR = 101.7 (between largest specimens FMR = 119.7),absolute eye size had FMR = 92.3 (Fig. 3).This was achieved despite the male's head being relatively smaller, FMR = 107.8,through the male's eye being greatly enlarged relative to the head, FMR = 90.6 (hypothesis 2b).
In all four samples where the FMR of eye dia meter-%HdL (Table 3) was significant (Fig. 3), the eye was larger, relative to HdL, in the smaller sex (sometimes the SSD of RA was clearer between maxima than between means).In two of these cases the FMR of relative HdL resembled the (insignificant) FMR of RA (Natrix tessel lata from the Levant and Crotalus cerastes, discussed below).If despite the insignificance such cases do occur, relative head size seems to increase the head-size difference between the sexes.But in the smaller sex, with smaller head, the eye was allometrically enlarged within the head.Therefore, in N. tessellata the FMR of eye size (in mm) resembled that of RA (hypothesis 2b).
In the two other samples with significant FMR of mean Eye%HdL, Natrix natrix and Platyceps tessella tus from Sinai (Fig. 4), the smaller sex had a relatively larger head and within the head relatively larger eyes, so that the FMR of absolute eye size was greatly moderated compared to the FMR of RA, the difference approximately halved (hypotheses 2a plus 2b).
The ontogenetic allometry of eye size sexual dimorphism is exemplified in Fig. 5, Natrix tessellata representing the majority trend (eye larger in the larger sex), with intraspecific variation.Figure 5A shows the increase in HdL as a function of RA, Figure 5B shows the increase of actual eye size as a function of HdL, and Figure 5C shows the decrease of relative eye size with increasing HdL (see also Table 3).In each, the regression lines of males and females differ in intercept; the difference between their slopes approaches significance only for absolute Eye%HdL (Fig. 5B).
Interspecific observations: differences between families.Before exploring interspecific relations among characters, we heeded that morphology varies among snake families (Rieppel, 1988;lee & scanlon, 2002) and asked whether interspecific analysis of characters should be applied to the pooled material or separately by family.For each sex, we compared each character between Colubridae and Viperidae (T-test and CD), as shown in Table 4.The number of taxa per character was 12 -14 in Colubridae and 12 in Viperidae.As a group, Colubridae had greater RA length than Viperidae (significantly in both sexes).In each family, female RA exceeded male RA.The FMR was similar in the two families (resp.FMR = 104.5 and 105.3, the difference was not signifi cant).In contrast, absolute eye diameter (mm) was greater in the Viperidae as a group than in the Colubridae (significantly in both sexes).This resulted from two allometric differences: Both HdL PERCRA, and eye%HdL, were greater in the Viperidae.The latter differences were not statistically significant but the picture appeared coherent.
Interspecific observations: the dependence of FMR on species size.We explored the effect of body size on the FMR of the eye, by comparing the FMRs of different measures of eye size, to those of body size.In view of the differences between Colubridae and Viperidae (Table 4), we computed the interspecific correlations among FMR values for the pooled taxa (Colubridae and Viperidae, Table 5A) but also separately among Colubridae (Table 5B) and among Viperidae (Table 5C).Initially the correlations were calculated based in turn on three RA sets, mean male RA, mean female RA, and their average.This detail was inconsequent and we present only the results using male sizes.
The pooled families (Table 5A) showed highly significant correlations of the FMR of absolute eye diameter (mm) with those of RA (based on means) and of relative eye diameter (PERCRA).Further details differed between the families.
In the Colubridae (Table 5B), the FMRs of RA based on means and based on maxima were correlated.The FMR of eye size (mm) correlated with both RA FMRs but the FMRs of relative eye size (as PERCRA and as%HdL) negatively correlated with both.Eye diameter PERCRA was correlated with HdL PERCRA.But absolute eye size (mm) and Eye size (%HdL) were correlated negatively.
In contrast, among the Viperidae (Table 5C) the only significant correlations were that the two FMRs of relative eye size (PERCRA, and as%HdL) were correlated and each was negatively correlated with that of RA (from means).
Interspecific observations: correlations among FMRs of characters.Is sexual dimorphism expressed similarly in different morphological characters, as it would under isometry?Inter-specifically, the FMR of absolute eye size was significantly correlated with that of body length (RA)  ).However, while throughout RA FMR ≤ 100 (i.e., male-biased sexual dimorphism) the sample averages belonging to either family were scattered on both sides of the equality line, throughout RA FMR ≥ 100 (i.e., female biased sexual dimorphism) the sample averages were below the equality line.Overall, eye size FMR was smaller (closer to 100) than RA FMR.

Discussion
Aspects of sexual dimorphism in snakes.In snakes SMD has been investigated mainly in total length, RA length, tail length and head length; sometimes proportions within the head; but only exceptionally spectacle diameter, as reviewed in the Introduction.
All these and diergic characters (fecundity, diet) interact.Our discussion of sexual dimorphism focuses on eye size.In our material most taxa showed some SMD, confirming earlier conclusions that in snakes usually females are longer than males (Fitch, 1981;cox et al., 2007).The values of SSD and other SMD vary geographically and temporally (Madsen & shine, 1993a), increasing the variation in our data.
For an individual specimen 'length' is the easiest character to measure.However, for a population (or sex) it is the most difficult character to define, due i.a. to ontogeny (Fitch, 1981, seiFan et al., 2009).
C Fig. 5.The ontogeny of sexual dimorphism in eye size, exemplified in Natrix tessellata.A: HdL as a function of RA.The slopes did not significantly differ between the sexes (P slopes = 0.19, F = 1.76), so the lines may be pooled as y = 0.035x + 4.927.Note that the head allometrically grows less than the body.B: Mean absolute eye size as function of HdL.The slopes did not significantly differ between the sexes (P slopes = 0.08, F = 3.14), so the lines may be pooled as y = 0.1x + 0.976.Note that the eye allometrically grows less than the head.C: Mean eye size relative to HdL, as a function of HdL.The slopes did not significantly differ between the sexes (P slopes = 0.33, F = 0.98), so the lines may be pooled as y = -0.16x+ 18.093.Note how relative eye size allometrically diminishes.The ontogeny of size and sexual size difference -who is adult?Reptiles continue growing after sexual maturity (andReWs, 1982;shine & chaRnov, 1992).They grow allometrically, changing proportions among body parts.Therefore discussion of SSD and SMD requires defining which individuals are included.This definition depends on the context.For an ecological question whether in a species with the males having larger heads, the sexes eat different prey sizes, we should use all sexed or sexually mature individuals.But if we investigate the sexual dimorphism of species to characterize their morphology, we better use full-sized individuals that have realized their growth curves (seiFan et al., 2009).

A B
When dealing with proportions among body parts this dilemma can be bypassed by using their allometric growth equations.This option is unavailable for body size.Its assessment has therefore been addressed in several investigations.One proposal to estimate maximum size uses the largest individuals in large samples (staMps & andReWs, 1992;staMps, 1993;staMps, KRishnan & andReWs, 1994).
A new difficulty in defining the representative size of a taxon accentuates the need for adequate samples.The length of young squamates is phenotypic, mitigating the interest in body size and sexual dimorphism.Individual snakes may grow faster and become larger in response  peteRson, 1989).Little is known of the later ontogeny.In Vipera berus: juvenile females grow faster than juvenile males, reach maturity at older age and are larger (Madsen & shine, 1994).Moreover, in Thamnophis sirtalis, a male-biased SSD in RA at birth reversed later, females be coming the longer adults (KRause & buRGhaRdt, 2007).At another level, shine & chaRnov (1992) suggested to derive the maximum RA from size at maturity by a relatively constant proportion between these two variables.However, of 17 species they reported, in two maximum size was ≥ 200% of the size at sexual maturity, but in two others, ≤ 116%.Moreover, maxima derive from ranges, ranges depend on sample size, but sample sizes were not given.
Herein our pragmatic solution for defining the body length of samples comprised three measures.(1) Using only specimens of known sex; (2) assessing the body size of a taxon (or sample) both from the average and from the largest individuals, and (3) viewing the size of body parts in terms of proportions.We lack calculations of asymptotic sizes (staMps & andReWs, 1992) but consider that what functions in the animals' life, and sustains selective pressure, is the actual body-part size prevalent in the population.
In the evolution of SSD proximate and ultimate factors interact simultaneously (duvall & beaupRe, 1998).We pragmatically investigate one factor at a time.The proximate causes for SSD may be genotypic and may operate through any of four mechanisms and their combinations.(1) Early differentiation during embryonic development.In some squamate species, SSD occurs already in hatchlings, remaining isometric during ontogeny.To the species with FMR not changing with RA listed by Fitch (1981) we add besides Natrix tessellata (herein) also Natrix natrix (GReGoRy, 2004) and the lizard Acanthodactylus boskianus (seiFan et al., 2009).Among four natricine species the differences in body persist, increase, or decrease (KinG et al., 1999).( 2) Faster growth of one sex (length, relative head length, relative tail length, existing from birth, may occur during onto geny Madsen, 1988;FoRsMan, 1991;GReeR, 1997).(3) Extend ed growth period of one sex (shine, 1994).In Natrix natrix females this mechanism operates together with mechanism 2, faster growth (Madsen, 1983).(4) Longer life-span of one sex (MinaKaMi, 1979).
Additionally, proximate causes for SSD may also be phenotypical, through environmental effects differing between the sexes (KRause, buRGhaRdt & GillinGhaM, 2003;tayloR & denaRdo, 2005).The sexually differing growth rate and ensuing SSD in Vipera berus was ascribed to different responses to prey abundance (FoRsMan, 1991).The differing growth rate and consequent SSD in wild populations failed to recur in the laboratory, in Natrix natrix (Madsen & shine, 1993b) and Crotalus atrox (John-aldeR, cox & tayloR, 2007).
Males of many snake species have relatively longer heads, paralleling the situation in lacertid lizards.The male lizard's relatively longer head may reflect the female's trunk becoming allometrically elongated for reproduction (bRaña, 1996;KRatochvíl et al., 2003).This may apply also to snakes, at least as a contributing factor.Furthermore, a male's enlarged head may serve in combat (loWe, 1948;shine et al., 1981).
However, some largest females benefit more from non-reproductive-ecological advantages.In these, maximum fertility may occur in intermediate-sized females (bonnet et al., 2000).
Male-biased SSD in snakes presumably relates to male-male combating (andRén, 1986), affecting reproductive success (Madsen et al., 1993;capula & luiselli, 1997).The generalization that combating males are relatively large (boGeRt & Roth, 1966) preceded the linking of combating to male-biased SSD.But there is a strong interspecific correlation of the male being the larger, with occurrence of male combats (shine et al., 1981).Among 374 snake species, male-male combats occur in 124 species.In most of these the males grow larger than females relative to related non-combating species (shine, 1978, 1994).Furthermore, at least in Thamnophis sirtalis pa rietalis the larger males are more successful in forcibly inseminating females (shine & Mason, 2005).
However, because fecundity selection for enlarging the female and sexual selection for enlarging the male are competing, exceptions are possible.In Vipera berus the females are the larger sex despite the males' combating, suggesting stronger selection of female size for fecundity (Madsen, 1988).Similarly in Natrix spp.mating aggregations (boRcZyK, 2007) longer males prevail (Madsen & shine, 1993c) even without combat (steMMleR-MoRath, 1935;capula & luiselli, 1997).
Ophidian SMD includes differences in head and gape sizes, and sometimes these are allometrically further increased in the larger sex.Snakes being gape-limited predators, and prey size tending to correlate with gape size (WeRneR, 1994;piZZatto, MaRQues & FacuRe, 2009), head enlargement may lead to food-resource partitioning between the sexes (caMilleRi & shine, 1990;FoRsMan & shine, 1997;shine & Wall, 2007), presumably enabling a denser population, as discovered in lizards (schoeneR, 1967).This is not always the case and in some lizards (bRaña, 1996;staMps, losos & andReWs, 1997) and in Naja melanoleuca, despite differing relative head size, the sexes ate similar food.This dimorphism may have had other causes (luiselli et al., 2002).Yet such dimorphism might have evolved in relation to diet without the relation being always manifested.shine and Wall (2005) reviewed SSD and ecological sexual diergism in 52 snake species.Among those with larger female, prey size differed between the sexes in 20/35 species but among those with larger male, prey size differed only in 2/13 species.Females ate larger prey also in the 1/4 species lacking SSD.Hence females appear to prefer large prey independently of their gape size.
Sexual dimorphism in head size, head structure, or both, even without SSD but due to allometry, enables feeding diergism, e.g., in Agkistrodon piscivorus (vincent, heRRel & iRschicK, 2004).Only rarely does allometric head enlargement in the smaller sex annul the morphological basis for dietary differentiation (shine, 1989b).
The correlation of prey size and gape size is reciprocal, and available prey may phenotypically affect head size (QueRal-ReGil & KinG, 1998;Krause, buRGhaRdt & GillinGhaM, 2003;schuett et al., 2005).Furthermore, other experimenters have questioned the concept that the correlation of prey size with gape size is due to active selection of larger prey by larger snakes (doWnes, 2002).
Are larger species more size-dimorphic?Do larger species show greater SSD (Reiss, 1986;shine, 1994)?Within groups the correlation often occurs: In Australian Typhlopidae (as viewed before the revision of hedGes et al., 2014) the females are larger and FMR correlates with RA (shine and Webb, 1990).Elapidae are male-biased and the larger species show greater SSD (shine, 1989a;GReeR, 1997).
Females gain a reproductive advantage from (3a) being long, or (3b) merely having a long abdomen (shine, 1992).When the species is relatively small, this factor becomes dominant; females are larger than males.The smaller the species, the greater this SSD.In larger species the male is the larger sex, and the larger the species, the greater the SSD.These relations are depicted in FaiRbaiRn &pReZiosi (1994) andabouheiF &FaiRbaiRn (1997).
These SSD trends have been called Rensch's Rule (abouheiF & FaiRbaiRn, 1997;FaiRbaiRn 1997) although Rensch (1950, 1959) never explicitly formulated it (seiFan et al., 2009).For reptiles the rule that among related species the direction and extent of SSD depend on species size was apparently first formulated by Fitch (1981) when reviewing SSD across Reptilia.His text ended with "Fig.9. Average adult size in lizards and snakes correlated with SSD showing that in both groups SSD (especially with male superiority) tends to be greater in species of large body size and less in small species".The FMR axis ranged 70 -155.
Data supporting Rensch's rule have been reported from assorted squamate groups.Among Elapidae, generally in smaller species the female was the larger sex but in larger species the male was larger (shine, 1991a).Five Israeli Eirenis (Colubrinae) species conspicuously displayed Rensch's rule (WeRneR & ventuRa, 2010, 2011) and a sixth Iranian species (sadeGhi, RasteGaR-pouyani & youseFKhani, 2014) fit into the same regression of FMR over RA.Most reptile lineages with frequent male combat and male-biased SSD followed Rensch's rule (Cox et al., 2007).Recently the validity of Rensch's rule was discussed for turtles and demonstrated in the Testudo graeca complex (WeRneR et al., 2015).Some snake and turtle lineages indicated an opposite pattern but significantly so only in natricine snakes.The ultimate explanations for both the general trend and its exceptions remain unclear (cox et al., 2007;WeRneR et al., 2015).
Head size and eye size.Environmental effects on head size and shape during embryogenesis have been reported only from a lizard (ulleR & olsson, 2003) and are unknown in snakes.However, postnatal food availability may affect head size and shape in snakes (QueRal-ReGil & KinG, 1998;KRause et al., 2003).
Among 114 snake species, in 47% of the species relative HdL showed significant SMD.In most species the female was the larger sex and additionally had a relatively larger head, enabling diet divergence; often the difference was present from birth, e.g., in Natrix natrix (shine, 1991b;GReeR, 1997;GReGoRy, 2004).At least in Dendrelaphis punctulata (Colubridae) in which female RA ≤ 200 cm while male RA only ≤ 110 cm, and the female has a relatively larger head, the female's jaw bones are further enlarged relative to head size (caMilleRi & shine, 1990).Strong female-biased SSD augmented by head enlargement has dietary consequences in Acrochordus arafurae (shine, 1986).Also when the larger sex is the male can its head be further enlarged, e.g. in Hierophis viridiflavus (FoRnasieRo et al., 2007).In Agkistrodon pis civorus the male's gape is enlarged through elongation of the quadrate bones, without significant head enlargement (vincent et al., 2004).
The frequent further enlargement of the feeding apparatus in the larger sex fits the hypothesis that SSD arises for ecological reasons, viz.prey partitioning (shine, 1989b).Though head size and prey size often agree (WeRneR, 1994;vincent & heRRel, 2007), this hypothesis seems countered by the smaller sex often having a relatively enlarged head, mitigating head SMD and reducing the basis for dietary differentiation.This occurs in both colubrids and viperids (vitt, 1980;vitt & vanGildeR, 1983; herein Table 3): For example, Natrix natrix RA FMR = 135.4but HdL PERCRA FMR = 99.4; and Echis c. terraesanc tae RA FMR = 96.4but HdL PERCRA FMR = 105.3;and 12 other taxa in which RA is greater in one sex and HdL PERCRA in the other.Conceivably sometimes the advantage of broadening the range of prey sizes available to the smaller sex, exceeds the advantage of reducing the food competition between the sexes.Almost all head SMD reports mentioned have considered prey ingestion, but not the eye that often detects the prey.Regnum-wide, eye size sexual dimorphism is not rare.Among 16 butterfly species, the eye was generally larger in the males (RutoWsKi, 2000).In chickens (Gallus gallus domesticus linnaeus, 1758) male eyes average larger than female eyes (Zhu et al., 1995).The situation in geckos was summarized in the Introduction.But for snakes, beyond the cases reviewed in the Introduction, we found few data of apparent, statistically insignificant, sexual dimorphism of eye size (toMovic et al., 2002;cottone & baueR, 2009a,b,c).
Herein few species showed isometric eye size, the eyes having similar relative size in the sexes, the larger sex having larger eyes.In these the FMR of absolute eye size was nevertheless more moderate than that of RA (Table 3).In the remaining taxa usually either the sexes had similar RA, or absolute eye size was similar despite SSD.This overall situation is interpreted as reflecting an ecological advantage for the smaller sex to share the eye size and eyesight of the larger sex.But in four taxa the eyes were larger (in mm) in the smaller sex -all males -than in the females.Of these, Coronella austriaca and Eirenis c. coronella were diurnal, and Crotalus cerastes (Fig. 3) and Echis borkini were nocturnal.Though statistically insignificant, this masculine connection may reflect additional tasks for the male's eyes, e.g., finding females.
The corrective equating of eye size between the sexes, sometimes overshooting to exaggerated eye size in the smaller male, is achieved in different ways.Each hypothetical allometric route foreseen in the Introduction was realized in some taxon: enlarging the eye within the head, enlarging the head relative to the body, or both.The details can vary within a genus, e.g., Psammophis (cottone & baueR, 2009a,b,c; and herein).
One wonders about eye-size in the species whose head size has already been reported elsewhere.Three such species are included here.Our Hierophis viridifla vus data agree with the literature: the male is larger with a relatively yet larger head.From our data (although statistically insignificant) eye size relative to the head appears to be larger in the female, so the sexual dimorphism in absolute eye size is more moderate than the SSD.Our Natrix natrix data agree with the literature that the female is larger; in our sample the female's head is not further enlarged; Eye%HdL is significantly greater in the male, and hence the sexual dimorphism in absolute eye size is more moderate than the SSD.Our Crotalus cerastes data agree with the literature (KlaubeR, 1956): the female is a little larger than the male, and has the head somewhat proportionately enlarged.In our data Eye%HdL is significantly greater in the male, and in absolute terms his eye is larger than the female's.These observations fit a hypothesis that eye size affects the microevolution of head size.
There is no SMD of head size in the pythons, that have strong female-biased SSD but across species, FMR (of RA) is not correlated with RA (GReeR, 1997).Conceivably many are large enough for the size of the eye not to be critical.Indeed, it seems useful to investigate such questions separately in different evolutionary units.We found profound inter-family differences (Tables 4, 5).Colubridae average longer than Viperidae but absolute eye size is greater in the Viperidae.In both families females are larger than males.HdL PERCRA appears greater in the Viperidae.In both families it is similar in the sexes (near isometry), so that absolute HdL is a little greater in the females.Eye size is greater in the Viperidae also in relative terms, in PERCRA and in %HdL.Its SMD differs between the families: In Colubridae, eye diameter (%HdL) is slightly greater in the males, eye diameter PERCRA is about the same in the sexes, and absolute eye size is a little greater in females.Among Viperidae, eye diameter (%Head length), eye diameter PERCRA and absolute eye size are greater in the males.It remains unclear whether the mostly nocturnal viperids having larger eyes reflects the families' heritages or ecological adaptations (capRette et al., 2004).
In computing these inter-family differences we have not screened the data for "phylogenetic contrasts", namely whether the number of events of a shift from diurnal to nocturnal life had been smaller than the number of nocturnal species.In the context of behavioural ecology, the relevant variable seems to be, how many extant discreet taxa thrive with a given combination of characters.Moreover, at least in gekkonoid lizards, eye morphology and the correlated diel activity cycle are highly plastic as seen among assorted diurnal genera (Röll, 2001) and in the genus Ptyodactylus (WeRneR & seiFan, 2006).
We are not contesting the prevalent hypotheses about the selective forces driving SSD and SMD in snakes.We merely hold that head SMD is sometimes modulated also by the requirements of eyesight.Moreover, it remains to be seen to what extent eye size in snakes may be correlated (positively or negatively) with the sizes of the other major sensory organs (nuMMela et al., 2013).

Conclusions
1. Most snakes are sexually size-dimorphic.Of 26 samples (species, subspecies, geographical populations), 12 (46.2%)showed significant SMD in at least one of 3 -6 mensural or computed characters.2. Snake SMD may show intraspecific geographical variation of unpredictable pattern; its study should take such variation into consideration.3. Of the mensural characters, RA was significantly greater in females in 10/21 samples of sufficient size (significantly in 4/10), in males in 8/21 samples (significantly in 3/8), and equal in three samples.4. Relative HdL tended to be male-biased in taxa with female-biased RA and female-biased in taxa with male-biased RA. 5.The relatively longer HdL in males may result in part from the elongation of the females' abdomen as a reproductive adaptation.
6. Species varied in the SMD of absolute eye size; generally this was mitigated compared to SSD of RA, due to allometric relationships among eye size, head size, and RA.Sometimes the eye was even larger in the smaller sex.These observations fit our hypothesis: eyesight may affect the evolution of head size.7. The FMR of few characters correlated with the FMR of RA, and sometimes differently in Colubridae and Viperidae, at least as sampled in the Levant.8. Before generalizing, it may be useful to study such issues separately in different evolutionary units.Herein, Colubridae exceeded Viperidae in RA but Viperidae had larger eyes.In Colubridae the females tended to have slightly larger eyes and in Viperidae the males tended to have slightly larger eyes.

Fig. 1 .
Fig. 1.Distribution of FMR values of mensural characters among snake taxa (N = 26 samples).White, Colubridae; black, Viperidae.A (left), The FMR of RA; B (right), The FMR of eye diameter relative to head length.Note that the ranges of FMR values are wider in A than in B.

Fig. 4 .
Fig. 4. Sexual dimorphism of eye size, compared in Natrix natrix and Platyceps tessellatus (pooled regions).In both species the dimorphism seen in absolute eye size, is reversed in terms of eye size relative to head size.A and C: Frequency distribution of absolute eye size, in N. natrix (A) greater in females, in P. tessellatus (C) slightly greater in males.B and D: frequency distribution of eye diameter relatively to HdL, in N. natrix (B) greater in males, in P. tessellatus (D) greater in females.
. Hence Table 1 lists 26 samples of Colubridae and Viperidae.Sample sizes range 2 -70 per sex.Nine samples represent data used by RaZZetti et al. (2007) from specimens in the museums listed in the Acknowledgements; the others are from the literature quoted in Table

Table 1 .
List of taxa with sample sizes by sex (M, F) and source references.*

Table 2B .
Characters of snake samples, including mean ± SD, min-max, for males (M) and females (F) separately: Eye diameter (relative and absolute) and FMRs.Boldface, significant at P ≤ 0.05.

Table 4 .
Comparing characters between the families Colubridae and Viperidae.Numbers of taxa are after excluding samples of N < 10.CD = coefficient of difference.P value was obtained by independent sample T-test in SPSS v.17.Boldface, significant at P ≤ 0.05.

Table 5 .
Correlations among FMR values of characters.A: Across all species; B: Across Colubridae; C: Across Viperidae.Sample sizes as in Table 4. Boldface, significant at P ≤ 0.05.