Morphology and burrowing energetics of semi-fossorial skinks (Liopholis spp.)

Terrestrial locomotion, such as running, is more energetically expensive than flying or swimming for an animal of similar mass (Schmidt-Nielsen, 1972), but considerably less costly than travelling through a dense, cohesive medium such as soil (Vleck, 1979; Seymour et al., 1998). A specialised burrower such as the Namib Desert golden mole (Eremitalpa granti namibensis) expends 26 times more energy burrowing through loose sand (80 J m⁻¹) than running (3 J m⁻¹) on the surface of the sand, though the cost of ‘swimming’ through loose sand is less than a tenth of that expended by mammals that tunnel through compact soil (Seymour et al., 1998). A non-specialised burrower such as the spinifex hopping mouse (Notomys alexis), can expend 5000 times more energy burrowing than running (7.1 kJ m⁻¹ compared with 1.2 J m⁻¹; White et al., 2006b). Despite the considerable energetic cost, burrowing has many benefits. These include food storage, access to underground food, a secure micro-environment free from predators and extreme environmental gradients (Robinson and Seely, 1980), nesting (Seymour and Ackerman, 1980), hibernation (Moberly, 1963) and enhanced acoustics to facilitate communication (Bennet-Clark, 1987).

Animals utilise a range of methods to burrow through soil, depending on soil characteristics (density, particle size and moisture content) and body morphology (limbed or limbless). Regardless of the method of burrowing, for animals that live and forage underground (fossorial species), the energy taken up must exceed the energy invested in burrowing. Fossorial mammals have therefore evolved ways to maximise burrowing capacities and efficiency and show convergent features that include reduction of hind-limbs, tail, eyes and external ears (Heffner and Heffner, 1990). Compared with mammals, burrowing reptiles tend to show different morphological features, such as limb reduction, body elongation and general size reduction (Wiens and Slingluff, 2001; Navas et al., 2004), strengthening of the cranium (Lee, 1998), shortening of the head and lower rostral angulation (Andrews et al., 1987; Barros et al., 2011), shortening of the tail (Shine and Wall, 2008) and streamlining of scales (Jackson and Reno, 1975). More specialised fossorial reptiles display reduction of both eyes and ears, fixation of the lower eyelid, a greater number of vertebrae and ribs associated with elongation of the body and atrophy of one lung (Bellairs, 1969).

The work required to excavate soil increases exponentially with body diameter, and fossorial animals therefore tend to be smaller than surface dwellers. Burrow size depends on animal morphology; bipedal animals such as birds construct significantly larger burrows than mammals to accommodate space for their beaks and feet to dig (White et al., 1978). Reptiles, however, tend to be more elongate than birds and mammals of a similar mass, so their burrows have a smaller cross-sectional area (White, 2005). Iguanas are more elongated than fossorial mammals of similar mass and construct smaller burrows (Rand and Dugan, 1983). The small cross-sectional area of burrows constructed by reptiles may therefore reduce their cost of burrowing, but this hypothesis remains untested. The hypothesis would be supported if reptiles are found to have lower burrowing costs than birds and mammals of similar mass.

Compared with fully fossorial species, semi-fossorial animals (facultative burrowers) use burrows as retreats and forage at the surface, or construct burrows only for nesting purposes (Seymour and Ackerman, 1980). Semi-fossorial animals construct less complex burrows than fully fossorial species, despite similar cross-sectional area (White, 2005), but their lack of structural adaptations for burrowing may require them to expend more energy per unit of cross-sectional area (White et al., 2006b).

Early work that considered the energetics of burrowing comprised either speculative accounts that featured no direct measurements (Grinnell, 1923; Tryon and Cunningham, 1968; Vaughan, 1974), or considered only basal metabolism and thermoregulatory costs (McNab, 1966). The first studies of burrowing energetics were conducted by Seymour (1973), who measured the metabolic rates of burrowing spadefoot toads (Spea multiplicata; prev. Scaphiopus multiplicatus) and Vleck (1979), who calculated the net energetic cost of burrowing (NCOB: the net energy cost of constructing a unit length of burrow, excluding maintenance costs associated with resting metabolism) of pocket gophers (Thomomys bottae). Since then, many studies of burrowing energetics have been conducted on a variety of burrowing mammals (e.g. Seymour et al., 1998; Ebensperger and Bozinovic, 2000a; Withers et al., 2000; White et al., 2006b), and have shown that the ambient air temperature (Luna and Antinuchi, 2007) and different substrate characteristics (Luna and Antinuchi, 2006; Zelová et al., 2010) can greatly affect the energetic cost of burrowing. For example, the cost of burrowing for mole rats (Bathyergidae) is up to 3.7 times higher when burrowing in dry sand relative to damp sand (Lovegrove, 1989) and burrowing metabolic rate is lowest for tuco-tucos Ctenomys talarum burrowing at ambient temperatures within their thermoneutral zone (Luna and Antinuchi, 2007).

To date, there have been no experimental studies of the cost of burrowing in reptiles. Burrowing is an important form of locomotion in reptiles (Lee, 1998) and one-third of Australian skinks are burrowing species that spend most of their lives underground (Wilson and Swan, 2013). The night skink (Liopholis striata) and the desert skink (Liopholis inornata) are nocturnal, semi-fossorial skinks from the genus Liopholis (previously Egernia; Gardner et al., 2008). In their natural habitat they are important bioturbators that modify the desert environment and produce burrows that provide shelter for other fauna including prickly geckos (Heteronotia binoei), knob-tailed geckos (Nephrurus levis) and king brown snakes (Pseudechis australis) (Pianka and Giles, 1982). These skinks occupy desert habitats ranging from sandy deserts to harder soils in Acacia deserts of Western Australia (Storr, 1978). Their burrows provide them with protection from surface sand temperatures that can exceed 40°C in the summer and from seasonal fires in spinifex grasslands (Wilson and Swan, 2013).

Adult L. striata ranges in size from 41 to 112 mm (snout–vent length; SVL) and construct elaborate burrow systems, with several interconnected openings (Pianka and Giles, 1982). The smaller L. inornata range in size from 32 to 84 mm (SVL) and construct simple U-shaped burrows roughly 30 cm deep (Storr, 1978). They live individually and often have two burrows 10–20 m apart (Pianka and Giles, 1982). The present study aimed to provide the first estimates of the NCOB in L. striata and L. inornata and examined the effect of temperature and substrate characteristics on burrowing energetics, testing the following four hypotheses: (1) because of their elongated body form, skinks will construct narrower burrows than other burrowing animals of similar mass (White, 2005) and will exhibit lower NCOB than a mammal of similar mass. (2) As fine sand is more cohesive than coarse sand, burrowing speed will be higher in coarse sand relative to fine sand (Zelová et al., 2010) and digging metabolic rate will be higher in fine sand than coarse sand (Luna and Antinuchi, 2006). NCOB incorporates costs associated with both shearing soil from the excavation face, and transporting soil away from the excavation face (Vleck, 1979). Changes in water content or state of compaction influence the soil density, cohesiveness, and shear strength (Collis-George, 1959). Thus, because the cost of shearing soil contributes to NCOB, NCOB should, all else being equal, increase with the cost of shearing soil (Vleck, 1979), so NCOB will be higher in fine sand compared with coarse sand. (3) The NCOB will be independent of ambient air temperature. This is because the NCOB reflects the mechanical cost of excavation, which should be independent over the range of temperature at which skinks burrow, and excludes maintenance costs (which are temperature dependent in ectotherms). (4) Species with preferences for burrow retreats will exhibit morphological specialisation for burrowing, such as elongated bodies and reduced limbs compared with non-burrowing species, because morphology contributes to burrowing efficiency.

Hypothesis 1 was tested by comparing the dimensions of burrows constructed by skinks with those constructed by other animals. Hypotheses 1–3 were tested by measuring the effects of soil characteristics and temperature on the burrowing energetics and NCOB for L. striata and L. inornata. Hypothesis 4 was tested by comparing morphometric measurements of L. striata and L. inornata with related skinks of the Egernia group (Gardner et al., 2008), which consists of seven genera (Bellatorias, Corucia, Cyclodomorphus, Egernia, Liopholis, Lissolepis and Tiliqua), to determine the relationship between size-independent body shape and retreat preferences.

The mean ambient air temperatures were 22.6±0.7°C (mean±s.d.) and 35.3±0.4°C in the 23 and 35°C treatment, respectively. The mean sand temperature at 10 cm depth was lower than the ambient air temperature by 1.0°C (21.6±0.8°C) in the 23°C treatment while in the 35°C treatment, the sand temperature was lower by 3.0°C (32.2±1.3°C). Both temperature treatments showed significant differences between sand and air temperatures (paired t-test, t₄₆=8.64, P<0.001). The mean density of the coarse sand treatment was 1.57±0.02 g cm⁻³ and mean density of the fine sand treatment was 1.60±0.02 g cm⁻³ (Student’s t-test, t₃₀=−3.68, P<0.001). Moisture content differed between sand treatments, where the coarse sand treatment contained 3.6±0.4% water and the fine sand treatment contained 5.4±1.4% water (Student’s t-test, t₃₅=−6.52, P<0.001).

For L. striata, resting metabolic rate (RMR) and digging metabolic rate (DMR) was significantly positively affected by temperature (t₁₄=2.23, P=0.04; t₁₄=2.61, P=0.02, respectively). Sand treatments did not have a significant effect on RMR (t₁₄=0.33, P=0.74, Fig. 1A, filled symbols) or DMR (t₁₄=0.50, P=0.62, Fig. 1A, open symbols). For L. inornata, RMR was significantly positively affected by temperature (t₁₂=4.53, P=0.0007), but not significantly affected by sand treatments (t₁₂=0.30, P=0.77, Fig. 1B, filled symbols). DMR was not affected by temperature (t₁₂=1.83, P=0.09) or sand treatment (t₁₂=0.11, P=0.91, Fig. 1B, open symbols). There were no significant interactions between temperature and sand type (P>0.05 in all cases). Data for both L. striata and L. inornata are compared with resting metabolic rates of other reptiles (White et al., 2006a) and digging metabolic rates of giant burrowing cockroaches Macropanesthia rhinoceros (Xu et al., 2014) in Fig. 2.

The ambient air temperature had a positive effect on burrowing rate for both L. striata (t₁₄=6.45, P<0.0001, Fig. 3A) and L. inornata (t₁₂=3.25, P=0.007, Fig. 3C). Air temperature had a negative effect on the NCOB for L. striata (t₁₄=−3.97, P=0.001, Fig. 3B) but not for L. inornata (t₁₂=−1.25, P=0.24, Fig. 3D). There was no significant effect of sand treatments on burrowing rate for both species (L. striata, t₁₄=1.88, P=0.08; L. inornata, t₁₂=0.97, P=0.35). NCOB was not significantly affected by sand treatments (L. striata, t₁₄=−1.62, P=0.13; L. inornata, t₁₄=−0.72, P=0.48). Interactions between temperature and sand type were always non-significant (P>0.05 in all cases). The NCOB was negatively associated with burrowing rate for L. striata (t₁₆=−5.13, P<0.0001) but not L. inornata (t₁₄=−1.4, P=0.18).

Interspecific comparisons of the NCOB with body mass revealed, on average, that both skink species have lower mean NCOB (L. striata, 316±160 J m⁻¹; L. inornata, 188±58 J m⁻¹, averaged over all substrate types and temperatures) than burrow-constructing mammals of similar mass (Fig. 4), but higher than sand-swimming mammals that burrow through loose dry sand. The NCOB for both skink species was higher than the predicted net cost of pedestrian transport (NCOT) for runners and walkers by over two orders of magnitude (predicted NCOT of L. striata, 0.91 J m⁻¹ and L. inornata, 0.54 J m⁻¹).

The mean burrow cross-sectional area constructed by L. striata was 5.3±1.4 cm² and 2.6±0.7 cm² for L. inornata. The body width of L. striata, on average took up 51% of their constructed burrow space. The body width of L. inornata took up 56% of the space of their constructed burrow. Video recordings showed skinks would often turn around halfway along a completed burrow and rest in a C shape, with their head and tail end towards the entrance, taking up all the space in the burrow.

Interspecific comparisons of burrow cross-sectional area (A_b) with body mass (M_b) revealed allometric scaling for all animals (Fig. 5). Three specific groups were distinguished from the grouped data; birds (A_b=5.46M_b^0.62, r²=0.84), reptiles (A_b=0.46M_b^0.74, r²=0.99) and vermiforms (A_b=0.39M_b^0.63, r²=0.99). Reptiles (excluding tortoises) constructed relatively narrower burrows but still within the variation of the grouped data (Tukey's HSD, P=0.02). Vermiforms constructed significantly smaller burrows (Tukey's HSD, P<0.0001) and birds constructed significantly larger burrows than the overall grouped animals of similar mass (Tukey's HSD, P<0.0001).

Linear discriminant analysis (LDA) revealed distinct separations for all retreat groups [hollow logs/rock crevices, hollow logs/burrows, burrows, vegetation (under scrub, grass or bush) and trees (arboreal), Fig. 6] and Wilk's lambda for size-corrected residual values revealed nine body morphology variables were significantly different among retreat preferences (F_4,19=5.26, P<0.0001): hindfoot length, head length, pelvis height, tail width, body width, head width, upper hind leg length, upper foreleg length, and lower foreleg length (supplementary material Table S2). The first discriminant function (LD1) reduced total variance by 67% and was positively loaded for body width and head length (loading value >1) while negatively loaded for pelvis height, upper hindleg length and hindfoot length. Tree species were loaded negatively, revealing longer hind leg (upper hindleg length and hindfoot length) and pelvic height, whereas vegetation species were loaded positively, with larger heads and bodies, and smaller limbs (Fig. 6).

The second discriminant function (LD2) accounted for 20% of the total variation (supplementary material Table S2) and loaded positively for lower foreleg length, upper hindleg length and head width, but was negatively loaded for upper foreleg length, tail width and body width (Fig. 6). The second function loaded burrowing species positively, revealing longer upper hindleg, shorter upper foreleg, and narrower body width and tail width. Species living in hollow logs and rock crevices showed the opposite traits, with longer upper foreleg length, wider body width and tail width and shorter upper hindleg and head width.

The value of λ>1 indicates that species traits are more similar than expected under Brownian motion (Cooper et al., 2010; Münkemüller et al., 2012). Our value of λ was high (1.42), and significantly different from zero (likelihood ratio test P<0.0001), suggesting that related species are more similar to one another than they are to unrelated species.

RMRs of both L. striata and L. inornata are toward the lower range of measurements of other reptiles at similar temperatures (Fig. 2). L. striata and L. inornata are both desert-adapted species, and arid species are often shown to have lower metabolic rates than related non-arid species (e.g. McNab and Morrison, 1963; Lovegrove, 1986; Lighton et al., 2001; Tieleman et al., 2003). There is, however, no association between field metabolic rate and aridity for free-living reptiles (Nagy et al., 1999) and we are not aware of any broad-scale tests for an association between RMR and aridity in reptiles. Thus, although the low RMRs of L. striata and L. inornata are consistent with the hypothesis that species from arid environments have low RMR, this hypothesis remains to be verified for reptiles more generally.

DMRs of L. striata and L. inornata at 23°C are around 24–40% lower than the DMR of similarly sized giant burrowing cockroaches Macropanesthia rhinoceros measured at 25°C (Fig. 2). DMR increased with temperature in both L. striata (Q₁₀=1.28) and L. inornata (Q₁₀=1.29), revealing weak temperature dependence relative to those observed for physiological traits in other species (values of Q₁₀ typically fall between 2 and 3; Withers, 1992). For example, the temperature dependence of DMR of the Liopholis species considered in the present study is lower than that of a related habitat generalist, Liopholis whitii (Bellamy, 2006), which has a Q₁₀ of 1.6 for metabolic rate during activity (Huey and Bennett, 1987).

Digging is an energetically demanding process, resulting in skinks expending 350 times more energy moving the same distance than the predicted cost of terrestrial locomotion (Fig. 4). Both Liopholis skinks have a similar NCOB to spadefoot toads (Spea multiplicata) (Seymour, 1973) and expend less energy per unit distance than a mammal of similar mass (Fig. 4). Although among-species variation in NCOB is positively correlated with body mass, there is considerable variation in the NCOB that is not explained by mass (Fig. 4). Differences in air temperature have been shown to affect the NCOB of ectotherms; as temperature increases, the NCOB of scorpions (Urodacus yaschenkoi) decreases (White, 2001), as is also generally the case for Liopholis skinks in the present study, although the effect of temperature is not significant for L. inornata (Fig. 3). This trend was also not observed in S. multiplicata (Seymour, 1973).

NCOB is also dependent on the physical and chemical properties of the substrate through which animals burrow (Collis-George, 1959; Vleck, 1979; Zelová et al., 2010). In the present study, the NCOB was not affected by substrate for either species (Fig. 3B,D). Similarities in the NCOB between coarse and fine sand may be due to small differences in density (difference of 0.03 g cm⁻³) and moisture content (difference of 1.79%) relative to other studies. The densities of the ‘hard’ and ‘soft’ soil treatments employed by Luna and Antinuchi (2006), for example, differed in density by 0.61 g cm⁻³, and they found that the NCOB was significantly higher in the ‘hard’ soil treatment compared with the ‘soft’ soil treatment. Similarly, Vleck (1979) used a variety of substrates from fine sand (1.37 g cm⁻³) to clay (1.84 g cm⁻³) and observed that burrowing energetics were highest in clay substrates and were lowest in gravelly sand substrates. The ‘dry’ and ‘damp’ sand treatments utilised by Lovegrove (1989) had moisture contents of 0% and 7.9%, respectively, and resulted in the NCOB being highest when burrowing in dry sand relative to damp sand. Finally, sand-swimming mammals expended less energy to ‘swim’ through loose un-compacted sand than both burrowing mammals and skinks. Since dry loose sand has similar properties to a fluid (Shimada et al., 2009), it is likely that adopting a swimming type of locomotion (e.g. undulatory) in this environment will reduce the energy expenditure during excavation. An example can be seen in sand-swimming lizards, where they have been observed transitioning from quadrupedal locomotion at the surface to undulatory locomotion when submerged in the sand (Maladen et al., 2009; Sharpe et al., 2013).

The average burrowing rate of the Liopholis skinks increased at higher air temperature (Fig. 3A,C), as has previously been shown for scorpions (White, 2001). Sand treatment did not significantly affect the burrowing speed in Liopholis skinks; however, other studies have shown that different substrate characteristics affect burrowing speed (Lovegrove, 1989; Luna and Antinuchi, 2006; Zelová et al., 2010). The relationship between the energy expenditure during locomotion and locomotory speed has been well documented (Taylor et al., 1970; Full et al., 1990; Seymour et al., 1998). All show a rapid decline in the cost of transport as speed increases. Although total power output increases approximately linearly with speed (Margaria et al., 1963; Heglund et al., 1982), the energy expended to move a given distance decreases non-linearly as speed increases. Liopholis skinks also follow this pattern, where the NCOB decreases with increasing burrowing rate, although the relationship is not significant for L. inornata. Irrespective of the medium travelled through, it seems the cost of transport per unit distance is more efficient at higher speed. However, if an animal travels outside its range of preferred speed without changing gait, then the cost of transport tends to increase (e.g. Hoyt and Taylor, 1981). It is therefore likely that the NCOB will not decrease indefinitely as speed increases, but animals presumably avoid burrowing at speeds that would require the use of anaerobic metabolism (Seymour, 1973) and avoid speeds that are high enough to cause an increase in NCOB. Thus, selecting a burrowing speed that avoids anaerobic metabolism and minimises NCOB allows burrowing animals to tunnel economically.

The size of a burrow is fundamentally dictated by the body shape and method of burrowing employed by the animal that constructed it. Elongated animals (e.g. marine worms, eels) construct narrower burrows compared with globular animals (e.g. birds) of similar body mass (White, 2005). The advantage of smaller, narrower bodies is that animals can expend less energy excavating burrows, because the energetic cost of burrowing is proportional to the amount of substrate removed (Vleck, 1981). Animals with spherical body shapes are therefore required to undertake more work per unit distance to excavate their wider burrows. Fossorial mammals minimise the cost of burrow construction by developing shorter and stronger limbs (Nevo, 1979) to increase power output and reduce the quantity of soil that must be excavated to burrow a given distance. Fossorial mammals in general are also smaller than semi-fossorial mammals (White, 2003). Fossorial reptiles like lizards and snakes generally have elongated bodies and reduced limbs to reduce energy expenditure during burrowing, and by increasing muscle mass and muscle cross-sectional area longitudinally they are able to do so without sacrificing power (Navas et al., 2004). Both Liopholis skinks examined in the present study constructed smaller burrows than the predicted burrow cross-sectional area, on the basis of their body mass (Fig. 5), but were within the variation observed in the grouped data.

Behavioural adaptations such as utilising a sit-and-wait foraging strategy from the safety of a burrow may allow energy conservation and reduce the risk of predation. Active foraging lizards have daily rates of energy expenditure about 1.3–1.5 times greater than sit-and-wait lizards in the same habitats, however the net food gain is about 1.3–2.1 times greater for foraging lizards (Huey and Pianka, 1981). Both Liopholis skink species use a sit-and-wait strategy where they sit inside the entrance of their burrows and wait for prey that pass by (Pianka and Giles, 1982), although some L. striata are occasionally seen foraging at night. Sociality in subterranean animals has been shown to facilitate the partitioning of burrowing workload among multiple individuals, thereby reducing each individual's total energy cost (Hansell, 1993; Ebensperger and Bozinovic, 2000b). Sociality allows the construction of complex multi-entrance burrows, which provide protection from predators (Rand and Dugan, 1983) and, for endotherms, provides a greater ability to thermoregulate (Yahav and Buffenstein, 1991; Kauffman et al., 2003). Given their higher individual energy costs, solitary species tend to be more efficient diggers than social species, as compared in two African mole rats (Bathyergidae, Rodentia). Solitary Heliophobius argenteocinereus expend less energy digging over a given distance than communal-living Fukomys mechowii, but F. mechowii shares the workload of burrow construction in a cooperative group (Zelová et al., 2010). Most Egernia group skinks, including the semi-fossorial skinks, show some degree of social communal living among closely related kin (Pianka and Giles, 1982; McAlpin et al., 2011; Fenner et al., 2012), which, in combination with the relatively low NCOB afforded by an elongate body form, may contribute to minimising the individual cost of burrow construction.

The relationship between body shape and habitat specialisation has been well studied (Vitt et al., 1997; Thompson and Withers, 2005; Grizante et al., 2012). Some studies have shown no relationship between morphology and habitat preference in lizards (Jaksić et al., 1980). Others found anti-predator escape (distance a lizard moved away from potential predator) was correlated with body shape [particularly body width and pelvic dimensions (Schulte et al., 2004)]. Egernia skinks occupy a wide range of habitats (Chapple, 2003) and show diverse body shapes, from very elongated, short-limbed Cyclodomorphus species to the large, heavy built Tiliqua (Wilson and Swan, 2013). Divergence of body shapes in the Egernia skinks relating to retreat preferences seems to be conserved and dependent on phylogeny (λ=1.42) as related species have similar retreat preferences (supplementary material Fig. S1). However, morphological differences between retreat preferences have been observed at a sub-species level (e.g. cranial differences in Egernia depressa; Doughty et al., 2011; Hollenshead, 2011).

LDA revealed distinct separation between rock crevices, hollow logs and burrow retreat groups. Burrowing species have narrower bodies, smaller heads, hindfoot and upper forelimb, and longer upper hindlimbs (Fig. 6). Similar specialisations for burrowing as those observed in the present study for Egernia group skinks have also been identified in Australian Ctenophorus (Agamidae) and Varanus (Varanidae), where burrowing representatives of all three groups have wider heads and longer, narrower bodies than their non-burrowing relatives (Thompson and Withers, 2005; Thompson et al., 2008). There is no consistent association between burrowing and limb dimensions; however, burrowing skinks and varanids have relatively long upper hindlimbs, while burrowing skinks and agamids have relatively short upper forelimbs. Shorter forelimbs for both skinks and agamids may allow them to increase their power output during excavation as they tend to burrow head first with their front limbs. However, the benefits of burrowing with shorter limbs can only be properly examined though biomechanical and kinematic studies.

In conclusion, digging requires a high level of specialisation to ensure that the benefits of burrowing outweigh the cost of a burrowing lifestyle. Locomotion via burrowing has been shown to greatly affect energy expenditure in various animals. The present study has provided the first estimates of the energy expenditure of burrowing in skinks and reveals that the semi-fossorial skinks, L. striata and L. inornata exhibit specialisation towards a subterranean lifestyle. These features include a relatively low NCOB compared with other tunnel-constructing species, low temperature dependence of metabolic rate during burrowing, construction of narrower burrows than mammals, and exhibition of morphological traits such as narrower bodies and smaller limbs compared with other Egernia group species. Future research on the energetic cost of burrowing in specialised fossorial reptiles (e.g. Lerista, Amphisbaenia and Serpentes) should be compared with the measurements of semi-fossorial reptiles obtained in the present study, to verify whether fossorial species expend less energy on burrow excavation than semi-fossorial reptiles, and establish the causality of why fully fossorial reptiles show convergence towards legless, elongated bodies and lower metabolic rate.

Six Liopholis striata (formerly Egernia striata Sternfeld 1919) (mean±s.d. SVL and mass of 93.6±3.4 mm and 27.8±3.7 g, respectively) were collected from the goldfields region of Western Australia (Government of Western Australia Department of Environment and Conservation Licence SF008358) in October 2011. Six Liopholis inornata (formerly Egernia inornata Rosén 1905) (mean±s.d. SVL and mass of 76.4±3.5 mm and 12.8±1.3 g, respectively) were collected from Big Desert State Forest, Victoria (Victoria Department of Sustainability and Environment Permit 10005993) in October 2011. Skinks were housed individually in white plastic tubs (60×40×26 cm) which contained sand (25–30 mm deep) (Ki-carma^®, Ormeau, Australia) in a temperature-controlled room (20±5°C). Each tub was maintained under two linear fluorescent bulbs with a 12 h:12 h light:dark photoperiod cycle; one bulb emitted only visible radiation (Crompton Lighting, Padstow, NSW, Australia) and the other bulb emitted visible, ultraviolet-A (320–400 nm) and ultraviolet-B (290–320 nm) radiation (Repti Glo 10.0, Exo Terra^®, Rolf C. Hagen Inc., Montreal, QC, Canada). Skinks were provided with two black plastic refuges: one refuge was situated at one end of the tub directly under a 50 W halogen lamp (Crompton Lighting, Padstow, NSW, Australia) that heated the top of the refuge to 35±2°C, the inside of the refuge to 30±2°C, and the far end of the tub to 25±2°C for 8 h in the middle of the 12 h light cycle; the second refuge was positioned at the other end of the tub away from the halogen lamp with a wet sponge positioned on top to maintain a mean relative humidity of 60% in the tub.

Skinks were given access to water at all times and were maintained on a diet of finely processed raw food that consisted of 50% vegetables (butternut pumpkin, green beans and rocket), 40% meat (turkey mince) and 10% fruit (strawberries). This food mix was supplemented with a reptile-specific multi-vitamin (Herptivite™, Rep-Cal, Los Gatos, CA, USA) and calcium powder (phosphorus-free calcium with vitamin D₃ Ultrafine, Rep-Cal) at the recommended dose of 15 ml of each supplement per 1 kg of food. L. striata were given 2.5 ml and L. inornata were given 1.2 ml of this food and supplement mix once or twice a week. Faeces were removed and water was replaced twice a week; the sand was replaced every six months. All skinks were handled in accordance with the Queensland Department of Environment and Resource Management Scientific Purposes Permit WISP10698712 and the University of Queensland Animal Ethics Approval Certificate SBS/288/11/ARC.

To determine whether temperature and substrate characteristics affect the NCOB, each skink was individually subjected to an environment with two variables: air temperature (23 and 35°C) and substrate characteristics (coarse sand and fine sand), which were presented in a full factorial combination.

Two grades of commercial sand were used to produce sand treatments that varied in particle size distribution. Washed fine sand (Joint Fill fine graded sand, Cement Australia Pty Ltd, Darra, QLD, Australia) consisting of >95% silica dioxide sand and <5% mineral and organic impurities (particle size: 0.06–0.25 mm) and washed coarse sand (Easy mix Tiler's coarse sand, River Sands Pty Ltd, Carbrook, Australia) consisting of <1% silt (particle size: 0.5–1.5 mm).

Sand bulk density (compacted) was measured as weight of soil per cubic centimetre (g cm⁻³), and the moisture content (%) of sand during burrowing trials was regulated by adding measured amounts of water to dry sand until a standard consistency was achieved (damp enough to be moulded by hand; White, 2001; White et al., 2006b). The coarse sand treatment consisted of a mixture of 70% coarse sand and 30% fine sand, because coarse sand alone would not bind at all without the addition of some fine sand. The fine sand treatment consisted of 100% fine sand. Soil temperature during burrowing trials was measured 10 cm under the surface of the sand using a type K thermocouple (QM1538 Digitech^®, www.jaycar.com.au).

Positive pressure flow-through respirometry (Lighton, 2008) was used to measure resting metabolic rate (RMR) and digging metabolic rate (DMR) as the rate of CO₂ production (V̇_CO2, ml h⁻¹). A gas analyser sub-sampler pump (SS-3, Sable Systems International, Las Vegas, NV, USA) was used to pump outside air scrubbed of CO₂ (using soda lime, Chem-Supply, Adelaide, Australia) and water vapour (using Drierite, W. A. Hammond Drierite Co. Ltd, Xenia, OH, USA) to a mass flow controller (GFC17, Aalborg Instruments & Controls Inc., Orangeburg, NY, USA) that regulated flow rate to a nominal value of 400 ml min⁻¹ (for L. striata) or 300 ml min⁻¹ (for L. inornata). The mass flow controller was calibrated using a NIST-traceable bubble film flow meter (1-10-500 ml, Bubble-O-Meter, Dublin, OH, USA). After passing through the mass flow controller, air was pushed through a respirometry chamber, which was a 2 l airtight clear polypropylene container (111×111×283 mm) holding 1.2 l of sand. After the respirometry chamber, air was rescrubbed of water vapour (using Drierite) before passing through an infrared CO₂ gas analyser (LI-820, LI-COR^® Biosciences Inc., Lincoln, NE, USA). The fractional concentration of CO₂ in the ex-current air (Fe_CO2) was recorded at a frequency of 1 Hz using Li-Cor software (LI-820 software version 2.0). The CO₂ analyser was calibrated with dry CO₂-free air and a certified gas mix (0.386±0.008% CO₂ in N₂, BOC Gases, Wetherill Park, Australia).

Each skink was fasted for 3–4 days prior to measurement to ensure a post-absorptive state (Secor, 2009). The background fractional CO₂ concentration of the ex-current air from the respirometry chamber was measured for a minimum of 2 h prior to the introduction of the animal. Before the skink was placed in the chamber, body mass was measured to 0.1 g using a digital scale (Mettler Toledo XS4001S Precision Balance, Port Melbourne, Victoria, Australia). Each individual was measured once for each treatment for approximately 5–7 h beginning around dusk, with the average resting V̇_CO2 recorded for approximately 5 min when V̇_CO2 was low and stable (e.g. Fig. 7). We refer to this measurement as resting metabolic rate (RMR) rather than standard metabolic rate because animals were measured during the active phase of their circadian cycle. The average DMR was taken over a 5 min period of consistent burrowing (e.g. Fig. 7). During the experiment, skink activities were filmed using an infrared (IR) camera (R-IR-60A, Airtight Security Plus, Rockville, Maryland) and recorded using GeoConcept Multiviewer 1.0 software (GeoConcept, Bagneux, France). The respirometry chamber was housed in a temperature control cabinet (ERI140, ProSciTech, Thuringowa, Australia) that regulated the air treatment temperatures at ±1°C. Average burrow dimensions (length, width and height) were measured to the nearest mm with a digital vernier caliper (Part no: 2351, Kincrome^® Australia Pty Ltd., Victoria, Australia) at the conclusion of the burrowing trial. The respirometry chamber was angled at approximately 10 deg, which generally allowed the skinks to burrow at the top, making it easier to measure burrow parameters.

where V̇_CO2 is rate of CO₂ production (ml CO₂ min⁻¹), V̇_i is rate of incurrent airflow (ml min⁻¹), Fe_CO2 is ex-current fraction of CO₂ and RER is respiratory exchange ratio, which was assumed to be 0.8. Rate of burrowing energy expenditure (J h⁻¹) was calculated by subtracting resting V̇_CO2 from burrowing V̇_CO2 and multiplying by the energy equivalent of 1 ml CO₂ production (25.6 J; Withers, 1992). The NCOB (J m⁻¹) was determined by dividing rate of energy expenditure by burrowing rate (m h⁻¹).

Comparative data for NCOB and body mass were compiled from the literature for a variety of vertebrate and invertebrate studies (supplementary material Table S3). Species were grouped taxonomically (mammals, reptiles, amphibians and invertebrates), and the effects of temperature and substrate were examined. Data for NCOB were compared with the predicted scaling relationship for the net cost of pedestrian transport (NCOT) of runners and walkers from Full et al. (1990).

The average burrow cross-sectional area (A_b, cm²) for L. striata and L. inornata was calculated based on an ellipse shape: A_b =παβ, where α is half of the burrow width and β is half of the burrow height. Additionally the proportion (%) of body width space taken up within the burrow (burrow width) was compared with the total burrow width. For comparisons between burrow dimensions with other animals, published measurements of burrow cross-sectional area were obtained from White (2005), supplemented with additional studies (supplementary material Table S4). If multiple values were available, the average burrow dimension was calculated and when body mass was not stated, an appropriate mass was obtained from multiple published sources. Data were log₁₀ transformed and classified into the following groups: grouped data (mammals, fish, amphibians and invertebrates), birds, reptiles, and vermiforms (worm-like shape). Scaling exponents of burrow area with mass (g) from each group were calculated by linear regression.

Body proportions of skink species from the Egernia group were compared with L. striata and L. inornata. A digital vernier caliper (Part no: 2351, Kincrome^® Australia Pty Ltd., Victoria, Australia) or one metre ruler (for larger specimens) was used to measure 17 body variables to 0.01 mm or 1 mm (tail length), respectively (Fig. 8). Measurements were taken from seven live species (81 individuals) kept at the University of Queensland and 24 ethanol-preserved species (121 individuals) from the Queensland Museum. The mean of each morphological variable was calculated for each species. Furthermore, species were grouped into five different retreat preferences: hollow logs/rock crevices, hollow logs/burrows, burrows, vegetation (under scrub, grass or bush) and trees (arboreal) based on the retreat with which they are most commonly associated in published accounts (supplementary material Table S1). Although tail length has been shown to be significantly associated with retreat type in the literature (Kohlsdorf et al., 2001; Bickel and Losos, 2002; Schulte et al., 2004; Velasco and Herrel, 2007), this association was not considered in the present study because a large number of museum specimens had missing or regenerated tails.

Analyses were performed in R 3.0.1 (R Development Core Team, 2013). An independent student’s t-test was used to test the null hypothesis that sand density and moisture do not differ between treatments and a paired t-test was used to determine if sand temperature was significantly different from the ambient air temperature. The effect of air temperature (23 or 35°C) and substrate characteristics (coarse or fine) on the NCOB and burrowing rate for L. striata and L. inornata were analysed using linear mixed effects models in the R ‘nlme’ package (Pinheiro et al., 2013) with sand and temperature as fixed effects and individual identity as a random effect to account for repeated measurements of each individual. Two individual L. striata were repeated twice in the experiment. Means±s.d. are presented, α was set at 0.05 for all statistical tests.

Analysis of covariance (ANCOVA) was used to test for differences in burrow cross-sectional area among species [grouped data (mammals, fish, amphibians and invertebrates), birds, reptiles, and vermiforms] with mass as a fixed continuous predictor.

Linear discriminant analysis (LDA) was used to calculate a set of weightings which allowed each pre-determined group to be distinguished. Morphology data were log₁₀ transformed and corrected for size by obtaining residuals from body length for each morphology variable using linear models prior to LDA. A forwards stepwise model using greedy.wilks function from the ‘klaR’ package (Weihs et al., 2005) was performed to extract significant variables depending on the Wilk's lambda criterion. The results were used for the following discriminant function analysis by the lda function from ‘MASS' package (Venables and Ripley, 2002). Phylogenetic signal was also calculated using LDA scores to determine if related species resemble one another using (Pagel, 1999) lambda (λ).

We thank Pieter Arnold for advice and comments on an earlier version of the manuscript, and Andrew Amey (Collection Manager of Amphibians and Reptiles) and Patrick Couper (Curator of Amphibians and Reptiles) from the Queensland Museum for providing access to museum specimens. Two reviewers provided comments that helped us improve an earlier version of the manuscript.