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Hindawi Publishing Corporation International Journal of Zoology Volume 2012, Article ID 627470, 16 pages doi:10.1155/2012/627470 Research Article Effects of Surface Roughness on the Locomotion of a Long-Tailed Lizard, Colobodactylus taunayi Amaral, 1933 (Gymnophthalmidae: Heterodactylini) 1 2 1 Elizabeth Hoﬂing, ¨ Sabine Renous, Felipe Franco Curcio, 3 4 AndreE ´ terovic, and Persio ´ de Souza Santos Filho Departamento de Zoologia, Instituto de Biociˆencias, Universidade de Sao ˜ Paulo, Rua do Matao ˜ , Travessa 14 No. 101, 05508-090 Sao ˜ Paulo, SP, Brazil UMR 7205, Mus´eum National d’Histoire Naturelle, 57 Rue Cuvier, 75231 Paris Cedex 05, France Centro de Ciˆencias Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados, No. 5001, 09210-170 Santo Andre, SP, Brazil Departamento de Ecologia, Instituto de Biociˆencias, Universidade de Sao ˜ Paulo, Rua do Matao ˜ , Travessa 14 No. 101, 05508-900 Sao ˜ Paulo, SP, Brazil Correspondence should be addressed to Elizabeth Hoﬂing ¨ , ehoﬂing@usp.br Received 7 June 2012; Revised 10 October 2012; Accepted 29 November 2012 Academic Editor: Erin Leone Copyright © 2012 Elizabeth Hoﬂing ¨ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We analyzed the locomotor behavior of a long-tailed, forest ﬂoor, and leaf litter lizard, Colobodactylus taunayi, a species that retains the generalized Gymnophthalmidae Bauplan whilst presenting the discrete toe reduction associated with the Bachia-like pattern of limb reduction. We videotaped individuals moving on four substrates with increasing degrees of roughness: plastic, wooden board, glued sand, and glued gravel. Signiﬁcantly higher speeds occurred on the last two substrates. As with most other limbed animals, increased speed was signiﬁcantly correlated with simultaneous increases in both stride length and stride frequency. Independently of the kind of substrate, C. taunayi used rather slow lateral sequence walking trots. In contrast to other ectothermic tetrapods, and especially other Gymnophthalmidae, this species lacked perceptible lateral ﬂexion of either the trunk or the tail to eﬀectuate these slow gaits. 1. Introduction catimbau, and also species of Bachia), a general gymnoph- thalmid Bauplan would characterize them as small-sized The family Gymnophthalmidae comprises around 230 spe- lizards (<6 cm snout-vent length), with a thin and elongated cies of new world lizards , occurring from Central Amer- body, short limbs (loss of ﬁngers and toes is rather frequent), ica to most of South America [2–4]. Over the last decade, and a well-developed tail [3, 4]. This body plan plays an several gymnophthalmid taxa have been described on the important role for locomotion among Gymnophthalmini basis of comprehensive phylogenetic approaches and/or sensu Pellegrino and coauthors [11–16]and amongHetero- detailed studies of alpha taxonomy [5–10], suggesting that dactylini . the real diversity of the family must be underestimated by Body proportions, such as leg or tail length, and the abil- the present data. ity to produce large undulations of the trunk control locomo- Gymnophthalmids show considerable variation regard- ing morphofunctional patterns as a consequence of adap- tor skills in terrestrial lizards. Stride length (the amplitude of limb movement) and stride frequency (the rhythm of limb tations to diverse habitats. Despite some highly specialized forms with remarkable body elongation and limb reduction movement), both components of speed (speed = stride (Calyptommatus spp., Notobachia ablephara, Scriptosaura frequency × stride length), are directly related to the body 2 International Journal of Zoology geometry and to the amplitude of body curvature (increasing four specimens were kept at the Instituto de Biociencias, ˆ the girdle inclination to gain forward displacement for the Universidade de Sao ˜ Paulo, in individual terraria reproduc- limb) . The intensity of body undulation may provide an ing their natural conditions in tropical forest litter rich in additional contribution to stride length, where the increased moss and dry leaves (see ), at an average temperature of body length results from an increase in the number of 25 C, and fed on nymphs of captive cockroaches (Nauphoeta presacral or tail vertebrae. Limb frequency is related to the cinerea). motor control  characterizing each species and is based 2.2. Body Proportions and Number of Presacral Vertebrae. The on the time taken by both phases of the limb cycle: stance and body form of C. taunayi (Figure 1(a))ismarkedlydorsoven- swing duration. trally ﬂattened and notably laterally keeled, mainly at tail According to this Bauplan, which is representative of level. The tail length in this species is remarkable, represent- a speciﬁc morphofunctional status, modulation of both ing between 2.1 and 2.8 times the snout-vent length (SVL). frequency and amplitude of movement adjust locomotion These data were compared with the body proportions of to the environmental mosaic. However, the mean adopted lizards from other gymnophthalmids [11, 23]collected from by the animal to cope with environmental constraints also literature [27–35] or by direct measurement of specimens includes the grip of the limbs (substrate roughness enhanc- used in previous studies [12, 14–16]. In all cases, we selected ing the exchange of forces during the stance phase) and the the highest values for the tail length provided by authors. selection of an appropriate gait so as to reach a kinematic Thenumberofpresacral vertebrae(PSV) of C. taunayi performance that minimizes energy expenditure [19, 20]. was counted directly in cleared and stained specimens; for As ﬁrst noted in lizards by Sukhanov , locomotion diﬀers according to the nature of the substratum in which the other species data were taken from literature [23, 33, 35, 36]. movement occurs. The gait can be characterized by diﬀerent time lags between successive footfalls of the four limbs and 2.3. Experimental Protocol. For imaging, animals could move by the relative proportion of stance and swing periods in the freely inside a 0.6 × 0.4 m opaque plastic box that allowed limb cycle. the introduction of diﬀerent kinds of 0.3 × 0.4 m hori- Colobodactylus has been scarcely explored regarding zontal supports within the ﬁeld of a camera. To mitigate locomotion patterns found in other Gymnophthalmidae. Its stress, the lizards returned to the terraria between ﬁlming external shape reveals an elongated body with a strikingly sequences. Specimens were videotaped under natural light long tail and toe reduction. The only two species, C. taunayi −1 at 60 frames∗s , with a camera (Panasonic PV-DV910) and C. dalcyanus, are restricted to the Brazilian Atlantic Rain on a tripod set perpendicularly to the 0.3 × 0.4 m ﬁlming Forest . Pellegrino and coauthors  and Rodrigues ﬁeld. A 0.01 m scale was a reference for calculation of still and coauthors  placed Colobodactylus among the Hetero- enlargements. dactylini, as a sister-group of Heterodactylus, and also related As previously used for the study of other gymnoph- to Acratosaura, Alexandresaurus, Colobosaura, Iphisa, and thalmid lizards [12–15] and caecilians , specimens inside Stenolepis. According to these authors, the Heterodactylini the box were able to freely pass over one of four diﬀer- and Gymnophthalmini comprise the subfamily Gymnoph- ent substrates: polyethylene plastic (PLAS), wooden-board thalmidae. Colobodactylus taunayi, the species studied here, (WOOD), glued sand (SAND), and glued gravel (GRAV) is distributed along Southeastern Brazil, occurring on the (Figure 1(b)). Average roughness (RA) was estimated for ﬁve Atlantic Plateau, in the lowlands at sea level and on local diﬀerent samples (5.0 mm )fromeachsubstrate type.For islands [22, 24, 25]. It is clearly associated with leaf litter on PLAS and WOOD, RA was measured with a proﬁllometer the ﬂoor of forest areas, and such an environment indicates (Kosaka Subcorder 1700 α). For SAND and GRAV, RA was a heterogeneous substrate in terms of roughness, which estimated from direct measurement of grains under an probably inﬂuences lizard performance. optical microscope. So, the four substrates can be rated in This study addresses the following questions. (i) Does an increasing RA spectrum: PLAS = 3.0, WOOD = 9.8, surface roughness aﬀect the kinematic variables of C. taunayi SAND = 546.0, and GRAV = 1560.0. Trials indicate that the locomotion, especially those linked to speed modulation? (ii) animals were unable to move on perspex (RA = 0.2). This Are these eﬀects similar to other Gymnophthalmidae [12– slippery substrate (methyl methacrylate) probably represents 16] under the same experimental conditions? the limit for motion in such extremely unnatural conditions. 2. Material and Methods 2.4. Data Acquisition. Film sequences showing several cycles 2.1. Animals Studied. Individuals of Colobodactylus taunayi of limb and spine motions on each substrate were initially (Figure 1(a)) were collected in three localities in Sao ˜ Paulo analyzed frame-by-frame using an image processing software State, Brazil (Miguel T. Rodrigues, Proc. Ibama 02001 006003/ selector (SigmaScan, Jandel). Data for graphical analysis 2002-12: 046/2006-cgfau/lic and M. Dixo, Proc. Ibama were stored directly as computer spread sheets. On frame 02010.002890/05-13: 0177/05-RAN). Variation in morpho- intervals of 1/60 s, the touchdown of each limb was detected logical parameters among them (n = 4) was small (mean from dorsal view by two simultaneous criteria: start of hand ± standard deviation; range in parenthesis): weight = 2.3 ± (or foot) immobility and start of body motion. We only 0.72 g (1.5–3.3), snout-vent length (SVL) = 4.8 ± 0.50 cm selected sequences in a straight-line motion for displace- (4.2–5.3), and tail length = 12.1 ± 1.7 cm (10.9–14.6). The ment, discarding those showing sharp change of direction. International Journal of Zoology 3 5 mm 100 µm (a) (b) Figure 1: (a) Colobodactylus taunayi on litter; (b) experimental substrates with a gradient of increasing roughness average (RA): 1, plastic (RA = 3);2,wooden board(RA = 9.765); 3, glued sand (RA = 546), and 4, glued gravel (RA = 1560). Within the continuous phase of a sequence, we retained 18 Wilcoxon tests (both pairing by individuals) to examine all cycles for each individual, yielding 72 data points for each six pairwise combinations of the four substrates. A Bonfer- of the four substrates, a total of 288 cycles for all individuals roni correction was used to maintain the experiment wise α- on all substrates. Since there are elements for two diﬀerent level at 0.05. Both contrast tests were applied with 100,000 diagonal pairs, only kinematic variables of the ipsi-lateral randomizations of the data, minimizing intra individual limb cycles (right, fore, and hindlimbs) were used. dependence. Thefollowing variableswererecordedfor each stride Previous ﬁndings [14, 15] have indicated that locomo- −1 cycle: ASP = absolute speed observed (measured in m∗s ), tion performance should respond to a roughness gradient ASL = absolute stride length or the horizontal distance across substrates. Substrate roughness varied by four orders traveled (in m), SFR = stride frequency or the inverse of the of magnitude, justifying the use of their log transformed −1 period (s ), STA = stance duration or the duration of foot values. Moreover, log transforming the nine kinematic contact with the substrate during the stride cycle (s), SWI variables reduced departures from normality. A straight = swing duration or the duration of absence of substrate forward expectation was that the log means of such variables contact by the foot (s), SDU = stride duration or the period would be linearly related to log roughness. We tested whether of a stride cycle (s), and DUT = duty factor or the stance the response of kinematic variables ﬁtted this model by (i) duration as a fraction of the stride cycle. To adjust individual examining the coeﬃcient of determination of such relation- size diﬀerences, SVL was used to calculate relative measure- ship and (ii) examining the residuals for each substrate in ments, despite Gatesy and Biewener’s  preference for the these linear regressions. The experimental design leads to use of hip height in this correction. This provides two new data dependence due to several measurements with the same variables: RSP = relative speed or the ratio of absolute speed individuals, resulting in variance underestimation, which −1 to SVL (in SVL∗s )and RSL = relative stride length or may inﬂate the value of test statistics in comparisons . the ratio of absolute stride length to SVL (in SVL units). However, contrasts among substrates are reliable because These relative values allow direct comparisons with other such eﬀects would be the same in each of them, as the same published works. individuals were the source of data. All movements recorded for the lizards were “voluntary” The causal relationship between relative speed, relative and correspond to spontaneous locomotion adopted without stride length, and stride frequency in uniform movement any artiﬁcial stimulus such as treadmills. Note that, in (RSP = RSL∗SFR) could be explained by the additive model uniform movement, we expected ASP = ASL∗SFR and, con- log RSP = log a + b ∗ log RSL + b ∗ log SFR + e; where log 1 2 sequently, RSP = RSL∗SFR. So, stride length and stride fre- a, b ,and b are parameters of a multiple linear regression 1 2 quency are direct determinants of speed. Also note that SDU (MLR), and e is the random error. The expected values for = STA + SWI and DUT = STA/SDU, indicating that stance aperfect ﬁt (r = 1) are a = b = b = 1and e = 0. 1 2 and swing duration are causal components of duty factor. Any signiﬁcant discrepancy corresponds to nonlinearities in the relationship among the model’s variables, that is, 2.5. Statistical Analyses. Data from all substrates were pooled an accelerating movement. It should be noted that RSL so as to gauge the performance across a wide range of rough- and SFR are not fully independent variables, as any given ness such as are likely to be encountered by these leaf litter value of speed may be attained by several combinations of dwelling lizards. Analyses of contrast in locomotor perfor- stride frequency and stride length, and they could even be mance on diﬀerent substrates focused on the kinematic inversely related. But multicollinearity does not aﬀect the variables with nonparametric Friedman and a posteriori MLR analysis, except for rendering large standard errors for 4 International Journal of Zoology coeﬃcients . Comparison of regression coeﬃcients for The comparison of progression on four substrates showed (i) the MLR model between pairs of substrates were made by t a greater rigidity of the body on all substrates at low speed; tests (with a Bonferroni correction for multiple contrasts). (ii) a greater ﬂexibility of the trunk and the root of the tail −1 Modulation of speed was studied within stride cycles by (through large undulations) at higher speeds (>5SVL∗s ) direct examination of the relationship between stride length on the substrates having the highest roughness, SAND, and and stride frequency. Z-transformation of both RSL and SFR GRAV; (iii) such undulations were rarely seen on smoother was employed so as to render the modulation of each variable substrates, PLAS, and WOOD. with respect to the other interpretable in the same units (standard deviations (SD)). 3.3. Contrasts among Substrates. Considering all substrates −1 For the two substrates SAND and GRAV, maximum aver- together, ASP had a minimum of 0.048 m∗s on WOOD −1 age values for RSP, RSL, and SFR obtained for C. taunayi were and a maximum of 0.578 m∗s on SAND (Table 1). In compared with those obtained for other gymnophthalmid terms of RSP, minimum and maximum were, respectively, −1 −1 species, namely, Vanzosaura rubricauda, Procellosaurinus 1.0 SVL∗s on PLAS and 12.6 SVL∗s on SAND. RSP tetradactylus (see ), Colobosaura modesta, and Micrable- signiﬁcantly diﬀered among substrates (Friedman χ = 95.3; pharus maximiliani (see ). P< 0.001), and in a posteriori tests, all pairs of substrates signiﬁcantly diﬀered, except SAND and GRAV. 3. Results ASL pooled for all substrates had a minimum of 0.0116 m on WOOD and a maximum of 0.0617 m on GRAV (Table 1). 3.1. The Bauplan of C. taunayi within the Gymnophthalmidae. RSL varied between 0.34 SVL on GRAV and 1.26 SVL on Body proportions (SVL and tail length) and PSV of some SAND (Table 1). The contrast of RSL among substrates was Gymnophthalmidae species show some notable diﬀerences. signiﬁcant (Friedman χ = 49.1; P< 0.001), and pairwise The tail of the Gymnophthalmidae is long in four-footed comparisons resulted in PLAS diﬀering from all, with no forms with more than 1.5 times SVL, although species with signiﬁcant diﬀerences among the other substrates. short tails also occur in the four tribes. The longest tails are SDU on all substrates pooled for all had a minimum found in the Cercosaurini; the Heterodactylini also possesses of 0.083 s on SAND and a maximum of 0.443 s on PLAS a slightly longer tail than the great majority of the Gymnoph- (Table 1). Accordingly, SFR varied across substrates from −1 −1 thalmini (Figure 2). In general, in the limbless taxa, long- 2.26 s on PLAS to 12.00 s on SAND (Table 1). A well- tail (Bachia spp.) or short-tail (Calyptommatus spp.) designs established principle for limbed vertebrate locomotion is that are not related to PSV. Overall, tail length generally is in when animals move at a given constant speed, the values accordance with the limb reduction process that occurs in the of stride frequency are similar at fore and hindlimbs. Both Gymnophthalmidae; that is, a more pronounced reduction SDU and SFR diﬀered among substrates (resp., Friedman: 2 2 of the hindlimbs is associated with the long-tail design, χ = 80.1, P< 0.001 and χ = 86.7, P< 0.001). 3 3 and a more pronounced reduction of the fore limbs is Pairwise comparisons between substrates for both variables associated with the short-tail design. In the Cercosaurini, were broadly in agreement: no diﬀerence was found between most species of the genus Bachia show a more pronounced PLAS and WOOD, but all other pairs of substrates showed reduction of the hindlimbs than of the fore limbs, and the signiﬁcant contrasts. genera Heterodactylus, Colobosaura, Colobodactylus (Hetero- Both STA and SWI were monotonically and positively dactylini), and Anotosaura (Ecpleopini) have been referred to correlated with SDU (resp., r = 0.875 and r = 0.652; s s as examples of this Bachia-like hindlimb reduction, whereas n = 288 andP< 0.001 for both), when all substrates are con- the Gymnophthalmini Calyptommatus spp. shows an inverse sidered together. Thus, longer stride durations were due to process of limb reduction, the fore limbs being absent and increases in both stance and swing duration. SDU was non- possessing vestigial hindlimbs. Nothobachia and, to a lesser linearly related to STA (log-transformed variables: b = 0.727; degree, Psilophthalmus (Gymnophthalmini) are also exam- r = 0.795) and to SWI (log-transformed variables: b = ples of this Calyptommatus-like process of limb reduction 0.513; r = 0.426). As the slopes of the above relationships [11, 28]. This pattern was indicated for Calyptommatus indicate, as the lizards moved more slowly they increased the in the phylogenetic analysis of the Gymnophthalmidae. time the foot was oﬀ the ground at a slower rate than the rate of increase for the time the foot was on the ground. Both 3.2. General Patterns in C. taunayi Locomotion. Individuals STA and SWI signiﬁcantly diﬀered among substrates (resp., 2 2 of C. taunayi placed on the four substrates used gaits Friedman: χ = 73.0and χ = 23.9; P< 0.001 for both, 3 3 between walk and trot, which corresponded to moderately Table 1). Pairwise comparisons between substrates showed slowspeedsasdeﬁnedbyHildebrand. The walking that there were no signiﬁcant diﬀerences in STA between trot is characterized by a lateral sequence, which is typical either PLAS and WOOD or SAND and GRAV, but all other of Squamata-quadruped locomotion. The kind of limb contrasts were signiﬁcant. Only PLAS × WOOD and WOOD coordination does not change and is independent of the × GRAV showed signiﬁcant diﬀerence in SWI. substrate used. During displacement under experimental DUT signiﬁcantly diﬀered among substrates (Friedman conditions at ground level, whatever the gait adopted there χ = 24.7; P< 0.001). DUT on PLAS diﬀered from all was no lateral bending of the vertebral axis, especially in the other substrates, which did not diﬀer among themselves tail, which remains stretched throughout the limb movement (Table 1). Interestingly, DUT had the smallest coeﬃcient of sequence. Large undulation only appeared at higher speeds. variation of all variables studied (CV = 5.5%), indicating International Journal of Zoology 5 Total body length (%) 0 102030405060708090 100 (A) Dryadosaura nordestina (25) Leposoma scincoides (25) Arthrosaura reticulata (25) Ecpleopus gauchichaudii (26) (B) Proctoporus unicolor Echinosaura horrida Euspondylus acutirostris Ptychoglossus plicatus Placosoma glabellum (25) Cercosaura ocellata (25) Anadia rhombifera Bachia bresslaui (45) Prionodactylus argulus (28) Pholidobolus aﬃnis Neusticurus rudis Pantodactylus schreibersii (26) (C) Colobosaura modesta (27) Iphisa elegans (29) Colobodactylus taunayi (30) Heterodactylus imbricatus (34) (D) ∗∗ Calyptommatus leiolepis (45) Tretioscincus agilis (27) ∗∗ Nothobachia ablephara (43) Gymnophthalmus pleii (29) Procellosaurinus tetradactylus (27) Vanzosaura rubricauda (30) ∗∗ Psilophthalmus paeminosus (30) Micrablepharus maximiliani (30) Figure 2: Body proportions of representatives from four Gymnophthalmidae tribes (sensu Pellegrino and coauthors ). Snout-vent length (dark grey) and tail length (light gray) are shown as relative measures of total body length. When available, the number of presacral vertebrae is shown in parenthesis. (a) Ecpleopini; (b) Cercosaurini; (c) Heterodactylini; (d) Gymnophthalmini. ∗Bachia-like limb reduction. ∗∗Calyptommatus-like limb reduction. that, at the voluntary speeds chosen by the lizards, DUT adiﬀerence in both SDU and SFR and in DUT, between the was maintained within a restricted range. Despite the two pairs of substrates. In addition, there was a diﬀerence in autocorrelation involved, as in the calculation of DUT the ASL and in RSL between these pairs of substrates. Altogether, denominator is SDU, it is of interest to note that there was these diﬀerences caused diﬀerences in both ASP and in RSP a positive, rather than negative, correlation between them in the two pairs of substrates. (r = 0.132; P = 0.025; n = 288); note, however, that as Both WOOD × SAND and WOOD × GRAV formed lizards moved slower, DUT tended to increase slightly, but contrasting pairs for which the pattern of similarities (and the explained variance is only 1.7%. dissimilarities) was exactly the same. Both SDU components, In the contrast to the raw variables (Table 1)for PLAS namely, STA and SWI, were diﬀerent between substrates and WOOD, there were diﬀerences in SDU components, in each case. These diﬀerences were responsible for the namely, SWI and DUT, but these were not suﬃcient to cause diﬀerencesdetectedinbothSDU andSFR andweresuﬃcient adiﬀerence between the substrates in either SDU or in SFR. to cause a signiﬁcant diﬀerence in RSP. Note, however, Note that the diﬀerence in DUT occurred despite the absence that there was also a diﬀerence in ASP and in ASL in of diﬀerences in either STA or SDU. The diﬀerence in RSL both contrasts between pairs of substrates. The contrast alone was suﬃcient to cause a diﬀerence in RSP between SAND × GRAV resulted in the lowest number of diﬀerences PLAS and WOOD. The pattern of similarities and diﬀerences between substrates: only SDU and SWI diverged. The latter was the same for the contrasts PLAS × SAND and PLAS × diﬀerences were insuﬃcient to cause a diﬀerence in SFR. GRAV. The diﬀerence found in STA was suﬃcient to cause Moreover, as there was no diﬀerence in RSL, no diﬀerence 6 International Journal of Zoology Table 1: Kinematic variables recorded for Colobodactylus taunayi on diﬀerent substrates. Mean ± SD, range in parenthesis, and n = 72 for each cell. Relative measures result from raw values divided by individual snout-vent length (SVL). Friedman tests indicated signiﬁcant diﬀerences (P< 0.001) among substrates for all variables. After Bonferroni correction, signiﬁcant Wilcoxon pairwise contrasts among substrates for each variable were shown as diﬀerent letters (a, b, and c). Substrate Variable PLAS WOOD SAND GRAV Total a a b b 12.5 ± 5.10 13.0 ± 4.11 19.2 ± 10.77 18.0 ± 8.27 15.7 ± 8.06 ASP (5.1–29.3) (4.8–23.3) (6.6–57.8) (5.9–40.0) (4.8–57.8) a a b b 2.96 ± 0.816 3.09 ± 0.914 3.60 ± 0.951 3.39 ± 1.064 3.26 ± 0.969 ASL (1.81–4.89) (1.16–5.44) (2.20–5.78) (1.78–6.17) (1.16–6.17) a b c c 2.7 ± 1.15 2.9 ± 0.92 4.0 ± 2.31 3.8 ± 1.76 3.3 ± 1.72 RSP (1.0–6.4) (1.2–4.6) (1.4–12.6) (1.1–7.8) (1.0–12.6) a b b b 0.63 ± 0.193 0.70 ± 0.144 0.75 ± 0.207 0.71 ± 0.209 0.70 ± 0.195 RSL (0.37–1.06) (0.41–1.07) (0.43–1.26) (0.34–1.21) (0.34–1.26) a a b b 4.16 ± 0.830 3.95 ± 0.852 5.03 ± 1.712 5.20 ± 1.401 4.58 ± 1.361 SFR (2.26–6.00) (2.5–6.00) (2.73–12.00) (2.86–8.57) (2.26–12.00) a a b b 0.172 ± 0.0409 0.170 ± 0.0502 0.134 ± 0.0463 0.132 ± 0.0433 0.152 ± 0.0489 STA (0.113–0.283) (0.083–0.287) (0.033–0.283) (0.067–0.250) (0.033–0.287) a b a a 0.079 ± 0.0265 0.093 ± 0.0244 0.085 ± 0.0367 0.074 ± 0.0258 0.083 ± 0.0295 SWI (0.050–0.160) (0.050–0.133) (0.033–0.217) (0.033–0.150) (0.033–0.217) a a b c 0.251 ± 0.0578 0.263 ± 0.0558 0.219 ± 0.0647 0.206 ± 0.0555 0.235 ± 0.0627 SDU (0.167–0.443) (0.167–0.400) (0.083–0.367) (0.117–0.350) (0.083–0.443) a b b b 0.688 ± 0.0650 0.640 ± 0.0910 0.614 ± 0.1070 0.636 ± 0.0912 0.644 ± 0.0934 DUT (0.500–0.813) (0.385–0.851) (0.333–0.850) (0.462–0.857) (0.333–0.857) −2 −1 −2 −1 Variables are ASP: absolute speed (×10 m ∗ s ), ASL: absolute stride length (×10 m), RSP: relative speed (SVL ∗ s ), RSL: relative stride length −1 (SVL), SFR: stride frequency (s ), STA: stance duration (s), SWI: swing duration (s), SDU: stride duration (s), and DUT: duty factor. Substrates are PLAS: polyethylene plastic, WOOD: wooden board, SAND: glued sand, and GRAV: glued gravel. in RSP was found. The same applies to ASP. When only variables two types of responses, either closely following the the kinematic variables directly responsible for determining gradient or deviating from the gradient, could be shown to speed, namely, RSL and SFR were considered, an interesting correspond to two groups of substrates. pattern emerged. Thus, the only diﬀerence found between PLAS and WOOD was in RSL. The contrasts PLAS × SAND 3.5. Determination of Speed. When pooling all substrates and PLAS × GRAV yielded diﬀerences in both RSL and (n = 288), speed increased nonlinearly with both increasing stride length and stride frequency (Figures 3(a) and 3(b)), SFR. The contrasts WOOD × SAND and WOOD × GRAV resulted in a diﬀerence only in SFR. Finally, no diﬀerences in as the relationships between (log transformed) RSP and RSL any of the direct determinants of speed were found between (b = 1.446, 95% (conﬁdence interval) CI = 1.349–1.543) and between RSP and SFR (b = 1.387, CI = 1.270–1.504) resulted SAND and GRAV. in slopes that diﬀered signiﬁcantly from unity. Hence, lizards 3.4. Responses of Kinematic Variables to a Roughness Gradient. increased their speed by simultaneously increased stride For all nine variables, the log-transformed data for all length and stride frequency. In addition, RSL and SFR were substrates together were signiﬁcantly correlated with log signiﬁcantly correlated (r = 0.465; P< 0.001). roughness (P< 0.001; n = 288). However, the log mean of The combined action of stride length and stride fre- such variables was signiﬁcantly correlated to log roughness quency explained from 87.8% (WOOD) to 99.8% (GRAV) only forASP,RSP,STA,and SDU(Table 2). The small mag- of the observed variation in speed (Table 3), thus supporting nitude of some residuals in Table 2 indicated that kinematic the assumption of constant speed for the empirical data on variables, for certain substrates, responded accordingly to stride cycles. However, the observed speed (the recorded RSP the roughness gradient, even when the linear regression as a values) was diﬀered from the theoretical speed (product of whole was not signiﬁcant. Interestingly, there was a tendency recorded RSL and SFR values), as can be gauged by the coeﬃ- for very small residuals to occur concurrently as groups of cients of determination of the linear regression (r )between two substrates. Thus, PLAS-WOOD formed a group for RSP them on each substrate (PLAS = 0.972, WOOD = 0.779, and ASL, while SAND-GRAV formed another group for SFR SAND = 0.992, and GRAV = 0.998; all highly signiﬁcant). and SDU (see Table 2). Hence, there were kinematic variables The slopes for these relationships were as follows (b,withits that responded closely to the gradient in roughness, whilst conﬁdence intervals in parenthesis): PLAS = 0.905 (0.869– other variables did not, indicating overall a heterogeneity 0.941), WOOD = 0.908 (0.794–0.923), SAND = 1.002 in response patterns. In addition, for certain kinematic (0.981–1.024), and GRAV = 1.005 (0.994–1.016), which International Journal of Zoology 7 Table 2: Results of linear regression between the logarithm of means of nine kinematic variables and the logarithm of roughness for four substrates (codes as in Table 1). Coeﬃcients of determination r and their associated probabilities P are presented. Sample size is n = 4for each linear regression. Absolute residuals of these linear regressions for each substrate are also shown, with small values (<0.01) in bold. Absolute residuals Variable r P PLAS WOOD SAND GRAV ASP 0.926 0.0380 0.0060 0.0144 0.0336 0.0252 ASL 0.822 0.0930 0.0053 0.0023 0.0207 0.0177 RSP 0.936 0.0330 0.0024 0.0032 0.0295 0.0240 RSL 0.553 0.2560 0.0199 0.0209 0.0175 0.0185 SFR 0.901 0.0510 0.0194 0.0250 0.0054 0.0003 STA 0.983 0.0080 0.0051 0.0080 0.0084 0.0055 SWI 0.173 0.5840 0.0382 0.0424 0.0228 0.0269 SDU 0.904 0.0490 0.0160 0.0190 0.0032 0.0063 DUT 0.553 0.2570 0.0132 0.0142 0.0099 0.0109 Table 3: Results of multiple linear regression of log-transformed WOOD (CI log a = 0.283–0.472), where the ﬁt of empirical relative speed (RSP) versus log-transformed relative stride length data to the constant speed model was the poorest (Table 3). (RSL) and stride frequency (SFR) for each substrate (codes as in Increases in both stride length and stride frequency Table 1). The coeﬃcients of determination (r ) were shown, as resulting in nonlinear increases in speed were corroborated well as the intercepts (a) and the partial regression coeﬃcients by the sum of partial regression coeﬃcients, which were (b for RSL, b for SFR), with respective t tests and P values. 1 2 greater than unity on all substrates, indicating increasing β is standardized partial regression coeﬃcients for each variable. returns to scale (Table 3). It should be noted that the sum Sample size for each substrate is n = 72. Only for WOOD the partial of β values (the standardized slopes, which are independent regression coeﬃcients for both RSL and SFR diﬀered signiﬁcantly in of measurement units) tended to increase according to the pairwise comparisons among substrates. gradient in roughness (β values versus log roughness, r = Substrate PLAS WOOD SAND GRAV 0.9123, P = 0.045, and n = 4). To evaluate the relative Fit r 0.972 0.878 0.992 0.998 contribution of each independent variable in changing the dependent variable by one unit, a rough comparison of β a 0.018 0.378 0.001 0.001 values indicates that, on WOOD, RSL has a much higher SE 0.044 0.047 0.017 0.008 Intercept eﬀectonRSP thanSFR (Table 3). t 0.42 7.95 0.08 0.18 For individuals on all four substrates, with increas- P 0.6770 0.0005 0.9380 0.8570 ing speed, duty factor varied markedly (Figure 3(f)). This b 0.892 1.322 1.000 1.008 variability was highest on WOOD and PLAS, whereas on SE 0.042 0.069 0.024 0.009 the others, it decreased at the highest speeds. However, RSL t 21.31 19.14 41.28 111.65 generally, with increasing speed the animals decreased duty P 0.0005 0.0005 0.0005 0.0005 factor values. For example, on SAND, a DUT value of 0.86 −1 β 0.615 0.826 0.525 0.643 1 corresponds to a relative speed of 0.017 m∗s , whereas that −1 of 0.33 is for a relative speed of 0.126 m∗s . b 0.924 0.460 1.004 1.002 The modulation of speed on each substrate was made SE 0.060 0.073 0.021 0.010 through simultaneous increases in both stride frequency and SFR t 15.39 6.33 47.65 101.04 relative stride length, as gauged by the magnitude of the P 0.0005 0.0005 0.0005 0.0005 coeﬃcient of determination of the relationship between RSL β 0.444 0.273 0.606 0.581 and SFR (Table 4). When all substrates were pooled, SFR increased at a rate that was 0.471 SD units of the rate of increase for RSL, showing that speed modulation within the all together indicated a slight underestimation of the actual stride cycles was mainly through an increase in the latter. In relative speed observed. Deviation from the constant speed each substrate, an increase in one SD unit led to increases model indicated the occurrence of acceleration in some stride in SFR (also in SD units) of 0.496 (PLAS), 0.216 (WOOD), cycles. 0.696 (SAND), and 0.332 (GRAV). In the MLR framework, a perfect ﬁt of the empirical data to the constant speed model would result in partial slopes 3.6. Comparison with Other Gymnophthalmid Lizards. The equalling unity, and this occurred on SAND and GRAV, but comparison of the maximum speed achieved by C. taunayi not on PLAS (CI b = 0.809–0.976, b = 0.804–1.044) and with those of some other gymnophthalmids on rough 1 2 WOOD (CI b = 1.184–1.460, b = 0.315–0.605) (Table 3). substrates, as expressed by the mean of the maximum speed 1 2 Also, it would be expected that the intercept (log a) should reached by each of the studied individuals of each species, be zero. A null intercept was found on all substrates, except showed that C. taunayi was faster than the phylogenetically 8 International Journal of Zoology 0 5 10 15 0 0.5 1 1.5 −1 SFR (s ) RSL (SVL) (a) (b) 0 0.1 0.2 0.3 0 0.1 0.2 0.3 STA (s) SWI (s) (c) (d) 14 14 12 12 0 0.2 0.4 0.6 0 0.3 0.6 0.9 SDU (s) DUT (e) (f) Figure 3: Relative speed plotted against other kinematic parameters of C. taunayi on four substrate types with increasing roughness level: polyethylene plastic (PLAS, black squares), wooden board (WOOD, white squares), glued sand (SAND, “+”), and glued gravel (GRAV, “×”). Relative speed (RSP) is measured in snout-vent length units per second. (a) Relative stride length (RSL, in SVL units), (b) stride frequency −1 (SFR, in s ), (c) stance duration (STA, in s), (d) swing duration (SWI, in s), (e) stride duration (SDU, in s), and (f) duty factor (DUT). All six Spearman correlations are highly signiﬁcant (P< 0.01). −1 close species Procellosaurinus tetradactylus, a sand specialist speed of 22.70 SVL∗s , and at the initial phase of such a (Figure 4(a)). However, it was slower than more generalist hop, the frequency of limb movements is always superior to −1 speciessuchas Micrablepharus maximiliani and Vanzosaura 16 s . rubricauda,especiallyonsand(Figure 4(a)). The fast lizard The mean value for the maximum stride frequency M. maximiliani even has the capacity of hopping at a relative was rather low in comparison to that of most other species ∗ −1 ∗ −1 ∗ −1 RSP (SVL s ) RSP (SVL s ) RSP (SVL s ) ∗ −1 ∗ −1 ∗ −1 RSP (SVL s ) RSP (SVL s ) RSP (SVL s ) International Journal of Zoology 9 Sand Gravel 12 12 8 8 4 4 0 0 12345 12345 (a) 20 20 12 12 8 8 4 4 0 0 (b) 1.8 1.8 1.2 1.2 0.6 0.6 0 0 (c) Figure 4: Comparison of the (a) maximal relative speed, (b) maximal stride frequency, and (c) maximal relative stride length of ﬁve Gymnophthalmidae species running on sand and gravel. 1 = Vanzosaura rubricauda (n = 16), 2 = Procellosaurinus tetradactylus (n = 16), 3 = Micrablepharus maximiliani (n = 4), 4 = Colobosaura modesta (n = 4), and 5 = Colobodactylus taunayi (n = 16). These are average maximal values reach by studied individuals in each species. Bars are SD. Data other than for species 5 are from Renous and coauthors  (1-2) and Renous and coauthors  (3-4). Max relative stride length (SVL) Max frequency (Hz) Max relative speed (SVL/s) Max relative stride length (SVL) Max frequency (Hz) Max relative speed (SVL/s) 10 International Journal of Zoology Table 4: Results of linear regressions through the origin (zero a consequence of the propulsion that derives mainly from intercept) of both Z-transformed values of stride frequency (SFR) the limbs acting in conjunction with a relatively rigid trunk. and relative stride length (RSL). The angular coeﬃcients (b), their Inversely, on the rough substrates, some mobility of the trunk respective standard errors (SE), and P values are shown with the evinced, as a weak undulation could amplify the stride length coeﬃcients of determination (r ) and the Spearman correlation generated by the limbs. This longer stride length, which coeﬃcients (r ). Sample size is n = 72 for each substrate and is a characteristic feature found in all Gymnophthalmidae n = 288 for all substrates pooled. Only WOOD × SAND (t = 2.1, studied, can eﬀectively contribute to increase the speed. P< 0.05) resulted in a signiﬁcant pairwise contrast among slopes for diﬀerent substrates. 4.2. Variation in the Components of the Stride Cycle. Anum- Substrate PLAS WOOD SAND GRAV All ber of aspects of our results may provide some insights into b 0.496 0.216 0.696 0.332 0.471 the locomotion process used by C. taunayi: (i) the highest SE 0.050 0.121 0.113 0.118 0.052 velocities were only found when individuals moved on sand and gravel, substrates that present a marked degree of rough- P 0.0005 0.0790 0.0005 0.0070 0.0005 2 ness in the experimental conditions, whereas lower velocities r 0.586 0.043 0.347 0.100 0.222 characterized the progression on smoother substrates, plas- r 0.747 0.289 0.564 0.329 0.457 tic, and wooden board; (ii) the maximum values reached by the relative stride length and the highest stride frequencies were obtained on sand and gravel; (iii) in contrast, the of gymnophthalmid lizards, except for P. tetradactylus high speeds on sand and gravel were obtained by marked (Figure 4(b)). In contrast, mean value for the maximum increase of the stride frequency and more moderate increase relative stride length of C. taunayi was rather similar to the of a long stride length; (iv) in fact, this high value of the data obtained for the fast M. maximiliani on gravel and P. stride length on the substrates having a high degree of tetradactylus on sand (Figure 4(c)). Indeed, on gravel, this roughness was reached by all individuals. Facilitation pro- value was the highest for this group of lizards, underlining vided by the axial muscular-skeletal system could explain the importance of the stride length in the locomotion of C. the diﬀerence observed for the relative stride length on the taunayi, a species in which the SVL is rather similar to that rougher substrates. of V. rubricauda and P. tetradactylus, and four times shorter There is a general biomechanical expectation that short than that of Colobosaura modesta, an allied heterodactylini limbs should limit stride length, and hence short-limbed species. lizards should have short stride lengths. Irschick and Jayne’s data  on ﬁve lizard species showed a range from 2.32 to 4.20 BL (mean stride lengths by mean total body lengths, 4. Discussion with BL obtained by adding average SVL to tail lengths). 4.1. Bauplan Constraints to Locomotion. Colobodactylus tau- Colobodactylus taunayi had an average RSL of 0.70 SVL, nayi belongs to the assemblage Colobodactylus, Heterodacty- ranged from 0.34 to 1.26 SVL (so, with tail excluded). lus that diﬀers from the remaining Heterodactylini by their The maxima relative stride lengths of V. rubricauda and more elongated body and degree of limb reduction , and Procellosaurinus tetradactylus were, respectively, 0.99 and it is included in the Bachia-like limb reduction group . 0.67 BL . Thus, gymnophthalmids show short relative It moves in the superﬁcial leaf litter using a lateral walking stride lengths as compared to the ﬁve species studied by trot without the aid of body undulation. Considering that Irschick and Jayne . the trot is the basic form for quadrupedal fast movement in Mean stride frequency of these species rangedfrom −1 lizards , it is notable that C. taunayi is also able to adopt 11.23 to 14.50 s ; maxima were not reported. Mean stride this gait for relatively low speeds. frequency of Hemidactylus garnotii, which has relatively short −1 In our experimental conditions, this species scarcely limbs, was 13.00 s . The maximum frequency of the used body undulation, with the trunk curving little and the gymnophthalmid species P. tetradactylus and V. rubricauda, tail remaining rather rigid, especially at low velocities. The as means of the four largest frequencies attained by four contribution made by girdle rotations to progress was individuals of each species , were, respectively, 8.92 −1 insigniﬁcant, and likewise, that of the vertebral system to and 14.41 s . The maxima in stride frequency for one four-footed movement also appeared to be largely negligible individual each of C. modesta and M. maximiliani were, −1 when compared with other forms . Rather, the limbs respectively, 12.50 and 16.67 s . Therefore, apparently, both became the main propellers; the stride length adopted by this short-limbed and long-limbed species can show relatively heterodactylini lizard on the smoothest substrates should high stride frequencies. However, Iguana iguana has a low −1 be attributed to the limb action rather than to any body maximum stride frequency of 1.4 s , sensu Brinkman , −1 undulation, since in straight-line displacements C. taunayi and so does Varanus exanthematicus,1.8s , sensu Jayne and did not use axial undulations. This option can constitute a coauthors . loss of eﬃciency, and the maximum extension of the limbs Alexander  proposed a simple rule for distinguishing constitutes a limit for the stride length value (approximately gaits based on duty factor values; namely, duty factors below 1 SVL). The great variability of the swing duration, which 50% refer to running gaits, and those above 50% refer to necessarily forms part of the stride duration and also walking gaits. Hildebrand’s classiﬁcation  utilizes, in inﬂuences the value of the duty factor, is probably due to addition to duty factor, the relative limb phase, and an even International Journal of Zoology 11 more complex determination of gaits relies on the gait furnish kinematics elements that could rather characterize a mechanics (e.g., ). The discussion that follows focuses litter specialist. exclusively on duty factor because there are more compara- tive data for this kinematic variable than for gait mechanics. 4.3. Responses of Kinematic Variables to a Gradient of Rough- The average duty factor for the 18 lizard species, studied by ness. Surface texture has a multidimensional nature which McElroy and coauthors , independently of gait, is 53.61% comprises roughness (the average distance between peaks (SD = 13.05; n = 23). Species using walking gait mechanics and valleys, that is, vertical deviations of a real surface from 65.14% (SD = 8.82; n = 7) and running gait mechanics its ideal form), waviness (the repeating irregularities with 48.56% (SD = 11.37; n = 18) diﬀered statistically (Z = spacing greater than roughness), lay (the overall pattern cre- 3.012; P = 0.003; n = 7; n = 18) in the expected direction; ated by the production process), and ﬂaw (any unintentional 1 2 that is, running gaits showed a lower duty factor. Indeed there surface irregularity that may be random or repeating, such as was a negative correlation between absolute speed and duty cracks and inclusions). It should thus be kept in mind that factor (r =−0.859; P = 0.0005; n = 22) for these species. roughness can only partially describe the complexity of the Duty factor in C. taunayi ranged from 33.33% to 85.71% surface texture of the substrates used, and lizard locomotion and had an average of 64.36% (SD = 0.0935; n = 288). Mean could conceivably respond to unmeasured aspects of the duty factors for the ﬁve lizard species studied by Irschick and gradient. Jayne  ranged from 17% to 35%, and these low means Previous studies of other short-limbed and elongated corresponded to the high mean absolute speeds of these gymnophthalmid lizard species have shown variation in species, as a negative correlation was also found between locomotor performance on diﬀerent substrates including these variables (r =−0.900; P = 0.037; n = 5). Mean duty perspex, plastic, cardboard, sand, and gravel [14, 15]. The factor for Hemidactylus garnotii was 43% . substrates used in the present paper, namely, polyethylene Thus, short-limbed lizards, such as the Gymnophthalmi- plastic, wood, sand, and gravel formed a nonlinear gradient dae, seem to have (i) relatively short relative stride lengths, in roughness which encompassed four orders of magnitude 0 3 (ii) mean stride frequencies as high as those of some long- (10 –10 ). Both polyethylene plastic and wood were machine limbed lizard species, (iii) much lower average and max- ﬁnished, the former according to industrial standards. But imum speeds than long-limbed lizards, and (iv) relatively neither the glued sand nor the glued gravel was subjected to high duty factors. However, these are only general trends, such processes. As roughness is only one of the components which should be subjected to a more rigorous comparative of surface texture; it is probable that the experimental analysis due to the procedural diﬀerences in data collection substrates diﬀered also in these additional properties, which by diﬀerent authors. comprised the combination of all imperfections present. Finally, depending on the kind of substrate encountered, The total surface area of the sand and gravel substrates C. taunayi can use diﬀerent methods to progress. On rough is larger than that of the other two substrates due to the substrates (sand and gravel), it can adopt the general mech- higher geometrical complexity, and the probability that anism found in most lizards, that of combining the action cracks and other discontinuities were larger in wood than in of a horizontal undulation of axial muscular skeletal system the polyethylene substrate, which has the most homogeneous with movement of the limbs. This mechanical association surface of them all. Although such substrate diﬀerences results in a long stride length which only needs a slight probably surpassed the simple diﬀerences in roughness, these increase to furnish higher speeds. Conversely, on the smooth additional characteristics were not measured. The remark- substrates (plastic and wood), C. taunayi can maintain its able diﬀerences between wood and the other substrates axial system rigid and only use the limbs to progress. This shown for the relative contributions of both stride frequency option, which also requires an adjustment of the stride and relative stride length were due to accelerations (positive frequency, may have an important energetic cost; it is also or not) being more common on wood, and thus yielding likely to be uncomfortable and is probably avoided in natural discrepancies between the two speed estimates, that is, the conditions. The adoption of this particular locomotion independent estimate that based on the within stride cycle strategy on smooth substrates and the use of a classic lizard data. strategy of locomotion on sand and gravel may indicate Colobodactylus taunayi may use sandy substrates, as well that the species is better adapted to substrates with a high as leaf litter and hence be exposed to a wide range of substrate roughness coeﬃcient. This agrees with the ecological context, properties. The leaf litter is a very heterogeneous substrate since C. taunayi is classiﬁed as a habitat specialist living in in terms of the surface textures and their spatial orientation, superﬁcial leaf litter of the Neotropical rainforests where it and sand presents peculiar sliding properties associated with is semifossorial. The strategy of such ombrophilous animals, locomotion. Given the diversity of substrates that the species when avoiding light, is to hide under dead leaves, a dense, and is exposed to, one might expect it to be a “jack of all trades” heterogeneous environment composed of many rough ele- regarding locomotor performance, rather than a specialist ments. Given the well-generalized habitat in the gymnoph- in one of the substrates to which it is normally exposed. thalmid lizards, the long-tail pattern shown by C. taunayi The experimental gradient in roughness that would thus does not seem to be directly related to its habitat. However, likely encompass the range of substrates C. taunayi would the use of the basic locomotion of lizards only on sand and encounter during its ontogeny. One would expect the plantar gravel and its modiﬁcation (by elimination of the mechan- surface of the feet and of the digits of C. taunayi to have ical action of the body undulation) on smooth surfaces suitable coeﬃcients of friction with the type of surfaces 12 International Journal of Zoology commonly encountered by individuals, and hence it is physiology, and biochemistry. Hence it can be expected that noteworthy that C. taunayi is unable to progress forward on below a lower threshold for some substrate properties—such perspex, while other gymnophthalmids are able to do so [14, as roughness and friction—performance will be nil, and at an 15]. This locomotor limitation in C. taunayi indicates a lower upper threshold for such substrate properties, performance threshold value of roughness below which propulsive friction will be maximized (and thus cannot increase), for instance, if does not occur; that is, there is a constraint in performance adhesion is optimal. Surfaces have friction values that impose imposed by very low friction substrates, although, obviously, such lower and upper thresholds for locomotor perfor- none of the cited gymnophthalmids are exposed to such low mances (the lower threshold in friction for C. taunayi on per- friction coeﬃcients in their natural habitats. spex has been already mentioned). Furthermore, there will When lizards are made to move on diﬀerent substrates be a range of values for the substrate property in which per- one wishes to associate variation in the substrate properties formance is directly correlated with the substrate property to variation in locomotor performance, ideally to identify values. This simple model can be slightly modiﬁed to account which substrate properties induce variation in kinematic for diﬀerential performances of diﬀerent kinematic variables variables, and more speciﬁcally, the direction and magnitude in the same substrate by stating that their upper and lower of the variation induced. In other words, one wishes to asso- thresholds do diﬀer. In addition, the slopes of the responses ciate substrate properties, such as roughness, with speciﬁc of kinematic variables to the same range of variation of the ways in which lizards apply forces to the substrate to gen- substrate property may themselves be diﬀerent. erate forward thrust, and how diﬀerent substrates inﬂuence When the log means of kinematic variables correlated the ﬁnal performance, as measured by speed. signiﬁcantly with log roughness, we take that to mean that Based on our previous analyses of other gymnoph- performance was in the region of a linear response (between thalmids [14, 15] we predicted that the locomotor perfor- thresholds), and a parsimonious explanation as to why a mance should increase according to a gradient in friction, given kinematic variable did not signiﬁcantly ﬁt the model here roughly approximated by the gradient in roughness. log means × log roughness on all substrates, but only some of Overall, these predictions have received support in the them would be that the performance for such a variable and present study; namely, (i) in the MLR analysis there was a for a given substrate was either below the lower or above the positive correlation between the sum of the partial slopes upper thresholds of response. In addition, one cannot rule of RSL and SFR and the logarithm of roughness, thus out that deviation from such log-log model for particular showing that modulation of speed responded to the gradient, kinematic variables, and for particular combinations of and the sums of slopes were greater than unity revealing kinematic variables and substrates, could be due to inﬂuence increasing returns to scale according to increasing roughness; of additional, nonidentiﬁed, and properties of the substrates (ii) the pattern of pairwise diﬀerences between substrates for besides roughness. Also, it should be noted that a broader the univariate analysis of each kinematic variable expected range of values for relative speed, stance duration, and swing if they responded to the rank order in roughness; (iii) duration,aswellasanarrower rangeofvaluesfor duty some kinematic variables had log means that correlated factor, were recorded only on sand and gravel. The absence signiﬁcantly with log roughness; (iv) even when a kinematic of a range of values in diﬀerent orders of magnitude on variable did not statistically ﬁt the model log means × log certain substrates—namely, plastic and wood—might have roughness, some substrates ﬁtted the expectation well, judged also inﬂuenced detected patterns. by the small magnitude of their residuals in the linear ﬁt. However, the analyses of locomotor performance under 4.4. Determination of Speed. The spontaneous absolute the gradient in roughness also uncovered some important speeds recorded for C. taunayi ranged from 0.05 to −1 deviations: (i) some kinematic variables did not show the 0.58 m∗s . McElroy and coauthors  reported the aver- expected pattern of pairwise diﬀerences for the gradient, (ii) age speed for 18 lizard species. Pooling the data provided by some kinematic variables simply did not show a signiﬁcant these authors for their lizard species for both running and −1 correlation between log means and log roughness, and (iii) walking, the average speeds ranged from 0.16 to 1.84 m∗s . −1 in those cases where the kinematic variable did not ﬁt the The average speed of C. taunayi (0.16 m∗s ) was the same model either all substrates signiﬁcantly deviated from its as that of Tracheloptychus petersi . Van Damme and expectation or at least two substrates did so. These results coauthors  provided absolute speeds for 11 lizard species −1 raise the following additional questions: why did certain which ranged from 1.25 to 3.20 m∗s , without mentioning kinematic variables behave according to this model whilst total body lengths (BL) of the specimens. But, as recorded others did not? And why did some other variables, and for by Irschick and Jayne , other lizards with relatively certain substrates, deviate from the model and others did longer limbs than C. taunayi attained much higher average −1 not? speeds, For example, Callisaurus draconoides:4.00m∗s , −1 In order to explain the heterogeneity of responses shown Uma scoparia:3.90m∗s ,and Phrynosoma platyrhinos: −1 by the kinematic variables and the additional heterogeneity 2.10 m∗s . Thus, as already mentioned by Renous and between substrates in the response of a given kinematic coauthors , gymnophthalmids seem to achieve low variable, that is, an interaction between kinematic response average spontaneous speeds. Note, however, that Irschick and and substrate, we need a model which considers the rela- Jayne  data were obtained on treadmills, whilst. McElroy tionship between locomotor performance and roughness. and coauthors  allowed individuals to run on a level Animals have biomechanical limits imposed by morphology, track, as with gymnophthalmids ([14, 15] present paper). International Journal of Zoology 13 Maximum or sprinting speeds was not measured for Colobodactylus taunayi individuals were allowed to C. taunayi.The spontaneous maximum speed recorded was choose voluntary speeds on the substrates, and thus a range −1 0.58 m∗s . Hemidactylus garnotii, with a similar total body of speeds was obtained, and increases in speed were attained length and relatively short limbs, had maximum speed by simultaneously increasing both stride length and stride −1 of 0.84 m∗s . Another gecko, Coleonyx variegatus, frequency, as found in other lizard species (e.g., [15, 45, 46, −1 reached 5.03 m∗s , and a skink with short limbs, Eumeces 53, 57]). Thus it can be argued that speed modulation should −1 skiltonianus, reached 0.75 m∗s . The lizards studied by be best viewed within the MLR framework in which (i) the McElroy and coauthors  had maximum speeds ranging joint eﬀect of both stride length and of stride frequency −1 from 0.20 to 3.57 m∗s , but these included both walking can be examined concurrently, and (ii) the interdependence and running mechanics. The maximum speeds for species among these two variables is taken into account in the very −1 using walking mechanics ranged from 0.20 to 1.23 m∗s , structure of the MLR equation. Moreover, the possibility while those utilizing running mechanics ranged from 0.28 of rigorously examining the partial regression coeﬃcients −1 to 3.57 m∗s . Vanhooydonck and coauthors reported allows for the statistical control of the eﬀect of either maximum speeds for 11 lizard species that ranged from independent variable, maintaining it ﬁxed, whilst examining −1 1.09 to 3.34 m∗s , but without mentioning total body the eﬀect on speed of one unit change in the other variable. lengths of the specimens. Among the Gymnophthalmidae, Hence we view the use of the logarithmized form of the the maximum absolute speed recorded for Micrablepharus constant speed model, that is, the fully parameterized MLR −1 maximiliani was 0.41 m∗s , and that for Colobosaura framework, as enabling a higher internal consistency in this −1 modesta was 0.50 m∗s (see Renous and coauthors ). type of kinematic analysis. Maximum relative speeds (the means of the four largest According to Vanhooydonck and coauthors and speeds of each individual studied, on all substrates) recorded McElroy and coauthors  short-limbed lizards would for V. rubricauda and P. tetradactylus were, respectively, be expected to increase speed mainly by increasing stride −1 9.91 and 4.37 BL∗s , whilst for C. taunayi it was frequency. In our study, as revealed by the MLR analysis, −1 8.21 BL∗s . Only one individual each of M. maximiliani increases in speed—on all substrates, except wood—were and of C. modesta were studied by Renous and coauthors attained by joint increases in both stride length and stride , and the means of the four highest speeds attained frequency with equal relative contributions of each. On −1 by each individual were, respectively, 4.69 and 3.49 BL∗s . wood, however, the increase in stride length was three times These maxima for all gymnophthalmids are low relative higher than the increase in stride frequency when individuals speeds, even when compared to mean relative speeds (not increased speed. Such asymmetrical contributions are most maximum relative speeds) of other lizard species. For probably due to the two independent ways, the speeds were example, Kohlsdorf and coauthors reportedmean measured, and that, in the MLR approach, variation in speed −1 running speeds of 23.8 BL∗s for Tropidurus itambere is to be necessarily explained by the within stride cycle mea- −1 and 29.1 BL∗s for T. oreadicus. Reilly and Delancey surements. Thus, on wood, there probably occurred acceler- −1 data reported9.15BL∗s for Sceloporus clarkii.The ations and decelerations responsible for diﬀerences between mean relative speeds of ﬁve lizard species running on the speeds measured within and outside the stride cycle. treadmills studied by Irschick and Jayne are Cal- There was thus signiﬁcant heterogeneity in the way speed −1 −1 lisaurus draconoides 52.6 BL∗s , Uma scoparia 48.8 BL∗s , was modulated through variation in its direct determinators −1 Phrynosoma platyrhinos 26.6 BL∗s , Dipsosaurus dorsalis among substrates. −1 −1 41.4 BL∗s ,and Cnemidophorus tigris 36.5 BL∗s . Further, Nonetheless, when speed modulation was examined the sprinting speeds of some of these species are even higher; using only those variables measured for each stride cycle, for example, Callisaurus draconoides may reach more than namely, RSL and SFR, no diﬀerence in the relative modula- −1 50 BL∗s [44, 56]. Although, admittedly, the spontaneous tion of stride frequency with respect to relative stride length speeds attained by gymnophthalmids on level substrates are was found among substrates, indicating a similar relative not directly comparable to the speeds of lizards forced to run covariation of both variables in all substrates. Note, however, on treadmills or to sprinting speeds, the available data sug- that the relative contributions of such variables to speed gests that gymnophthalmids have low absolute and relative variation was such that for each SD unit in RSL, only a speeds, associated with the short length of their limbs. fractional unit in SFR occurred, showing speed modulation In the constant speed model the joint eﬀect of stride to be mainly through relative stride length. Furthermore, for length and stride frequency is multiplicative, and both larger values of RSL, a higher variation in SFR was found, variables are correlated with each other. Hence it can be indicating relative modulation of these two variables with argued that simple bivariate analyses relating either RSL respect to one another to be tighter for smaller RSL values. or SFR to RSP are not really informative regarding speed modulation because these analyses assume independent 5. Epilogue eﬀects of each variable on speed. Modulation of speed can be made conceptually clearer by considering that any given Ultimately, precise knowledge of the response pattern of speed can be the result of several combinations of stride kinematic variables to the gradient in roughness demands length and frequency values. Thus, these combinations imply more precise investigations of the biomechanics of locomo- an inverse relationship between RSL and SFR, which further tion when only a single property of the substrate varies in highlights their interdependence. the gradient, thus allowing accurate and precise association 14 International Journal of Zoology of biomechanical characteristics of the locomotor system of References the individuals and the speciﬁc property being examined.  P. Uetz, “The reptile database,” 2012, http://www.reptile- Nonetheless, despite the multidimensional nature of the database.org/. properties of the substrates in our experimental setup, inter-  W. 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