The differing limb dynamics and postures of small and large terrestrial animals may be mechanisms for minimising metabolic costs under scale-dependent muscle force, work and power demands; however, empirical evidence for this is lacking. Leghorn chickens (Gallus gallus domesticus) are highly dimorphic: males have greater body mass and relative muscle mass than females, which are permanently gravid and have greater relative intestinal mass. Furthermore, leghorns are selected for standard (large) and bantam (small) varieties and the former are sexually dimorphic in posture, with females having a more upright limb. Here, high-speed videography and morphological measurements were used to examine the walking gaits of leghorn chickens of the two varieties and sexes. Hindlimb skeletal elements were geometrically similar among the bird groups, yet the bird groups did not move with dynamic similarity. In agreement with the interspecific scaling of relative duty factor (DF, the proportion of a stride period with ground contact for any given foot) with body mass, bantams walked with greater DF than standards, and females walked with greater DF than males. Greater DF in females than in males was achieved via variety-specific kinematic mechanisms, associated with the presence/absence of postural dimorphism. Females may require greater DF in order to reduce peak muscle forces and minimise power demands associated with lower muscle to reproductive tissue mass ratios and smaller body size. Furthermore, a more upright posture observed in the standard, but not bantam, females, may relate to minimising the work demands of being larger and having proportionally larger reproductive tissue volume. Lower DF in males relative to females may also be a work-minimising strategy and/or due to greater limb inertia (as a result of greater pelvic limb muscle mass) prolonging the swing phase.

The size of an animal influences its walking kinematics. When moving at the same speed (U, m s−1), larger animals generally take longer and fewer strides per unit time than smaller animals. Comparison of the walking kinematics of different-sized animals can be conducted at speeds at which the ratios of inertial to gravitational forces acting upon the body centre of mass (CoM) are equal, using either the Froude number (Fr=U2/ghhip) or its square root, often termed relative speed:
formula
(1)

where hhip is hip height (m) and g is gravitational acceleration (9.81 m s−2) (Alexander, 1976; Alexander and Jayes, 1983). Dynamic similarity of motion between different-sized animals requires geometric similarity in body plan and equal values of dimensionless kinematic parameters (scaled appropriately to negate the effects of size) for a given relative speed (Alexander, 1976; Alexander and Jayes, 1983; Hof, 1996).

Animals may move in such a way as to minimise metabolic cost. The metabolic cost of transport (CoT) is the energy required to move a unit body weight over a unit distance [power/(body weight×speed)]. Geometrically similar animals of different size moving in a dynamically similar fashion are expected to have equal CoT (Alexander and Jayes, 1983). The dynamic similarity hypothesis of Alexander and Jayes (1983) postulated that different quadrupedal mammals would locomote with dynamic similarity at equivalent relative speeds. Within non-cursorial (<1 kg) and cursorial (>10 kg) mammalian groups (Jenkins, 1971), the hypothesis was supported. Observed kinematic differences between the two groups, however, were not accounted for (Alexander and Jayes, 1983). Furthermore, between avian species of small and large body size, there is considerable deviation from dynamic similarity of locomotion (Gatesy and Biewener, 1991; Abourachid and Renous, 2000; Abourachid, 2001). However, a general pattern exists across these vertebrates, whereby smaller species move with greater relative duty factor (DF, the proportion of a stride with ground contact for any given foot) and relative stride lengths. These deviations from dynamic similarity of locomotion have been attributed to differences in the relative lengths of the limb segments and limb posture (Alexander and Jayes, 1983; Gatesy and Biewener, 1991; Abourachid and Renous, 2000; Abourachid, 2001). Crouched and upright limb postures are generally adopted by small and large vertebrate species, respectively, which are clear departures from geometric similarity in body form (Biewener, 1989; Gatesy and Biewener, 1991).

The differing gait kinematics and postures of small and large terrestrial animals may be mechanisms for minimising metabolic costs under scale-dependent muscle force, work and power demands; however, empirical evidence for this is lacking. Body weight (∝l3v1, where l is length and v is volume) increases at a faster rate with body size than the strength (i.e. ability to resist forces, ∝cross-sectional area ∝l2v2/3) of the biological materials that must support it (Biewener, 1989). An erect limb aligns body weight with each limb bone's long axis, reducing mechanical loading on the muscles associated with turning moments about the joints (Biewener, 1989). The ‘cost of muscle force’ hypothesis for the scaling of limb posture and gait with body size states that the more upright limbs of larger species serve to reduce the large forces that would otherwise have to be exerted by the limb muscles (Biewener, 1989). An alternative to the cost of muscle force approach is that animals of differing size optimise active muscle volume under scale-dependent muscle work and power demands (Usherwood, 2013). A more erect limb requires shorter stance (push-off) periods, reducing fore–aft speed fluctuations and, consequently, muscle work (J kg−1) requirements (Usherwood, 2013). Although the same benefits of an upright limb (in terms of reducing muscle work) would apply to smaller animals, theoretically, their muscle power (J s−1 kg−1) requirements may be disproportionately high (Usherwood, 2013). Therefore, a more crouched limb, requiring a longer push-off period, may act to minimise power requirements in smaller animals (Usherwood, 2013). Indeed, for a given relative speed, human (Homo sapiens) toddlers were found to deviate more from work-minimising gaits than adults, via longer relative stance periods (Hubel and Usherwood, 2015).

List of symbols and abbreviations
     
  • B

    female bantams

  •  
  • B

    male bantams

  •  
  • CoM

    centre of mass

  •  
  • DF

    duty factor

  •  
  • Fr

    Froude number

  •  
  • fstride

    stride frequency

  •  
  • relative stride frequency

  •  
  • g

    gravitational acceleration

  •  
  • hback

    back height

  •  
  • hhip

    hip height

  •  
  • hhiplsegs

    posture index

  •  
  • L

    female standards

  •  
  • L

    male standards

  •  
  • lfem

    femur length

  •  
  • lstride

    stride length

  •  
  • relative stride length

  •  
  • ltars

    tarsometatarsus length

  •  
  • ltib

    tibiotarsus length

  •  
  • Mb

    body mass

  •  
  • tstance

    stance duration

  •  
  • relative stance duration

  •  
  • tswing

    swing duration

  •  
  • relative swing duration

  •  
  • relative speed

  •  
  • U

    speed

  •  
  • wfem

    femur width

  •  
  • wpelv

    pelvis width

  •  
  • wtars

    tarsometatarsus width

  •  
  • wtib

    tibiotarsus width

  •  
  • Σlsegs

    sum of the hindlimb long bone lengths

Understanding of the gaits and postures of different-sized animals is compromised because the majority of comparisons are conducted between different species (Alexander and Jayes, 1983; Gatesy and Biewener, 1991; Abourachid and Renous, 2000; Abourachid, 2001). Intraspecifically, the sexes may differ not only in body size (Lislevand et al., 2009; Remes and Szekely, 2010) but also in morphological proportions, which are likely to influence muscle force, work and power demands. For example, in many vertebrate species, the relative proportions of total body mass (Mb) allocated to different somatic and reproductive components are usually biased towards males and females, respectively (Shine et al., 1998; Hammond et al., 2000; Lourdais et al., 2006). Furthermore, female reproductive specialisation may even require specific skeletal proportions [e.g. a wider pelvis (Baumel, 1953; Smith et al., 2002; Cho et al., 2004) or posture, during pregnancy (Franklin and Conner-Kerr, 1998) or gravidity (Rose et al., 2015b)]. Most studies on gait kinematics, however, have been conducted using individuals of only one sex (Reilly, 2000); without comparing sexes (Rubenson et al., 2004; Watson et al., 2011); or using individuals whose sexes were not reported (Gatesy and Biewener, 1991; Abourachid, 2000, 2001; Abourachid and Renous, 2000; Griffin et al., 2004; Nudds et al., 2010). Previous studies have identified sex differences in walking kinematics in humans (Bhambhani and Singh, 1985) and two species of bird (Lees et al., 2012; Rose et al., 2014), but whether size variations alone or both size and additional unidentified sexual dimorphisms were behind the differences in kinematics was not determined.

The leghorn chicken, Gallus gallus domesticus (Linnaeus 1758) is highly dimorphic, with males having greater body size and muscle mass than females (Mitchell et al., 1931; Rose et al., 2016a). Female leghorns have greater digestive organ masses than males and remain permanently gravid (Mitchell et al., 1931). Furthermore, leghorns are selectively bred for standard (large) and bantam (small) varieties, and only the standard variety is sexually dimorphic in limb posture, with females possessing a more upright limb than males at mid-stance during a walking gait (Rose et al., 2015b). For a given sex, the two varieties are expected to be closer to geometric similarity in anatomical proportions (a prerequisite for dynamic similarity of motion). Whilst the males of the two varieties are geometrically similar in their axial and appendicular skeletons, the bantam males adopt a more upright posture at mid-stance than the standards during a walking gait (Rose et al., 2015a). The morphological variations that have resulted from selective breeding in these leghorns provide a novel opportunity to investigate the effects of limb posture and differing relative locomotor muscle, digestive and reproductive tissue masses (i.e. varied muscle force, work and power demands) on walking dynamics.

Here, high-speed videography and morphological measurements were used to test the hypothesis that male and female standard and bantam varieties of leghorn show clear departures from dynamic similarity of motion associated with their morphological variations.

Animals

Male and female bantam brown leghorns (B and B) and standard-breed white leghorns (L and L) were obtained from local suppliers and housed in the University of Manchester's Animal Unit. All leghorns (>16 weeks, <1 year) had reached sexual maturity and females were gravid. Sexes and varieties were housed separately with ad libitum access to food, water and nesting space. Birds were trained daily for a week to sustain locomotion for ∼5 min within a Perspex® chamber mounted upon a Tunturi T60 (Turku, Finland) treadmill. The kinematics of 24 of the 28 leghorns used for the simultaneously collected metabolic measurements described in Rose et al. (2015b) are presented here (B: N=9, 1.39±0.03 kg; B: N=5, 1.04±0.03 kg; L: N=5, 1.92±0.13 kg; L: N=5, 1.43±0.06 kg; means±s.e.m.). All experiments were approved by the University of Manchester's ethics committee, carried out in accordance with the Animals (Scientific procedures) Act (1986) and performed under a UK Home Office Project Licence held by J.R.C. (40/3549).

Kinematics

The left greater trochanter of the hip of each bird was located by hand and any overlying feathers were removed and replaced with a reflective marker. Each leghorn was exercised at a minimum speed of 0.28 m s−1 and at increasing increments of 0.14 m s−1 (in a randomised order), up to the maximum they could sustain without showing signs of fatigue. The birds were rested between speed trials. All trials were filmed from a lateral view (left of each bird) using a video camera (HDR-XR520VE, Sony, Japan; 100 frames s−1).

All video recordings were analysed using Tracker software (Open Source Physics). Distance was calibrated for each video recording using a known distance from the front to the back of the respirometry chamber. This allowed for the alignment of a calibration tool through the line of travel of each bird (always passing through digit 3), eliminating any error that could be incurred by a bird's displacement from it (i.e. the bird's position on the treadmill/distance from the camera did not affect our distance calibration). At each speed, the phasing of the sum of the vertical kinetic and gravitational potential energies with the horizontal kinetic energy of the body CoM (approximated by the trochanter marker) was determined using spatial and temporal data. Unlike the males, the female leghorns are either unable or unwilling to use grounded running gait mechanics (Rose et al., 2015b). Hence, only data for speeds at which the birds used walking gait mechanics (out of phase fluctuation of gravitational potential and horizontal kinetic energy) were used in the analyses.

The left foot of each bird was tracked across ∼10 continuous strides (constant speed and position) to obtain the times of toe-on and toe-off, which were used to calculate DF, stride frequency (fstride, Hz), stride length (lstride=U/fstride, m), swing duration (tswing, s) and stance duration (tstance, s). A single fixed measure of hip height (hhip) was used per individual (see ‘Morphological measurements’, below) as the characteristic length for normalising their speed and gait kinematic parameters. U was normalised for size differences as the square root of Fr, here termed relative speed . Kinematic parameters were normalised based on the Hof (1996) record of non-dimensional forms of mechanical quantities as: relative stride length , relative stride frequency, relative swing duration and relative stance duration .

Morphological measurements

For each experimental bird, hhip was measured from a video recording (accuracy, ±1 mm) of a slow walking speed (0.28 m s−1) for a minimum of 7 strides. hhip was taken (using the same method as in Rose et al., 2015a,b) as the distance from the treadmill belt (where digit 1 meets the base of the tarsometatarsus) to the hip marker at 90 deg to the direction of travel during mid-stance, when it is at its greatest. Back height (hback) was measured in the same way as hhip. Digital Vernier callipers (accuracy, ±0.01 mm) were used to measure hindlimb long bone (femur, tibiotarsus and tarsometatarsus) length (lfem, ltib, ltars) and width (wfem, wtib, wtars). Total leg length (Σlsegs) was calculated as the sum of the three element lengths. Note that Σlsegs does not represent the true functional length of the hindlimb, because the measurements were taken from dried bones excluding the inter-joint soft tissue. The measurements were taken as the shortest distance between the most proximal and distal grooves of each element, which would further decrease the value of Σlsegs relative to the maximum potential length of the three leg segments if they were vertically aligned. Therefore, a posture index near the value of 1.00 at mid-stance in the present study is not indicative of a completely upright limb. The width of the pelvis (wpelv, the distance between the left and right acetabula) was also measured.

Soft-tissue components from five experimental individuals of each bird group were dissected and weighed upon electronic scales (accuracy, ±0.01 g). Thirteen major muscles of the right pelvic limb (m. iliotibialis cranialis, m. iliotibialis lateralis, m. iliofibularis, m. flexor cruris lateralis pars pelvica, m. flexor cruris medialis, m. iliotrochantericus caudalis, m. femerotibialis medialis, m. pubioischiofemoralis pars lateralis, m. pubioischiofemoralis pars medialis, m. gastrocnemius pars lateralis, m. gastrocnemius pars medialis, m. fibularis lateralis and m. tibialis cranialis) were dissected for a sister study on variety- and sex-specific muscle architectural properties (Rose et al., 2016a). The masses of these muscles were summed to give a comparable total pelvic limb muscle mass between chicken groups. The right breast muscles (m. pectoralis and m. supracoracoideus) and the intestines (small and large combined) were also weighed. Reproductive tissue mass (developing eggs, ovaries and oviduct) was measured from female birds only and was assumed negligible in males in terms of influencing locomotion dynamics. For the bantam females, four of the five reproductive tissue masses measured were from individuals whose experimental data were not included in the present study. These individuals, however, were from the same cohort and underwent the same training and experimental process as the birds for which kinematic data are presented here. All anatomical components were compared between varieties and sexes as a percentage of dead bird body mass.

Statistical analyses

All statistical analyses were conducted in R (v3.0.2 GUY 1.2 Snow Leopard build 558; R Development Core Team, 2011). The Car package (Fox and Weisberg, 2011) was used for all analyses of variance (ANOVA) in which variety and sex were included as fixed factors. Shapiro–Wilk tests were performed on the standardised residuals generated by all statistical models to ensure the data conformed to a normal distribution. Where morphological data (Table 1) did not conform to a normal distribution even after log transformation, a Kruskal–Wallis test was conducted to compare the means of the four groups: B, B, L and L. Dunn post hoc tests were used to indicate which groups differed. The relationships between absolute and relative kinematics variables with U and were compared between the bird groups using linear models. U and were included in the models as covariates and all potential interaction terms were considered before a stepwise backwards deletion of non-significant interaction terms was conducted to simplify the models. Outputs from the final models are reported. Best-fit lines were obtained from the coefficients tables of the final statistical models and were back-transformed where data had been log transformed.

Table 1.

Results of the one- and two-way ANOVA that tested for variety and sex differences in morphological measurements/indices

Results of the one- and two-way ANOVA that tested for variety and sex differences in morphological measurements/indices
Results of the one- and two-way ANOVA that tested for variety and sex differences in morphological measurements/indices

Morphological measurements

Body mass (Mb, Fig. 1A) and total leg length (Σlsegs, Fig. 1B) were greater in the standard than in the bantam variety, and greater in males than in females (Table 1). Hip height (hhip, Fig. 1C), however, was greater in males than in females in the bantam variety, but, conversely, greater in females than in males in the standard variety (Table 1). Posture index (hhiplsegs; Fig. 1D) did not differ between the sexes of the bantam variety; in contrast, the posture index of L was ∼27% greater than that of L, indicative of a more erect limb (Table 1).

Fig. 1.

Morphological measurements for the variety and sex combinations of leghorn chicken. (A) Body mass (Mb). (B) Total leg length (Σlsegs, sum of the three skeletal element lengths). (C) Hip height (hhip). (D) Posture index (hip height:total leg length). Bars represent means±s.e.m. for standard males (L, grey), standard females (L, purple), bantam males (B, blue) and bantam females (B, red). Significant variety, sex and variety×sex interaction terms are denoted by V, S and I, respectively (***P<0.001). Results of the two-way ANOVA conducted to test for variety and sex differences are in Table 1. These morphological differences have been reported previously (Rose et al., 2015b) for a different sample size.

Fig. 1.

Morphological measurements for the variety and sex combinations of leghorn chicken. (A) Body mass (Mb). (B) Total leg length (Σlsegs, sum of the three skeletal element lengths). (C) Hip height (hhip). (D) Posture index (hip height:total leg length). Bars represent means±s.e.m. for standard males (L, grey), standard females (L, purple), bantam males (B, blue) and bantam females (B, red). Significant variety, sex and variety×sex interaction terms are denoted by V, S and I, respectively (***P<0.001). Results of the two-way ANOVA conducted to test for variety and sex differences are in Table 1. These morphological differences have been reported previously (Rose et al., 2015b) for a different sample size.

Each hindlimb segment was a similar proportion of Σlsegs (Table 2) in all of the groups excluding B, which had a relatively longer lfem, and concomitantly shorter ltars, resulting in a small, but nonetheless statistically significant, difference (Table 2). The width of each limb segment (Table 2) was a similar proportion of its respective segment length in all groups (Table 2). The finding of a more erect posture in L when compared with the other three groups was further supported by indices incorporating the height of the back (hback). hhip:hback did not differ between the bird groups, and Σlsegs:hback was lower in L than in the other three groups (Table 2). wpelv, relative to Σlsegs (Table 2), did not differ between the sexes, but was ∼1% greater in the bantams than in the standards (Table 2).

Table 2.

Mean (±s.e.m.) morphometric indices and results of the statistical tests conducted to investigate whether the indices differ between varieties and sexes

Mean (±s.e.m.) morphometric indices and results of the statistical tests conducted to investigate whether the indices differ between varieties and sexes
Mean (±s.e.m.) morphometric indices and results of the statistical tests conducted to investigate whether the indices differ between varieties and sexes

Total pelvic limb muscle mass (the sum of the masses of 13 pelvic limb muscles) was a greater percentage of body mass (Fig. 2) in males than in females in both varieties (Table 1). Total pelvic limb muscle mass was also greater in the bantam than in the standard variety (Fig. 2, Table 1). The observed differences between varieties, however, were small in comparison to the sexual dimorphisms. The same statistical outcomes obtained for the total pelvic limb muscle mass were mirrored by the breast muscles, m. pectoralis and m. supracoracoideus (Fig. 2, Table 1). Intestine mass as a proportion of body mass (Fig. 2) was greater in females than in males (Table 1). The two varieties, however, shared similar relative intestinal masses. The reproductive tissue mass as a percentage of body mass was greater in L (11.49±0.56%) than in B (8.40±0.08%).

Fig. 2.

Anatomical components as a percentage of body mass for the variety and sex combinations of leghorn chicken. Bars represent means±s.e.m. for L (grey), L (purple), B (blue) and B (red). Limb muscle mass was calculated as the sum of 13 major pelvic limb muscles on the right limb. M. pectoralis and M. supracoracoideus mass expressed as a percentage of body mass (Mb) is for the right side of the body only. Reproductive tissue mass was assumed negligible in males in terms of influencing gait. Significant variety and sex effects are denoted by V and S, respectively. Significance levels: *P<0.05, **P<0.01 and ***P<0.001. Results of the one- and two-way ANOVA conducted to test for variety and sex differences are in Table 1.

Fig. 2.

Anatomical components as a percentage of body mass for the variety and sex combinations of leghorn chicken. Bars represent means±s.e.m. for L (grey), L (purple), B (blue) and B (red). Limb muscle mass was calculated as the sum of 13 major pelvic limb muscles on the right limb. M. pectoralis and M. supracoracoideus mass expressed as a percentage of body mass (Mb) is for the right side of the body only. Reproductive tissue mass was assumed negligible in males in terms of influencing gait. Significant variety and sex effects are denoted by V and S, respectively. Significance levels: *P<0.05, **P<0.01 and ***P<0.001. Results of the one- and two-way ANOVA conducted to test for variety and sex differences are in Table 1.

Therefore, all four groups were similar in their hindlimb skeletal bone geometry (a prerequisite of dynamic similarity of locomotion). The sexes, however, differed markedly in each of the measured anatomical masses when expressed as percentage body mass. In contrast, with the exception of limb posture and the relative mass of the female reproductive system, for a given sex, the two varieties of leghorn were more similar in their anatomical proportions.

Walking kinematics and dynamics

DF, tswing and tstance were negatively correlated with U, and lstride and fstride were positively correlated with U. The same correlations were also found for the relationship between size-normalised kinematics parameters and . For all four groups of leghorns, the exponents describing the relationships between absolute or size-normalised parameters and U or were similar, unless stated otherwise below.

Across all speeds, DF (Fig. 3A) was greater in females than in males (∼2%) and greater in the bantam than in the standard variety by ∼2% (Table 3). At comparable , DF was, similarly, greater in females than in males in both varieties and this sex difference was greater in the bantams. In addition, DF was greater in the bantam than in the standard variety (Fig. 3B, Table 3).

Fig. 3.

Absolute gait kinematics parameters versus speed and relative gait kinematics parameters versus relative speed. Duty factor (DF; A,B), stride frequency (fstride, C), relative stride frequency (, D), stride length (lstride, E), relative stride length (, F), swing duration (tswing, G), relative swing duration (, H), stance duration (tstance, I) and relative stance duration (, J) are shown versus speed (U, left) and relative speed ( , right). Each data point (L, grey circles; L, purple crosses; B, blue circles; and B, red crosses) represents a single trial for an individual bird. Best-fit line equations and the results of the linear models conducted to test for variety and sex differences are in Table 3.

Fig. 3.

Absolute gait kinematics parameters versus speed and relative gait kinematics parameters versus relative speed. Duty factor (DF; A,B), stride frequency (fstride, C), relative stride frequency (, D), stride length (lstride, E), relative stride length (, F), swing duration (tswing, G), relative swing duration (, H), stance duration (tstance, I) and relative stance duration (, J) are shown versus speed (U, left) and relative speed ( , right). Each data point (L, grey circles; L, purple crosses; B, blue circles; and B, red crosses) represents a single trial for an individual bird. Best-fit line equations and the results of the linear models conducted to test for variety and sex differences are in Table 3.

Table 3.

Results of the linear models that tested for sex differences in absolute/normalised kinematics with speed

Results of the linear models that tested for sex differences in absolute/normalised kinematics with speed
Results of the linear models that tested for sex differences in absolute/normalised kinematics with speed

fstride (Fig. 3C) was greater in females than in males at any given U (0.11 Hz; Table 3). Absolute fstride and the rate of increase in fstride with U were significantly greater in the bantam than in the standard variety. At comparable , was greater in females than in males in the standard variety but, contrastingly, greater in males than in females in the bantam variety (Fig. 3D, Table 3).

At any given U, lstride was greater in males than in females, and by a larger amount in the standard variety (70 mm) than in the bantam variety (20 mm) (Fig. 3E, Table 3), and was associated with a greater difference between the males of the two varieties than between the females of the two varieties. At any given , (Fig. 3F), was greater in females than in males in the bantam variety, but, contrastingly, it was greater in males than in females in the standard variety (Table 3).

At each U, tswing (Fig. 3G) was greater in males than in females and this difference was smaller in the bantam (0.02 s) than in the standard (0.04 s) variety (Table 3). In the bantams, (Fig. 3H), was similar in the two sexes, whilst in the standard variety, it was significantly greater in males compared with females at a given .

tstance (Fig. 3I) was similar in B and B, but was greater in L than in L by 0.03 s at all U (Table 3). Across all , (Fig. 3J, Table 3) was greater in B than in B, yet lower in L than in L.

Therefore, none of the sex or variety differences in gait kinematics were accounted for by correcting for body size differences. The two varieties differed in the mechanisms by which females had elevated DF relative to males. In the bantams, females had relatively longer stance durations than males (Fig. 3J) and the sexes shared similar swing dynamics (Fig. 3H). In the standard variety, females had shorter swing and stance durations than males, but the sex difference in was much greater than that in (Fig. 3H,J).

This study represents the first detailed comparison of the gait of the sexes in any species. Leghorn chickens, although all similar in their hindlimb segment geometry, show considerable variation in limb posture and the relative contributions of anatomical components (skeletal muscle, digestive organs and reproductive tissues) to total body mass. In association with these morphological differences, and in agreement with our hypothesis, none of the leghorn groups walked with dynamic similarity.

Incremental responses of absolute kinematics parameters to increasing U are generally greater in smaller species (Gatesy and Biewener, 1991). However, with the exception of fstride, which increased at a faster rate in bantams than in the standard variety, all birds in the present study showed similar incremental kinematic responses to U, despite the size differences associated with sex and variety. Most of the sex differences in absolute kinematic parameters paralleled interspecies differences, associated with body size (Gatesy and Biewener, 1991). In females of the two varieties, fstride was greater, and lstride, tswing and tstance smaller, at any given U compared with that in their conspecific males, which had greater body size (except for tstance in the bantams, which was similar between the sexes). Similarly, fstride was greater, and lstride, tswing and tstance shorter, at any given U in the bantams compared with the standards. The only parameter that was not comparable to interspecies patterns associated with body size for a given absolute speed was DF. Interspecific scaling patterns would predict the heavier and longer-legged animal to have a greater DF than the lighter, shorter-legged one, at the same U (Gatesy and Biewener, 1991). In contrast, here, females walked with greater DF than males, and bantams walked with greater DF than standards.

In agreement with body size-dependent interspecies differences in DF measured at equivalent relative speeds (Alexander and Jayes, 1983; Gatesy and Biewener, 1991), we found that at any given relative speed, DF was still higher in the smaller bantam relative to the standard variety, and in females relative to males. Deviations from dynamic similarity of motion with increasing body mass are usually associated with increasing limb erectness, i.e. an increasing hhip to Σlseg ratio (Biewener, 1987, 1989; Gatesy and Biewener, 1991). Smaller, more crouched, species can achieve greater lstride relative to their hhip because they can extend the crouched limb, which in turn allows a greater DF (Gatesy and Biewener, 1991). In contrast, a more erect limb is constrained in terms of the range of lstride and DF it can achieve, relative to a given hhip (Gatesy and Biewener, 1991). The similar pelvic limb skeletal geometry of the birds in the present study provides a control for the potential effects of limb segment proportions on walking dynamics and allows investigation into the potential influences of additional morphological characteristics, including limb posture. Despite L having the most-upright limbs, and the lowest relative stride lengths (Fig. 3F), they still produced a greater DF relative to hhip than did the L, whose limbs were more crouched. Furthermore, as sexual dimorphism in limb posture was exclusive to the standards, limb posture cannot explain the similar sex difference in DF in the two varieties. The sexual dimorphism in posture in the standard variety only was reflected in the opposite sex-specific dynamics of , , and at any given between the two varieties (i.e. the sex differences in gait were variety specific, yet ultimately led to greater DF in females than in males). The lower in L than in B and higher in L than in B are consistent with the general consensus that a more upright limb limits the length of a step relative to hhip (Gatesy and Biewener, 1991).

By adopting a more upright limb posture, larger animals reduce the forces per unit area that the muscles must exert and that the bones must resist to counteract joint moments, which would otherwise scale geometrically (stress∝Mb1/3) (Biewener, 1989). Until recently, this has been considered the principal reason for the scaling of limb posture and gait in vertebrates (Biewener, 1989). Why smaller animals do not also have upright limbs so that they could have relatively more gracile and lighter bones, however, is not accounted for by this explanation. Proposed reasons for a more crouched limb include that it may improve manoeuvrability (Biewener, 1989) and stability (Gatesy and Biewener, 1991) or minimise the cost of work associated with bouncing viscera (Daley and Usherwood, 2010). Another potential explanation, however, is that animals optimise muscle mechanical work and power demands during push-off (which are scale dependent) in order to minimise the volume of active muscle for a given size (Usherwood, 2013). In this case, a crouched limb at mid-stance (allowing longer DF) for small animals may serve to reduce power demands (which are high because at any given U, shorter legs require quicker stances), whilst a more upright limb suits the work demands of being large (which are high because a disproportionate amount of body weight must be supported).

The females in the present study may, therefore, benefit from a greater DF, which would decrease the elevated power demands associated with having small limbs, yet greater body weight to support per unit of muscle mass because of gravidity. The L in the present study may have adopted kinematic and postural mechanisms for reducing both the elevated work demands due to gravity (via upright limbs) and the power demands of being small (via longer DF, achieved without a crouched posture). It is possible that L may require a more upright limb than B because of their greater relative reproductive tissue mass. In B, minimising power via a greater relative DF (exceeding that in L) appears to be more important. In guinea fowl, Numida meleagris, adding trunk loads equivalent to 23% of Mb did not affect tswing but led to a 4% increase in tstance (Marsh et al., 2006). In contrast, in several additional avian species, no changes in gait kinematics were associated with the application of trunk loads (McGowan et al., 2006; Tickle et al., 2010, 2013). These experiments, however, involve unnatural loads applied in backpacks and may not represent a true gravid loading condition. The hypothesis that the kinematics of leghorn hens are influenced by muscle mechanical demands associated with gravidity is further supported by the finding than DF increases with the onset of egg laying during sexual maturation in leghorn hens (Rose et al., 2016b). Equally, males may benefit from lower DF via the minimisation of work demands associated with changes in fore–aft acceleration and deceleration, because of being larger.

The hypothesis of Usherwood (2013) that animals adopt kinematic and postural mechanisms to minimise active muscle volume (according to work and power demands) in order to minimise metabolic costs is supported by the present findings together with previously published data on locomotor energy metabolism collected simultaneously from the same birds (Rose et al., 2015a,b). The metabolic cost of transport in gravid female leghorns is in fact lower than allometric predictions based on body mass (Van kampen, 1976; Rose et al., 2015b) and also lower than that of male leghorns (Rose et al., 2015b), which can be linked to their comparatively greater DF. A lower metabolic cost of transport in L than in B (Rose et al., 2015b) can also be linked to more-upright limbs. Additionally, greater relative DF and more upright limb posture may contribute to a lower than expected metabolic cost of transport in B for their body mass and the lack of scaling in the metabolic cost of transport between males of the two varieties (Rose et al., 2015a).

Alternatively/additionally, the greater DF in females relative to males may be a mechanism for reducing peak muscle forces in supporting body weight, which may again be particularly important when carrying proportionally more weight (because of the greater digestive/reproductive tissue volume) with proportionally less muscle volume. Furthermore, chickens artificially selected for egg production are well known to suffer from osteoporosis associated with the utilisation of calcium from medullary limb bone in order to form egg shells (Dacke et al., 1993; Whitehead, 2004). A greater proportion of ground contact throughout the stride to reduce peak forces exerted on the bones may reduce the risk of bone fracture. This argument may be particularly pertinent to L because the pelvic limb skeletal element diameter of the two varieties conformed to geometric, and not elastic (positive allometry), scaling as is found between species (Doube et al., 2012). The bones of L are, therefore, not expected to be any more robust than those of B to assist with supporting proportionally more weight of the reproductive system. The same reasoning may also explain the upright limbs of L.

It is also possible that additional sexual dimorphisms, perhaps in muscle physiology or morphology, are linked to the sex differences in dynamics. For example, simply the distribution of mass across the limb segments may be responsible. In a recent study in which the swing phase kinematics of different charadriiform birds were compared, Northern lapwings (Vanellus vanellus) and Eurasian oystercatchers (Haematopus), which share similar hindlimb long bone proportions, shared similar tswing at any given speed despite oystercatchers having longer and heavier limbs overall (Kilbourne et al., 2016). In comparison to these two species, pied avocets (Recurvirostra avosetta) moved with longer swing durations at higher speeds linked to a more distal concentration of hindlimb mass (Kilbourne et al., 2016). The greater relative pelvic limb muscle mass in males, relative to females (Mitchell et al., 1931; Rose et al., 2016a), may similarly increase limb moment of inertia and prolong the swing phase of the limb, increasing its contribution to the stride period.

In summary, this study represents the first detailed comparison of male and female gait in a bird. Clear departures from dynamic similarity of motion were evident between the sexes in standard and bantam varieties of leghorn chicken. Females walked with greater DF than males at any given relative speed, but this sex difference was achieved through alternative kinematic mechanisms in each variety and linked to variety differences in sex-specific posture. L carry a greater relative reproductive tissue mass than B and potentially represent the first documented example of an animal adopting mechanisms for minimising the demands of both work (via an upright limb, relative to B) and power (via a longer DF than their heavier, more crouched male conspecifics).

We thank two anonymous reviewers for their helpful comments on an earlier version of this manuscript.

Author contributions

R.L.N., J.R.C. and K.A.R. designed the study and contributed to the manuscript. K.A.R. conducted the experiments and statistical analyses with advice from R.L.N. and J.R.C.

Funding

This research was funded by the Biotechnology and Biological Sciences Research Council (G01138/1 and 10021116/1 to J.R.C.). K.A.R. was supported by a Natural Environment Research Council DTA stipend and CASE partnership with the Manchester Museum.

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Competing interests

The authors declare no competing or financial interests.