Impact of hindlimb length variation on jumping dynamics in the Longshanks mouse

In terrestrial vertebrates, jumping is a type of locomotor behavior characterized by a phase of push-off against the substrate, during which both hindlimbs simultaneously extend to provide a propulsive thrust, resulting in an organism becoming airborne (Emerson, 1985; Graham and Socha, 2019). Jumping behaviors can be divided into two broad categories: saltatorial locomotion and leaping. Saltatorial locomotion consists of a series of hops performed in succession to produce a gait with cyclic elastic storage (Harty, 2010). In contrast, leaping is defined by a single-output or acyclic jumping behavior during which all mechanical energy is derived from muscle contraction during take-off, i.e. without energy recovery from previous hops (Günther et al., 1991).

Jumping is phylogenetically widespread, with numerous distantly related groups having convergently evolved jumping behaviors, either as their main mode of travel (e.g. kangaroos) or as a secondary mode of locomotion used in specific ecological or functional contexts, such as predator escape (jerboas and other desert rodents) and prey capture (frogs), or to provide initial acceleration for flight (birds and bats) (James et al., 2007; Marsh, 1999; Schutt et al., 1997). For example, jumping has evolved independently five times in mammals alone (McGowan and Collins, 2018; Moore et al., 2015). Even primarily cursorial mammals, such as lagomorphs, will often also leap as an evasion strategy, because the escape velocity generated by leaping is higher than in running (Djawdan and Garland, 1988; Higham et al., 2017; Williams et al., 2007), and the escape trajectories are less predictable (Bartholomew and Caswell, 1951; Howell, 1932; Moore et al., 2017a). In extant arboreal primates, leaping is typically used to cross gaps in the canopy, as moving on the ground between trees is time consuming, risky and energetically expensive (Günther et al., 1991; Legreneur et al., 2010).

Mammals that frequently engage in leaping behaviors tend to have longer hindlimb skeletal elements relative to body mass than closely related species (Berman, 1985; Christiansen, 1999; Emerson, 1985; James et al., 2007; Marchini et al., 2014; Toro et al., 2003). For example, North American jumping mice (Zapus spp.), Australian hopping mice (Notomys spp.) and jerboas (Family Dipodidae) have convergently evolved slender and elongated hindlimbs compared with related non-jumping rodents (Harty, 2010; Krutzsch, 1954; Wu et al., 2014). Similarly, among primates, galagos and tarsiers have hindlimbs that are significantly longer relative to body size than those of more generalized primates (Günther et al., 1991; Alexander, 1995).

The extensive convergent evolution of elongated hindlimb skeletal morphology among leaping animals strongly suggests that relatively longer hindlimbs evolve adaptively, i.e. under natural selection, because they improve jumping performance. Functionally, hindlimb elongation has been hypothesized to improve jumping performance in two non-mutually exclusive ways: (1) by increasing the capacity of jumping specialists to generate force and hence acceleration (Alexander, 1995; Günter et al., 1991; Harty, 2010; Krutzsch, 1954; Wu et al., 2014), and (2) by extending the take-off period, allowing for a longer period of force application, and therefore a greater impulse (Alexander, 1995; Rankin et al., 2018). Even among animals that are not specialized jumpers, these hypothesized benefits should still convey a performance advantage. If true, then relatively longer hindlimbs should increase evolutionary fitness (reproductive success) within populations of conspecifics that jump. While the ultimate impacts of performance on evolutionary fitness are challenging to measure directly, the effect of morphological variation among conspecifics on performance, as a proxy for evolutionary fitness, can be tested empirically (Arnold, 1983).

Investigation within species, however, has yielded mixed results regarding the effect of limb length on jumping ability. For example, in mammals, jump performance of domestic cats (Felis silvestris catus), specifically take-off velocity, is significantly positively correlated with relative hindlimb length (Harris and Steudel, 2002). Intraspecific studies of individual species of frogs (Choi and Park, 1996) and anole lizards (Losos et al., 1989; Toro et al., 2003) have found no significant impact of limb length on jumping performance. Toro et al. (2003) only detected an intraspecific hindlimb effect on acceleration in one of three Anolis species, and thus concluded hindlimb length was a poor predictor of performance below the species level.

As a complementary approach to comparing conspecific jumping performance, this study sought to determine which aspects of jumping performance and muscular morphology, if any, are altered within a population following selection for hindlimb elongation. The Longshanks artificial selection experiment was established to study the mechanistic basis of microevolutionary change in hindlimb morphology (Marchini et al., 2014; Marchini and Rolian, 2018), and its functional consequences (Sparrow et al., 2017). By selectively breeding an outbred mouse stock (CD-1) for increased tibia length relative to body mass, we established two replicate lines of mice (Longshanks lines LS1 and LS2) with tibiae that are on average 15% longer, but with the same average body mass, as random-bred controls from the same genetic background (Marchini et al., 2014). When mice from the Control line are pooled with Longshanks mice, an ‘artificial’ population with a bimodal distribution of relative hindlimb length is obtained. This creates an idealized population, reared under identical conditions, with an increased range of variation in a single trait of interest.

The aim of this study was to test whether differences in relative hindlimb length within a population are associated with predictable differences in jumping performance. The measures of performance considered in this study were both behavioral and biomechanical in nature. Specifically, we assessed (1) self-selected maximum jump height, and (2) aspects of jump dynamics and biomechanics at standardized vertical distances. Our general hypothesis was that the elongated hindlimb bones of Longshanks mice alter how their hindlimbs move during take-off compared with controls, leading to two specific hypotheses regarding their jumping performance. First, from a behavioral standpoint, we predicted that Longshanks mice would jump higher on average and achieve a greater maximal jump height (hypothesis 1). Second, we hypothesized that – when jumping to the same height – Longshanks mice would exhibit differences in hindlimb biomechanics that reflect improved jumping/propulsive performance when compared with controls (hypothesis 2). Specifically, at each of three standard heights, we predicted greater take-off duration (in s), take-off velocity (whole body, in m s⁻¹) and angular velocities (in deg s⁻¹) of the hindlimb joints, and greater propulsive forces (standardized to body weight) in the Longshanks mice.

Complementary to this, we also investigated plantarflexor morphology to determine whether there had been changes in soft tissue anatomy that are associated with the observed increase in tibia length in Longshanks mice. We hypothesized skeletal elongation would be associated with altered plantarflexor morphology (hypothesis 3). The gastrocnemius was analyzed because it is a functionally significant biarticular muscle that spans the region that underwent the most elongation in response to artificial selection in Longshanks mice (the tibia). This musculotendinous unit was also chosen because of its functional importance during high acceleration tasks such as leaping, by acting both as a plantarflexor to generate power at the ankle and as a biarticular strut transferring proximally derived power from the hip and knee distally to be delivered at the ankle (Biewener and Blickhan, 1988; Moore et al., 2017b; Schwaner et al., 2018). We predicted muscle volume, cross-sectional area and length of the Longshanks mice gastrocnemius muscle bellies and tendon would be proportionally greater than in controls, essentially ‘filling in’ the space added by tibia elongation.

To address our hypotheses and predictions, we collected behavioral, kinetic, kinematic and anatomical data on a cohort of newly weaned Longshanks and Control mice, the ‘jumping’ or JMP cohort (Fig. 1A). Mice were trained to jump onto a platform over 30 or more training sessions, while behavioral data on their jumping were collected (hypothesis 1). Once all mice were trained and had achieved their individual behavioral maximum, we filmed their jumps to collect kinetic and kinematic data at specific heights (hypothesis 2). Finally, we sampled some of the JMP cohort to dissect and evaluate plantarflexor anatomy (hypothesis 3). For this part of the study, we compared members of the JMP cohort with a ‘sedentary’ or SED cohort to confirm that any changes in muscle architecture were not due to training or to jumping habitually from a young age.

The Health Sciences Animal Care Committee at the University of Calgary approved all procedures involving live animals (protocol AC13-0077), and these procedures were conducted in accordance with best practices from the Canadian Council on Animal Care. This experiment used a sample of mice from the 22nd generation of the Longshanks selection experiment (F22). Details on husbandry and selective breeding protocols used to generate the Longshanks mouse lines can be found in Marchini et al. (2014).

The JMP sample included 36 mice in total: nine Control mice from three separate litters, 12 Longshanks Line 1 mice (hereafter LS1) from four litters, and 15 Longshanks Line 2 mice (hereafter LS2) from five litters. The JMP sample was randomly split into three training groups that contained individuals from all three lines. The SED sample included 24 mice in total: nine Controls from four litters, seven LS1 from four litters and eight LS2 from four litters. To remove the potentially confounding effects of sex on locomotor behaviors and overall body mass (Beatty, 1979, 1984; Dalla and Shors, 2009), only female mice were used in all experimental groups. After reaching adult body mass (when mean mass converged at 30±10 g and mass measurements on 5 consecutive days varied by less than 5 g) the JMP mice were put on a restricted diet capped at 15% body mass per day (Pico-Vac lab rodent chow, 20% protein, 4.5% fat) and fasted overnight prior to training sessions, in order to increase their incentive to earn a food reward. The SED mice were fed the same low-fat chow, ad libitum.

All training and filming sessions took place within a custom-built Plexiglas enclosure (Fig. 1B). The bottom of the enclosure had an integrated force plate (HE6X6 Hall Effect Low Load Miniature Force Platform, AMTI, Watertown, MA, USA), flush with the floor, to collect ground reaction forces (GRFs). One end of the enclosure was fitted with an adjustable opaque platform that could be raised or lowered to the desired height.

Training of the JMP mice began immediately after weaning and was based on positive reinforcement protocols (Staddon and Cerutti, 2003; Zbinden, 1981). A detailed explanation of the training protocol is available in the Supplementary Materials and Methods. Briefly, mice were placed in the Plexiglas enclosure for 15 min to acclimate, and then engaged in a 15 min training session 2–3 times per week and on non-consecutive days. A peanut butter reward and clicker were used to get the mouse to jump onto the platform, which was raised in 2 cm increments following a successful jump.

Behavioral performance, specifically the frequency of each locomotor behavior and height of the platform the mice attempted to reach, started to plateau after ∼10 training sessions. All mice had achieved a behavioral plateau by 15 training sessions (Fig. 2). Behavioral data collection began after 15 training sessions. After at least 30 training sessions, filming and force trials for biomechanical data began (Fig. 1A).

During each data collection session, the locomotor method used to get onto the raised platform was qualitatively described throughout 15 min sessions as: (1) bimanual pull-up: a slow, forelimb-dominated movement with little hindlimb involvement; (2) lunge-jump: a quick, hindlimb-dominated movement with a punctuated acceleration phase where the forelimbs are primarily used as a strut, for balance and redirection of the center of mass (COM) on the platform (Graham and Socha, 2019; also referred to as a ‘vault jump’ in Crompton and Sellers, 2007); or (3) bipedal leap: a hindlimb-dominated movement fully powered by the hindlimbs without using the forelimbs for balance. The height achieved was measured vertically from the floor of the enclosure to the bottom of the platform.

Jumping events and behaviors, including limb kinematics, were filmed at 250 frames s⁻¹ using three high-resolution AOS S-PRIplus cameras with 50 mm f0.95 lenses. Film data were collected using AOS Imaging Studio version 3.9.5.4 (AOS Technologies AG). During each filming session, the platform was placed at one of three predetermined heights, and the mouse remained in the enclosure until two films had been collected. Predetermined heights of 6, 10 and 14 cm were selected to standardize the biomechanical data across individuals and groups. Based on our observations during the behavioral data collection, the platform heights represented a low, easily achievable jump (6 cm), a medium jump (10 cm), and a jump near the behavioral maximum (14 cm). To capture joint positions, landmarks were placed externally on hindlimb joints (Fig. 1C). Mice were first anesthetized by isoflurane inhalation and the relevant areas were shaved; the joint was then palpated and marked with permanent marker. The following landmarks were selected: hip – the outer surface of where the femur articulates with the acetabulum; knee – the femoral–tibial articulation; ankle – the tibial–talar junction; MT – the metatarsophalangeal joint; tail – the base of the tail; and eye – the middle of the eye (landmark added during digitization).

Video data were digitized using ProAnalyst 3D Professional Edition v.1.5.8.0 (XCitex, Woburn, MA, USA). Video footage was calibrated in 3D space using a fixture with 96 known points. Footage was digitized from initiation, defined here as the time point at which a mouse crouched and reached the minimum 3D linear (Euclidean) distance between its hip and ankle landmarks, to take-off, defined here as the frame when the feet were no longer touching the force plate and the mouse was no longer interacting with the substrate (F_resultant≈0 N).

To ensure that data analysis was based on comparable behaviors, only lunge-jumps were compared, while bipedal leaps and bimanual pull-ups were excluded. Bipedal leaps occurred too infrequently to allow robust comparison, because many mice (crucially, all individuals from the Control line) never executed a bipedal leap (see Results). Lunge-jumps were distinguished from bimanual pull-ups by a pronounced acceleration phase in the force trace and qualitative visual cues such as the position of the forepaws and a conspicuous crouch at initiation that was absent during bimanual pull-ups.

Exclusion criteria were established prior to analysis. Films where the landmarks went out of plane, due to either camera position or body rotation, were not used. Jumps identified on footage as being propelled by a single leg were also removed. If ProAnalyst identified a spatial uncertainty of landmarks greater than 5 mm within a trial, the trial was re-digitized. If following re-digitization, the error/uncertainty remained greater than 5 mm, the trial was excluded from analysis.

Whole-body instantaneous take-off velocity was calculated from the hip landmark, as this marker is near the animal's COM. During kinematic analysis, whole-body instantaneous velocity was processed using a 4th order low-pass Butterworth filter with a cut-off frequency of 50 Hz (Erer, 2007). Average velocity, contact time, joint (hip, knee and ankle) displacement, joint (hip, knee and ankle) angular velocity, and effective limb length were also extracted from the 3D footage. All jump sequences were standardized in duration from 0% (initiation) to 100% (take-off) to facilitate comparisons of whole-body and joint-specific angular velocities among individuals and jumps. Analysis of jump dynamics was performed in R v.4.1.1 (http://www.R-project.org/).

Effective limb length, or the emergent length of the limb as it functions as a strut (Pontzer, 2007), was calculated as the distance between the hip landmark and the metatarsophalangeal (MT) landmark, as the hip landmark most closely approximates the COM of the mouse and the MT landmark is the last point to contact the ground. This estimate of effective limb length was measured at jump initiation (0% contact time) and during maximal excursion. Joint angles were calculated using the joint of interest as the vertex between the articulating limb segments.

An AMTI HE6X6 force plate positioned below the platform (Fig. 1B) recorded force data at 1000 Hz calibrated to a global sign convention with the origin at the center of the force plate using the factory 6X12 calibration array (AMTI). The calibration was tested prior to each filming session using a series of known weights. The impulse (the product of force and the time interval over which that force is applied) and power (rate of work) of the whole push-off phase (where the COM is moving in a positive direction) were calculated using the measured GRF.

The following equations were used to calculate kinematics from the landmark positions in the digitized films.

The following equations were used to calculate kinetics from the digitized film and the integrated force plate.

The sample for musculoskeletal morphometrics comprised five JMP Control mice, as well as nine additional sedentary controls from the same litters (SED), 10 JMP LS1, seven SED LS1, seven JMP LS2 and eight SED LS2 mice. After the jumping trials were concluded, JMP and SED mice were euthanized by CO₂ inhalation and their hindlimbs were dissected for analysis of the tibia and gastrocnemius muscle complex, using diffusible iodine-based contrast enhanced computed tomography (dice-CT). Dice-CT uses a staining agent to render soft tissues radio-opaque, thus increasing their contrast during scanning (Charles et al., 2016; Gignac et al., 2016; Metscher, 2009; Pauwels et al., 2013). We opted for non-destructive dice-CT instead of cadaveric dissection to ensure the entirety of the hindlimb musculoskeletal geometry was preserved and standardized, especially the position and stretch of the calcaneal tendon. Moreover, dice-CT presents another advantage in that, by differentially staining connective tissues at high resolution, it can be used to differentiate soft tissues with greater precision than gross dissection on fresh cadaveric tissues (Metscher, 2009; Gignac et al., 2016). This is especially beneficial to tease apart muscle bellies and musculotendinous structures in small and tightly packed muscle compartments, as is typically the case in a mouse hindlimb.

Because of the variable efficacy of dice-CT protocols and the known risk of tissue shrinkage from the staining process, a standardized staining protocol optimized to meet the conditions of this experiment was developed (Vickerton et al., 2013). Following euthanasia, mice were either immediately dissected to isolate the hindlimbs and pelvic girdle (Fig. S1) or stored at 4°C. During dissection, we removed the skin, fatty tissue and other viscera, which exposed the muscles directly to the solution to enable the muscular tissue to take up the stain faster (Gignac et al., 2016) and in a more predictable manner. Dissected specimens were fixed using 10% neutral buffered formalin (NBF) for 48 h at room temperature. Following fixation, limbs were rinsed in water for 1 h to remove excess NBF and placed in 1× phosphate-buffered saline (PBS) at 4°C. Using a prepared aqueous 2.0% I₂KI solution, hindlimbs were stained for 72 h under foil to prevent photo-oxidation (Gignac et al., 2016), then placed into 70% ethanol for 48 h to increase contrast between hard and soft tissues. We used as low a concentration of I₂KI as possible (2%), as solutions stronger than 10% I₂KI greatly increase the chances of specimen destruction and soft-tissue shrinkage (Cox and Faulkes, 2014; Gignac et al., 2016; Vickerton et al., 2013). Most importantly, because our protocol was rigorously applied in a standard way across the specimens in all three groups, we believe any existing among-group differences in muscle morphology would be preserved.

Micro-computed tomography (micro-CT) scans were acquired on a SkyScan 1173 micro-CT scanner (Bruker, Kontich, Belgium), at an isotropic resolution of 15.6 µm (122 kV, 65 µA) with a 1.0 mm aluminium filter. The dissected specimens were held on a mount designed to keep the limb position constant between individual scans (Fig. S1). To prevent desiccation during scanning, specimens were wrapped in 1× PBS-soaked gauze.

Only the right hindlimb was analyzed. The gastrocnemius muscle and the proximal and distal epiphyses of the tibia were volumized and landmarked (defined in Fig. S2) in 3D using Amira software v.5.3.3 (Visage Imaging, Berlin, Germany). Muscles were volumized with masking to remove the vasculature and other non-muscular soft tissues from volume renderings. The lateral and medial gastrocnemius muscle bodies were treated as a single muscular complex. Gastrocnemius and tibia lengths were determined using landmark distances, while gastrocnemius volume was collected from the volume rendering.

To compare behavioral outcomes during training sessions (mean jump height after 15 sessions and maximum jump height achieved), a one-way repeated measures ANOVA was performed treating line as a categorical factor and individual mouse as a random factor. A post hoc Tukey's honest significant difference (HSD) test was used to evaluate the statistical significance of pairwise differences between lines. Tukey's HSD test relies on the assumption of homogeneity of variance between groups. To test for homogeneity of variance, a Levene's test was used (Schultz, 1985).

Linear mixed models (ANOVA) were used to test group-wide effects of mouse line on dynamics while treating the individual as a random factor. Mouse line (Control, LS1, LS2) was treated as a fixed effect, and because of the replicate Longshanks lines (LS1 and LS2), the degrees of freedom were reduced to two (Garland and Rose, 2009). We used the model Yijk=μ+αi+βj+(αβ)ij+εijk, where αi is the fixed effect of line I, βj is the random effect of individual j and (αβ)ij is the corresponding interaction between individual and line. As above, Tukey's HSD was used to evaluate statistical significance of pairwise differences between lines.

A statistical comparison of angular velocity–time curves was carried out using the R package SplinectomeR (Shields-Cutler et al., 2018). SplinectomeR conducts pairwise comparisons of time series data by fitting a spline to represent the average time series between groups and then calculating the between-group difference as the absolute area between the splines, as well as a random permutation to create a random distribution of curves over the time series using the underlying distributions and patterns of individual time series curves. The P-value of the difference between average time series is calculated from the distances within this distribution of null curves compared with the observed distance between groups.

A full factorial model analysis of covariance (ANCOVA) was used to analyze the morphological data. Line and exercise were treated as fixed factors (with their interaction included) and body mass was treated as a covariate. To analyze group mean differences using appropriately scaled covariates, the least squares mean of gastrocnemius volume was adjusted for mean body mass (g), while tibia length, gastrocnemius length and calcaneal tendon length were corrected for cube root body mass (g^0.33) and mid-body cross-sectional area (CSA) was corrected for cube root body mass squared (g^0.66). For each variable, a post hoc Tukey's HSD was performed to evaluate the statistical significance of pairwise differences, followed by a Levene's test for homogeneity of variance.

Over the course of both the behavioral and biomechanics data collection trials, the Control mice were larger on average than both the LS1 and LS2 mice (Table 1). Mice in all lines (Control, LS1, LS2) reached their maximum voluntary height after approximately 15 training sessions (Fig. 2). The most common mode of movement onto the platform was a forelimb-dominant bimanual pull-up. Despite standardized training, there were notable behavioral differences among individuals. A third of mice, including all Control mice, never leaped onto the platform bipedally (powered exclusively by hindlimbs without forelimb contribution), and the rest rarely utilized a fully bipedal leap. Instead, mice would frequently use a lunge-jump behavior with a limited aerial phase (Graham and Socha, 2019) to access the raised platform. The maximum platform height (n=9 Control, 12 LS1, 15 LS2) reached by LS1 and LS2 mice was 2 cm higher than that for Control mice (ANOVA, Tukey's HSD Control–LS1 P=0.015, Control–LS2 P=0.003; Table 1). Similarly, the mean platform heights achieved over 784 sessions (18–23 post-plateau sessions per mouse, n=36 mice) by LS1 and LS2 mice were 2.37 cm higher and 4.45 cm higher, respectively, than those reached by Control mice (repeated-measures ANOVA, Tukey's HSD Control–LS1 P<0.001, Control–LS2 P<0.001; Table 1). LS2 mice also jumped significantly higher on average than LS1 mice (repeated-measures ANOVA, Tukey's HSD LS1–LS2 P<0.005).

Dynamics at three standard platform heights (6, 10 and 14 cm) are summarized in Table 1. Whole-body velocity (measured at the hip) reached its peak during the final 25% of contact time at the three heights (Fig. 3), consistent with a lunge-jump's acceleration phase (Graham and Socha, 2019). Maximal whole-body velocity was relatively consistent across the three heights and among lines (Table 1). At 10 cm, whole-body velocities of LS1 and LS2 mice were initially lower but following a period of acceleration at 75–100% of contact time, LS1 and LS2 mice reached marginally higher whole-body velocities than Control mice before leaving the ground. At 14 cm, all lines maintained similar whole-body velocities until 25–85% Contact time, when the whole-body velocity of Control mice was greater than that of both Longshanks lines. At roughly 85% of the jump, however, both Longshanks lines accelerated their COM, achieving a whole-body velocity closer to that of the controls at the point of take-off (Table 1, Fig. 3).

At 6 cm platform height, contact time was marginally different across lines (mixed model ANOVA P=0.059), with Longshanks mice maintaining contact with the substrate 20–35% longer (Fig. 4, Table 1). Similarly, at 14 cm, Longshanks mice contact times were 46–76% longer than those of controls. In contrast, at 10 cm, mean contact time did not vary significantly between LS2 and controls, but controls had contact times on average 26% longer than those of LS1 mice (Tukey's HSD P=0.009) (Fig. 4, Table 1).

Initial and final joint angles are reported in Table S1. These angles did not significantly differ between the groups, with the exception of the initial angle of the ankle at 10 cm, where the controls had a smaller initial angle than both Longshanks lines (Tukey HSD Control–LS1 P=0.02, Control–LS2 P=0.03), and the final angle of the ankle at 14 cm, where LS1 mice had a smaller final angle than LS2 mice (Tukey HSD LS1–LS2 P=0.028). The only difference in the observed dynamic range of motion (ROM) (summarized in Table S1) occurred at the knee at 6 cm, where LS2 mice had a greater difference between the initial and final angles than the other two groups (Tukey HSD LS1–LS2 P=0.014, Control–LS2 P=0.016). However, there are no systematic differences in the range of motion displayed during the take-offs we analyzed. At 6 cm, LS1 mice began their jumps with a significantly greater mean effective limb length than Control or LS2 mice at initiation (Tukey's HSD Control–LS1 P=0.02, LS1–LS2 P=0.01), and greater than Control mice at maximal excursion, i.e. take-off (Tukey's HSD Control–LS1 P=0.001) (Fig. 4, Table 1). At 10 cm, mean effective limb lengths were approximately the same across lines at initiation, but were significantly greater in LS1 mice at maximal excursion (Table 1; Tukey's HSD control–LS1 P=0.002, LS1–LS2 P=0.05). At 14 cm, effective limb length did not differ significantly among lines, but individual mouse (a random factor in our model) was significantly correlated with effective limb length (mixed model ANOVA P=0.03 at initiation and P=0.002 at maximal excursion for the random factor).

At 6 cm, the shape of the time series curve of angular velocity of the hip and ankle (Fig. S3) was significantly different across the whole contact time between Control and LS2 mice (P=0.03). While the overall shape of the angular velocity curves at these joints did not differ significantly between Control and LS1 mice (P=0.11), Control mice had significantly greater angular velocity (Figs S3 and S4) at the hip between 50% and 100% of contact time, and at the ankle around 75% of contact time. No differences in angular velocity curves were observed at the knee (Figs S3 and S4). At 10 cm, the shape of the angular velocity curves of all joints was not significantly different over the whole time series (Figs S3 and S4).

At 14 cm, hip angular velocity was higher in Controls (Figs S3 and S4), which likely generated similar take-off velocities to those of Longshanks mice (Fig. 4, Table 1) despite shorter contact times (Table 1). The spline fit to the control group's hip angular velocity was significantly different from that for the LS1 group over the entire time series (P=0.02), and from LS2 pointwise during a period from 50% to 100% of contact time (Fig. S4). At the knee, the spline-fit model indicated the trajectories of the angular velocity curves of LS1 mice were significantly different from those of LS2 mice overall (P=0.02) and from controls during 75–100% of contact time (Fig. S4, P=0.09 overall). No consistent differences in angular velocity curves at the ankle were observed among lines.

At 6 cm, maximum GRF expressed as a multiple of body weight (Fig. 5A, Table 1) did not differ significantly between LS1 and Control mice, or LS2 and Control mice. The mean impulse in excess of body weight also did not differ significantly between lines (Fig. 5B, Table 1). The mean power output of controls was 30% greater than that of LS2 mice (Tukey's HSD P=0.024). At a standardized platform height of 10 cm, there was no significant difference in maximal GRF, impulse or power among lines (Fig. 5, Table 1).

In contrast to the lower platform heights, the maximum GRF produced by controls at 14 cm (approximately 1.8 times body weight) was significantly higher than that of both Longshanks lines (1.5 times body weight) (Fig. 5A, Table 1). Despite this difference in maximum GRF, however, the average force, impulse and power over the whole contact time remained consistent (ANOVA P=0.07 and P=0.53, respectively; Fig. 5, Table 1).

All morphometric results are summarized in Table 2. As in the behavioral, kinematic and force trials, the Control mice were larger on average than both the LS1 and LS2 mice. Tibia length differed significantly among lines (ANOVA P=0.001) and was independent of exercise and body mass. The mean tibia length of both Longshanks lines was approximately 15% longer than that of the Controls, consistent with previous work using Longshanks mice (Marchini and Rolian, 2018). Body length, however, did not differ among lines. Within line, all muscular morphological traits (tendon length, muscle volume, length or mid-body CSA) were independent of exercise when controlled for body mass. Therefore, the mice from the two exercise groups were pooled within line to increase statistical power, then morphological traits were compared among lines with an ANCOVA using body mass as a covariate.

Gastrocnemius muscle–body length (Fig. 6, Table 2) differed by line (ANCOVA P=0.0007). When adjusted for body mass, the least squares mean length of the LS1 and LS2 gastrocnemius was 10.4% longer than that in controls (Tukey's HSD P=0.0025 Control–LS1, P=0.0005 Control–LS2) (Fig. 6, Table 2). Similarly, the least squares mean calcaneal tendon length of LS1 mice was 18.4% longer than that of the Controls (Tukey HSD P=0.008), and the least squares mean tendon length of LS2 mice was 15.8% longer than that of the Controls (Tukey's HSD P=0.047) (Table 2). Gastrocnemius volume differed among lines after controlling for body mass (ANCOVA P<0.001). The least squares mean gastrocnemius volume of LS1 mice was lowest (Tukey's HSD P<0.0005 LS1–LS2, P=0.0137 Control–LS1) and LS2 volume was greatest (Tukey's HSD P<0.0005 LS1–LS2, P=0.22 Control–LS2) (Fig. 6, Table 2). This pattern was echoed in the gastrocnemius mid-body CSA, where the effect of line was again significant (ANCOVA P<0.001).

In this study, we examined the jumping/lunging behaviors, hindlimb dynamics and plantarflexor morphology of Longshanks mice, which were selectively bred over 22 generations for increased tibia length relative to body mass. We tested whether increased tibia length was associated with predictable behavioral and biomechanical differences in jumping and leaping dynamics, and whether selection for tibia length was associated with changes in the musculature of the leg segment. Hindlimb elongation was associated with greater average and maximal jump heights (Fig. 2, Table 1), and lower maximum GRFs to reach the highest platform height (Fig. 5A). This was associated with changes in movement dynamics during take-off, especially longer contact times in both Longshanks lines.

While the dynamic range of motion for each individual joint (ankle, knee and hip) lacks systematic differences among groups (Table S1), small differences in joint angles compound to produce postural differences (i.e. effective limb length) among lines at different platform heights. At 6 and 10 cm, Control mice tended to leave the substrate with shorter effective limb lengths (Fig. 4, Table 1). At 14 cm, however, controls still tended to flex their hips more, but subsequently extended their knees and ankles beyond the typical LS1 angles to reach knee and ankle angles observed in LS2 mice towards maximal excursion. This slightly greater limb joint extension may compensate for their shorter length, resulting in an effective limb length equivalent to that of the Longshanks lines at maximal excursion prior to leaving the substrate.

Once off the ground, all mice relied on their forelimbs, likely to redirect the trajectory of the COM to get onto the platform (Fig. 7). This is unlike specialized bipedal jumping rodents, which tend to use the tail as a balancing organ (Bartholomew and Caswell, 1951; Crompton and Sellers, 2007). However, lunge-jumping where the forelimb is incorporated as a strut has been observed in other quadrupeds, such as arboreal primates that are not specialized for vertical clinging and leaping (Crompton and Sellers, 2007).

Take-off velocity did not differ between lines at any height. Unexpectedly, the take-off velocity was highest at 6 cm. This may be in part due to the greater horizontal displacement at 6 cm (Fig. 7). Alternatively, as the initiation posture at 14 cm was more orthograde than that at 6 cm and was coupled with a digitigrade stance, the COM was intrinsically raised. This posture has been posited previously to increase jump distance without increasing exertion in some small-bodied leaping-specialist primates (Boyer et al., 2013; Gebo, 2011).

Ideally, hindlimb extension moves the COM mostly in the desired direction to produce the momentum that will carry the animal through the air after the limbs are fully extended (Boyer et al., 2013). How this multi-joint extension is coordinated can impact the distance covered during a dynamic movement because it determines the trajectory of the COM, as well as the transfer and delivery of muscular force to the substrate (Bobbert and van Ingen Schenau, 1988; Bobbert and van Soest, 1994). A proximodistal pattern of joint extension, where an early extension of the hip joint is followed by knee and late ankle extension, occurs during jumping and other dynamic behaviors for many species (Aerts, 1998; Günther et al., 1991; Rodacki et al., 2001; Schwaner et al., 2017). This pattern of extension is thought to transfer proximal muscle power to the distal joints (Hogan, 1985). However, few consistent differences were observed among lines or platform heights in joint-specific kinematics, suggesting different individuals achieve the desired behavioral outcomes using different limb dynamics, regardless of any morphological differences. All mice in this study lacked a clear proximodistal sequence, which likely affected power transfer and delivery. Using lunge-jumps with minimal aerial periods may have reduced the need for stereotyped proximodistal sequences to achieve a given platform height.

At both 6 and 10 cm, the maximum GRF produced by all lines neared 1.5 times body weight (Table 1). In contrast, while the maximum GRFs produced by LS1 and LS2 mice at 14 cm remained roughly 1.5 times body weight, the mean maximum GRF in controls increased 20% to 1.8 times body weight (Table 1). This result is similar to interspecific comparisons between lemurs wherein the greatest forces relative to body weight were applied by generalists (Lemur catta and Eulemur rubriventer), not by leaping specialists (Propithecus verreauxi) when jumping to the same height (Demes et al., 1995, 1999). How did Longshanks mice gain the same platform height, average power, impulse and take-off velocity as Control mice while maintaining a lower maximum GRF?

Explosive/dynamic movements such as bipedal jumps and lunge-jumps are limited by the kinetic energy generated during take-off. A moving body's kinetic energy is determined by its velocity, which itself depends on the acceleration of that body's COM, and the distance over which this acceleration is generated (Harris and Steudel, 2002). For a given platform height, the elongated Longshanks hindlimbs provide more acceleration distance than do those of controls, enabling a lower force (and thus lower acceleration) to produce adequate kinetic energy to reach the platform. Related to this, whole-body acceleration (as well as take-off velocity) can also be maintained with lower applied forces via longer take-off durations. Likewise, as impulse is the time integral of force, longer take-off times enable lower applied force to still produce the same impulse. In this study, both Longshanks lines had on average 46–76% longer contact times than controls (Fig. 4, Table 1), suggesting that part of the reduced force output but equal impulses in Longshanks mice versus Control mice is associated with their longer take-off durations.

Complementary to increasing take-off durations, performance (i.e. vertical height) remains consistent even with reduced mass-specific force if there is a concomitant increase in the push-off distance determined by the normal extension range (Samozino et al., 2010). In our study, the mean change in effective limb length (essentially, push-off distance) of LS1 (10.5 mm) and LS2 (11.7 mm) mice was, respectively, 21% and 34% greater than that of controls (8.7 mm). This may provide a complementary strategy in Longshanks mice to achieve desired performance outcomes with lower mass-specific forces.

While our data do support a performance advantage from longer contact times during take-off and push-off distance determined by changes in effective limb length, the lower maximum GRF produced by Longshanks mice at 14 cm could instead be an intrinsic constraint of their muscle architecture and hindlimb geometry. The relationship between force output and musculature relies on the moment arm, muscle CSA, duty factor (time available to produce force) and the force–velocity relationship of the muscle. Power production is generally proportional to muscle volume and muscle mass, while muscles with longer fascicle lengths generally produce less force and higher shortening velocities (Banus and Zetlin, 1938; Williams et al., 2007). With their longer gastrocnemius (Table 2, Fig. 6), Longshanks mice may simply be unable to generate the same mass-specific force as controls.

We approximated physiological CSA by measuring mid-body CSA. When controlled for covariation with body mass, LS2 CSA and volume were larger than those of the LS1 and Control mice, while the LS1 gastrocnemius volume and CSA were significantly lower than those of both the Control and the LS2 mice (Fig. 6). If the LS1 mice were unable to produce high muscular force because of a reduced CSA, they may overcome those constraints by tightly modulating the activation and coordination of joint extension. More robust analyses of muscle activation and coordination will be necessary to test this hypothesis.

It is also possible that LS1 and LS2 mice each achieved force reduction relative to controls at 14 cm using different strategies. LS1 mice had significantly longer contact times and smaller gastrocnemius muscles (in terms of both volume and mid-body CSA). LS1 mice may be intrinsically constrained by their smaller muscles and must compensate by extending contact time. LS2 mice had non-significantly longer contact times, increased gastrocnemius mid-body CSA and volume, and a greater increase in the distance the COM travels during push-off determined by total range of extension when compared with LS1 mice. In this case, the LS2 mice may not have been intrinsically constrained by muscle architecture but instead experienced force reduction at 14 cm due to a combination of greater COM displacement during take-off and slightly longer contact times (Gray, 1953; Samozino et al., 2010).

There is no general agreement on which mechanical characteristics of the lower limb maximize work, power or impulse, and which of these parameters, if any, best determines changes in performance that improve fitness (Adamson and Whitney, 1971; Knudson, 2009; Marsh, 1994; Roberts et al., 2011; Samozino et al., 2010). Our results suggest that for a given height, maximum force production can be reduced in individuals with longer limbs while impulse and power remain consistent. This perhaps indicates that instead of hindlimb elongation maximizing power, impulse and work, it instead, or additionally, allows a longer time period for force application.

We speculate that if the lower maximal GRF observed in Longshanks mice is associated with less muscular work, then this may represent a selectable advantage in terms of performance, and ultimately evolutionary fitness. Specifically, it would suggest Longshanks mice use less metabolic energy to achieve the same outcome (vertical height). However, it should be noted that if Longshanks mice use the same metabolic energy but are unable to properly translate muscular force into usable torque (for example, because of their musculoskeletal morphology), then Longshanks mice would instead be at a performance disadvantage.

Take-off duration can also affect the metabolic cost of a dynamic behavior. For example, across primate species (Cheirogaleus major, Galago garnetti, Galago moholi, Microcebus murinus, Mirza coquereli, Lemur catta), jumps with a longer take-off period were more efficient (Sellers and Crompton, 1994) and escape jumps with a shorter take-off were more energetically expensive (Sellers and Crompton, 1994). If this is also true in mice, then Longshanks mice expend less energy than controls.

Our results show that aspects of locomotor performance were altered solely through selection for tibial elongation. Thus, a forward-engineered morphological trait of interest can have discernible effects on performance. The Longshanks model provides an opportunity to examine the interplay between musculoskeletal morphology and measures of biomechanical performance in a controlled environment. However, selection experiments with model organisms can potentially yield results that do not adequately reflect behaviors or performance in natural populations (Garland, 2003). In this study, for example, behavioral and morphological characters were decoupled as the Longshanks mice were bred for increases in relative tibia length only, and not locomotor ability (Arnold, 1983).

In addition, unlike the acrobatic jumps performed by bipedal rodents and arboreal leaping specialists, the most common dynamic behavior we observed was a lunge-jump, which involved incorporation of the forelimbs. Our analyses were guided by the assumption that forelimb involvement is roughly equivalent in all three lines, and is limited to redirecting the COM after the acceleration phase. However, this assumption was not directly tested and should be addressed by future studies. Regardless of forelimb involvement, a lunge-jump is easier to execute and safer than a bipedal jump as, among other factors, advanced trunk control during the aerial phase is not required. With their longer hindlimbs, Longshanks mice may be able to reach the platform at a greater distance while rearing, allowing them to use a low consequence lunge-jump over taller vertical gaps. In a hypothetical ancestral population under selection for jumping performance, this suggests longer limbed individuals would be able cross larger gaps safely and effectively.

Macroevolutionary phenomena, such as convergent evolution, are hard to test directly because of the relatively large time scales involved; however, the microevolutionary patterns found with experimental approaches can inform macroevolutionary hypotheses (Garland and Rose, 2009). Artificial selection experiments, like the Longshanks mice, allow the investigator to be very specific about what is under selection (Garland, 2003). As the Longshanks mice were under selection strictly for morphology, not behavior or mechanics, we could test whether predictable functional differences inevitably arose with a specific morphological change (here, elongated tibiae). While the replicate Longshanks lines were consistent in many ways, there were also notable differences in both their mechanics and muscular morphology, despite undergoing selection for the exact same limb skeletal phenotype. This suggests that even if taxa converge on analogous morphology, they may not have analogous mechanics during locomotor tasks and may not have arrived at their similarities under selection for the same functional outcomes. Simply put, selection for the same functional outcomes (e.g. improved jumping performance) can and does often lead to convergent morphology, but the reverse is not necessarily true: selection for the same morphological outcomes (e.g. increased limb length) does not necessarily produce convergent performance outcomes.

We thank Rocio Araujo and the staff at the University of Calgary Mouse Halfway House for their animal care, Peter Byrne for the construction of the jumping enclosure, and Alexis DeMong and Robin Goodfellow for their help during mouse training. The authors also thank Jason Anderson and Jessica Theodor for SkyScan 1173 micro-CT scanner access. Portions of the Results/Discussion in this paper are reproduced from the Master's thesis of M.B.-C. (Bradley, 2019).