Walking animals often vary the temporal and spatial coordination of their limb movements to move at different speeds or to navigate different terrains. During forward planar walking, for example, insects generally transition from a pentapodal coordination at slow speeds to a tripod stepping pattern during fast walking (Fig. 1). Recent studies have shown that transitions between inter-leg coordination patterns (ICPs) in insects occur in a probabalistic, continuous manner (Wosnitza et al., 2013; Szczecinski et al., 2018; DeAngelis et al., 2019). This is in contrast with observations in vertebrates (although, see Geyer et al., 2006), where switches between ICPs are often accompanied by a discontinuous transition in at least one kinematic parameter (e.g. duty factor or inter-leg phase relationship) and reliably occur at a characteristic speed (Alexander and Jayes, 1983; Alexander, 1989). This apparent lack of distinct gaits in insects implies that a single underlying controller may be able to generate their entire repertoire of ICPs (DeAngelis et al., 2019). Furthermore, commonalities in coordination patterns across a range of invertebrate species (Fig. 2) excitingly suggest the possibility of a shared control circuit that extends even beyond insects (Nirody, 2021).

Fig. 1.

Observed transitions in inter-leg coordination patterns with walking speed across panarthropod species. Spectrum of idealized forward walking inter-leg coordination patterns (ICPs) in panarthropods with various numbers of legs (from top to bottom): insects, nlegs=6; arachnids, nlegs=8; myriapods, nlegs>10. Numbering denotes the order of footfalls within a full stride cycle; the timing of footfalls is also denoted from lighter to darker coloring. Swing phases of ipsilateral legs on adjacent segments do not overlap, with lift-offs occurring in a posterior-to-anterior wave (Wilson, 1966). As walking speed increases, stance duration is reduced; this increases the frequency of the traveling wave of swing initiations and decreases the number of legs involved in one wavelength of swing initiations (ncycle).

Fig. 1.

Observed transitions in inter-leg coordination patterns with walking speed across panarthropod species. Spectrum of idealized forward walking inter-leg coordination patterns (ICPs) in panarthropods with various numbers of legs (from top to bottom): insects, nlegs=6; arachnids, nlegs=8; myriapods, nlegs>10. Numbering denotes the order of footfalls within a full stride cycle; the timing of footfalls is also denoted from lighter to darker coloring. Swing phases of ipsilateral legs on adjacent segments do not overlap, with lift-offs occurring in a posterior-to-anterior wave (Wilson, 1966). As walking speed increases, stance duration is reduced; this increases the frequency of the traveling wave of swing initiations and decreases the number of legs involved in one wavelength of swing initiations (ncycle).

Fig. 2.

Changes in phase relationships between ipsilateral (left) and contralateral (right) leg pairs with walking speed across panarthropod species. Ipsilateral phase relationships are reported with an anterior observed leg and a reference posterior leg (e.g. observed leg R2, reference leg R3). Running mean from data for Drosophila (Szczecinski et al., 2018) is shown as a gray line. Mean values are reported in other species; for studies in which distributions were made available, I report only means from normally distributed data. Expected ipsilateral phase offsets as animals vary walking speed are shown as shaded bands ranging from wave (yellow, φC<1/3) to tetrapod-like (red, φC=1/3) to tripod (yellow, φC=1/2) coordination. All ideal canonical coordinations across speeds and species show an anti-phase contralateral coordination (shaded in blue, φC=1/2). Figure modified from Nirody (2021). Data sources are indicated in the key (Grabowska et al., 2012; Weihmann et al., 2015; Nirody et al., 2021; Manton, 1950, 1952b, 1954; Couzin-Fuchs et al., 2015; Pearson et al., 1984; Merrienne et al., 2020; Szczecinski et al., 2018).

Fig. 2.

Changes in phase relationships between ipsilateral (left) and contralateral (right) leg pairs with walking speed across panarthropod species. Ipsilateral phase relationships are reported with an anterior observed leg and a reference posterior leg (e.g. observed leg R2, reference leg R3). Running mean from data for Drosophila (Szczecinski et al., 2018) is shown as a gray line. Mean values are reported in other species; for studies in which distributions were made available, I report only means from normally distributed data. Expected ipsilateral phase offsets as animals vary walking speed are shown as shaded bands ranging from wave (yellow, φC<1/3) to tetrapod-like (red, φC=1/3) to tripod (yellow, φC=1/2) coordination. All ideal canonical coordinations across speeds and species show an anti-phase contralateral coordination (shaded in blue, φC=1/2). Figure modified from Nirody (2021). Data sources are indicated in the key (Grabowska et al., 2012; Weihmann et al., 2015; Nirody et al., 2021; Manton, 1950, 1952b, 1954; Couzin-Fuchs et al., 2015; Pearson et al., 1984; Merrienne et al., 2020; Szczecinski et al., 2018).

The idea of a shared controller across panarthropods echoes an early observation of walking in Onychophora (velvet worms, which along with Tardigrada and Arthropoda, constitute Panarthropoda): onychophoran stepping patterns are ‘sufficiently wide to provide a common origin for all the more specialized types’ of arthropod walking patterns (Manton, 1952b). One proposed ‘universal’ circuit consists of mutual inhibition between contralateral leg pairs and a posterior-to-anterior inhibition on each ipsilateral side (DeAngelis et al., 2019; Nirody et al., 2021; Nirody, 2021). The broad framework of this model relies on the existence of distinct and largely autonomous central pattern generators (CPGs), each controlling the movement of a single limb; this idea has support from neurophysiological and biomechanical studies in several insects (Pearson and Franklin, 1984; Wosnitza et al., 2013; Ayali et al., 2015; Cruse, 1990; Cruse et al., 1995; Dürr et al., 2018). The nature of the connectivity between these CPGs, however, is far less obvious. While the above circuit can successfully generate the spectrum of panarthropod ICPs observed during forward planar walking, whether it can be extended to walking in more complex environments is unclear.

Here, I begin by detailing the structure of this phenomenological model and highlighting the commonalities in ICPs across panarthropods that form its basis (Fig. 3). I then extend this framework to accommodate movement beyond forward walking on flat terrain to situations in which variability in coordination (from the intra-individual to the inter-species level) becomes more apparent. Do the ‘universal’ patterns observed on flat ground persist when more complex environments are considered?

Fig. 3.

A phenomenological model that generates the observed spectrum of forward-walking inter-leg coordination patterns across panarthropod species. Analysis of a large kinematic dataset from walking Drosophila puts forward a simple model for forward walking ICPs. The model comprises hemisegmental central pattern generators (CPGs) (shown as circles), each controlling the movement of a leg. The following coupling scheme is able to generate all observed coordination patterns across walking speeds: mutual inhibitory connections between contralateral leg pairs and a posterior-to-anterior inhibition on each ipsilateral side. Inhibitory connections are shown as capped vertical lines with associated (–) signs. The neural basis of such a circuit remains unknown, but its structure is rooted in the structure of the thoracic ganglia of the ventral nerve cord (VNC). Schematic modified from Nirody (2021).

Fig. 3.

A phenomenological model that generates the observed spectrum of forward-walking inter-leg coordination patterns across panarthropod species. Analysis of a large kinematic dataset from walking Drosophila puts forward a simple model for forward walking ICPs. The model comprises hemisegmental central pattern generators (CPGs) (shown as circles), each controlling the movement of a leg. The following coupling scheme is able to generate all observed coordination patterns across walking speeds: mutual inhibitory connections between contralateral leg pairs and a posterior-to-anterior inhibition on each ipsilateral side. Inhibitory connections are shown as capped vertical lines with associated (–) signs. The neural basis of such a circuit remains unknown, but its structure is rooted in the structure of the thoracic ganglia of the ventral nerve cord (VNC). Schematic modified from Nirody (2021).

Inter-leg coordination patterns in panarthropods probably result from the interplay between CPG-driven output and sensory feedback from the environment. Many locomotive challenges faced by panarthropods [e.g. climbing over gaps (Blaesing and Cruse, 2004); walking over compliant or shifting substrates: (Humeau et al., 2019; Nirody et al., 2021); walking upside down (Ramdya et al., 2017); dealing with rough or three-dimensional terrain (Sponberg and Full, 2008)] necessitate that stepping patterns be constantly updated based on environmental and internal cues. There is evidence that even the ‘universal’ coordination patterns observed during walking on flat terrain also require both CPG activity and sensory feedback: electrophysiological studies of reduced insect preparations often show ICPs that deviate significantly from those observed in freely walking animals (Dürr et al., 2018).

Within the context of the above leg CPG model framework, I consider the contribution of two general types of sensory information: load sensing and proprioception. Broadly speaking, load sensing is relevant during the stance phase of walking (when the leg is in contact with the ground) and proprioceptive feedback is relevant during the swing phase (when the leg is lifted during a step). Sensory receptors responsive to both of these forms of information are prevalent in various panarthropods: campaniform sensilla in insects (Zill et al., 2011, 2012, 2015) and slit sensilla in spiders (French et al., 2002) monitor interaction forces with the substrate as strains in the exoskeleton, while hair fields near leg joints provide proprioceptive feedback in several insect species (Dürr et al., 2018; Mendes et al., 2013). Feedback from these receptors has been reported to impact leg movements and inter-leg coordination (Berg et al., 2013; Zill et al., 2009; Dallmann et al., 2017), as well as entrain CPG motor activity (Borgmann et al., 2009); this further emphasizes the importance of considering the effect of environmental feedback on panarthropod stepping patterns.

Throughout this review, I compile and present data from a range of studies on panarthropod coordination patterns during forward walking. In the first section, I begin with a discussion of the speed-dependent continuum of ICPs observed during walking on flat terrain in a wide range of panarthropod taxa. In the sections following, I explore deviations from this ICP spectrum, focusing on coordination patterns that arise in environments with challenging substrate material properties (which provide variable loading feedback) and with challenging substrate geometry (which compromise walking stability by disrupting swing-to-stance transitions).

Alongside data from biomechanical studies, I also report complementary results from neurophysiological analyses of various panarthropod species wherever appropriate. With this work, I hope to emphasize the value of: (1) performing experiments with an eye towards studying locomotion in naturalistic situations (e.g. walking over complex terrain, which often provides variable sensory feedback); (2) integrating results from neurophysiological studies with kinematic analyses; and (3) diversifying our repertoire of study systems across panarthropod taxa.

Within a lifetime (and often within a single hour), an animal must be able to walk at a wide range of speeds to achieve various behavioural goals: foraging for food requires relatively slow walking over long distances, while escaping a predator necessitates bursts of fast running. This can be done both by varying the dynamics of a single leg, as well as by modulating inter-leg coordination. With regard to single-leg dynamics, panarthropods vary both the length of their steps (stride length) and the time each step takes (stride frequency) to tune their walking speed. Increasing stride length beyond the limit imposed by leg morphology requires the insertion of an aerial phase, a strategy rarely used by panarthropod species (Full and Tu, 1991; Goldman et al., 2006; Wosnitza et al., 2013; Reinhardt and Blickhan, 2014; Pfeffer et al., 2019). Modulating stride frequency can be done by either shortening the time dedicated to swing (during which the leg is lifted) or stance (during which the leg is in contact with the ground). The majority of panarthropod species change walking speed by varying the duration of stance, with swing duration generally decreasing only slightly from low to medium speeds and remaining constant at higher walking speeds (Mendes et al., 2013;Wosnitza et al., 2013; Dürr et al., 2018).

The relative coordination between leg movements also varies with walking speed and has been reported to be optimized for stability in insects (Wosnitza et al., 2013; Szczecinski et al., 2018). Insects keep five feet on the ground in a ‘wave gait’ at slow speeds, walk using a tetrapod stepping pattern at intermediate speeds and prefer a tripod pattern during fast walking (Fig. 1). Wilson (1966) summarized the commonalities in walking patterns between slow and fast insects in a set of simple observations: (1) swing duration is independent of walking speed; (2) stride frequency increases with speed and is modulated by varying stance duration; (3) initiation of swing (lift-off of a leg) occurs in a posterior to anterior wave along each ipsilateral side; (4) contralateral leg pairs move in anti-phase.

Recent work on Drosophila more quantitatively characterized the structure of variability in observed coordination patterns on flat terrain across a wide range of walking speeds (Wosnitza et al., 2013; Szczecinski et al., 2018; DeAngelis et al., 2019). These studies show that flies transition smoothly between stepping patterns in a probabalistic manner, often making use of multiple ICPs at the same speed. Although these stepping patterns are often called ‘gaits’ in the literature (Nishii, 2000; Dürr et al., 2004; Bender et al., 2011), DeAngelis et al. (2019) show that flies actually progress through walking speeds along a speed-dependent continuum.

In agreement with Wilson's first and second observations, DeAngelis et al. (2019) showed that varying stance duration alone allows for the generation of the entire spectrum of Drosophila stepping patterns across walking speeds: from wave gait to tetrapod to tripod coordination. Varying stance duration also suffices to describe coordination patterns observed ‘beyond’ tripod in many fast-running hexapod species, such as the bipod and monopod stepping patterns observed in cockroaches, beetles and ants (Hughes, 1952; Full and Tu, 1991; Wahl et al., 2015).

These observations can also be easily generalized beyond hexapods. Coordination patterns in several non-insect panarthropods (Manton, 1950; 1952a; Spagna et al., 2011; Nirody et al., 2021) seem to follow the same patterns even though they do not show the exact progression of ICPs in insects (Fig. 1). For example, Wilson's third observation implies that swing phases of ipsilateral legs on adjacent segments do not overlap, with lift-offs occurring in a posterior-to-anterior wave. In a generalized panarthropod with leg number nlegs, this results in ipsilateral phase offset increasing from at low speeds, to a maximum offset of at the highest speeds (⁠ results in a retrograde wave of swing initiations that travels from anterior to posterior). Broadly, reducing stance duration increases the frequency of the traveling wave of swing initiations and a decrease in the number of leg pairs involved in each cycle ncycle (‘the wavelength’) with walking speed; this corresponds to an increase in the phase offset between ipsilateral legs (Nirody, 2021).

In hexapods (nlegs=6), this corresponds to a continuum varying smoothly with speed from in wave coordination, to in tetrapods and in tripods (Fig. 1). In myriapods, the same fundamental control rules manifest in a metachronal wave coordination across all walking speeds (Manton, 1952a). In this manner, arthropods with many legs can reach very high speeds during grounded running with a relatively high number of feet on the ground at any given time (i.e. maintain a high duty factor at high speeds) (Manton, 1952a; Kuroda et al., 2018 preprint; Yasui et al., 2019). Finally, in agreement with Wilson's fourth observation, contralateral phase offset φC=0.5 remains constant across speeds in a wide range of panarthropod species (Fig. 2).

Wilson's observations can be quantified in the form of a simple model, composed of distinct central pattern generators (CPGs) in each leg (DeAngelis et al., 2019; Schilling and Cruse, 2020; Nirody, 2021). The existence of hemisegmental CPGs gains support from a long history of studies in insects, including experiments in the stick insect that showed that rhythmic leg movements are still generated in preparations transected along the midline of the thoracic ganglia (Büschges et al., 1995). This and other early work on deafferented animals determined that central neuronal networks in the thoracic ganglia are able to generate rhythmic activity in insect leg motor neurons without descending or sensory input when activated by applying the muscarinic agonist pilocarpine (Mantziaris et al., 2020). For example, work in locusts reported that coordinated activity akin to stepping could be observed in similar preparations (Ryckebusch and Laurent,1993, 1994; Knebel et al., 2017).

Within this simple model, each pair of contralateral legs displays mutual inhibitory coupling, while a posterior-to-anterior inhibitory coupling exists between ipsilateral legs on each side (Fig. 3). Much remains to be understood about the organization of these CPGs within the panarthropod nervous system, and whether these similarities in ICPs across panarthropod taxa suggest an underlying common neural mechanism is unclear.

Much of the neural circuitry for walking in panarthropods is contained within the ventral nerve cord (VNC), the topology of which is largely conserved across taxa: each ganglion (neuromere) is made up of a grouping of neurons that are responsible for dealing with the sensory inputs and motor outputs for the leg pair on the associated segment. Each thoracic neuromere is further subdivided into two halves (neuropil), each of which controls the motor neurons and muscles in a leg (Yang et al., 2016; Niven et al., 2008). Within this general framework, however, there exists significant morphological diversity; in particular, the position of each neuromere relative to adjacent ones, as well as to the segment they innervate, is highly variable among panarthropods (Niven et al., 2008).

It requires less time and metabolic energy to transmit signals between closely placed neurons, and several modelling studies have suggested that nervous systems in both vertebrates and invertebrates are organized to minimize total wiring cost (Laughlin, 2001). The distance between neighboring neuromeres and between a neuromere and the segment it innervates, then, may represent competing selective forces in shaping the structure of the nerve cord: as posterior neuromeres are drawn forward to ‘fuse’ with their anterior neighbor, they are drawn away from the leg pair that they are responsible for controlling (Niven et al., 2008). Comparative studies of extant and fossil morphology suggest that the ancestral VNC featured thoracic neuromeres that were ‘unfused’ (Yang et al., 2016) and the pattern of diversity of fusion patterns of the thoracic ganglia among extant taxa imply that multiple fusion and separation events have likely occurred (Niven et al., 2008). Whether the phylogenetic pattern of neuromere positioning suggests a functional trade-off between inter-neuromere and peripheral connectivity remains unclear: very little variation in coordination between ipsilateral limbs has been reported across panarthropod taxa, with tardigrades, fruit flies and centipedes showing the same general stepping pattern during forward walking on flat surfaces (Fig. 1).

Coupling between contralateral (intrasegmental) limb CPGs is generally far more variable than coupling between ipsilateral legs, both intraspecifically and among different panarthropod species (Dürr, 2005; Nirody, 2021). Studies in onychophorans may hint at a possible structure–function relationship here: kinematic analyses report that velvet worms display little coordination between contralateral limb pairs, even on flat terrain (Oliveira et al., 2019), while structural studies show a lateralized VNC architecture with completely unfused and distantly located intrasegmental neuropil across Onychophora (Yang et al., 2016). However, neural coupling between contralateral leg pairs is generally quite weak across panarthropod species and whether the observed variability in coordination actually corresponds to VNC morphology is far from clear. The variability in panarthropod coordination patterns observed during walking on flat terrain is very likely the tip of the iceberg. Apparent ‘universal’ features observed in planar stepping patterns may be misleading and phenomenological models rooted in these commonalities probably fall short of providing the full picture of panarthropod walking.

There is mounting evidence that inter-leg coordination arises from a complex – and possibly species-specific – combination of central and peripheral influences. For instance, the pattern of central interactions between leg CPGs in pharmacologically stimulated insect preparations varies between species. Pilocarpine application in cockroach (David et al., 2016) and hawk moth (Johnston and Levine, 2002) preparations resulted in a tripod-like walking pattern with anti-phase contralateral coordination as in intact animals; CGPs in the stick insect (Mantziaris et al., 2017) and locust (Knebel et al., 2017), however, tended towards in-phase coordination. This deviation from observations in freely behaving animals may be due to the influence of sensory input, which has been hypothesized to affect coordination more strongly in slow-walking insects (such as stick insects and locusts) than in fast-walking animals (such as cockroaches and hawk moths) (Mantziaris et al., 2020).

The neural underpinning of these influences remains largely unknown. Even more elusive is how analogous combinations of descending control and sensory feedback generate locomotive strategies in more complex environments, as well as in other behaviors such as grooming or searching. In particular, uncovering whether similarly convergent coordination strategies across species arise in more complex maneuvers will require deeper and more comprehensive investigation of walking in a wider range of environments and in a wider range of panarthropod species.

Legged locomotion encompasses a variety of terrain, which can pose a range of locomotive challenges. One such challenge relevant to a number of natural environments is walking over substrates that are slippery, compliant (tendency to flow) or otherwise unsteady. For example, arthropods such as mites and ladybirds must move along deformable –