Animal locomotion is controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of generating a rhythmic output. The spatio-temporal symmetries of the quadrupedal gaits walk, trot and pace lead to plausible assumptions about the symmetries of locomotor CPGs. These assumptions imply that the CPG of a quadruped should consist of eight nominally identical subcircuits, arranged in an essentially unique matter. Here we apply analogous arguments to myriapod CPGs. Analyses based on symmetry applied to these networks lead to testable predictions, including a distinction between primary and secondary gaits, the existence of a new primary gait called 'jump', and the occurrence of half-integer wave numbers in myriapod gaits. For bipeds, our analysis also predicts two gaits with the out-of-phase symmetry of the walk and two gaits with the in-phase symmetry of the hop. We present data that support each of these predictions. This work suggests that symmetry can be used to infer a plausible class of CPG network architectures from observed patterns of animal gaits.

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In this paper we continue the analysis of a network of symmetrically coupled cells modeling central pattern generators for quadruped locomotion proposed by Golubitsky, Stewart, Buono, and Collins. By a cell we mean a system of ordinary differential equations and by a coupled cell system we mean a network of identical cells with coupling terms. We have three main results in this paper. First, we show that the proposed network is the simplest one modeling the common quadruped gaits of walk, trot, and pace. In doing so we prove a general theorem classifying spatio-temporal symmetries of periodic solutions to equivariant systems of differential equations. We also specialize this theorem to coupled cell systems. Second, this paper focuses on primary gaits; that is, gaits that are modeled by output signals from the central pattern generator where each cell emits the same waveform along with exact phase shifts between cells. Our previous work showed that the network is capable of producing six primary gaits. Here, we show that under mild assumptions on the cells and the coupling of the network, primary gaits can be produced from Hopf bifurcation by varying only coupling strengths of the network. Third, we discuss the stability of primary gaits and exhibit these solutions by performing numerical simulations using the dimensionless Morris-Lecar equations for the cell dynamics.

The assessment of disturbance effects on wildlife and resulting mitigation efforts are founded on edge-effect theory. According to the classical view, the abundance of animals affected by human disturbance should increase monotonically with distance from disturbed areas to reach a maximum at remote locations. Here we show that distance-dependent movement taxis can skew abundance distributions toward disturbed areas. We develop an advection-diffusion model based on basic movement behavior commonly observed in animal populations and parameterize the model from observations on radio-collared caribou in a boreal ecosystem. The model predicts maximum abundance at 3.7 km from cutovers and roads. Consistently, aerial surveys conducted over 161,920 km(2) showed that the relative probability of caribou occurrence displays nonmonotonic changes with the distance to anthropogenic features, with a peak occurring at 4.5 km away from these features. This aggregation near disturbed areas thus provides the predators of this top-down-controlled, threatened herbivore species with specific locations to concentrate their search. The edge-effect theory developed here thus predicts that human activities should alter animal distribution and food web properties differently than anticipated from the current paradigm. Consideration of such nonmonotonic response to habitat edges may become essential to successful wildlife conservation.