On self-similar patterns in coupled parabolic systems as non-equilibrium steady states.

We consider reaction-diffusion systems and other related dissipative systems on unbounded domains with the aim of showing that self-similarity, besides the well-known exact self-similar solutions, can also occur asymptotically in two different forms. For this, we study systems on the unbounded real line that have the property that their restriction to a finite domain has a Lyapunov function (and a gradient structure). In this situation, the system may reach local equilibrium on a rather fast time scale, but on unbounded domains with an infinite amount of mass or energy, it leads to a persistent mass or energy flow for all times; hence, in general, no true equilibrium is reached globally. In suitably rescaled variables, however, the solutions to the transformed system converge to so-called non-equilibrium steady states that correspond to asymptotically self-similar behavior in the original system.

Many morphs: Parsing gesture signals from the noise.

Parsing signals from noise is a general problem for signallers and recipients, and for researchers studying communicative systems. Substantial efforts have been invested in comparing how other species encode information and meaning, and how signalling is structured. However, research depends on identifying and discriminating signals that represent meaningful units of analysis. Early approaches to defining signal repertoires applied top-down approaches, classifying cases into predefined signal types. Recently, more labour-intensive methods have taken a bottom-up approach describing detailed features of each signal and clustering cases based on patterns of similarity in multi-dimensional feature-space that were previously undetectable. Nevertheless, it remains essential to assess whether the resulting repertoires are composed of relevant units from the perspective of the species using them, and redefining repertoires when additional data become available. In this paper we provide a framework that takes data from the largest set of wild chimpanzee (Pan troglodytes) gestures currently available, splitting gesture types at a fine scale based on modifying features of gesture expression using latent class analysis (a model-based cluster detection algorithm for categorical variables), and then determining whether this splitting process reduces uncertainty about the goal or community of the gesture. Our method allows different features of interest to be incorporated into the splitting process, providing substantial future flexibility across, for example, species, populations, and levels of signal granularity. Doing so, we provide a powerful tool allowing researchers interested in gestural communication to establish repertoires of relevant units for subsequent analyses within and between systems of communication.

NetFACS: Using network science to understand facial communication systems.

Understanding facial signals in humans and other species is crucial for understanding the evolution, complexity, and function of the face as a communication tool. The Facial Action Coding System (FACS) enables researchers to measure facial movements accurately, but we currently lack tools to reliably analyse data and efficiently communicate results. Network analysis can provide a way to use the information encoded in FACS datasets: by treating individual AUs (the smallest units of facial movements) as nodes in a network and their co-occurrence as connections, we can analyse and visualise differences in the use of combinations of AUs in different conditions. Here, we present 'NetFACS', a statistical package that uses occurrence probabilities and resampling methods to answer questions about the use of AUs, AU combinations, and the facial communication system as a whole in humans and non-human animals. Using highly stereotyped facial signals as an example, we illustrate some of the current functionalities of NetFACS. We show that very few AUs are specific to certain stereotypical contexts; that AUs are not used independently from each other; that graph-level properties of stereotypical signals differ; and that clusters of AUs allow us to reconstruct facial signals, even when blind to the underlying conditions. The flexibility and widespread use of network analysis allows us to move away from studying facial signals as stereotyped expressions, and towards a dynamic and differentiated approach to facial communication.

Tropical rainforest flies carrying pathogens form stable associations with social nonhuman primates.

Living in groups provides benefits but also incurs costs such as attracting disease vectors. For example, synanthropic flies associate with human settlements, and higher fly densities increase pathogen transmission. We investigated whether such associations also exist in highly mobile nonhuman primate (NHP) Groups. We studied flies in a group of wild sooty mangabeys (Cercocebus atys atys) and three communities of wild chimpanzees (Pan troglodytes verus) in Taï National Park, Côte d'Ivoire. We observed markedly higher fly densities within both mangabey and chimpanzee groups. Using a mark-recapture experiment, we showed that flies stayed with the sooty mangabey group for up to 12 days and for up to 1.3 km. We also tested mangabey-associated flies for pathogens infecting mangabeys in this ecosystem, Bacillus cereus biovar anthracis (Bcbva), causing sylvatic anthrax, and Treponema pallidum pertenue, causing yaws. Flies contained treponemal (6/103) and Bcbva (7/103) DNA. We cultured Bcbva from all PCR-positive flies, confirming bacterial viability and suggesting that this bacterium might be transmitted and disseminated by flies. Whole genome sequences of Bcbva isolates revealed a diversity of Bcbva, probably derived from several sources. We conclude that flies actively track mangabeys and carry infectious bacterial pathogens; these associations represent an understudied cost of sociality and potentially expose many social animals to a diversity of pathogens.

Local control of globally competing patterns in coupled Swift-Hohenberg equations.

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model.

We revisit the model for a two-well phase transformation in a linearly elastic body that was introduced and studied in Mielke et al. (2002 Arch. Ration. Mech. Anal. 162: , 137-177). This energetic rate-independent system is posed in terms of the elastic displacement and an internal variable that gives the phase portion of the second phase. We use a new approach based on mutual recovery sequences, which are adjusted to a suitable energy increment plus the associated dissipated energy and, thus, enable us to pass to the limit in the construction of energetic solutions. We give three distinct constructions of mutual recovery sequences which allow us (i) to generalize the existence result in Mielke et al. (2002), (ii) to establish the convergence of suitable numerical approximations via space-time discretization and (iii) to perform the evolutionary relaxation from the pure-state model to the relaxed-mixture model. All these results rely on weak converge and involve the H-measure as an essential tool.

Impact of dominance rank specification in dyadic interaction models.

Dominance rank is a vital descriptor of social dynamics in animal societies and regularly used in studies to explain observed interaction patterns. However, researchers can choose between different indices and standardizations, and can specify dyadic rank relations differently when studying interaction distributions. These researcher degrees of freedom potentially introduce biases into studies and reduce replicability. Here, I demonstrate the impact of researcher choices by comparing the performance of different combinations of rank index, standardization, and model specification when explaining dyadic interaction patterns in sooty mangabeys (Cercocebus atys atys). I show that while no combination consistently performed best across interaction types (aggression, grooming, proximity, supplants), model specifications allowing for nonlinear patterns performed better than other models on average. Choices made in pre-processing and model building impacted model performance and subsequent interpretation of results. Researchers could end up describing social systems differently based on the same data. These results highlight the impact of researcher choices in the processing of behavioural data and potential limitations when using indirect species comparisons in animal behaviour research. To increase repeatability, researchers could make the impact of their processing choices more transparent and report results using a variety of indices and model specifications.

Fine Properties of Geodesics and Geodesic λ-Convexity for the Hellinger-Kantorovich Distance.

We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger-Kantorovich problem (HK), providing sufficient conditions for the solvability of the primal Monge formulation. We also establish new regularity properties for the solution of the Hamilton-Jacobi equation arising in the dual dynamic formulation of HK, which are sufficiently strong to construct a characteristic transport-growth flow driving the geodesic interpolation between two arbitrary positive measures. These results are applied to study relevant geometric properties of HK geodesics and to derive the convex behaviour of their Lebesgue density along the transport flow. Finally, exact conditions for functionals defined on the space of measures are derived that guarantee the geodesic λ-convexity with respect to the Hellinger-Kantorovich distance. Examples of geodesically convex functionals are provided.

Higher social tolerance is associated with more complex facial behavior in macaques.

The social complexity hypothesis for communicative complexity posits that animal societies with more complex social systems require more complex communication systems. We tested the social complexity hypothesis on three macaque species that vary in their degree of social tolerance and complexity. We coded facial behavior in >3000 social interactions across three social contexts (aggressive, submissive, affiliative) in 389 animals, using the Facial Action Coding System for macaques (MaqFACS). We quantified communicative complexity using three measures of uncertainty: entropy, specificity, and prediction error. We found that the relative entropy of facial behavior was higher for the more tolerant crested macaques as compared to the less tolerant Barbary and rhesus macaques across all social contexts, indicating that crested macaques more frequently use a higher diversity of facial behavior. The context specificity of facial behavior was higher in rhesus as compared to Barbary and crested macaques, demonstrating that Barbary and crested macaques used facial behavior more flexibly across different social contexts. Finally, a random forest classifier predicted social context from facial behavior with highest accuracy for rhesus and lowest for crested, indicating there is higher uncertainty and complexity in the facial behavior of crested macaques. Overall, our results support the social complexity hypothesis.

Chimpanzee play sequences are structured hierarchically as games.

Social play is ubiquitous in the development of many animal species and involves players adapting actions flexibly to their own previous actions and partner responses. Play differs from other behavioural contexts for which fine-scale analyses of action sequences are available, such as tool use and communication, in that its form is not defined by its function, making it potentially more unpredictable. In humans, play is often organised in games, where players know context-appropriate actions but string them together unpredictably. Here, we use the sequential nature of play elements to explore whether play elements in chimpanzees are structured hierarchically and follow predictable game-like patterns. Based on 5,711 play elements from 143 bouts, we extracted individual-level play sequences of 11 Western chimpanzees (Pan troglodytes verus) of different ages from the Bossou community. We detected transition probabilities between play elements that exceeded expected levels and show that play elements form hierarchically clustered and interchangeable groups, indicative of at least six games that can be identified from transition networks, some with different roles for different players. We also show that increased information about preceding play elements improved predictability of subsequent elements, further indicating that play elements are not strung together randomly but that flexible action rules underlie their usage. Thus, chimpanzee play is hierarchically structured in short games which limit acceptable play elements and allow players to predict and adapt to partners' actions. This "grammar of action" approach to social interactions can be valuable in understanding cognitive and communicative abilities within and across species.