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Marmosets mutually compensate for differences in rhythms when coordinating vigilance [1]
['Nikhil Phaniraj', 'Institute Of Evolutionary Anthropology', 'University Of Zurich', 'Zurich', 'Neuroscience Center Zurich', 'Eth Zurich', 'Rahel K. Brügger', 'Judith M. Burkart', 'Center For The Interdisciplinary Study Of Language Evolution', 'Isle']
Date: 2024-07
Synchronization is widespread in animals, and studies have often emphasized how this seemingly complex phenomenon can emerge from very simple rules. However, the amount of flexibility and control that animals might have over synchronization properties, such as the strength of coupling, remains underexplored. Here, we studied how pairs of marmoset monkeys coordinated vigilance while feeding. By modeling them as coupled oscillators, we noted that (1) individual marmosets do not show perfect periodicity in vigilance behaviors, (2) nevertheless, marmoset pairs started to take turns being vigilant over time, a case of anti-phase synchrony, (3) marmosets could couple flexibly; the coupling strength varied with every new joint feeding bout, and (4) marmosets could control the coupling strength; dyads showed increased coupling if they began in a more desynchronized state. Such flexibility and control over synchronization require more than simple interaction rules. Minimally, animals must estimate the current degree of asynchrony and adjust their behavior accordingly. Moreover, the fact that each marmoset is inherently non-periodic adds to the cognitive demand. Overall, our study provides a mathematical framework to investigate the cognitive demands involved in coordinating behaviors in animals, regardless of whether individual behaviors are rhythmic or not.
Research suggests that synchronized animal behaviors often emerge from simple interaction rules. Mathematical models have been instrumental in revealing these underlying rules. Here, we employed mathematical modeling to study how marmoset monkeys coordinate vigilance and feeding behaviors in a situation where doing both actions simultaneously is not possible. We found that pairs of marmosets progress to a state where they show opposite behaviors, i.e., when one individual is feeding, the other is vigilant, and vice-versa. In order to achieve such coordinated state, the individuals must influence each other’s behaviors, i.e., couple. We found that marmosets can couple flexibly and that they couple more strongly if they are initially out-of-sync with their partner. Such ability to detect the current state of synchrony and adapt behavior accordingly is cognitively demanding. Our research thus demostrates that animals with more complex cognitive abilities can do much more than following simple interaction rules to synchronize with other individuals. Overall, our research (1) establishes marmosets as a strong candidate species for studying the cognitive aspects of social timing, (2) provides a novel mathematical framework that is tailored for studying synchronization in biological systems, and (3) underlines the implications of synchrony for marmosets and other animals.
Introduction
Rhythmic phenomena involving multiple animals are widespread in nature [1–3]. From synchronized flashings of fireflies [4,5], call synchronization in frogs [6,7] to coupled neuronal activity in bats [8] or synchronized heart rates in humans [9]–synchronicity can be found in a huge variety of organisms in different behavioral contexts, at varying levels and serving multiple functions. Synchronicity not only includes patterns where individuals behave in the same way at the same time, as in the impressive synchronous light flashes of fireflies or coordinated movements of starling flocks [10]. Many phenomena show anti-phase synchronization in which individuals alternate behavior [11], as in vocal turn-taking in marmoset monkeys [12,13], meerkats [14], elephants [15] and plain-tailed wrens [16] or gestural exchanges of mother-infant dyads in chimpanzees and bonobos [17]. Whereas in-phase and anti-phase synchrony are the two extremes and frequently occur in nature, synchronization can, in principle, occur at any phase lag (e.g., [18]). Throughout this paper, we use ’synchronization’ to refer to the phenomena of individuals showing repetitive behavior at the same rate, with any phase difference between them.
However, the complexity of these phenomena does not necessarily imply complex cognitive mechanisms. There is extensive evidence from invertebrates that synchronized patterns can emerge as epiphenomena of animals following very simple rules: fireflies, for example, simply flash sooner than usual whenever a neighbor flashes and the resulting synchrony emerges from these small changes in local interactions [19–21]. In such cases, where individuals are not synchronized to begin with, individuals need to interact in such a way that they influence the behavior of each other, i.e., ’couple’, to reach a synchronized state. These simple mechanistic rules predict patterns of synchronization that are quite uniform, with minimal variation of rhythmic rates between individuals that are coupled and across behavioral bouts. Animals are also expected to show a limited range of possible adjustments to their inherent rhythm, making it difficult to adjust to more dissimilar stimulus rhythms [3]. This is especially important when looking at contexts such as gait synchronization [22,23] since the skeletal and motor system inherently limits the movement frequencies of animals [3]. When looking at patterns of behavior such as gestural exchanges these limiting factors to the flexibility of rhythmic rates might be less constrained but in turn synchronization might be more difficult to achieve.
What remains underexplored is how flexible synchronization patterns are in non-human animals with more complex cognitive abilities compared to invertebrates. Most studies investigating cognitive mechanisms underlying rhythmic behaviors focus on the perception and production of rhythmic patterns [24]. For example, typical rhythm perception tasks are performed as go/no-go tasks where animals are trained to respond to regular (isochronous) rhythms but not irregular (anisochronous) ones. The same previously trained animals are then confronted with novel regular and, importantly, irregular sequences ("anisochrony detection"). Individuals are expected to generalize the patterns of regularity to the novel sequences, i.e., they should again respond to regular sequences but not to irregular ones. Both rats [25] and starlings [26,27] are capable of solving such tasks (but not zebra finches: [28] and pigeons: [29]). Other studies use approach behavior (i.e., moving closer to one of two sound sources) to discern whether animals can discriminate between rhythmic patterns. These tasks seem especially promising when used with mating calls of frogs or insects, where animals seem to show species-specific rhythmic preferences [30,31]. Rhythm production studies in vertebrate animal models rely heavily on training (and rewarding anticipatory movements) and a laboratory setting (i.e., [32–34]. These studies show that primates [34,35], rats [36] and birds [33,37] can successfully achieve synchronization in tasks where they are required to synchronize a motor action such as pressing a lever or pecking a key to an audio or visual metronome stimulus (even with adaptations to changes in tempo). The most flexible rhythm production has been shown by a sea lion and two parrots who were capable of synchronizing to the beat of real music at varying tempos (sea lion: [38,39]; parrots: [40,41]), thus indicating that coupling is not restricted to a certain rate. Even though these lab-based studies offer a very controlled environment to investigate the cognitive flexibility of synchronization abilities, they also heavily rely on motivational factors that do not necessarily relate to how flexible rates of rhythmic abilities can be adjusted. These factors might sometimes be overlooked, and potentially lead to false negative results [3]. The other avenue that has been taken is relying on more naturalistic observation where rhythmic abilities from a species-specific behavioral repertoire are used (e.g., chimpanzee walking: [42]). Critically, this approach can be further enhanced when combined with mathematical modeling [2].
One such context where animals are expected to show high motivation for temporal coordination and that is under high selection pressures, is anti-predator vigilance. There is ample evidence that individuals living in bigger groups spend less time being vigilant [43–45], perhaps because they simply feel safer (i.e., the many eyes effect [46]) or because they actually take others’ vigilance into account. For several species it has been shown that individuals’ vigilance levels are indeed not independent of each other but rather synchronized at the group level (e.g., birds: [47,48]; mammals: [49–51]), leading to periods of higher and lower vigilance. Intriguingly, vigilance can also be coordinated in anti-phase synchronization (i.e., animals maximizing the feeding time when any group member is vigilant [52]), leading to turn-taking-like patterns [53–55]. Such evidence for anti-phase synchrony is most prevalent in groups with sentinel systems and otherwise typically restricted to (mating) pairs (coral reef fish: [56,57]; birds [58,59]).
For the small, arboreal common marmosets, who are vulnerable to predation in the wild ([60], carnivores: [61], snakes: [62], raptors: [63]), vigilance is a key part of their survival strategy [64]. They follow the general trend of a negative group size effect with bigger groups being associated with lower levels of individual vigilance [65]. Some studies have claimed the presence of a sentinel system [66,67] and more recently, marmoset pairs have shown to coordinate their vigilance in a feeding situation by being more vigilant when the pair mate was feeding than when not [68]. Furthermore, when feeding in proximity to their mate, they maintained the same behavior for longer periods of time when showing opposite behaviors, i.e., one individual being vigilant and the other feeding [68]. These results suggest temporal coordination between individuals, but how this anti-phase synchrony develops or fades out is currently unknown.
Here, we dynamically modeled the vigilance and feeding behaviors of captive pairs of common marmosets as coupled oscillators (i.e., oscillators changing behaviors between vigilance and feeding) using the Kuramoto model. We used a feeding situation where being vigilant and feeding were mutually exclusive (namely, when marmosets were eating mash out of an opaque feeding bowl). Even in captive settings marmosets maintain high levels of vigilance, as for instance when responding to unfamiliar humans with antipredator behavior and emitting warning calls upon spotting birds of prey (personal observations by RKB & JMB). First, we described the general properties of marmosets’ vigilance and feeding bouts, especially comparing mean vigilance and feeding durations between times when animals were situated alone versus together on a feeding basket. Next, we modeled the two individuals as coupled oscillators according to the classic Kuramoto model [69,70] (henceforth ’Kuramoto model’). The Kuramoto model is one way to model the development of synchrony and its temporal variations. Other popularly used models include the integrate-and-fire model for pulse-coupled oscillators (when the oscillators interact only momentarily during a cycle, such as firefly flashes) [71] and the second-order Kuramoto model for oscillators with inertia (such as power grids) [72]. As our system does not fit these special cases, we started modeling our system using the classic Kuramoto model. However, the classic model assumes that the individual oscillators are inherently periodic. We thus additionally developed a non-periodic version of the Kuramoto model, as many biological systems are not expected to be inherently periodic [73,74].
An overview of analyses is summarized in Fig 1 and described in detail in the methods section. Briefly, we started studying marmoset vigilance behavior when they were feeding alone and simulated behavioral bouts based on this data. We then virtually paired the simulated bouts of the marmoset partners and fit the classic Kuramoto model to these instances (Fig 1A). These were the ’control bouts’, reflecting patterns of synchronization that would randomly occur. Next, we studied marmoset vigilance behavior when the marmosets were actually feeding together with their partner (and hence, were highly likely to be influenced by their behavior) and fit the classic Kuramoto model to these ’actual bouts’ (Fig 1B). Finally, we simulated several marmoset behavioral bouts using the non-periodic Kuramoto model and compared the simulations to empirical data. By fitting the classic and non-periodic Kuramoto models to the data, we were able to estimate how strongly one individual’s behavior influenced the other individual, i.e., the coupling strength–through the coupling constant. Positive and negative values of the coupling constant indicate the tendency to reach in-phase and anti-phase synchrony, respectively. We additionally derived the critical coupling constant (the threshold to reach a state of synchrony), using the classic Kuramoto model and the control model. For the classic Kuramoto model, we also obtained the time to reach anti-phase synchrony.
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TIFF original image Download: Fig 1. Overview of analyses. (A) The pipeline for analyzing control bouts. Individuals were observed when they were feeding alone, and their vigilance and feeding distributions were obtained (an individual sat on the basket and ate from the yellow bowl). The distributions were used to simulate 100 behavioral bouts per pair. These bouts underwent lowpass filtering and Hilbert transform, and the Kuromoto model was fit to the phases to obtain synchronization parameters. (B) The pipeline for analyzing actual bouts using the classic Kuramoto model. Individuals were observed when they were feeding together, and their vigilance and feeding distributions were obtained. Additionally, the time-series of when each individual was vigilant or feeding was obtained. These time-series (bouts) underwent lowpass filtering and Hilbert transform and Kuromoto model was applied on the phases to obtain synchronization parameters as in the control condition. (C) Non-periodic Kuramoto model. The distributions of vigilance and feeding durations were provided as inputs to the non-periodic Kuramoto model and a parameter sweep of coupling constants done to simulate 2 time-series of phases. From this, the time-series of phase difference was calculated and its angular distance from the time-series obtained from a behavioral bout of the ’together’ condition was determined. The coupling constant value, which gave the smallest angular distance (provided the ’best fit’) was the estimated coupling constant for that behavioral bout. Note that even though monkeys are depicted to be provided with one food bowl when alone and two food bowls when together, both one bowl and two bowl conditions were experienced by all animals to control for alternative explanations. See the methods sections for further details. Abbreviations: V = vigilance, F = feeding, K = coupling constant, K c = critical coupling constant, Ω = difference in natural frequencies, T = time to attain anti-phase synchrony, and τ = time-period for which an individual would remain in a particular behavioral state.
https://doi.org/10.1371/journal.pcbi.1012104.g001
Our predictions were threefold: 1) Most biological oscillators are not perfectly periodic, yet there are abundant examples of synchronization in the animal world. We did not expect marmoset head oscillations (i.e., their behavioral transitions from vigilance to feeding) to be periodic in the absence of any input from conspecifics, but we predicted that they would still show anti-phase synchrony with a partner, given that the probability of an individual being vigilant when its partner is feeding has been shown to be higher than chance [68,73–75]. 2) Animals that show a stereotyped periodic behavior and eventually synchronize, such as fireflies flashing or katydids chirping seem to do so following simple, fixed interaction rules. If marmosets were following simple, fixed interaction rules to coordinate vigilance, we would expect the coupling strengths to be more-or-less uniform across feeding bouts. Moreover, we would expect the synchronization dynamics to be uniform. As marmoset vigilance behavior is known to be variable and not very stereotyped [68], we predicted that there will be some variation in the coupling strengths across feeding bouts and that marmosets can synchronize flexibly. 3) If the coupling strength indeed varied across feeding bouts, we predicted that the differences in the initial rate of head oscillations can explain some of this variation. This was motivated by the fact that marmosets show sensitivity to initial conditions when synchronizing in other modalities. For example, marmosets converge with their pair-mates in acoustic space, i.e., sound more similar to their partner over time, in a process called vocal accommodation [76,77]. During this process, they also move through the acoustic space in a synchronized fashion [78]. The extent of vocal accommodation is proportional to the initial differences in vocal properties, with higher initial acoustic differences between partners leading to more vocal accommodation later [79].
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