Social tipping points in animal societies

Widespread cultural change in declining populations of Amazon parrots

Species worldwide are experiencing anthropogenic environmental change, and the long-term impacts on animal cultural traditions such as vocal dialects are often unknown. Our prior studies of the yellow-naped amazon (Amazona auropalliata) revealed stable vocal dialects over an 11-year period (1994-2005), with modest shifts in geographic boundaries and acoustic structure of contact calls. Here, we examined whether yellow-naped amazons maintained stable dialects over the subsequent 11-year time span from 2005 to 2016, culminating in 22 years of study. Over this same period, this species suffered a dramatic decrease in population size that prompted two successive uplists in IUCN status, from vulnerable to critically endangered. In this most recent 11-year time span, we found evidence of geographic shifts in call types, manifesting in more bilingual sites and introgression across the formerly distinct North-South acoustic boundary. We also found greater evidence of acoustic drift, in the form of new emerging call types and greater acoustic variation overall. These results suggest cultural traditions such as dialects may change in response to demographic and environmental conditions, with broad implications for threatened species.

Agonistic interactions and social behaviors in the Saharan Dorcas gazelle (Gazella dorcas neglecta): Using social network analysis to evaluate relationships and social structure in captive male groups

Social interactions, including agonistic behavior, are very important for the management and welfare of individuals forming groups in captivity. One of the main concerns for the stability and durability of adult male groups is a noticeable level of intraspecific aggression. This study comprises a Social Network Analysis to illustrate social structure in different groups of captive Saharan Dorcas gazelles (Gazella dorcas neglecta). Our main objectives were to examine the relationship between agonistic, affiliative, and association networks and their reciprocity, assessing also whether the agonistic networks can conform to a linear dominance hierarchy. For these purposes, we recorded the behavior of 23 adult males organized in five herds, three composed only of Saharan Dorcas gazelle males and two mixed herds in which there were also Mhorr gazelle males (Nanger dama mohor). Observations were carried out during 295 h through scan sampling. We found no correlation between the affiliative and association networks in any group, although there was a significant correlation between the agonistic and association networks in mixed-species groups which was not present in single-species groups. Overall, there was no consistent reciprocity in either affiliative nor agonistic networks and none of the agonistic networks showed a linear structure. These results indicate that affiliative behavior in Saharan Dorcas gazelles offers distinctive and valuable information about the bonds between individuals, however, their dominance structure is far more complex than previously thought. As information provided by affiliative and proximity behaviors is different in this species, we suggest considering affiliative interactions to stablish affinity between individuals. Evaluating different social behaviors and not only agonistic interactions in later studies, is also recommended to develop a more accurately daily management in zoos that guarantee group stability and individuals' welfare, which will improve the conservation of captive populations.

Optimal parameterizing manifolds for anticipating tipping points and higher-order critical transitions

A general, variational approach to derive low-order reduced models from possibly non-autonomous systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes more classical notions of invariant or slow manifolds when the breakdown of "slaving" occurs, i.e., when the unresolved variables cannot be expressed as an exact functional of the resolved ones anymore. The OPM provides, within a given class of parameterizations of the unresolved variables, the manifold that averages out optimally these variables as conditioned on the resolved ones. The class of parameterizations retained here is that of continuous deformations of parameterizations rigorously valid near the onset of instability. These deformations are produced through the integration of auxiliary backward-forward systems built from the model's equations and lead to analytic formulas for parameterizations. In this modus operandi, the backward integration time is the key parameter to select per scale/variable to parameterize in order to derive the relevant parameterizations which are doomed to be no longer exact away from instability onset due to the breakdown of slaving typically encountered, e.g., for chaotic regimes. The selection criterion is then made through data-informed minimization of a least-square parameterization defect. It is thus shown through optimization of the backward integration time per scale/variable to parameterize, that skilled OPM reduced systems can be derived for predicting with accuracy higher-order critical transitions or catastrophic tipping phenomena, while training our parameterization formulas for regimes prior to these transitions takes place.

Opposing Responses to Scarcity Emerge from Functionally Unique Sociality Drivers

AbstractFrom biofilms to whale pods, organisms across taxa live in groups, thereby accruing numerous diverse benefits of sociality. All social organisms, however, pay the inherent cost of increased resource competition. One expects that when resources become scarce, this cost will increase, causing group sizes to decrease. Indeed, this occurs in some species, but there are also species for which group sizes remain stable or even increase under scarcity. What accounts for these opposing responses? We present a conceptual framework, literature review, and theoretical model demonstrating that differing responses to sudden resource shifts can be explained by which sociality benefit exerts the strongest selection pressure on a particular species. We categorize resource-related benefits of sociality into six functionally distinct classes and model their effect on the survival of individuals foraging in groups under different resource conditions. We find that whether, and to what degree, the optimal group size (or correlates thereof) increases, decreases, or remains constant when resource abundance declines depends strongly on the dominant sociality mechanism. Existing data, although limited, support our model predictions. Overall, we show that across a wide diversity of taxa, differences in how group size shifts in response to resource declines can be driven by differences in the primary benefits of sociality.

The ecology of wealth inequality in animal societies

Individuals vary in their access to resources, social connections and phenotypic traits, and a central goal of evolutionary biology is to understand how this variation arises and influences fitness. Parallel research on humans has focused on the causes and consequences of variation in material possessions, opportunity and health. Central to both fields of study is that unequal distribution of wealth is an important component of social structure that drives variation in relevant outcomes. Here, we advance a research framework and agenda for studying wealth inequality within an ecological and evolutionary context. This ecology of inequality approach presents the opportunity to reintegrate key evolutionary concepts as different dimensions of the link between wealth and fitness by (i) developing measures of wealth and inequality as taxonomically broad features of societies, (ii) considering how feedback loops link inequality to individual and societal outcomes, (iii) exploring the ecological and evolutionary underpinnings of what makes some societies more unequal than others, and (iv) studying the long-term dynamics of inequality as a central component of social evolution. We hope that this framework will facilitate a cohesive understanding of inequality as a widespread biological phenomenon and clarify the role of social systems as central to evolutionary biology.

Hysteresis stabilizes dynamic control of self-assembled army ant constructions

Biological systems must adjust to changing external conditions, and their resilience depends on their control mechanisms. How is dynamic control implemented in noisy, decentralized systems? Army ants’ self-assembled bridges are built on unstable features, like leaves, which frequently move. Using field experiments and simulations, we characterize the bridges’ response as the gaps they span change in size, identify the control mechanism, and explore how this emerges from individuals’ decisions. For a given gap size, bridges were larger after the gap increased rather than decreased. This hysteresis was best explained by an accumulator model, in which individual decisions to join or leave a bridge depend on the difference between its current and equilibrium state. This produces robust collective structures that adjust to lasting perturbations while ignoring small, momentary shifts. Our field data support separate joining and leaving cues; joining is prompted by high bridge performance and leaving by an excess of ants. This leads to stabilizing hysteresis, an important feature of many biological and engineered systems.

Army ant bridges are a remarkable example of self-assembled living structures. Here, the authors investigate experimentally how army ant bridges respond to unstable ground, revealing how responses emerge from the decentralized actions of individuals.

The dynamics of dominance: open questions, challenges and solutions

Although social hierarchies are recognized as dynamic systems, they are typically treated as static entities for practical reasons. Here, we ask what we can learn from a dynamical view of dominance, and provide a research agenda for the next decades. We identify five broad questions at the individual, dyadic and group levels, exploring the causes and consequences of individual changes in rank, the dynamics underlying dyadic dominance relationships, and the origins and impacts of social instability. Although challenges remain, we propose avenues for overcoming them. We suggest distinguishing between different types of social mobility to provide conceptual clarity about hierarchy dynamics at the individual level, and emphasize the need to explore how these dynamic processes produce dominance trajectories over individual lifespans and impact selection on status-seeking behaviour. At the dyadic level, there is scope for deeper exploration of decision-making processes leading to observed interactions, and how stable but malleable relationships emerge from these interactions. Across scales, model systems where rank is manipulable will be extremely useful for testing hypotheses about dominance dynamics. Long-term individual-based studies will also be critical for understanding the impact of rare events, and for interrogating dynamics that unfold over lifetimes and generations. This article is part of the theme issue 'The centennial of the pecking order: current state and future prospects for the study of dominance hierarchies'.

Permutation Entropy as a Universal Disorder Criterion: How Disorders at Different Scale Levels Are Manifestations of the Same Underlying Principle

What do bacteria, cells, organs, people, and social communities have in common? At first sight, perhaps not much. They involve totally different agents and scale levels of observation. On second thought, however, perhaps they share everything. A growing body of literature suggests that living systems at different scale levels of observation follow the same architectural principles and process information in similar ways. Moreover, such systems appear to respond in similar ways to rising levels of stress, especially when stress levels approach near-lethal levels. To explain such communalities, we argue that all organisms (including humans) can be modeled as hierarchical Bayesian controls systems that are governed by the same biophysical principles. Such systems show generic changes when taxed beyond their ability to correct for environmental disturbances. Without exception, stressed organisms show rising levels of 'disorder' (randomness, unpredictability) in internal message passing and overt behavior. We argue that such changes can be explained by a collapse of allostatic (high-level integrative) control, which normally synchronizes activity of the various components of a living system to produce order. The selective overload and cascading failure of highly connected (hub) nodes flattens hierarchical control, producing maladaptive behavior. Thus, we present a theory according to which organic concepts such as stress, a loss of control, disorder, disease, and death can be operationalized in biophysical terms that apply to all scale levels of organization. Given the presumed universality of this mechanism, 'losing control' appears to involve the same process anywhere, whether involving bacteria succumbing to an antibiotic agent, people suffering from physical or mental disorders, or social systems slipping into warfare. On a practical note, measures of disorder may serve as early warning signs of system failure even when catastrophic failure is still some distance away.

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_c$$\end{document}qc in case of conformity is independent from the size of the source of influence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_a$$\end{document}qa in case of anticonformity. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_c=q_a=q$$\end{document}qc=qa=q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_c \ge q_a + \Delta q$$\end{document}qc≥qa+Δq, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta q=4$$\end{document}Δq=4 for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_a \le 3$$\end{document}qa≤3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta q=3$$\end{document}Δq=3 for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_a>3$$\end{document}qa>3. In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle k\rangle \le 150$$\end{document}⟨k⟩≤150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle k\rangle$$\end{document}⟨k⟩. Moreover, we show that for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_a < q_c - 1$$\end{document}qa<qc-1 pair approximation results overlap the Monte Carlo ones. On the other hand, for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_a \ge q_c - 1$$\end{document}qa≥qc-1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle k\rangle$$\end{document}⟨k⟩, as long as the pair approximation indicates correctly the type of the phase transition.

The thermal environment as a moderator of social evolution

Animal sociality plays a crucial organisational role in evolution. As a result, understanding the factors that promote the emergence, maintenance, and diversification of animal societies is of great interest to biologists. Climate is among the foremost ecological factors implicated in evolutionary transitions in social organisation, but we are only beginning to unravel the possible mechanisms and specific climatic variables that underlie these associations. Ambient temperature is a key abiotic factor shaping the spatio-temporal distribution of individuals and has a particularly strong influence on behaviour. Whether such effects play a broader role in social evolution remains to be seen. In this review, we develop a conceptual framework for understanding how thermal effects integrate into pathways that mediate the opportunities, nature, and context of social interactions. We then implement this framework to discuss the capacity for temperature to initiate organisational changes across three broad categories of social evolution: group formation, group maintenance, and group elaboration. For each category, we focus on pivotal traits likely to have underpinned key social transitions and explore the potential for temperature to affect changes in these traits by leveraging empirical examples from the literature on thermal and behavioural ecology. Finally, we discuss research directions that should be prioritised to understand the potentially constructive and/or destructive effects of future warming on the origins, maintenance, and diversification of animal societies.

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s \ge 2$$\end{document}s≥2 states. As in the original binary q-voter model, which corresponds to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s=2$$\end{document}s=2, at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-p$$\end{document}1-p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s>2$$\end{document}s>2 the model displays discontinuous phase transitions for any \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q>1$$\end{document}q>1, on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q>5$$\end{document}q>5. Moreover, unlike the case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s=2$$\end{document}s=2, for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s>2$$\end{document}s>2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

Using multilayer network analysis to explore the temporal dynamics of collective behavior

Social organisms often show collective behaviors such as group foraging or movement. Collective behaviors can emerge from interactions between group members and may depend on the behavior of key individuals. When social interactions change over time, collective behaviors may change because these behaviors emerge from interactions among individuals. Despite the importance of, and growing interest in, the temporal dynamics of social interactions, it is not clear how to quantify changes in interactions over time or measure their stability. Furthermore, the temporal scale at which we should observe changes in social networks to detect biologically meaningful changes is not always apparent. Here we use multilayer network analysis to quantify temporal dynamics of social networks of the social spider Stegodyphus dumicola and determine how these dynamics relate to individual and group behaviors. We found that social interactions changed over time at a constant rate. Variation in both network structure and the identity of a keystone individual was not related to the mean or variance of the collective prey attack speed. Individuals that maintained a large and stable number of connections, despite changes in network structure, were the boldest individuals in the group. Therefore, social interactions and boldness are linked across time, but group collective behavior is not influenced by the stability of the social network. Our work demonstrates that dynamic social networks can be modeled in a multilayer framework. This approach may reveal biologically important temporal changes to social structure in other systems.

Decrease in social cohesion in a colonial seabird under a perturbation regime

Social interactions, through influence on behavioural processes, can play an important role in populations’ resilience (i.e. ability to cope with perturbations). However little is known about the effects of perturbations on the strength of social cohesion in wild populations. Long-term associations between individuals may reflect the existence of social cohesion for seizing the evolutionary advantages of social living. We explore the existence of social cohesion and its dynamics under perturbations by analysing long-term social associations, in a colonial seabird, the Audouin’s gull Larus audouinii, living in a site experiencing a shift to a perturbed regime. Our goals were namely (1) to uncover the occurrence of long-term social ties (i.e. associations) between individuals and (2) to examine whether the perturbation regime affected this form of social cohesion. We analysed a dataset of more than 3500 individuals from 25 years of monitoring by means of contingency tables and within the Social Network Analysis framework. We showed that associations between individuals are not only due to philopatry or random gregariousness but that there are social ties between individuals over the years. Furthermore, social cohesion decreased under the perturbation regime. We sustain that perturbations may lead not only to changes in individuals’ behaviour and fitness but also to a change in populations’ social cohesion. The consequences of decreasing social cohesion are still not well understood, but they can be critical for the population dynamics of social species.

Fisheries-induced selection against schooling behaviour in marine fishes

Group living is a common strategy used by fishes to improve their fitness. While sociality is associated with many benefits in natural environments, including predator avoidance, this behaviour may be maladaptive in the Anthropocene. Humans have become the dominant predator in many marine systems, with modern fishing gear developed to specifically target groups of schooling species. Therefore, ironically, behavioural strategies which evolved to avoid non-human predators may now actually make certain fish more vulnerable to predation by humans. Here, we use an individual-based model to explore the evolution of fish schooling behaviour in a range of environments, including natural and human-dominated predation conditions. In our model, individual fish may leave or join groups depending on their group-size preferences, but their experienced group size is also a function of the preferences of others in the population. Our model predicts that industrial fishing selects against individual-level behaviours that produce large groups. However, the relationship between fishing pressure and sociality is nonlinear, and we observe discontinuities and hysteresis as fishing pressure is increased or decreased. Our results suggest that industrial fishing practices could be altering fishes' tendency to school, and that social behaviour should be added to the list of traits subject to fishery-induced evolution.

A network-based microfoundation of Granovetter's threshold model for social tipping

Social tipping, where minorities trigger larger populations to engage in collective action, has been suggested as one key aspect in addressing contemporary global challenges. Here, we refine Granovetter’s widely acknowledged theoretical threshold model of collective behavior as a numerical modelling tool for understanding social tipping processes and resolve issues that so far have hindered such applications. Based on real-world observations and social movement theory, we group the population into certain or potential actors, such that – in contrast to its original formulation – the model predicts non-trivial final shares of acting individuals. Then, we use a network cascade model to explain and analytically derive that previously hypothesized broad threshold distributions emerge if individuals become active via social interaction. Thus, through intuitive parameters and low dimensionality our refined model is adaptable to explain the likelihood of engaging in collective behavior where social-tipping-like processes emerge as saddle-node bifurcations and hysteresis.

Insights from the study of complex systems for the ecology and evolution of animal populations

Populations of animals comprise many individuals, interacting in multiple contexts, and displaying heterogeneous behaviors. The interactions among individuals can often create population dynamics that are fundamentally deterministic yet display unpredictable dynamics. Animal populations can, therefore, be thought of as complex systems. Complex systems display properties such as nonlinearity and uncertainty and show emergent properties that cannot be explained by a simple sum of the interacting components. Any system where entities compete, cooperate, or interfere with one another may possess such qualities, making animal populations similar on many levels to complex systems. Some fields are already embracing elements of complexity to help understand the dynamics of animal populations, but a wider application of complexity science in ecology and evolution has not occurred. We review here how approaches from complexity science could be applied to the study of the interactions and behavior of individuals within animal populations and highlight how this way of thinking can enhance our understanding of population dynamics in animals. We focus on 8 key characteristics of complex systems: hierarchy, heterogeneity, self-organization, openness, adaptation, memory, nonlinearity, and uncertainty. For each topic we discuss how concepts from complexity theory are applicable in animal populations and emphasize the unique insights they provide. We finish by outlining outstanding questions or predictions to be evaluated using behavioral and ecological data. Our goal throughout this article is to familiarize animal ecologists with the basics of each of these concepts and highlight the new perspectives that they could bring to variety of subfields.

The lag-time constraint for behavioural plasticity

Environmental instability (i.e. environments changing often) can select fixed phenotypes because of the lag time of plastically adapting to environmental changes, known as the lag-time constraint. Because behaviour can change rapidly (e.g. switching between foraging strategies), the lag-time constraint is not considered important for behavioural plasticity. Instead, it is often argued that responsive behaviour (i.e. behaviour that changes according to the environment) evolves to cope with unstable environments. But proficiently performing certain behaviours may require time for learning, for practising or, in social animals, for the group to adjust to one's behaviour. Conversely, not using certain behaviours for a period of time can reduce their level of performance. Here, using individual-based evolutionary simulations, we show that environmental instability selects for fixed behaviour when the ratio between the rates of increase and reduction in behavioural performance is below a certain threshold; only above this threshold does responsive behaviour evolve in unstable environments. Thus, the lag-time constraint can apply to behaviours that attain high performance either slowly or rapidly, depending on the relative rate with which their performance decreases when not used. We discuss these results in the context of the evolution of reduced behavioural plasticity, as seen in fixed personality differences.

Assessing the repeatability, robustness to disturbance, and parent-offspring colony resemblance of collective behavior

Groups of animals possess phenotypes such as collective behaviour, which may determine the fitness of group members. However, the stability and robustness to perturbations of collective phenotypes in natural conditions is not established. Furthermore, whether group phenotypes are transmitted from parent to offspring groups with fidelity is required for understanding how selection on group phenotypes contributes to evolution, but parent-offspring resemblance at the group level is rarely estimated. We evaluated the repeatability, robustness to perturbation and parent-offspring resemblance of collective foraging aggressiveness in colonies of the social spider Anelosimus eximius. Among-colony differences in foraging aggressiveness were consistent over time but changed if the colony was perturbed through the removal of individuals or via individuals' removal and subsequent return. Offspring and parent colony behaviour were correlated at the phenotypic level, but only once the offspring colony had settled after being translocated, and the correlation overlapped with zero at the among-colony level. The parent-offspring resemblance was not driven by a shared elevation but could be due to other environmental factors. The behaviour of offspring colonies in a common garden laboratory setting was not correlated with the behaviour of the parent colony nor with the same colony's behaviour once it was returned to the field. The phenotypes of groups represent a potentially important tier of biological organization, and assessing the stability and heritability of such phenotypes helps us better understand their role in evolution.

Structural trade-offs can predict rewiring in shrinking social networks

There is growing evidence that organisms can respond to declining population sizes by adapting their interactions with others. Regulating connections with others could underpin resilience of biological networks spanning from social groups to ecological communities. However, our ability to predict the dynamics of shrinking social networks remains limited. Network regulation involves several trade-offs. Removing nodes (and therefore their connections) from networks reduces the number of connections among remaining nodes. Responding by forming new connections then impacts other network properties. A simple way to minimize the impact of up-regulating network connections is to form new connections or to strengthen connections, between nodes that share a lost connection with a recently removed node. I propose a simple 'second-degree rewiring' rule as a biologically plausible regulatory mechanism in shrinking social networks. I argue that two individuals that have lost a connection with a common removed individual will both be more likely, or more willing, to form a new, or strengthen an existing, connection among themselves. I then show that such second-degree rewiring has less impact on important structural properties of the network than forming random new connections. For example, in a network with phenotypic assortment, second-degree nodes are more likely to be similar than any random pair of nodes, and connecting these will better maintain assortativity. This simple rule can therefore maintain network properties without individuals having any knowledge of the global structure of the network or the relative properties of the nodes within it. In this paper, I outline an algorithm for second-degree rewiring. I demonstrate how second-degree rewiring can have less impact than adding new, or increasing the strength of, random connections on both the individual and whole network properties. That is, relative to randomly adding or strengthening connections, second-degree rewiring has less impact on mean degree, assortativity, clustering and network density. I then demonstrate empirically, using social networks of great tits (Parus major), that individuals that previously shared connections to a removed conspecific were more likely to form a new connection or to strengthen their connection, relative to other individuals in the same population. This study highlights how developing a better mechanistic understanding of the structural properties of networks, and the consequences of adding new connections, can provide useful insights into how organisms are likely to regulate their interactions in shrinking populations.

What can a non-eusocial insect tell us about the neural basis of group behaviour?

Group behaviour has been extensively studied in canonically social swarming, shoaling and flocking vertebrates and invertebrates, providing great insight into the behavioural and ecological aspects of group living. However, the search for its neuronal basis is lagging behind. In the natural environment, Drosophila melanogaster, increasingly used as a model to study neuronal circuits and behaviour, spend their lives surrounded by several conspecifics of different stages, as well as heterospecifics. Despite their dynamic multi-organism natural environment, the neuronal basis of social behaviours has been typically studied in dyadic interactions, such as mating or aggression. This review will focus on recent studies regarding how the behaviour of fruit flies can be shaped by the nature of the surrounding group. We argue that the rich social environment of Drosophila melanogaster, its arsenal of neurogenetic tools and the ability to use large sample sizes for detailed quantitative behavioural analysis makes this species ideal for mechanistic studies of group behaviour.

Individual and collective encoding of risk in animal groups

The need to make fast decisions under risky and uncertain conditions is a widespread problem in the natural world. While there has been extensive work on how individual organisms dynamically modify their behavior to respond appropriately to changing environmental conditions (and how this is encoded in the brain), we know remarkably little about the corresponding aspects of collective information processing in animal groups. For example, many groups appear to show increased "sensitivity" in the presence of perceived threat, as evidenced by the increased frequency and magnitude of repeated cascading waves of behavioral change often observed in fish schools and bird flocks under such circumstances. How such context-dependent changes in collective sensitivity are mediated, however, is unknown. Here we address this question using schooling fish as a model system, focusing on 2 nonexclusive hypotheses: 1) that changes in collective responsiveness result from changes in how individuals respond to social cues (i.e., changes to the properties of the "nodes" in the social network), and 2) that they result from changes made to the structural connectivity of the network itself (i.e., the computation is encoded in the "edges" of the network). We find that despite the fact that perceived risk increases the probability for individuals to initiate an alarm, the context-dependent change in collective sensitivity predominantly results not from changes in how individuals respond to social cues, but instead from how individuals modify the spatial structure, and correspondingly the topology of the network of interactions, within the group. Risk is thus encoded as a collective property, emphasizing that in group-living species individual fitness can depend strongly on coupling between scales of behavioral organization.

Is Independence Necessary for a Discontinuous Phase Transition within the q-Voter Model?

We ask a question about the possibility of a discontinuous phase transition and the related social hysteresis within the q-voter model with anticonformity. Previously, it was claimed that within the q-voter model the social hysteresis can emerge only because of an independent behavior, and for the model with anticonformity only continuous phase transitions are possible. However, this claim was derived from the model, in which the size of the influence group needed for the conformity was the same as the size of the group needed for the anticonformity. Here, we abandon this assumption on the equality of two types of social response and introduce the generalized model, in which the size of the influence group needed for the conformity q c and the size of the influence group needed for the anticonformity q a are independent variables and in general q c ≠ q a . We investigate the model on the complete graph, similarly as it was done for the original q-voter model with anticonformity, and we show that such a generalized model displays both types of phase transitions depending on parameters q c and q a .

Exploring Interactions between the Gut Microbiota and Social Behavior through Nutrition

Microbes influence a wide range of host social behaviors and vice versa. So far, however, the mechanisms underpinning these complex interactions remain poorly understood. In social animals, where individuals share microbes and interact around foods, the gut microbiota may have considerable consequences on host social interactions by acting upon the nutritional behavior of individual animals. Here we illustrate how conceptual advances in nutritional ecology can help the study of these processes and allow the formulation of new empirically testable predictions. First, we review key evidence showing that gut microbes influence the nutrition of individual animals, through modifications of their nutritional state and feeding decisions. Next, we describe how these microbial influences and their social consequences can be studied by modelling populations of hosts and their gut microbiota into a single conceptual framework derived from nutritional geometry. Our approach raises new perspectives for the study of holobiont nutrition and will facilitate theoretical and experimental research on the role of the gut microbiota in the mechanisms and evolution of social behavior.