A Continuum Three-Zone Model for Swarms

We present a progression of three distinct three-zone, continuum models for swarm behavior based on social interactions with neighbors in order to explain simple coherent structures in popular biological models of aggregations. In continuum models, individuals are replaced with density and velocity functions. Individual behavior is modeled with convolutions acting within three interaction zones corresponding to repulsion, orientation, and attraction, respectively. We begin with a variable-speed first-order model in which the velocity depends directly on the interactions. Next, we present a variable-speed second-order model. Finally, we present a constant-speed second-order model that is coordinated with popular individual-based models. For all three models, linear stability analysis shows that the growth or decay of perturbations in an infinite, uniform swarm depends on the strength of attraction relative to repulsion and orientation. We verify that the continuum models predict the behavior of a swarm of individuals by comparing the linear stability results with an individual-based model that uses the same social interaction kernels. In some unstable regimes, we observe that the uniform state will evolve toward a radially symmetric attractor with a variable density. In other unstable regimes, we observe an incoherent swarming state.     

The kin composition of social groups: trading group size for degree of altruism

Why some social systems form groups composed of kin, while others do not, has gone largely untreated in the literature. Using an individual-based simulation model, we explore the demographic consequences of making kinship a criterion in group formation. We find that systems where social groups consist of one-generation breeding associations may face a serious trade-off between degree of altruism and group size that is largely mediated by their kin composition. On the one hand, restricting groups to close kin allows the evolution of highly altruistic behaviors but may limit group size to suboptimal levels, the more severely so the smaller the intrinsic fecundity of the species and the stricter the kin admission rule. Group size requirements, on the other hand, can be met by admitting nonkin into groups, but not without limiting the degree of altruism that can evolve. As a solution to this conundrum, we show that if helping roles within groups are assigned through a lottery rather than being genetically determined, maximum degrees of altruism can evolve in groups of nonrelatives of any size. Such a "lottery" mechanism may explain reproductive and helping patterns in organisms as varied as the cellular slime molds, pleometrotic ants, and Galapagos hawks.     

Population ecology, nonlinear dynamics, and social evolution. I. Associations among nonrelatives

Using an individual-based and genetically explicit simulation model, we explore the evolution of sociality within a population-ecology and nonlinear-dynamics framework. Assuming that individual fitness is a unimodal function of group size and that cooperation may carry a relative fitness cost, we consider the evolution of one-generation breeding associations among nonrelatives. We explore how parameters such as the intrinsic rate of growth and group and global carrying capacities may influence social evolution and how social evolution may, in turn, influence and be influenced by emerging group-level and population-wide dynamics. We find that group living and cooperation evolve under a wide range of parameter values, even when cooperation is costly and the interactions can be defined as altruistic. Greater levels of cooperation, however, did evolve when cooperation carried a low or no relative fitness cost. Larger group carrying capacities allowed the evolution of larger groups but also resulted in lower cooperative tendencies. When the intrinsic rate of growth was not too small and control of the global population size was density dependent, the evolution of large cooperative tendencies resulted in dynamically unstable groups and populations. These results are consistent with the existence and typical group sizes of organisms ranging from the pleometrotic ants to the colonial birds and the global population outbreaks and crashes characteristic of organisms such as the migratory locusts and the tree-killing bark beetles.     

Evolution of Gene Regulatory Networks by Fluctuating Selection and Intrinsic Constraints

Various characteristics of complex gene regulatory networks (GRNs) have been discovered during the last decade, e.g., redundancy, exponential indegree distributions, scale-free outdegree distributions, mutational robustness, and evolvability. Although progress has been made in this field, it is not well understood whether these characteristics are the direct products of selection or those of other evolutionary forces such as mutational biases and biophysical constraints. To elucidate the causal factors that promoted the evolution of complex GRNs, we examined the effect of fluctuating environmental selection and some intrinsic constraining factors on GRN evolution by using an individual-based model. We found that the evolution of complex GRNs is remarkably promoted by fixation of beneficial gene duplications under unpredictably fluctuating environmental conditions and that some internal factors inherent in organisms, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for the evolution of GRNs. The results indicate that various biological properties observed in GRNs could evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves. Our study emphasizes that evolutionary models considering such intrinsic constraining factors should be used as null models to analyze the effect of selection on GRN evolution.     

Modeling Group Formation and Activity Patterns in Self-Organizing Collectives of Individuals

We construct and analyze a nonlocal continuum model for group formation with application to self-organizing collectives of animals in homogeneous environments. The model consists of a hyperbolic system of conservation laws, describing individual movement as a correlated random walk. The turning rates depend on three types of social forces: attraction toward other organisms, repulsion from them, and a tendency to align with neighbors. Linear analysis is used to study the role of the social interaction forces and their ranges in group formation. We demonstrate that the model can generate a wide range of patterns, including stationary pulses, traveling pulses, traveling trains, and a new type of solution that we call zigzag pulses. Moreover, numerical simulations suggest that all three social forces are required to account for the complex patterns observed in biological systems. We then use the model to study the transitions between daily animal activities that can be described by these different patterns.     

GROUP FORMATION AND THE EVOLUTION OF SOCIALITY

In spite of its intrinsic evolutionary instability, altruistic behavior in social groups is widespread in nature, spanning from organisms endowed with complex cognitive abilities to microbial populations. In this study, we show that if social individuals have an enhanced tendency to form groups and fitness increases with group cohesion, sociality can evolve and be maintained in the absence of actively assortative mechanisms such as kin recognition or nepotism toward other carriers of the social gene. When explicitly taken into account in a game‐theoretical framework, the process of group formation qualitatively changes the evolutionary dynamics with respect to games played in groups of constant size and equal grouping tendencies. The evolutionary consequences of the rules underpinning the group size distribution are discussed for a simple model of microbial aggregation by differential attachment, indicating a way to the evolution of sociality bereft of peer recognition.     

Collective Learning and Optimal Consensus Decisions in Social Animal Groups

Learning has been studied extensively in the context of isolated individuals. However, many organisms are social and consequently make decisions both individually and as part of a collective. Reaching consensus necessarily means that a single option is chosen by the group, even when there are dissenting opinions. This decision-making process decouples the otherwise direct relationship between animals'' preferences and their experiences (the outcomes of decisions). Instead, because an individual''s learned preferences influence what others experience, and therefore learn about, collective decisions couple the learning processes between social organisms. This introduces a new, and previously unexplored, dynamical relationship between preference, action, experience and learning. Here we model collective learning within animal groups that make consensus decisions. We reveal how learning as part of a collective results in behavior that is fundamentally different from that learned in isolation, allowing grouping organisms to spontaneously (and indirectly) detect correlations between group members'' observations of environmental cues, adjust strategy as a function of changing group size (even if that group size is not known to the individual), and achieve a decision accuracy that is very close to that which is provably optimal, regardless of environmental contingencies. Because these properties make minimal cognitive demands on individuals, collective learning, and the capabilities it affords, may be widespread among group-living organisms. Our work emphasizes the importance and need for theoretical and experimental work that considers the mechanism and consequences of learning in a social context.     

Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations

In this paper we develop a general mathematical model describing the spatio-temporal dynamics of host-parasitoid systems with forced generational synchronisation, for example seasonally induced diapause. The model itself may be described as an individual-based stochastic model with the individual movement rules derived from an underlying continuum PDE model. This approach permits direct comparison between the discrete model and the continuum model. The model includes both within-generation and between-generation mechanisms for population regulation and focuses on the interactions between immobile juvenile hosts, adult hosts and adult parasitoids in a two-dimensional domain. These interactions are mediated, as they are in many such host-parasitoid systems, by the presence of a volatile semio-chemical (kairomone) emitted by the hosts or the hosts food plant. The model investigates the effects on population dynamics for different host versus parasitoid movement strategies as well as the transient dynamics leading to steady states. Despite some agreement between the individual and continuum models for certain motility parameter ranges, the model dynamics diverge when host and parasitoid motilities are unequal. The individual-based model maintains spatially heterogeneous oscillatory dynamics when the continuum model predicts a homogeneous steady state. We discuss the implications of these results for mechanistic models of phenotype evolution.P. Schofield gratefully acknowledges the financial support of the BBSRC and The Wellcome Trust.     

The socioecology of fission-fusion sociality in Orangutans

Fission-fusion systems can have the group or the individual as their primary unit. In group-based fission-fusion systems, predation risk reduction is the major benefit to grouping, in the individual-based ones the benefits are likely to be primarily social. Orangutans, like chimpanzees, are examples of an individual-based fission-fusion species. The orangutans inhabiting a Sumatran swamp forest (Suaq Balimbing) are more likely than elsewhere to form travel parties. As elsewhere, the main benefits of grouping are social: mating opportunities, protection from harassment and socialization of infants. Most animals also incur costs, but these are relatively low at Suaq Balimbing due to the high productivity of the swamp. Costs seem to be disproportionately high for females with mid-sized infants, who avoid parties.     

Multilevel selection favors fragmentation modes that maintain cooperative interactions in multispecies communities

Reproduction is one of the requirements for evolution and a defining feature of life. Yet, across the tree of life, organisms reproduce in many different ways. Groups of cells (e.g., multicellular organisms, colonial microbes, or multispecies biofilms) divide by releasing propagules that can be single-celled or multicellular. What conditions determine the number and size of reproductive propagules? In multicellular organisms, existing theory suggests that single-cell propagules prevent the accumulation of deleterious mutations (e.g., cheaters). However, groups of cells, such as biofilms, sometimes contain multiple metabolically interdependent species. This creates a reproductive dilemma: small daughter groups, which prevent the accumulation of cheaters, are also unlikely to contain the species diversity that is required for ecological success. Here, we developed an individual-based, multilevel selection model to investigate how such multi-species groups can resolve this dilemma. By tracking the dynamics of groups of cells that reproduce by fragmenting into smaller groups, we identified fragmentation modes that can maintain cooperative interactions. We systematically varied the fragmentation mode and calculated the maximum mutation rate that communities can withstand before being driven to extinction by the accumulation of cheaters. We find that for groups consisting of a single species, the optimal fragmentation mode consists of releasing single-cell propagules. For multi-species groups we find various optimal strategies. With migration between groups, single-cell propagules are favored. Without migration, larger propagules sizes are optimal; in this case, group-size dependent fissioning rates can prevent the accumulation of cheaters. Our work shows that multi-species groups can evolve reproductive strategies that allow them to maintain cooperative interactions.     

Multiscale analysis of collective motion and decision-making in swarms: An advection-diffusion equation with memory approach

We propose a (time) multiscale method for the coarse-grained analysis of collective motion and decision-making in self-propelled particle models of swarms comprising a mixture of ‘naïve’ and ‘informed’ individuals. The method is based on projecting the particle configuration onto a single ‘meta-particle’ that consists of the elongation of the flock together with the mean group velocity and position. We find that the collective states can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle, which we assume follows a continuous time random walk (CTRW). These properties can be accurately predicted at the macroscopic level by an advection-diffusion equation with memory (ADEM) whose parameters are obtained from a mean group velocity time series obtained from a single simulation run of the individual-based model.     

How the Spatial Position of Individuals Affects Their Influence on Swarms: A Numerical Comparison of Two Popular Swarm Dynamics Models

Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual''s Voronoi neighbors. The models include a tunable parameter that controls an individual''s relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.     

Travelling Waves in Hybrid Chemotaxis Models

Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant), which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations.     

Environmental quality mediates the ecological dominance of cooperatively breeding birds

Although social species as diverse as humans and ants are among the most abundant organisms on Earth, animals cooperate and form groups for many reasons. How these different reasons for grouping affect a species' ecological dominance remains unknown. Here we use a theoretical model to demonstrate that the different fitness benefits that animals receive by forming groups depend on the quality of their environment, which in turn impacts their ecological dominance and resilience to global change. We then test the model's key predictions using phylogenetic comparative analysis of >6500 bird species. As predicted, we find that cooperative breeders occurring in harsh and fluctuating environments have larger ranges and greater abundances than non-cooperative breeders, but cooperative breeders occurring in benign and stable environments do not. Using our model, we further show that social species living in harsh and fluctuating environments will be less vulnerable to climate change than non-social species.     

The Evolution of Different Forms of Sociality: Behavioral Mechanisms and Eco-Evolutionary Feedback

Different forms of sociality have evolved via unique evolutionary trajectories. However, it remains unknown to what extent trajectories of social evolution depend on the specific characteristics of different species. Our approach to studying such trajectories is to use evolutionary case-studies, so that we can investigate how grouping co-evolves with a multitude of individual characteristics. Here we focus on anti-predator vigilance and foraging. We use an individual-based model, where behavioral mechanisms are specified, and costs and benefits are not predefined. We show that evolutionary changes in grouping alter selection pressures on vigilance, and vice versa. This eco-evolutionary feedback generates an evolutionary progression from “leader-follower” societies to “fission-fusion” societies, where cooperative vigilance in groups is maintained via a balance between within- and between-group selection. Group-level selection is generated from an assortment that arises spontaneously when vigilant and non-vigilant foragers have different grouping tendencies. The evolutionary maintenance of small groups, and cooperative vigilance in those groups, is therefore achieved simultaneously. The evolutionary phases, and the transitions between them, depend strongly on behavioral mechanisms. Thus, integrating behavioral mechanisms and eco-evolutionary feedback is critical for understanding what kinds of intermediate stages are involved during the evolution of particular forms of sociality.     

Environmental flow assessment in estuaries taking into consideration species dispersal in fragmented potential habitats

Here, we propose an approach to environmental flow assessment that pays attention to species dispersal among fragmented potential habitat patches affected by river inflow and tidal currents in estuaries. The approach consists of three steps. In step one, potential suitable habitats were mapped and the Habitat Aggregation Index (HAI) was determined to understand the fragmentation of potential suitable habitats by integrating the requirements for critical environmental factors that have temporal and spatial variability. In the second step, an individual-based model was developed to simulate the dispersal of target species among potential habitat patches. The model provided the species distributions for altered hydrological processes. In the third step, environmental flows were defined by comparing the occupancy of suitable habitat patches by individual organisms and habitat aggregation for varying freshwater inflows. This approach was tested using a case study in the Yangtze River Estuary. We stressed the ecological importance of flood pulse, rather than average discharge, and recommend a Gaussian-type flood pulse, as provides a win–win point for both the numbers of individuals that could occupy suitable habitat and the HAI. We also demonstrated the importance of the peak flow and flood pulse duration in terms of affecting species distribution. Based on the results presented here, the proposed approach offers a flexible assessment of environmental flow for aquatic ecosystems.     

Population Responses to Environmental Change: Life History Variation, Individual-based Models, and the Population Dynamics of Short-lived Organisms

SYNOPSIS. We review two potentially important approaches topredicting the consequences of environmental change for populationsof short-lived organisms. First, we examine the concepts of"feasible life histories" and "feasible demographies" and presentthe results of a set of simulations in which the effects onpopulation growth rate of varying one of the demographic variables(average nest survival, average juvenile survival rates, averageannual adult survival rates, or age-specific fecundity) overa broad range of values while the others are maintained at long-termpopulation average values for the Grapevine Hills, Texas populationof the short-lived lizard Sceloporus merriami. The results ofthese simulations are compared to an analogous set of simulationsfor a Michigan population of the relatively long-lived snappingturtle (Chelydra serpentina, Congdon et al., 1994). The implicationsof differences in feasible demographies and life histories suchas described for these two species are discussed. We also discuss the approach of using individual-based, physiologicallystructured models to predict population response to environmentalvariation and present the results of simulations using a modeldeveloped for predicting population-level effects of operativeenvironmental variation in the lizard S. merriami under twodifferent climate change scenarios. This individual-based, physiologicallystructured model incorporates population-specific data on ecologicalenergetics, thermal and size dependence of digestive physiologyand metabolic rates, energetics of individual growth, allometricrelationships, social structure and mating system, and the dependenceof mortality rates on age, size, and social status of individuals.The data necessary to such models of population response toenvironmental variation can come only from detailed long-termstudies of individual populations.     

The evolutionary pathway to obligate scavenging in Gyps vultures

The evolutionary pathway to obligate scavenging in Gyps vultures remains unclear. We propose that communal roosting plays a central role in setting up the information transfer network critical for obligate scavengers in ephemeral environments and that the formation of a flotilla-like foraging group is a likely strategy for foraging Gyps vultures. Using a spatial, individual-based, optimisation model we find that the communal roost is critical for establishing the information network that enables information transfer owing to the spatial-concentration of foragers close to the roost. There is also strong selection pressure for grouping behaviour owing to the importance of maintaining network integrity and hence information transfer during foraging. We present a simple mechanism for grouping, common in many animal species, which has the added implication that it negates the requirement for roost-centric information transfer. The formation of a flotilla-like foraging group also improves foraging efficiency through the reduction of overlapping search paths. Finally, we highlight the importance of consideration of information transfer mechanisms in order to maximise the success of vulture reintroduction programmes.     

Mini-review: convection around biofilms

Water that flows around a biofilm influences the transport of solutes into and out of the biofilm and applies forces to the biofilm that can cause it to deform and detach. Engineering approaches to quantifying and understanding these phenomena are reviewed in the context of biofilm systems. The slow-moving fluid adjacent to the biofilm acts as an insulator for diffusive exchange. External mass transfer resistance is important because it can exacerbate oxygen or nutrient limitation in biofilms, worsen product inhibition, affect quorum sensing, and contribute to the development of tall, fingerlike biofilm clusters. Measurements of fluid motion around biofilms by particle velocimetry and magnetic resonance imaging indicate that water flows around, but not through biofilm cell clusters. Moving fluid applies forces to biofilms resulting in diverse outcomes including viscoelastic deformation, rolling, development of streamers, oscillatory movement, and material failure or detachment. The primary force applied to the biofilm is a shear force in the main direction of fluid flow, but complex hydrodynamics including eddies, vortex streets, turbulent wakes, and turbulent bursts result in additional force components.     

A community model of ciliateTetrahymena and bacteriaE. coli: Part I. Individual-based models ofTetrahymena andE. coli populations

The dynamics of a microbial community consisting of a eucaryotic ciliateTetrahymena pyriformis and procaryoticEscherichia coli in a batch culture is explored by employing an individual-based approach. In this portion of the article, Part I, population models are presented. Because both models are individual-based, models of individual organisms are developed prior to construction of the population models. The individual models use an energy budget method in which growth depends on energy gain from feeding and energy sinks such as maintenance and reproduction. These models are not limited by simplifying assumptions about constant yield, constant energy sinks and Monod growth kinetics as are traditional models of microbal organisms. Population models are generated from individual models by creating distinct individual types and assigning to each type the number of real individuals they represent. A population is a compilation of individual types that vary in a phase of cell cycle and physiological parameters such as filtering rate for ciliates and maximum anabolic rate for bacteria. An advantage of the developed models is that they realistically describe the growth of the individual cells feeding on resource which varies in density and composition. Part II, the core of the project, integrates models into a dynamic microbial community and provides model analysis based upon available data.