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Antarctic krill swarms are one of the largest known animal aggregations, and yet, despite being the keystone species of the Southern Ocean, little is known about how swarms are formed and maintained. Understanding the local interactions between individuals that provide the basis for these swarms is fundamental to knowing how swarms arise in nature, and what potential factors might lead to their breakdown. Here, we analysed the trajectories of captive, wild-caught krill in 3D to determine individual-level interaction rules and quantify patterns of information flow. Our results demonstrate that krill align with near neighbours and that they regulate both their direction and speed relative to the positions of groupmates. These results suggest that social factors are vital to the formation and maintenance of swarms. Furthermore, krill operate a novel form of collective organization, with measures of information flow and individual movement adjustments expressed most strongly in the vertical dimension, a finding not seen in other swarming species. This research represents a vital step in understanding the fundamentally important swarming behaviour of krill.

What will happen when two invasive species are competing and invading the environment at the same time? In this paper, we try to find all the possible scenarios in such a situation based on the diffusive Lotka-Volterra competition system with free boundaries. In a recent work, Du and Wu (Calc Var Partial Differ Equ, 57(2):52, 2018) considered a weak-strong competition case of this model (with spherical symmetry) and theoretically proved the existence of a “chase-and-run coexistence” phenomenon, for certain parameter ranges when the initial functions are chosen properly. Here we use a numerical approach to extend the theoretical research of Du and Wu (Calc Var Partial Differ Equ, 57(2):52, 2018) in several directions. Firstly, we examine how the longtime dynamics of the model changes as the initial functions are varied, and the simulation results suggest that there are four possible longtime profiles of the dynamics, with the chase-and-run coexistence the only possible profile when both species invade successfully. Secondly, we show through numerical experiments that the basic features of the model appear to be retained when the environment is perturbed by periodic variation in time. Thirdly, our numerical analysis suggests that in two space dimensions the population range and the spatial population distribution of the successful invader tend to become more and more circular as time increases no matter what geometrical shape the initial population range possesses. Our numerical simulations cover the one space dimension case, and two space dimension case with or without spherical symmetry. The numerical methods here are based on that of Liu et al. (Mathematics, 6(5):72, 2018, Int J Comput Math, 97(5): 959–979, 2020). In the two space dimension case without radial symmetry, the level set method is used, while the front tracking method is used for the remaining cases. We hope the numerical observations in this paper can provide further insights to the biological invasion problem, and also to future theoretical investigations. More importantly, we hope the numerical analysis may reach more biologically oriented experts and inspire applications of some refined versions of the model tailored to specific real world biological invasion problems.

Animal groups are often composed of individuals that vary according to behavioral, morphological, and internal state parameters. Understanding the importance of such individual-level heterogeneity to the establishment and maintenance of coherent group responses is of fundamental interest in collective behavior. We examined the influence of hunger on the individual and collective behavior of groups of shoaling fish, x-ray tetras (Pristella maxillaris). Fish were assigned to one of two nutritional states, satiated or hungry, and then allocated to 5 treatments that represented different ratios of satiated to hungry individuals (8 hungry, 8 satiated, 4:4 hungry:satiated, 2:6 hungry:satiated, 6:2 hungry:satiated). Our data show that groups with a greater proportion of hungry fish swam faster and exhibited greater nearest neighbor distances. Within groups, however, there was no difference in the swimming speeds of hungry versus well-fed fish, suggesting that group members conform and adapt their swimming speed according to the overall composition of the group. We also found significant differences in mean group transfer entropy, suggesting stronger patterns of information flow in groups comprising all, or a majority of, hungry individuals. In contrast, we did not observe differences in polarization, a measure of group alignment, within groups across treatments. Taken together these results demonstrate that the nutritional state of animals within social groups impacts both individual and group behavior, and that members of heterogenous groups can adapt their behavior to facilitate coherent collective motion.

Movement, positioning and coordination of player formations is a key aspect for the performance of teams within field-based sports. The increased availability of player tracking data has given rise to numerous studies that focus on the relationship between simple descriptive statistics surrounding team formation and performance. While these existing approaches have provided a high-level a view of team-based spatial formations, there is limited research on the nature of collective movement across players within teams and the establishment of stable collective states within game play. This study draws inspiration from the analysis of collective movement in nature, such as that observed within schools of fish and flocking birds, to explore the existence of collective states within the phases of play in soccer. Order parameters and metrics describing group motion and shape are derived from player movement tracks to uncover the nature of the team’s collective states and transitions. This represents a unique addition to the current body of work around the analysis of player movement in team sports. The results from this study demonstrate that sequences of ordered collective behaviours exist with relatively rapid transitions between highly aligned polar and un-ordered swarm behaviours (and vice-versa). Defensive phases of play have a higher proportion of ordered team movement than attacking phases, indicating that movements linked with attacking tactics, such as player dispersion to generate passing and shooting opportunities leads to lower overall collective order. Exploration within this study suggests that defensive tactics, such as reducing the depth or width to close passing opportunities, allows for higher team movement speeds and increased levels of collective order. This study provides a novel view of player movement by visualising the collective states present across the phases of play in football.

Emergent patterns of collective motion are thought to arise from local rules of interaction that govern how individuals adjust their velocity in response to the relative locations and velocities of near neighbours. Many models of collective motion apply rules of interaction over a metric scale, based on the distances to neighbouring group members. However, empirical work suggests that some species apply interactions over a topological scale, based on distance determined neighbour rank. Here, we modify an important metric model of collective motion (Couzin et al. in J Theor Biol 218(1):1-11, 2002), so that interactions relating to orienting movements with neighbours and attraction towards more distant neighbours operate over topological scales. We examine the emergent group movement patterns generated by the model as the numbers of neighbours that contribute to orientation- and attraction-based velocity adjustments vary. Like the metric form of the model, simulated groups can fragment (when interactions are influenced by less than 10-15% of the group), swarm and move in parallel, but milling does not occur. The model also generates other cohesive group movements including cases where groups exhibit directed motion without strong overall alignment of individuals. Multiple emergent states are possible for the same set of underlying model parameters in some cases, suggesting sensitivity to initial conditions, and there is evidence that emergent states of the system depend on the history of the system. Groups that do not fragment tend to stay relatively compact in terms of neighbour distances. Even if a group does fragment, individuals remain relatively close to near neighbours, avoiding complete isolation.

The emergent patterns of collective motion are thought to arise from application of individual-level rules that govern how individuals adjust their velocity as a function of the relative position and behaviours of their neighbours. Empirical studies have sought to determine such rules of interaction applied by ‘average’ individuals by aggregating data from multiple individuals across multiple trajectory sets. In reality, some individuals within a group may interact differently from others, and such individual differences can have an effect on overall group movement. However, comparisons of rules of interaction used by individuals in different contexts have been largely qualitative. Here we introduce a set of randomization methods designed to determine statistical differences in the rules of interaction between individuals. We apply these methods to a case study of leaders and followers in pairs of freely exploring eastern mosquitofish ( Gambusia holbrooki ). We find that each of the randomization methods is reliable in terms of: repeatability of p -values, consistency in identification of significant differences and similarity between distributions of randomization-based test statistics. We observe convergence of the distributions of randomization-based test statistics across repeat calculations, and resolution of any ambiguities regarding significant differences as the number of randomization iterations increases.

Antarctic krill swarms are one of the largest known animal aggregations. However, despite being the keystone species of the Southern Ocean, little is known about how swarms are formed and maintained, and we lack a detailed understanding of the local interactions between individuals that provide the basis for these swarms. Here we analyzed the trajectories of captive, wild-caught krill in 3D to determine individual level interaction rules and quantify patterns of information flow. Our results suggest krill operate a novel form of collective organization, with measures of information flow and individual movement adjustments expressed most strongly in the vertical dimension, a finding not seen in other swarming species. In addition, local directional alignment with near neighbors, and strong regulation of both direction and speed relative to the positions of groupmates suggest social factors are vital to the formation and maintenance of swarms. This research represents a first step in understanding the fundamentally important swarming behavior of krill.

The behaviour of animals is strongly influenced by the detection of cues relating to foraging opportunity or to risk, while the social environment plays a crucial role in mediating their behavioural responses. Despite this, the role of the social environment in the behaviour of non-grouping animals has received far less attention than in social species. Here, we present the results of an experiment on a cryptic species of goby (Pseudogobius sp.), which does not form social groups in its natural habitat. Gobies were presented sequentially with chemical cues relating to food, conspecific alarm and control, while in the presence of conspecifics. The intermittent locomotory behaviour of the gobies, which is typical of many cryptic animals, was influenced by the type of cues presented. Gobies decreased the duration of bouts of stasis in the presence of food cues and were generally more active. By contrast, those detecting alarm cues decreased the duration of movement bouts and were generally less active. In line with previous studies involving shoaling species, gobies in the presence of food cues adopted a more dispersed distribution, while clustering together in the presence of alarm cues. Finally, we used calculations of transfer entropy as a means of inferring information transfer among experimental subjects. In contrast to previous studies that have focused on social species, transfer entropy between gobies was detectable only in the conspecific alarm treatment. Taken together, our results show that members of this cryptic species detect and respond to chemical cues by adjusting their movement and distancing to conspecifics. Furthermore, they augment their own information with social cues but only when they perceive a threat. Animals are routinely exposed to an array of cues within their environment that convey valuable information about risk and foraging opportunities and must adapt their behaviour accordingly. To facilitate this, animals often use information arising from the behaviour of conspecifics to inform their own responses; however, this has rarely been considered in species which do not exhibit strong grouping tendencies. We used a non-shoaling fish, the goby (Pseudogobius sp.), to examine both their responses to ecologically relevant cues and the effect of the social environment on these responses. The gobies adapted their distances relative to one another according to the cues present and responded most strongly to information arising from conspecifics (measured as transfer entropy) in the presence of a potential threat. This demonstrates the potential importance of social information even to species that do not live in social groups with others of their own kind.

What will happen when two invasive species are competing and invading the environment at the same time? In this paper, we try to find all the possible scenarios in such a situation based on the diffusive Lotka-Volterra competition system with free boundaries. In a recent work, Du and Wu (Calc Var Partial Differ Equ, 57(2):52, 2018) considered a weak-strong competition case of this model (with spherical symmetry) and theoretically proved the existence of a "chase-and-run coexistence" phenomenon, for certain parameter ranges when the initial functions are chosen properly. Here we use a numerical approach to extend the theoretical research of Du and Wu (Calc Var Partial Differ Equ, 57(2):52, 2018) in several directions. Firstly, we examine how the longtime dynamics of the model changes as the initial functions are varied, and the simulation results suggest that there are four possible longtime profiles of the dynamics, with the chase-and-run coexistence the only possible profile when both species invade successfully. Secondly, we show through numerical experiments that the basic features of the model appear to be retained when the environment is perturbed by periodic variation in time. Thirdly, our numerical analysis suggests that in two space dimensions the population range and the spatial population distribution of the successful invader tend to become more and more circular as time increases no matter what geometrical shape the initial population range possesses. Our numerical simulations cover the one space dimension case, and two space dimension case with or without spherical symmetry. The numerical methods here are based on that of Liu et al. (Mathematics, 6(5):72, 2018, Int J Comput Math, 97(5): 959-979, 2020). In the two space dimension case without radial symmetry, the level set method is used, while the front tracking method is used for the remaining cases. We hope the numerical observations in this paper can provide further insights to the biological invasion problem, and also to future theoretical investigations. More importantly, we hope the numerical analysis may reach more biologically oriented experts and inspire applications of some refined versions of the model tailored to specific real world biological invasion problems.

The question of who leads and who follows is crucial to our understanding of the collective movements of group-living animals. Various characteristics associated with leadership have been documente ...

Most studies on collective decision making in honeybees have been performed on the cavity-nesting Western honeybee, Apis mellifera. In more recent years, the open-nesting red dwarf honeybee Apis florea has been developed as a model organism of collective decision making in the context of nest-site selection. These studies have shown that the specifics of the species’ nest-site requirements affect collective decision making. In particular, when potential nesting sites are abundant, as is the case in A. florea, the process of collective decision making can be simplified. Here, we ask if A. florea simply follows the availability of floral resources in their environment when deciding on an area to move into. We determined the locations danced for by three colonies the day before, of and after reproductive swarming. Our results suggest that colonies of A. florea indeed track the availability of forage in their environment and that swarms move in the general direction of forage rather than towards a specific nest site.

Humbug damselfish, Dascyllus aruanus, are a common coral reef fish that form stable social groups with size-based social hierarchies. Here we caught whole wild groups of damselfish and tested whether social groups tended to be comprised of animals that are more similar to one another in terms of their behavioural type, than expected by chance. First we found that individuals were repeatable in their level of activity and exploration, and that this was independent of both absolute size and within-group dominance rank, indicating that animals were behaviourally consistent. Secondly, despite the fact that individuals were tested independently, the behaviour of members of the same groups was significantly more similar than expected under a null model, suggesting that individual behaviour develops and is shaped by conformity to the behaviour of other group members. This is one of the first studies to demonstrate this group-level behavioural conformity in wild-caught groups.

Groups of animals coordinate remarkable, coherent, movement patterns during periods of collective motion. Such movement patterns include the toroidal mills seen in fish shoals, highly aligned parallel motion like that of flocks of migrating birds, and the swarming of insects. Since the 1970’s a wide range of collective motion models have been studied that prescribe rules of interaction between individuals, and that are capable of generating emergent patterns that are visually similar to those seen in real animal group. This does not necessarily mean that real animals apply exactly the same interactions as those prescribed in models. In more recent work, researchers have sought to infer the rules of interaction of real animals directly from tracking data, by using a number of techniques, including averaging methods. In one of the simplest formulations, the averaging methods determine the mean changes in the components of the velocity of an individual over time as a function of the relative coordinates of group mates. The averaging methods can also be used to estimate other closely related quantities including the mean relative direction of motion of group mates as a function of their relative coordinates. Since these methods for extracting interaction rules and related quantities from trajectory data are relatively new, the accuracy of these methods has had limited inspection. In this paper, we examine the ability of an averaging method to reveal prescribed rules of interaction from data generated by two individual based models for collective motion. Our work suggests that an averaging method can capture the qualitative features of underlying interactions from trajectory data alone, including repulsion and attraction effects evident in changes in speed and direction of motion, and the presence of a blind zone. However, our work also illustrates that the output from a simple averaging method can be affected by emergent group level patterns of movement, and the sizes of the regions over which repulsion and attraction effects are apparent can be distorted depending on how individuals combine interactions with multiple group mates.

Summary Foraging behaviour must be flexible enough to adapt to heterogeneities in the distribution and quality of food resources. Accurate models of optimal foraging behaviour should acknowledge the extent to which animals can detect and regulate their intake of food based on smaller scale differences in food types. In particular, consideration of macro-nutrient distribution and how animals perceive this is limited in studies of optimal foraging, particularly in vertebrates and for animals that forage in groups. Here, we track shoals of eight mosquitofish as they forage in two environments that contain equal amounts of available energy but differ in their distribution of macro-nutrients. We provide empirical evidence that fish will distribute themselves within an environment in relation to the distribution of specific macro-nutrients. Also, fish make foraging decisions based on the macronutrient composition of patches, such that their durations on patches are longer when they have a higher concentration of protein and lower concentration of carbohydrate. The ratio of protein to carbohydrate does not affect the probability of a fish joining a patch, however, with low numbers of fish on the patch the probability of a fish leaving is greater per unit time step in the patches with a low protein to carbohydrate ratio than the patches with a high protein to carbohydrate ratio. This study confirms the importance of considering the macro-nutrient composition of foods when considering the movement decisions of foraging groups and thus has important consequences for developing more accurate foraging models that take into account the distribution of macro-nutrients in the environment. The results suggest the spatial distribution of nutrients on a landscape scale could influence grouping patterns and social interactions, thus affecting population dynamics.

With the increased development of low-cost and miniature devices, sensors are increasingly being deployed as arrays of redundant sensors. However, little work has been done characterizing properties of these arrays. Here, we develop and test a Bayesian algorithm for estimating the limit of detection of sensor arrays. The algorithm is applicable for single sensors as well as sensor arrays, and works by reducing a vector in the signal domain to a univariate response in the measurand domain. We show that the new algorithm can reproduce results from a benchmark algorithm for single sensors, and then demonstrate the benefit of adding additional sensors to an array. Then, we provide guidelines that achieve numerical stability while minimising computational cost. Finally, we provide a real-world example using an array of ion-selective electrodes measuring carbonate in seawater. This application demonstrates how incorporation of a set of individual low-quality sensors into an array leads to a substantially reduced LOD that clearly meets the demands of the application.

Despite the frequency with which mixed-species groups are observed in nature, studies of collective behaviour typically focus on single-species groups. Here, we quantify and compare the patterns of interactions between three fish species, threespine sticklebacks ( Gasterosteus aculeatus ), ninespine sticklebacks ( Pungitius pungitius ) and roach ( Rutilus rutilus ) in both single- and mixed-species shoals in the laboratory. Pilot data confirmed that the three species form both single- and mixed-species shoals in the wild. In our laboratory study, we found that single-species groups were more polarized than mixed-species groups, while single-species groups of threespine sticklebacks and roach were more cohesive than mixed shoals of these species. Furthermore, while there was no difference between the inter-individual distances between threespine and ninespine sticklebacks within mixed-species groups, there was some evidence of segregation by species in mixed groups of threespine sticklebacks and roach. There were differences between treatments in mean pairwise transfer entropy, and in particular we identify species-differences in information use within the mixed-species groups, and, similarly, differences in responses to conspecifics and heterospecifics in mixed-species groups. We speculate that differences in the patterns of interactions between species in mixed-species groups may determine patterns of fission and fusion in such groups.

Honeybees use the dance language to communicate the location of profitable food resources to nestmates. During nectar foraging, bees alter the duration of the return phase of the dance to reflect the source’s quality. For more profitable resources, the return phase is shorter; this effectively makes the dance ‘livelier’. Bees also increase the number of dance circuits when the nectar source is more profitable, and they are more likely to dance for such sources. As a result, the colony focuses on high-quality nectar sources. Here we ask whether foragers similarly adjust aspects of their dance when foraging for pollen according to the pollen’s protein content. Pollen is essential for raising brood, and protein content varies substantially across plant species. We offered bees pollen, pollen substitutes or mixtures that differed in protein content and determined whether the duration of the return phase decreased and the number of dance circuits increased with increasing protein content. We further examined whether bees adjust return phase duration based on the protein content of naturally collected pollen. Lastly, we examined whether foragers are more likely to dance for pollen high in protein. Honeybees did not adjust the duration of the return phase or the number of dance circuits when mixtures contained more protein. Similarly, there was no relationship between protein content of natural pollen and return phase duration. Our results suggest that foragers cannot assess pollen’s protein content. Bees were more likely to dance when collecting pure pollen, suggesting an important role of pollen-based cues in the regulation of pollen foraging.

Groups of animals are often heterogeneously structured and may be composed of selfish individuals responding to different internal stimuli. Group-level behaviour can be determined by the slight differences in simple behavioural movement parameters structuring local interactions between conspecifics. To accurately understand individual behaviour within groups and how it affects whole-group behaviour, we need to measure the responses of individuals in groups to changes in internal state and examine the outcome of these responses within the social context. Therefore, we quantified the influence of nutritional state on the individual and group movement parameters of free swimming shoals of eight rainbow fish, Melanotaenia duboulayi. Individual fish were experimentally manipulated to be in one of two nutritional states, hungry or satiated, and were assayed in three group compositions: all-hungry (8:0 hungry/satiated), mixed (4:4) or all-satiated (0:8). We showed that the internal nutritional state of individual fish affected basic behaviours relating to spatial positioning. The interaction between pairs of fish was dependent on the nutritional state of both fish, and there was an additive effect of individual behaviour on group behaviour, which meant that group behaviour reflected the motivations of its individual members in such a way that allowed individuals to fulfil their own behavioural needs whilst still attaining the benefits of grouping.

The question of how hunger affects locomotory behaviour, in particular how it affects the kinematics of movement and an animal’s interaction with the physical structures in its environment is of broad relevance in behavioural ecology. We experimentally manipulated the hunger levels of individual mosquitofish (Gambusia holbrooki) and recorded their swimming behaviour in shoals of 4 fish. We found that hungry individuals in shoals moved at greater speeds and had higher turning speeds than satiated individuals in shoals, as well as a greater variance in speed and turning speeds. We also found that hungry individuals explored more of the arena and used more of its internal space, away from the square arena’s walls and displayed less wall-following behaviour than satiated individuals. A functional explanation for this change in swimming behaviour and interaction with environmental heterogeneity is discussed in the context of social foraging, as is the consequence of these results for models of search patterns and collective movement.

Funding: Australian Research Council. A.J.W.W. and T.M.S. were supported by a Discovery Project Grant from the Australian Research Council. D.J.T.S. and J.E.H.-R. were supported by a Knut & Alice Wallenberg Foundation Grant. Collective motion describes the global properties of moving groups of animals and the self-organized, coordinated patterns of individual behaviour that produce them. We examined the group-level patterns and local interactions between individuals in wild, free-ranging shoals of three-spine sticklebacks, Gasterosteus aculeatus. Our data reveal that the highest frequencies of near-neighbour encounters occur at between one and two body lengths from a focal fish, with the peak frequency alongside a focal individual. Fish also show the highest alignment with these laterally placed individuals, and generally with animals in front of themselves. Furthermore, fish are more closely matched in size, speed and orientation to their near neighbours than to more distant neighbours, indicating local organization within groups. Among the group level properties reported here, we find that polarization is strongly influenced by group speed, but also the variation in speed among individuals and the nearest neighbour distances of group members. While we find no relationship between group order and group size, we do find that larger groups tend to have lower nearest neighbour distances, which in turn may be important in maintaining group order. Publisher PDF

Many animals move in groups, but the mechanisms by which a group of animals form a consensus about where to move are not well understood. In honeybees group movement generally falls into two behavioural categories: reproductive swarming and colony migration. In both contexts the bees use the dance language to decide on a location to move to. During reproductive swarming bees choose between and dance for multiple discrete locations before departing towards one of them. In contrast, during migration bees select a single direction in which to fly, but information with respect to distance is highly variable. In this study we show that swarms of the giant Asian honeybee, Apis dorsata, when placed in a novel environment rapidly reach a general consensus on a single patch within the environment in a fashion similar to relocating swarms of the red dwarf honeybee, Apis florea. In the three swarms used in this study the patches for which bees danced prior to the swarm departing corresponded to a stand of trees. One of our swarms showed a dance pattern consistent with long-distance migration: dances during the final 15 min preceding swarm departure indicated a wide range of distances but a uniform direction. Unlike previous descriptions of migrating swarm behaviour, the direction indicated by dances on this swarm changed throughout the decision-making process. Our other two swarms landed within the canopy of the trees in the patches for which they danced in the last 15 min and then presumably searched the surrounding area for a specific location in which to construct their new comb. Crown Copyright 2014 Published on behalf of The Association for the Study of Animal Behaviour by Elsevier Ltd. All rights reserved.

Decision making in moving animal groups has been shown to be disproportionately influenced by individuals at the front of groups. Therefore, an explanation of state-dependent positioning of individuals within animal groups may provide a mechanism for group movement decisions. Nutritional state is dynamic and can differ between members of the same group. It is also known to drive animal movement decisions. Therefore, we assayed 6 groups of 8 rainbowfish foraging in a flow tank. Half of the fish had been starved for 24h and half had been fed 1h prior to experimental start. Groups were assayed again one week later but individuals were allocated to the opposite nutritional treatment. During the assay the positions of individually identified fish were recorded as were the number of food items they each ate and the position within the group they acquired them from. Food-deprived fish were more often found towards the front of the shoal; the mean weighted positional score of food-deprived fish was significantly larger than that of well-fed fish. Individuals were not consistent in their position within a shoal between treatments. There was a significant positive correlation between mean weighted positional score and number of food items acquired which displays an obvious benefit to front positions. These results suggest that positional preferences are based on nutritional state and provide a mechanism for state-dependent influence on group decision-making as well as increasing our understanding of what factors are important for group functioning.

Tetragonula hockingsi and T. carbonaria are two closely related species of Australian stingless bees. The primary species-specific character is the architecture of the brood comb. The brood comb of T. hockingsi is an open lattice comprising clumps of about ten cells that are connected by vertical pillars. In contrast, in T. carbonaria the brood comb is a compact spiral in which all brood cells (except on the margins) are connected by their walls to adjacent cells at the same height. We made detailed observations of the cell construction process in two colonies of each species. From these observations we formed a species-specific hypothesis about the algorithm followed by the bees during cell construction. The two algorithms allowed us to make predictions about the locations of new cells. Both T. hockingsi and T. carbonaria share a preference for constructing new brood cells in the clefts formed by two or three adjacent existing brood cells, but there are differences in detail for other components of the building process. The fundamental difference in the cell construction process of the two species is that for T. hockingsi, when a cluster of cells contains ten cells, the next cell added to the cluster is offset upwards by half a cell length, or, less often, a vertical pillar rather than a new cell is constructed. In T. carbonaria, cell construction is continuous at the comb margin so that there are no gaps between cells. Furthermore, it seems that T. hockingsi only makes use of local knowledge of the brood comb when deciding to place new brood cells, whereas T. carbonaria could make some building decisions based on knowledge of the total structure. We translated the species-specific algorithms into agent-based lattice swarm computer simulations of the cell construction process for the two species. These simulations produced representations of brood combs that are similar to those seen in vivo, suggesting that our biological rules are realistic.

This is the second of two papers devoted to the analysis of contour crossing errors that occur in contour-advective simulations of fluid motion, where either vorticity or potential vorticity is represented by contours. We begin with a detailed discussion on some of the potential mechanisms for contour crossing. Past work has suggested that the formation of contour crossings is due to inadequate spatial resolution of contours [1]. The implementation of two schemes for preventing contour crossings within the framework of the Contour-Advective Semi-Lagrangian (CASL) algorithm is detailed here. We then present an analysis of contour crossing errors in simulations of quasigeostrophic turbulence on the f-plane and the quasigeostrophic motion of an initially circular vortex patch on the @b-plane using the algorithm detailed in Part 1. We find that in general individual crossings occur at scales smaller than the inversion grid scale on which velocity is calculated, but at scales larger than that of the surgical scale that defines the smallest resolved features (vorticity) of a flow. If the resolution of a quasigeostrophic turbulence simulation on the f-plane is increased by doubling the number of grid points in each coordinate direction used in the calculation of the velocity field, then the total area in error due to contour crossings remains unchanged; a smaller number of crossings introducing larger scale area errors is replaced by a greater number of smaller local errors. Uniformly increasing the density of nodes along all contours and placement of nodes at points of close approach on contours are both effective methods for limiting contour crossings.

This is the first of two papers devoted to the analysis of contour crossing errors that occur in contour-advective simulations of fluid motion. Here an algorithm is presented for quantifying the error due to contour crossings. The first step is to determine the relative proximity of all possible pairs of contours. A digital representation of each contour is produced to aid in the corresponding calculation. Simple analysis of functions is then used to find any crossings between contours deemed close to each other by the digital representation method. Next, the area in error of a pair of crossing contours is calculated by identifying the polygon or polygons that approximately bound the erroneous region. Finally, some preliminary results of analysis of contour crossings that occur in contour-advective semi-lagrangian (CASL) simulations of single layer quasigeostrophic turbulence are presented. It is shown that the error due to contour crossings is small in the simulations considered here.

We present an agent-based model for the nest site selection process of the open-nesting red dwarf honeybee, Apis florea. Our main aim was to determine how nest site requirements affect the bees’ decision-making process. We either calculated our model parameters from experimental data or chose them so that our model would generate similar numbers of dancing bees and dance followers to those observed in real swarms with access to an abundance of suitable nest sites in all directions. We found that A. florea is less capable of making a collective decision on a new nest site when the area occupied by suitable sites is small compared to when suitable sites are abundant. Increasing the use of information regarding the location of potential nest sites or the accuracy of the information available enhanced the decision-making ability of A. florea when nest sites were scarce. We also found that swarm guidance might be hindered when suitable nest site areas are wide apart. We therefore examined two possible mechanisms for increasing directional agreement among dancers: mimicry of unverified dance information and self-regulation by inhibiting or changing dance behaviour based on observations of other dances. We show that, even at low levels, dance mimicry greatly enhances the ability of an A. florea swarm to make a decision and reduces the time to make a decision. However, in the presence of mimicry errors propagate through the swarm. Self-regulation had little or no effect, probably because of the overall low levels of dance activity present on the swarm at any given time. Our model results suggest that A. florea’s decision-making process allows swarms to locate a new nest site provided nest sites are abundant, even when they are of similar quality.

During reproductive swarming and seasonal migration, a honeybee swarm needs to locate and move to a new, suitable nest site. While the nest-site selection process in cavity-nesting species such as the European honeybee Apis mellifera is very precise with the swarm carefully selecting a single site, open-nesting species, such as Apis florea, lack such precision. These differences in precision in the nest-site selection process are thought to arise from the differing nest-site requirements of open- and cavity-nesting species. While A. florea can nest on almost any tree, A. mellifera is constrained by the scarcity of suitable nest sites. Here we show that imprecision in the nest-site selection process allows swarms to quickly reach a decision when many nest sites are available. In contrast, a very precise nest-site selection process slows down the decision-making process when nest sites are abundant. Nest-site selection in A. florea appears to be more similar to search-space sampling than to a decision-making process. Bees appear to scout the environment for general areas in which potential nest sites are abundant. Bees involved in searching the environment for suitable nest sites are also involved in guiding the swarm once the decision to depart has been made. Generally A. florea swarms exhibit a lack of consensus in the direction indicated by dancers prior to take-off. Because of this lack of consensus a swarm of A. florea will need to determine its exact direction of travel while in flight. We show that in the absence of directional consensus a swarm of bees can still be guided towards an area containing suitable nest sites provided directional dissent is not too great and nest sites are abundant. However, if the swarm needs to move to a very specific location (a single point in space), directional dissent should be avoided, resulting in a more lengthy decision-making process prior to departure. We further show that the guidance mechanism of bee swarms, so-called ‘streaking’, functions both when directional dissent is present and when it is absent, making it a more general mechanism of group movement than previously thought.

The Red Dwarf honeybee (Apis florea) is one of two basal species in the genus Apis. A. florea differs from the well-studied Western Hive bee (Apis mellifera) in that it nests in the open rather than in cavities. This fundamental difference in nesting biology is likely to have implications for nest-site selection, the process by which a reproductive swarm selects a new site to live in. In A. mellifera, workers show a series of characteristic behaviors that allow the swarm to select the best nest site possible. Here, we describe the behavior of individual A. florea workers during the process of nest-site selection and show that it differs from that seen in A. mellifera. We analyzed a total of 1,459 waggle dances performed by 197 scouts in five separate swarms. Our results suggest that two fundamental aspects of the behavior of A. mellifera scouts—the process of dance decay and the process of repeated nest site evaluation—do not occur in A. florea. We also found that the piping signal used by A. mellifera scouts to signal that a quorum has been reached at the chosen site, is performed by both dancing and non-dancing bees in A. florea. Thus, the piping signal appears to serve a different purpose in A. florea. Our results illustrate how differences in nesting biology affect the behavior of individual bees during the nest-site selection process.

Why are mitochondria almost always inherited from one parent during sexual reproduction? Current explanations for this evolutionary mystery include conflict avoidance between the nuclear and mitochondrial genomes, clearing of deleterious mutations, and optimization of mitochondrial-nuclear coadaptation. Mathematical models, however, fail to show that uniparental inheritance can replace biparental inheritance under any existing hypothesis. Recent empirical evidence indicates that mixing two different but normal mitochondrial haplotypes within a cell (heteroplasmy) can cause cell and organism dysfunction. Using a mathematical model, we test if selection against heteroplasmy can lead to the evolution of uniparental inheritance. When we assume selection against heteroplasmy and mutations are neither advantageous nor deleterious (neutral mutations), uniparental inheritance replaces biparental inheritance for all tested parameter values. When heteroplasmy involves mutations that are advantageous or deleterious (non-neutral mutations), uniparental inheritance can still replace biparental inheritance. We show that uniparental inheritance can evolve with or without pre-existing mating types. Finally, we show that selection against heteroplasmy can explain why some organisms deviate from strict uniparental inheritance. Thus, we suggest that selection against heteroplasmy explains the evolution of uniparental inheritance., Author Summary Mitochondria contain genes that encode the machinery needed to power cells. Unlike the nuclear genome, the mitochondrial genome is typically inherited from one parent only (uniparental inheritance). The most common explanation for uniparental inheritance is the genomic conflict theory, which states that uniparental inheritance evolved to prevent the spread of ‘selfish’ mitochondria that replicate quickly but produce energy inefficiently. Current explanations have a major problem: when using realistic parameters, mathematical models cannot show that uniparental inheritance can replace biparental inheritance. Clearly, we need a new explanation that fits with standard population-genetic theory. Recent evidence suggests cells may incur a cost when they carry multiple types of mitochondria. Here we show mathematically that uniparental inheritance could have evolved to avoid the costs of maintaining multiple mitochondrial lineages within a cell. Our results explain the long-standing evolutionary mystery of uniparental inheritance and provide insight into the evolution of mating types and binary sexes. Selection against heteroplasmy also has implications for the evolution of the mitochondrial genome because new mitochondrial haplotypes always lead to heteroplasmy before becoming fixed in the population. Thus, selection against heteroplasmy may explain why mtDNA coding-genes have slower substitution rates than analogous genes within the nucleus.

All honeybees use the waggle dance to recruit nestmates. Studies on the dance precision of Apis mellifera have shown that the dance is often imprecise. Two hypotheses have been put forward aimed at explaining this imprecision. The first argues that imprecision in the context of foraging is adaptive as it ensures that the dance advertises the same patch size irrespective of distance. The second argues that the bees are constrained in their ability to be more precise, especially when the source is nearby. Recent studies have found support for the latter hypothesis but not for the “tuned-error” hypothesis, as the adaptive hypothesis became known. Here we investigate intra-dance variation among Apis species. We analyse the dance precision of A. florea, A. dorsata, and A. mellifera in the context of foraging and swarming. A. mellifera performs forage dances in the dark, using gravity as point of reference, and in the light when dancing for nest sites, using the sun as point of reference. Both A. dorsata and A. florea are open-nesting species; they do not use a different point of reference depending on context. A. florea differs from both A. mellifera and A. dorsata in that it dances on a horizontal surface and does not use gravity but instead “points” directly toward the goal when indicating direction. Previous work on A. mellifera has suggested that differences in dance orientation and point of reference can affect dance precision. We find that all three species improve dance precision with increasing waggle phase duration, irrespective of differences in dance orientation, and point of reference. When dancing for sources nearby, dances are highly variable. When the distance increases, dance precision converges. The exception is dances performed by A. mellifera on swarms. Here, dance precision decreases as the distance increases. We also show that the size of the patch advertised increases with increasing distance, contrary to what is predicted under the tuned-error hypothesis.

Collective motion, where large numbers of individuals move synchronously together, is achieved when individuals adopt interaction rules that determine how they respond to their neighbors’ movements and positions. These rules determine how group-living animals move, make decisions, and transmit information between individuals. Nonetheless, few studies have explicitly determined these interaction rules in moving groups, and very little is known about the interaction rules of fish. Here, we identify three key rules for the social interactions of mosquitofish ( Gambusia holbrooki ): ( i ) Attraction forces are important in maintaining group cohesion, while we find only weak evidence that fish align with their neighbor’s orientation; ( ii ) repulsion is mediated principally by changes in speed; ( iii ) although the positions and directions of all shoal members are highly correlated, individuals only respond to their single nearest neighbor. The last two of these rules are different from the classical models of collective animal motion, raising new questions about how fish and other animals self-organize on the move.

Reproductive swarms of honeybees are faced with the problem of finding a good site to establish a new colony. We examined the potential effects of swarm size on the quality of nest-site choice through a combination of modelling and field experiments. We used an individual-based model to examine the effects of swarm size on decision accuracy under the assumption that the number of bees actively involved in the decision-making process (scouts) is an increasing function of swarm size. We found that the ability of a swarm to choose the best of two nest sites decreases as swarm size increases when there is some time-lag between discovering the sites, consistent with Janson & Beekman (Janson & Beekman 2007 Proceedings of European Conference on Complex Systems , pp. 204–211.). However, when simulated swarms were faced with a realistic problem of choosing between many nest sites discoverable at all times, larger swarms were more accurate in their decisions than smaller swarms owing to their ability to discover nest sites more rapidly. Our experimental fieldwork showed that large swarms invest a larger number of scouts into the decision-making process than smaller swarms. Preliminary analysis of waggle dances from experimental swarms also suggested that large swarms could indeed discover and advertise nest sites at a faster rate than small swarms.

How different levels of biological organization interact to shape each other's function is a central question in biology. One particularly important topic in this context is how individuals' variation in behaviour shapes group-level characteristics. We investigated how fish that express different locomotory behaviour in an asocial context move collectively when in groups. First, we established that individual fish have characteristic, repeatable locomotion behaviours (i.e. median speeds, variance in speeds and median turning speeds) when tested on their own. When tested in groups of two, four or eight fish, we found individuals partly maintained their asocial median speed and median turning speed preferences, while their variance in speed preference was lost. The strength of this individuality decreased as group size increased, with individuals conforming to the speed of the group, while also decreasing the variability in their own speed. Further, individuals adopted movement characteristics that were dependent on what group size they were in. This study therefore shows the influence of social context on individual behaviour. If the results found here can be generalized across species and contexts, then although individuality is not entirely lost in groups, social conformity and group-size-dependent effects drive how individuals will adjust their behaviour in groups.

Contour dynamics and contour-advective methods are commonly used numerical techniques for simulating inviscid fluid motions. In these methods the vorticity or potential vorticity of a flow is represented by a series of contours which are advected according to the prevailing velocity field. In some circumstances the contours may cross, eroding the accuracy of the numerical solution and violating the equations of motion. This paper describes an automated method for explicitly revealing such crossings, first considering the case of determining if two contours cross and then later the more general case of determining if and where an arbitrary number of contours cross.