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Second harmonic generation microscopy was performed on both normal and diseased breast tissue. Differences in the collagen fibre shape between normal, benign and malignant breast tissue were compared and quantified using elliptical Fourier analysis. Principal shape analysis of these coefficients provided an understanding of the key differences in collagen fibre shape between the three tissue types. A Gaussian model was also used to associate the shape of the fibre with the probability that it had been sampled from malignant breast tissue. These results provide quantitative evidence for the alteration of collagen fibre shape in both benign and malignant breast tissue.

1. Information about the density of wild honey bee (Apis spp.) colonies in an ecosystem is central to understanding the functional role of honey bees in that ecosystem, necessary for effective biosecurity response planning, and useful for determining whether pollination services are adequate. However, direct visual surveys of colony locations are not practical at ecosystem scales. Thus, indirect methods based on population genetic analysis of trapped males have been proposed and implemented.
2. In this review, indirect methods of assessment of honey bee colony densities are described, which can be applied at ecosystem scales. The review also describes how to trap males in the field using the Williams drone trap (or virgin queens) the appropriate genetic markers and statistical analyses, and discusses issues surrounding sample size.
3. The review also discusses some outstanding issues concerning the methods and the conversion of estimated colony number to colony density per km². The appropriate conversion factor will require further research to determine the area over which a drone trap draws drones.

We give a complete description of the long-time asymptotic profile of the solution to a free boundary model considered recently in [10]. This model describes the spreading of an invasive species in an environment which shifts with a constant speed, and the research of [10] indicates that the species may vanish, or spread successfully, or fall in a borderline case. In the case of successful spreading, the long-time behavior of the population is not completely understood in [10]. Here we show that the spreading of the species is governed by two traveling waves, one has the speed of the shifting environment, giving the profile of the retreating tail of the population, while the other has a faster speed determined by a semi-wave, representing the profile of the advancing front of the population.

This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor, and its long-time dynamical behavior can be described by a spreading-vanishing dichotomy. The main purpose of this paper is to determine the asymptotic spreading speed of the invading species when its spreading is successful, which involves two systems of traveling wave type equations.

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.

'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.

In this paper, we report some recent theoretical work of Du-Shi, Du-Liang and Du-Peng-Wang that examines the effect of environmental changes in three well-known diffusive population models, each modeling the interaction of two population species in a common habitat. For each model, we consider the situation that one of the two species is endangered and a simple protection zone is created in the habitat for the endangered species. The focus is on the effect of the protection zone on the dynamics of the two species systems. We demonstrate that, though the effects of the protection zone on the dynamical behavior of the three systems are significantly different from each other, they all share one important property, namely, there exists a critical patch size for the protection zone: If the protection zone is below this size, each model behaves similarly to the no-protection zone case, but every model undergoes profound changes in dynamical behavior once the protection zone is above the critical patch size, and in such a case the endangered species is always saved from extinction.

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.

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.

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.

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.

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.

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 nestsite 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.

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.

In this paper, we consider the diffusive Leslie predator-prey model with large intrinsic predator growth rate, and investigate the change of behavior of the model when a simple protection zone Ω₀ for the prey is introduced. As in earlier work [Y. Du, J. Shi. A diffusive predator-prey model with a protection zone. J. Differential Equations 229 [2006] 63-91: Y. Du. X. Liang. A diffusive competition model with a protection zone. J. Differential Equations 244 (2008) 61-86] we show the existence of a critical patch size of the protection zone, determined by the first Dirichlet eigenvalue of the Laplacian over Ω₀ and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when Ω₀ is above the critical patch size. However, our research here reveals significant difference of the model's behavior from the predator-prey model studies in [Y. Du, J. Shi, A diffusive predator-prey model with a protection some, J. Differential Equations 229 (2006) 63-91] with the same kind of protection zone. We show that the asymptotic profile of the population distribution of the Leslie model is governed by a standard boundary blow-up problem, and classical or degenerate logistic equations.

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.

Collective animal behavior is an emergent phenomenon arising from the local interactions of the members of animal groups. Considerable progress has been made in characterizing these interactions, particularly inferring rules that shape and guide the responses of animals to their near neighbors. To date, experimental work has focused on collective behavior within a single, stable context. We examine the individual and collective behavior of a schooling fish species, the x-ray tetra (Pristella maxillaris), identifying their response to changes in context produced by food cues or conspecific alarm cues. Fish exposed to alarm cues show pronounced, broad-ranging changes of behavior, including reducing speed and predictability in their movements. Alarmed fish also alter their responses to other group members, including enacting a smaller zone of repulsion and increasing their frequency of observation of, and responsiveness to, near neighbors. Fish subject to food cues increased speed as a function of neighbor positions and reduced encounter frequency with near neighbors. Overall, changes in individual behavior and the interactions among individuals in response to external cues coincide with changes in group-level patterns, providing insight into the adaptability of behavior to changes in context and interrelationship between local interactions and global patterns in collective behavior.

Hopfield's Lyapunov function is used to view the stability and topology of equilibria in neuronal networks for visual rivalry and pattern formation. For two neural populations with reciprocal inhibition and slow adaptation, the dynamics of neural activity is found to include a pair of limit cycles: one for oscillations between states where one population has high activity and the other has low activity, as in rivalry, and one for oscillations between states where both populations have the same activity. Hopfield's Lyapunov function is used to find the dynamical mechanism for oscillations and the basin of attraction of each limit cycle. For a spatially continuous population with lateral inhibition, stable equilibria are found for local regions of high activity (solitons) and for bound states of two or more solitons. Bound states become stable when moving two solitons together minimizes the Lyapunov function, a result of decreasing activity in regions between peaks of high activity when the firing rate is described by a sigmoid function. Lowering the barrier to soliton formation leads to a pattern-forming instability, and a nonlinear solution to the dynamical equations is found to be given by a soliton lattice, which is completely characterized by the soliton width and the spacing between neighboring solitons. Fluctuations due to noise create lattice vacancies analogous to point defects in crystals, leading to activity which is spatially inhomogeneous.

Understanding the nature of spreading of invasive species is a central problem in invasion ecology. This is a problem of nonequilibrium. If we represent the population distribution of an invasive species as a function of time t and space location 'x', written as 'u'('t','x'), then it is possible to establish mathematical models that govern the evolution of 'u'. We will look at several such mathematical models in this article, and discuss the predictions they offer for the invasion problem.

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.

The coordinated and synchronized movement of animals in groups often referred to as collective motion emerges through the interactions between individual animals within the group. Factors which affect these interactions have the potential to shape collective movement. One such factor is familiarity, or the tendency to bias behaviour towards individuals as a result of social recognition. We examined the effect of familiarity on the expression of collective motion in small shoals of female guppies ('Poecilia reticulata'). Groups comprising familiar individuals were more strongly polarized than groups of unfamiliar individuals, particularly when in novel surroundings. The ability to form more strongly polarized shoals potentially promotes information transfer and enhances the anti-predator benefits of grouping.

In this article, we study the dynamical behaviour of a new species spreading from a location in a river network where two or three branches meet, based on the widely used Fisher-KPP advection-diffusion equation. This local river system is represented by some simple graphs with every edge a half infinite line, meeting at a single vertex. We obtain a rather complete description of the long-time dynamical behaviour for every case under consideration, which can be classified into three different types (called a trichotomy), according to the water flow speeds in the river branches, which depend crucially on the topological structure of the graph representing the local river system and on the cross section areas of the branches. The trichotomy includes two different kinds of persistence states, and the state called "persistence below carrying capacity" here appears new.

1. 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. 2. 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. 3. 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. 4. 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.

All honey bees 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.

The last few years have seen a renewed interest in the mechanisms behind nest-site selection in honeybees. Most studies have focused on the cavity-nesting honeybee 'Apis mellifera', but more recently studies have included the open-nesting 'A. florea'. Amongst species comparisons are important if we want to understand how the process has been adapted over evolutionary time to suit the particular species' nest-site requirement. Here, we describe the behaviour of scout bees of the giant Asian honeybee 'A. dorsata' on three artificially created swarms to determine the mechanisms used to collectively decide on a location to move to, either in the same environment (nest-site selection) or somewhere further afield (migration). In all swarms, scouts' dances converged on a general direction prior to lift-off and this direction corresponded to the direction that swarms flew. Scouts from one swarm danced for sites that were far away. These dances did not converge onto a specific distance, implying they were migration dances. Dances for different sites differed in the number of circuits per dance suggesting that 'A. dorsata' scouts make an assessment of site quality. Similarly to 'A. florea', but in contrast to 'A. mellifera', 'A. dorsata' scouts did not reduce dance duration after repeated returns from scouting flights.We found that many scouts that dance for a non-preferred location changed dance location during the decision-making process after following dances for the consensus direction. We conclude that the consensus building process of 'A. dorsata' swarms relies on the interaction of scout bees on the swarm.

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.

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.

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.

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.

Honey bee foragers recruit other bees to visit productive patches of flowers by advertising, on their return to the hive, their source of nectar or pollen by a waggle dance to indicate the location and quality of the source. The distribution of foragers among sources, generated by this waggle dance recruitment, has been modeled with differential equations. Differential equation models either represent each stage of foraging - dancing, visiting forage sites, waiting as an unemployed forager, following a dance - or more simply divide the foraging force into pools of workers where each pool exploits a different site. Other models include receiver bees who work in the hive and modulate the foragers' dance response to the quality of forage sites. Simulation and individual-oriented models for honey bee foraging are briefly discussed as well as foraging in other social insects. A brief description of the application of ideas from honey bee foraging to create bee-based computer algorithms concludes the chapter.

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.

It is always very difficult to efficiently and accurately solve a system of differential equations coupled with moving free boundaries, while such a system has been widely applied to describe many physical/biological phenomena such as the dynamics of spreading population. The main purpose of this paper is to introduce efficient numerical methods within a general framework for solving such systems with moving free boundaries. The major numerical challenge is to track the moving free boundaries, especially for high spatial dimensions. To overcome this, a front tracking framework coupled with implicit solver is first introduced for the 2D model with radial symmetry. For the general 2D model, a level set approach is employed to more efficiently treat complicated topological changes. The accuracy and order of convergence for the proposed methods are discussed, and the numerical simulations agree well with theoretical results.

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 documented across a range of social taxa, including hunger, motivation, dominance and personality. Comparatively little is known about the physiological mechanisms that underlie leadership. Here, we tested whether the metabolic phenotype of individual fish (x-ray tetras, Pristella maxillaris) determined their relative position within a moving shoal and their tendency to act as leaders. In contrast to previous work, we found that individuals with low maximal metabolic rates and low aerobic scope tended to be more likely to be found at the front of shoals and were more likely to act as leaders. We suggest that leadership by low-performing individuals leads to greater group cohesion. However, in more challenging environmental contexts, such as flowing water, higher performing animals may be more likely to become leaders while low-performing individuals seek the more favourable hydrodynamic conditions at the rear of the group. Hence, the travelling speed of the group may mediate the relationship between metabolic phenotype and leadership.

This volume grew out from the "International Conference on Reaction-Diffusion Systems and Viscosity Solutions" held at Providence University, Taiwan, during January 3-6,2007. It consists mostly of selected articles representing the recent progress of some important areas of nonlinear partial differential equations. Some of the articles are research papers by participants of the conference, but most are invited survey papers by leading experts in the field, not necessarily participant of the conference. The topics included here reflect the themes of the above-mentioned conference and the research interests of the editors, and therefore are naturally biased and incomplete. Nevertheless, they cover a wide range of partial differential equations, from regularity of viscosity solutions, to symmetry properties of positive solutions of parabolic equations, to nonlinear Schrodinger equations, to mention but a few. A complete list can be found from the content pages.

The Fisher-Kolmogorov-Petrovsky-Piskunov model, also known as the Fisher-KPP model, supports travelling wave solutions that are successfully used to model numerous invasive phenomena with applications in biology, ecology and combustion theory. However, there are certain phenomena that the Fisher-KPP model cannot replicate, such as the extinction of invasive populations. The Fisher-Stefan model is an adaptation of the Fisher-KPP model to include a moving boundary whose evolution is governed by a Stefan condition. The Fisher-Stefan model also supports travelling wave solutions; however, a key additional feature of the Fisher-Stefan model is that it is able to simulate population extinction, giving rise to a spreading-extinction dichotomy. In this work, we revisit travelling wave solutions of the Fisher-KPP model and show that these results provide new insight into travelling wave solutions of the Fisher-Stefan model and the spreading-extinction dichotomy. Using a combination of phase plane analysis, perturbation analysis and linearization, we establish a concrete relationship between travelling wave solutions of the Fisher-Stefan model and often-neglected travelling wave solutions of the Fisher-KPP model. Furthermore, we give closed-form approximate expressions for the shape of the travelling wave solutions of the Fisher-Stefan model in the limit of slow travelling wave speeds, c≪1.

Tadpoles of the cane toad (Rhinella marina) form dense aggregations in the field, but the proximate cues eliciting this behavior are not well understood. We sampled water‐bodies in the Northern Territory of Australia, finding that the density of cane toad tadpoles increased with increasing temperature. Furthermore, we conducted laboratory experiments to explore the roles of biotic factors (attraction to conspecifics; chemical cues from an injured conspecific; food) and spatially heterogeneous abiotic factors (light levels, water depth, physical structure) to identify the cues that induce tadpole aggregation. Annulus and binary choice trials demonstrated weak but significant attraction between conspecifics. Tadpoles decreased swimming speeds, but did not increase grouping in response to cues from an injured conspecific. Larvae aggregated in response to abiotic cues (high levels of illumination and proximity to physical structures) and were strongly attracted to feeding conspecifics. Overall, aggregation by cane toad tadpoles is likely driven by weak social attraction coupled with a shared preference for specific abiotic features, creating loose aggregations that are then reinforced by movement toward feeding conspecifics.

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.

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.

We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary problem was studied recently in, but only rough bounds of the spreading speed were obtained there. We show in this paper that there exists an asymptotic spreading speed, which is determined by a certain traveling wave type system of one space dimension, called a semi-wave. This appears to be the first result that gives the precise asymptotic spreading speed for a two species system with free boundaries.