The impact of individual perceptual and cognitive factors on collective states in a data-driven fish school model

In moving animal groups, social interactions play a key role in the ability of individuals to achieve coordinated motion. However, a large number of environmental and cognitive factors are able to modulate the expression of these interactions and the characteristics of the collective movements that result from these interactions. Here, we use a data-driven fish school model to quantitatively investigate the impact of perceptual and cognitive factors on coordination and collective swimming patterns. The model describes the interactions involved in the coordination of burst-and-coast swimming in groups of Hemigrammus rhodostomus. We perform a comprehensive investigation of the respective impacts of two interactions strategies between fish based on the selection of the most or the two most influential neighbors, of the range and intensity of social interactions, of the intensity of individual random behavioral fluctuations, and of the group size, on the ability of groups of fish to coordinate their movements. We find that fish are able to coordinate their movements when they interact with their most or two most influential neighbors, provided that a minimal level of attraction between fish exist to maintain group cohesion. A minimal level of alignment is also required to allow the formation of schooling and milling. However, increasing the strength of social interactions does not necessarily enhance group cohesion and coordination. When attraction and alignment strengths are too high, or when the heading random fluctuations are too large, schooling and milling can no longer be maintained and the school switches to a swarming phase. Increasing the interaction range between fish has a similar impact on collective dynamics as increasing the strengths of attraction and alignment. Finally, we find that coordination and schooling occurs for a wider range of attraction and alignment strength in small group sizes.     

Stage duration distributions in matrix population models

Matrix population models are a standard tool for studying stage‐structured populations, but they are not flexible in describing stage duration distributions. This study describes a method for modeling various such distributions in matrix models. The method uses a mixture of two negative binomial distributions (parametrized using a maximum likelihood method) to approximate a target (true) distribution. To examine the performance of the method, populations consisting of two life stages (juvenile and adult) were considered. The juvenile duration distribution followed a gamma distribution, lognormal distribution, or zero‐truncated (over‐dispersed) Poisson distribution, each of which represents a target distribution to be approximated by a mixture distribution. The true population growth rate based on a target distribution was obtained using an individual‐based model, and the extent to which matrix models can approximate the target dynamics was examined. The results show that the method generally works well for the examined target distributions, but is prone to biased predictions under some conditions. In addition, the method works uniformly better than an existing method whose performance was also examined for comparison. Other details regarding parameter estimation and model development are also discussed.     

Effects of successive predator attacks on prey aggregations

We study the cumulative effect of successive predator attacks on the disturbance of a prey aggregation using a modelling approach. Our model intends to represent fish schools attacked by both aerial and underwater predators. This individual-based model uses long-distance attraction and short-distance repulsion between prey, which leads to prey aggregation and swarming in the absence of predators. When intermediate-distance alignment is added to the model, the prey aggregation displays a cohesive displacement, i.e., schooling, instead of swarming. Including predators, i.e. with repulsion behaviour for prey to predators in the model, leads to flash expansion of the prey aggregation after a predator attack. When several predators attack successively, the prey aggregation dynamics is a succession of expanding-grouping-swarming/schooling phases. We quantify this dynamics by recording the changes in the simulated prey aggregation radius over time. This radius is computed as the longest distance of individual prey to the aggregation centroid, and it is assumed to increase along with prey disturbance. The prey aggregation radius generally increases during flash expansion, then decreases during grouping until reaching a constant lowest level during swarming/schooling. This general dynamics is modulated by several parameters: the frequency, direction (vertical vs. horizontal) and target (centroid of the prey aggregation vs. random prey) of predator attacks; the distance at which prey detect predators; the number of prey and predators. Our results suggest that both aerial and underwater predators are more efficient at disturbing fish schools by increasing their attack frequency at such level that the fish cannot return to swarming/schooling. We find that a mix between aerial and underwater predators is more efficient at disturbing a fish school than a single type of attack, suggesting that aerial and underwater foragers may gain mutual benefits in forming foraging groups.     

Self-organized fish schools: an examination of emergent properties

Heterogeneous, "aggregated" patterns in the spatial distributions of individuals are almost universal across living organisms, from bacteria to higher vertebrates. Whereas specific features of aggregations are often visually striking to human eyes, a heuristic analysis based on human vision is usually not sufficient to answer fundamental questions about how and why organisms aggregate. What are the individual-level behavioral traits that give rise to these features? When qualitatively similar spatial patterns arise from purely physical mechanisms, are these patterns in organisms biologically significant, or are they simply epiphenomena that are likely characteristics of any set of interacting autonomous individuals? If specific features of spatial aggregations do confer advantages or disadvantages in the fitness of group members, how has evolution operated to shape individual behavior in balancing costs and benefits at the individual and group levels? Mathematical models of social behaviors such as schooling in fishes provide a promising avenue to address some of these questions. However, the literature on schooling models has lacked a common framework to objectively and quantitatively characterize relationships between individual-level behaviors and group-level patterns. In this paper, we briefly survey similarities and differences in behavioral algorithms and aggregation statistics among existing schooling models. We present preliminary results of our efforts to develop a modeling framework that synthesizes much of this previous work, and to identify relationships between behavioral parameters and group-level statistics.     

Schooling as a strategy for taxis in a noisy environment

Many aquatic animals face a fundamental problem during foraging and migratory movements: while their resources commonly vary at large spatial scales, they can only sample and assess their environment at relatively small, local spatial scales. Thus, they are unable to choose movement directions by directly sampling distant parts of their environment. A common strategy to overcome this problem is taxis, a behaviour in which an animal performs a biased random walk by changing direction more rapidly when local conditions are getting worse. Such an animal spends more time moving in right directions than wrong ones, and eventually gets to a favourable area. Taxis is inefficient, however, when environmental gradients are weak or overlain by noisy small-scale fluctuations. In this paper, I show that schooling behaviour can improve the ability of animals performing taxis to climb gradients, even under conditions when asocial taxis would be ineffective. Schooling is a social behaviour incorporating tendencies to remain close to and align with fellow members of a group. It enhances taxis because the alignment tendency produces tight angular distributions within groups, and dampens the stochastic effects of individual sampling errors. As a result, more school members orient up-gradient than in the comparable asocial case. However, overly strong schooling behaviour makes the school slow in responding to changing gradient directions. This trade-off suggests an optimal level of schooling behaviour for given spatio-temporal scales of environmental variations. Social taxis may enhance the selective value of schooling in pelagic grazers such as herrings, anchovies and Antarctic krill. Furthermore, the degree of aggregation in a population of schooling animals may affect directly the rate and direction of migration and foraging movements.     

Self-organized and highly ordered domain structures within swarms of Myxococcus xanthus

Coordinated group movement (swarming) is a key aspect of Myxococcus xanthus' social behavior. Here we report observation of domain structures formed by multiple cells within large three-dimensional swarming groups grown on amorphous glass substrates, using the atomic force microscope (AFM). Novel analyses revealed that 90% of the wild type swarms displayed some form of preferential cell alignment. In contrast, cells with mutations in the social and adventurous motility systems displayed a distinct lack of cell alignment. Video microscopy observations of domain features of in vivo swarming M. xanthus cells were also consistent with the AFM data. The results presented here reveal that unique domain formation within swarms of wild type cells is a biologically driven process requiring the social and adventurous motility systems and is not a statistical phenomenon or thermodynamic process arising from liquid crystal behavior.     

Why join groups? Lessons from parasite‐manipulated Artemia

Grouping behaviours (e.g. schooling, shoaling and swarming) are commonly explicated through adaptive hypotheses such as protection against predation, access to mates or improved foraging. However, the hypothesis that aggregation can result from manipulation by parasites to increase their transmission has never been demonstrated. We investigated this hypothesis using natural populations of two crustacean hosts (Artemia franciscana and Artemia parthenogenetica) infected with one cestode and two microsporidian parasites. We found that swarming propensity increased in cestode‐infected hosts and that red colour intensity was higher in swarming compared with non‐swarming infected hosts. These effects likely result in increased cestode transmission to its final avian host. Furthermore, we found that microsporidian‐infected hosts had both increased swarming propensity and surfacing behaviour. Finally, we demonstrated using experimental infections that these concurrent manipulations result in increased spore transmission to new hosts. Hence, this study suggests that parasites can play a prominent role in host grouping behaviours.     

The number of lines of descent and fixation probabilities of alleles in the pure genetic drift process: analytical approximations

Analysis of diversity between populations diverged from an evolutionarily small number of generations cannot be done under the assumption that allele frequencies reflect an equilibrium between genetic drift and mutations. An alternative to analysis through coalescence theory is proposed in this situation by developing analytical approximations. Using a Poisson approximation of its distribution, the expected number of genes from one generation whose copies make up the population after a number of generations characterized by fixation index F can be shown to be approximated by 2/F-1, irrespective of population size, and probabilities of fixation of alleles over a finite period of time can be also approximated. These expressions, which were checked numerically, should make it possible to calculate approximate likelihoods for allele frequency distributions promoted by drift.     

Natural variation of gliding motility in a centimetre-scale population of Myxococcus xanthus

A major challenge in microbial evolutionary ecology is to understand how fitness-related traits vary in natural populations of microorganisms at defined spatial scales and subsequently to identify the forces that maintain such variation. The Gram-negative soil bacterium Myxococcus xanthus is a model system for the study of gliding motility, which is driven by two complementary motility systems in this species and is central to its social lifestyle. We tested whether the ecological context of a centimetre-scale M. xanthus population allows the coexistence of diverse motility-related phenotypes. Swarming rates among 26 clones isolated at the centimetre scale were found to vary greatly in multiple laboratory environments. This variation appears to be motility-specific, as it is not explained by a correlated variation in intrinsic growth rate. In contrast to the common reference strain DK1622, most isolates swarmed faster on hard agar than on soft agar, highlighting the difficulty of inferring species characteristics from laboratory reference strains. These isolates also varied greatly in swarm morphology and in the effect of nutrient limitation on swarming rate. Our results show that diverse swarming phenotypes can coexist in a small-scale bacterial population.     

Spatial variance of mobile aquatic organisms: capelin and cod in Newfoundland coastal waters

Spatial variance in the distribution of aquatic mobile organisms differs from that of passive tracers such as phytoplankton or water temperature. On average, spatial variance of phytoplankton scales with sample unit as $L^2$ or equivalently with frequency as $f^{-2}$. Limited evidence suggests that spatial variance in the distribution of mobile organisms is concentrated at relatively small scales, with little increase over larger scales: spatial variance scales as $f^{-1}$ or less. We investigated whether spatial variance in distributions of a mobile predator, Atlantic cod (Gadus morhua), and a schooling prey, capelin (Mallotus villosus), also scale with frequency as $f^{-1}$. Acoustic surveys showed that at short time scales spatial variance in cod and capelin densities, as measured by spectral density, peaked at various scales ranging from 20 m to 10 km. At longer time scales, spatial variance of cod scaled as $f^{-1.08}$ at resolutions finer than 90 m, while scaling as $f^{-0.18}$ at coarser scales. Spatial variance of capelin scaled as $f^{-1.1}$ at resolutions finer than 400 m, while scaling as $f^{-0.21}$ at coarser scales. Spatial variance plots of krill and marine birds showed similar transitions from shallow to steep scaling. Shoaling, schooling and the aggregative response by predators to concentrations of prey were three processes hypothesized to influence spatial variance in distributions of mobile organisms. Numerical experiments showed that shoaling injects variance at large to intermediate scales, resulting in scalings flatter than $f^{-1}$. Additional experiments showed that schooling produces a transition from shallow to steep scaling as frequency increases. Spatial variance patterns in cod density were not due to aggregative responses by the predator to concentrations of capelin: there was no association, on average, at resolution scales from 20 m to 10 km. Exponent values for aquatic or terrestrial mobile organisms are predicted to be approximately two at the scale of an individual organism, 0.2 at scales that contain aggregations, and two at scales larger than that of populations. These findings suggest that relations between mobile organisms and large scale habitat variables will be difficult to detect, that stratified survey designs used to estimate commercial population sizes will be inefficient, and that rates of interaction between predator and prey will be underestimated if local observations are averaged over the spatial scale of the population.     

On the number of independent cultural traits carried by individuals and populations

In species subject to individual and social learning, each individual is likely to express a certain number of different cultural traits acquired during its lifetime. If the process of trait innovation and transmission reaches a steady state in the population, the number of different cultural traits carried by an individual converges to some stationary distribution. We call this the trait-number distribution. In this paper, we derive the trait-number distributions for both individuals and populations when cultural traits are independent of each other. Our results suggest that as the number of cultural traits becomes large, the trait-number distributions approach Poisson distributions so that their means characterize cultural diversity in the population. We then analyse how the mean trait number varies at both the individual and population levels as a function of various demographic features, such as population size and subdivision, and social learning rules, such as conformism and anti-conformism. Diversity at the individual and population levels, as well as at the level of cultural homogeneity within groups, depends critically on the details of population demography and the individual and social learning rules.     

Communally breeding Bechstein's bats have a stable social system that is independent from the postglacial history and location of the populations

Investigating macro-geographical genetic structures of animal populations is crucial to reconstruct population histories and to identify significant units for conservation. This approach may also provide information about the intraspecific flexibility of social systems. We investigated the history and current structure of a large number of populations in the communally breeding Bechstein's bat ( Myotis bechsteinii ). Our aim was to understand which factors shape the species' social system over a large ecological and geographical range. Using sequence data from one coding and one noncoding mitochondrial DNA region, we identified the Balkan Peninsula as the main and probably only glacial refugium of the species in Europe. Sequence data also suggest the presence of a cryptic taxon in the Caucasus and Anatolia. In a second step, we used seven autosomal and two mitochondrial microsatellite loci to compare population structures inside and outside of the Balkan glacial refugium. Central European and Balkan populations both were more strongly differentiated for mitochondrial DNA than for nuclear DNA, had higher genetic diversities and lower levels of relatedness at swarming (mating) sites than in maternity (breeding) colonies, and showed more differentiation between colonies than between swarming sites. All these suggest that populations are shaped by strong female philopatry, male dispersal, and outbreeding throughout their European range. We conclude that Bechstein's bats have a stable social system that is independent from the postglacial history and location of the populations. Our findings have implications for the understanding of the benefits of sociality in female Bechstein's bats and for the conservation of this endangered species.     

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of ‘global’ variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.     

Numerical Relations and Skill Level Constrain Co-Adaptive Behaviors of Agents in Sports Teams

Similar to other complex systems in nature (e.g., a hunting pack, flocks of birds), sports teams have been modeled as social neurobiological systems in which interpersonal coordination tendencies of agents underpin team swarming behaviors. Swarming is seen as the result of agent co-adaptation to ecological constraints of performance environments by collectively perceiving specific possibilities for action (affordances for self and shared affordances). A major principle of invasion team sports assumed to promote effective performance is to outnumber the opposition (creation of numerical overloads) during different performance phases (attack and defense) in spatial regions adjacent to the ball. Such performance principles are assimilated by system agents through manipulation of numerical relations between teams during training in order to create artificially asymmetrical performance contexts to simulate overloaded and underloaded situations. Here we evaluated effects of different numerical relations differentiated by agent skill level, examining emergent inter-individual, intra- and inter-team coordination. Groups of association football players (national – NLP and regional-level – RLP) participated in small-sided and conditioned games in which numerical relations between system agents were manipulated (5v5, 5v4 and 5v3). Typical grouping tendencies in sports teams (major ranges, stretch indices, distances of team centers to goals and distances between the teams'' opposing line-forces in specific team sectors) were recorded by plotting positional coordinates of individual agents through continuous GPS tracking. Results showed that creation of numerical asymmetries during training constrained agents'' individual dominant regions, the underloaded teams'' compactness and each team''s relative position on-field, as well as distances between specific team sectors. We also observed how skill level impacted individual and team coordination tendencies. Data revealed emergence of co-adaptive behaviors between interacting neurobiological social system agents in the context of sport performance. Such observations have broader implications for training design involving manipulations of numerical relations between interacting members of social collectives.     

Tactical population movements and distributions for ideally motivated competitors

The spatial distributions of populations are a reflection of underlying rules for movement behavior in the context of the environment encountered by individuals. Here I study how ideal directed movement--in which individuals travel in the direction offering the most immediate perceived improvement to their personal fitness--dictates the spatial position of two populations occupying the same relative niche and engaged in competition via interference to an individual's ability to gather resources. Drawing on the analytic derivation of equilibria, numerical simulations, and graphical assessments, I provide conditions under which sympatry, parapatry, or regional exclusion is expected during different phases of the community's development. I also demonstrate that specific competitive asymmetries produce distinguishable distributions and invasion patterns and identify which populations are found centrally or peripherally. Dynamic and dispersal equilibria were examined for differences in the sensitivity to spatial variations in fitness, per capita mortality, metabolic efficiency, the strength of interspecific interference, resource collection speed, and the optimal location of each population along an environmental cline. These asymmetries were studied both in isolation and pairwise in fitness trade-off scenarios.     

Past climate change drives current genetic structure of an endangered freshwater mussel species

Historical‐to‐recent climate change and anthropogenic disturbance affect species distributions and genetic structure. The Rio Grande watershed of the United States and Mexico encompasses ecosystems that are intensively exploited, resulting in substantial degradation of aquatic habitats. While significant anthropogenic disturbances in the Rio Grande are recent, inhospitable conditions for freshwater organisms likely existed prior to such disturbances. A combination of anthropogenic and past climate factors may contribute to current distributions of aquatic fauna in the Rio Grande basin. We used mitochondrial DNA and 18 microsatellite loci to infer evolutionary history and genetic structure of an endangered freshwater mussel, Popenaias popeii, throughout the Rio Grande drainage. We estimated spatial connectivity and gene flow across extant populations of P. popeii and used ecological niche models (ENMs) and approximate Bayesian computation (ABC) to infer its evolutionary history during the Pleistocene. structure results recovered regional and local population clusters in the Rio Grande. ENMs predicted drastic reductions in suitable habitat during the last glacial maximum. ABC analyses suggested that regional population structure likely arose in this species during the mid‐to‐late Pleistocene and was followed by a late Pleistocene population bottleneck in New Mexico populations. The local population structure arose relatively recently, perhaps due to anthropogenic factors. Popenaias popeii, one of the few freshwater mussel species native to the Rio Grande basin, is a case study for understanding how both geological and anthropogenic factors shape current population genetic structure. Conservation strategies for this species should account for the fragmented nature of contemporary populations.     

Genetic Determinants of Swarming in Rhizobium etli

Swarming motility is considered to be a social phenomenon that enables groups of bacteria to move coordinately atop solid surfaces. The differentiated swarmer cell population is embedded in an extracellular slime layer, and the phenomenon has previously been linked with biofilm formation and virulence. The gram-negative nitrogen-fixing soil bacterium Rhizobium etli CNPAF512 was previously shown to display swarming behavior on soft agar plates. In a search for novel genetic determinants of swarming, a detailed analysis of the swarming behavior of 700 miniTn5 mutants of R. etli was performed. Twenty-four mutants defective in swarming or displaying abnormal swarming patterns were identified and could be divided into three groups based on their swarming pattern. Fourteen mutants were completely swarming deficient, five mutants showed an atypical swarming pattern with no completely smooth edge and local extrusions, and five mutants displayed an intermediate swarming phenotype. Sequence analysis of the targeted genes indicated that the mutants were likely affected in quorum-sensing, polysaccharide composition or export, motility, and amino acid and polyamines metabolism. Several of the identified mutants displayed a reduced symbiotic nitrogen fixation activity.