Power-law versus exponential distributions of animal group sizes

There has been some confusion concerning the animal group size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; as power-law decay with exponent 3/2 was proposed in physical analogy to aerosol condensation. Here I show that the animal group-size distribution follows a power-law decay with exponent 1, and is truncated at a cut-off size which is the expected size of the groups an arbitrary individual engages in. An elementary model of animal aggregation based on binary splitting and coalescing on contingent encounter is presented. The model predicted size distribution holds for various data from pelagic fishes and mammalian herbivores in the wild.     

Interactions among social monitoring,anti-predator vigilance and group size in eastern grey kangaroos

Group size is known to affect both the amount of time that prey animals spend in vigilance and the degree to which the vigilance of group members is synchronized. However, the variation in group-size effects reported in the literature is not yet understood. Prey animals exhibit vigilance both to protect themselves against predators and to monitor other group members, and both forms of vigilance presumably influence group-size effects on vigilance. However, our understanding of the patterns of individual investment underlying the time sharing between anti-predator and social vigilance is still limited. We studied patterns of variation in individual vigilance and the synchronization of vigilance with group size in a wild population of eastern grey kangaroos (Macropus giganteus) subject to predation, in particular focusing on peripheral females because we expected that they would exhibit both social and anti-predator vigilance. There was no global effect of group size on individual vigilance. The lack of group-size effect was the result of two compensating effects. The proportion of time individuals spent looking at other group members increased, whereas the proportion of time they spent scanning the environment decreased with group size; as a result, overall vigilance levels did not change with group size. Moreover, a degree of synchrony of vigilance occurred within groups and that degree increased with the proportion of vigilance time peripheral females spent in anti-predator vigilance. Our results highlight the crucial roles of both social and anti-predator components of vigilance in the understanding of the relationship between group size and vigilance, as well as in the synchronization of vigilance among group members.     

Group-size diversity in public goods games

Public goods games are models of social dilemmas where cooperators pay a cost for the production of a public good while defectors free ride on the contributions of cooperators. In the traditional framework of evolutionary game theory, the payoffs of cooperators and defectors result from interactions in groups formed by binomial sampling from an infinite population. Despite empirical evidence showing that group-size distributions in nature are highly heterogeneous, most models of social evolution assume that the group size is constant. In this article, I remove this assumption and explore the effects of having random group sizes on the evolutionary dynamics of public goods games. By a straightforward application of Jensen's inequality, I show that the outcome of general nonlinear public goods games depends not only on the average group size but also on the variance of the group-size distribution. This general result is illustrated with two nonlinear public goods games (the public goods game with discounting or synergy and the N-person volunteer's dilemma) and three different group-size distributions (Poisson, geometric, and Waring). The results suggest that failing to acknowledge the natural variation of group sizes can lead to an underestimation of the actual level of cooperation exhibited in evolving populations.     

Single origin of human commensalism in the house sparrow

The current, virtually worldwide distribution of the house sparrow (Passer domesticus) is a result of its commensal relationship with humans. It has been suggested that long before the advent of agriculture, an early glacial advance resulted in two disjunct ranges of ancestral house sparrows - one in the Middle East and another on the Indian subcontinent. Differentiation during this period of isolation resulted in two major groups of subspecies: the domesticus group and the indicus group. According to this hypothesis, commensalism with humans would have evolved independently in the two regions and at least twice. An alternative hypothesis is that morphological differences between the subspecies represent very recent differentiation, following expansions from a single source. To test between these hypotheses, we analysed genetic variation at the mitochondrial DNA control region and at three nuclear loci from several house sparrow populations in Europe, Asia and North Africa. No differentiation between the indicus and domesticus groups was found, supporting the single origin hypothesis. One of the subspecies in the indicus group, P. d. bactrianus, differs ecologically from other house sparrows in being migratory and in preferentially breeding in natural habitat. We suggest that bactrianus represents a relict population of the ancestral, noncommensal house sparrow. When agricultural societies developed in the Middle East about 10 000 years ago, a local house sparrow population of the bactrianus type adapted to the novel environment and eventually became a sedentary, human commensal. As agriculture and human civilizations expanded, house sparrows experienced a correlated and massive expansion in range and numbers. The pattern of genetic variation analysed here is consistent with this scenario.     

Risk allocation and competition in foraging groups: reversed effects of competition if group size varies under risk of predation

Animals often feed more quickly when in larger groups. This group-size effect is often explained by safety advantages for groups but an alternative explanation is that animals feed faster in larger groups because of greater scramble competition for limited food. We show that predation risk enhances the group-size effect if groups vary in size. By contrast, competition leads to the group-size effect only when individuals feed in groups of constant size. When individuals feed in groups that vary in size, the best strategy for dealing with competition is to feed intensely when in smaller groups and feed little when in larger (more competitive) groups. In all situations, the effects of competition interact with the effects of predation risk in a simple multiplicative way. Our results suggest that scramble competition is not a general explanation for the group-size effect on vigilance in situations where group size changes relatively rapidly.     

The group-size paradox: effects of learning and patch departure rules

In many species, foraging in groups can enhance individual fitness.However, groups are often predicted to be larger than the sizethat maximizes individual fitness. This is because individualforagers are expected to continue joining a group until thefitness in the group falls to the level experienced by solitaryforagers. If such a process were pervasive, social foraging,paradoxically, would provide little evolutionary advantages.We propose a solution to the group-size paradox by allowingforagers to learn about habitat quality and leave food patcheswhen their current intake rate falls below that expected forthe whole habitat. By using a simulation model, we show thatunder a wide range of population sizes, foragers using suchrules abandon under- and overcrowded patches, ensuring thatgroup size remains close to the optimal value. The results holdin habitats with varying patch quality, but we note that thelack of food renewal in patches can disrupt the process of groupformation. We conclude that groups of optimal sizes can occurfrequently if fitness functions are peaked and resources patchilydistributed, without the need to invoke relatedness betweenjoiners and established group members, group defense againstjoiners, or other mechanisms that were proposed earlier to preventgroups from becoming too large.     

A first principles derivation of animal group size distributions

Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.     

Group Effects and Background Color Patterns Affect the Exploratory Behavior of Tree Sparrows

Exploratory behavior serves the function of acquiring information when facing environmental uncertainty, thus plays an important role for animals living on patchy or ephemeral resources. Our study tested the hypothesis that exploratory behavior is affected by ecological factors associated with the risk of predation. We conducted experiments to examine exploration behavior of wild‐caught Eurasian tree sparrows (Passer montanus) under the influences of background color patterns (white or camouflaged) and group sizes (single vs. five sparrows). We further conducted two‐pattern choice experiments and offered sparrows backgrounds combining those two color patterns. In comparisons with single sparrows, flocking sparrows had shorter landing latencies, started exploring sand patches earlier, spent less total time on the ground before pecking at the first patch and nearly successfully located and pecked all patches. In contrast, sparrows responded nearly indifferently to the two single‐pattern backgrounds; yet when given a choice, sparrows still favored the camouflaged portion in the two‐pattern backgrounds and first landed more frequently there. Twice as many patches were left untouched on the two‐pattern backgrounds, mostly by single sparrows, than on both types of single‐pattern backgrounds. In tests of flocks, sparrows that first landed on the ground to initiate exploration had a higher chance to also first explore a sand patch than random expectation on single‐pattern backgrounds, but not necessarily on two‐pattern backgrounds. Our results demonstrate context‐specific effects of social exploration, suggest possible influence of individual variation and offer evidence for advantages of group living in situations where explorers have to cope with environmental uncertainty.     

From individuals to aggregations: the interplay between behavior and physics

This paper analyses the processes by which organisms form groups and how social forces interact with environmental variability and transport. For aquatic organisms, the latter is especially important-will sheared or turbulent flows disrupt organism groups? To analyse such problems, we use individual-based models to study the environmental and social forces leading to grouping. The models are then embedded in turbulent flow fields to gain an understanding of the interplay between the forces acting on the individuals and the transport induced by the fluid motion. Instead of disruption of groups, we find that flows often enhance grouping by increasing the encounter rate among groups and thereby promoting merger into larger groups; the effect breaks down for strong flows. We discuss the transformation of individual-based models into continuum models for the density of organisms. A number of subtle difficulties arise in this process; however, we find that a direct comparison between the individual model and the continuum model is quite favorable. Finally, we examine the dynamics of group statistics and give an example of building an equation for the spatial and temporal variations of the group-size distribution from the individual-based simulations. These studies lay the groundwork for incorporating the effects of grouping into models of the large scale distributions of organisms as well as for examining the evolutionary consequences of group formation.     

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

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

The effect of size-dependent growth and environmental factors on animal size variability

The origin of variation in animal growth rate and body size is not well understood but central to ecological and evolutionary processes. We develop a relationship that predicts the change in relative body size variation within a cohort will be approximately equal to the relative change in mean per unit size growth rate, when only size-dependent factors affect growth. When modeling cohort growth, relative size variation decreased, remained unchanged, or increased, as a function of growth rate-size scaling relationships, in a predictable manner. We use the approximation to predict how environmental factors (e.g., resource level) affect body size variation, and verified these predictions numerically for a flexible growth model using a wide range of parameter values. We also explore and discuss the assumptions underlying the approximation. We find that factors that similarly affect mean growth rate may differently affect size variation, and competition may increase body size variation without changing size-independent relationships. We discuss implications of our results to the choice of growth equations used in models where body size variation is an important variable or output.     

Individual variation in response to simulated territorial challenge among territory-holding song sparrows

Lack (1946) suggested that male songbirds exhibit consistent individual differences in the vigor or manner in which they defend their territories against intrusion. The causes and consequences of such individual variation have not been incorporated into models of territoriality, however, because of a lack of experimental data confirming Lack's suggestion. In this paper, we test the possibility that male song sparrows Melospiza melodia who are successful territory holders differ consistently in the vigor with which they defend their territory, by conducting repeated song playback trials with the same set of territory-holding subjects across a breeding season. We found only relatively weak seasonal trends in responsiveness: the amount birds sang in response to playback increased significantly across the breeding season and responsiveness was generally lower when a male's social mate was egg laying. By contrast, we found extensive variation among males in how closely they approached a simulated territorial intrusion. These individual differences remained significantly consistent across four rounds of playback trials that spanned the breeding season as determined by Kendall's coefficient of concordance. Our results confirm that some individual song sparrows are consistently more vigorous than others in territory defense, at least in one conspicuous aspect of their behavior, and suggest that further work is needed to understand the nature and consequences of variation in patterns of defense among successful territory holders.     

Intraspecific variation in group size in the blackbuck antelope: the roles of habitat structure and forage at different spatial scales

The main ecological factors that are hypothesized to explain the striking variation in the size of social groups among large herbivores are habitat structure, predation, and forage abundance and distribution; however, their relative roles in wild populations are not well understood. I combined analyses of ecological correlates of spatial variation in group size with analyses of individual behaviour in groups of different sizes to investigate factors maintaining variation in group size in an Indian antelope, the blackbuck Antilope cervicapra. I measured group size, habitat structure, forage, and the occurrence of predators in ten blackbuck populations, and, at a smaller spatial scale, within an intensively studied population. To examine the processes by which these ecological factors influence group size, I used behavioural observations and an experiment to estimate the shape of the relationship between group size and potential costs and benefits to individuals. Group size varied extensively both among and within populations. Analyses of spatial variation in group size suggested that both forage and habitat structure influence group size: large-scale, among-population variation in group size was primarily related to habitat structure, while small-scale, within-population variation was most closely related to forage abundance. Analyses of individual behaviour suggested that larger groups incur greater travel costs while foraging. However, individuals in larger groups appeared to experience greater benefits, namely the earlier detection of a “predator”, a reduction in vigilance, and an increase in the time spent feeding. Overall, these findings suggest that individuals in groups experience a trade-off between predation-related benefits and costs arising from feeding competition. Habitat structure and forage likely influence the nature of this trade-off; thus, variation in these ecological factors may maintain variation in group size. The role of predation pressure and other factors in explaining the remaining variation needs further exploration. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Experimental and model analyses of the effects of competition on individual size variation in wood frog (Rana sylvatica) tadpoles

1. Size variation is a ubiquitous feature of animal populations and is predicted to strongly influence species abundance and dynamics; however, the factors that determine size variation are not well understood. 2. In a mesocosm experiment, we found that the relationship between mean and variation in wood frog (Rana sylvatica) tadpole size is qualitatively different at different levels of competition created by manipulating resource supply rates or tadpole density. At low competition, relative size variation (as measured by the coefficient of variation) decreased as a function of mean size, while at high competition, relative size variation increased. Therefore, increased competition magnified differences in individual performance as measured by growth rate. 3. A model was developed to estimate the contribution of size-dependent factors (i.e. based on size alone) and size-independent factors (i.e. resulting from persistent inherent phenotypic differences other than size that affect growth) on the empirical patterns. 4. Model analysis of the low competition treatment indicated that size-dependent factors alone can describe the relationship between mean size and size variation. To fit the data, the size scaling exponent that describes the dependence of growth rate on size was determined. The estimated value, 0-83, is in the range of that derived from physiological studies. 5. At high competition, the model analysis indicated that individual differences in foraging ability, either size-based or due to inherent phenotypic differences (size-independent factors), were much more pronounced than at low competition. The model was used to quantify the changes in size-dependent or size-independent factors that underlie the effect of competition on size-variation. In contrast to results at low competition, parameters derived from physiological studies could not be used to describe the observed relationships. 6. Our experimental and model results elucidate the role of size-dependent and size-independent factors in the development of size variation, and highlight and quantify the context dependence of individual (intrapopulation) differences in competitive abilities.     

Environmental influence and cohort effects in a sexual ornament in the house sparrow, Passer domesticus

Presence of phenotypic variation is necessary for selection to occur, yet processes affecting variation in sexually selected characters in natural populations are poorly understood. Here we examine whether variation in a sexual ornament (badge size) of male house sparrows ( Passer domesticus ) is dependent on individual variation in the conditions during early ontogenetic stages, and whether this variation and the population-wide effects of external variables such as weather or population size jointly will generate consistent differences among cohorts later in life. Variation in badge size was independent of adult body size, whereas heavier fledglings and fledglings in good body condition developed smaller visible badges as adults. Furthermore, strong cohort-effects were present, caused by a combined effect of density-dependence and weather during the early development in the moulting period and autumn after hatching. Thus, badge size is an environmentally-dependent trait in house sparrows, and likely to be under the influence of both natural and sexual selection.     

Theory and method in studies of vigilance and aggregation

Predation is considered one of the most important selective pressures on free-ranging animals. Our understanding of it derives mainly from studies of individual vigilance (visual scanning of the surroundings beyond the immediate vicinity) and aggregation in prey. Vigilance bears a direct relationship to aggregation, because animals in groups may rely on associates for early warning of danger. This review addresses the relationship between vigilance and aggregation with particular attention to the prediction that individual vigilance declines with increasing group size. Contrary to most other animals studied, primates do not support the prediction. Exploring this, I examined the assumptions underlying vigilance theory in the light of primate behaviour. First I tested whether manual harvesting and upright processing of food as seen among primates might permit them to feed and scan simultaneously. I found no support for this idea. Next I examined the targets of primate vigilance and found that one component (within-group vigilance) might explain the differences between primates and other animals. Finally, I evaluated whether individual primates in large groups face a lower risk of predation than those in small groups. A conclusion was impossible, but by separating group-level from individual-level risk, I was able to identify several common circumstances in which group size would not predict individual risk or vigilance. These circumstances arose for primates and nonprimates alike. I concluded that the relationship of vigilance to aggregation is not straightforward. The absence of a group-size effect on vigilance among primates is probably due to functional differences in vigilance behaviour or safety in groups, not to methodological differences. Furthermore, future work on animal vigilance and aggregation must fully consider both the targets of glances, and the assumption that larger groups are safer from predators. I predict that animals will not relax vigilance in larger groups if conspecific threat increases with group size. Group size will not predict individual risk of predation nor individual vigilance rates when predators do not rely on surprise, or when predators select a small subset of highly vulnerable group members. Copyright 2000 The Association for the Study of Animal Behaviour.     

Strong and weak cross-sex correlations govern the quantitative-genetic architecture of social group choice in Drosophila melanogaster

When genotypes differ in niche-constructing traits, genotypes are expected to differ in which environments they experience, providing a novel causal relationship between genotypes, environments, and behavior. Such genetic variation in niche construction (or, more precisely, environment construction) is predicted to be especially important for social environments, yet the quantitative-genetic parameters governing such variation are still poorly understood. Here, we examine genetic variation and cross-sex genetic correlations for social environment-constructing behaviors. We focus on whether genetic variation in patch use—the tendency to spend time near food patches where conspecifics may be present—and group-size preference—the specific group size chosen when individuals are affiliating—is correlated or decoupled across sexes in the fruit fly, Drosophila melanogaster. Across three choice treatments, we find genotype and sex differences in how much time individuals spend near patches, and which group sizes they prefer. We find that the genetic basis of patch use is strongly coupled across sexes, whereas the genetic basis of group-size preference is completely decoupled across sexes. We discuss how these findings augment and complicate our understanding of the evolutionary genetics of social behaviors.     

Vigilance in Przewalski's gazelle: effects of sex, predation risk and group size

Vigilance in social animals is often aimed at detecting predators. Many social and environmental factors influence vigilance, including sex, predation risk and group size. During the summer of 2007, we studied Przewalski's gazelle Procapra przewalskii , an endemic ungulate to the Qinghai-Tibet Plateau, to test whether and how these three factors affect vigilance. We distinguished groups consisting of males, mothers with lambs and females without lambs making observations on groups in the presence or absence of nearby predators. We assessed the group-size effect on vigilance and how this varied with levels of predation risk and sex. Males and mothers scanned longer and with a higher frequency than females without lambs. Individuals were more vigilant under direct predation threat. Although vigilance generally decreased with group size, the extent of the decrease was independent of predation risk and was not significant in males. The results suggest that mothers are more vigilant suggesting greater vulnerability and that males may have increased their vigilance to compete for higher social ranks. The positive correlation between vigilance and predation risk and the negative correlation between vigilance and group size are consistent with earlier findings, but we failed to find an interaction between group size and predation risk on vigilance perhaps because vigilance levels are low even in small groups, thus making similar vigilant upward adjustments in both small and large groups.     

Individual foraging specialisation in a social mammal: the European badger (Meles meles)

Individual specialisation has been identified in an increasing number of animal species and populations. However, in some groups, such as terrestrial mammals, it is difficult to disentangle individual niche variation from spatial variation in resource availability. In the present study, we investigate individual variation in the foraging niche of the European badger (Meles meles), a social carnivore that lives in a shared group territory, but forages predominantly alone. Using stable isotope analysis, we distinguish the extent to which foraging variation in badgers is determined by social and spatial constraints and by individual differences within groups. We found a tendency for individual badgers within groups to differ markedly and consistently in their isotope values, suggesting that individuals living with access to the same resources occupied distinctive foraging niches. Although sex had a significant effect on isotope values, substantial variation within groups occurred independently of age and sex. Individual differences were consistent over a period of several months and in some instances were highly consistent across the two years of the study, suggesting long-term individual foraging specialisations. Individual specialisation in foraging may, therefore, persist in populations of territorial species not solely as a result of spatial variation in resources, but also arising from individuals selecting differently from the same available resources. Although the exact cause of this behaviour is unknown, we suggest that specialisation may occur due to learning trade-offs which may limit individual niche widths. However, ecological factors at the group level, such as competition, may also influence the degree of specialisation.     

Open capture-recapture models with heterogeneity: I. Cormack-Jolly-Seber model

In open population capture-recapture studies, it is usually assumed that similar animals (e.g., of the same sex and age group) have similar survival rates and capture probabilities. These assumptions are generally perceived to be an oversimplification, and they can lead to incorrect model selection and biased parameter estimates. Allowing for individual variability in survival and capture probabilities among apparently similar animals is now becoming possible, due to advances in closed population models and improved computing power. This article presents a flexible framework of likelihood-based models which allow for individual heterogeneity in survival and capture rates. Heterogeneity is modeled using finite mixtures, which have enough flexibility of distribution shape to accommodate a wide variety of different patterns of individual variation. The models condition on the first capture of each animal, and include as a special case the Cormack-Jolly-Seber model. Model selection is done either using Akaike's information criterion or by likelihood ratio tests, making available checks of different influences on survival rates. Bias in parameter estimates is reduced by including individual heterogeneity. Model selection and bias reduction are important in population studies and for making informed management decisions.