When is bigger better? The effects of group size on the evolution of helping behaviours.

Understanding the evolution of sociality in humans and other species requires understanding how selection on social behaviour varies with group size. However, the effects of group size are frequently obscured in the theoretical literature, which often makes assumptions that are at odds with empirical findings. In particular, mechanisms are suggested as supporting large-scale cooperation when they would in fact rapidly become ineffective with increasing group size. Here we review the literature on the evolution of helping behaviours (cooperation and altruism), and frame it using a simple synthetic model that allows us to delineate how the three main components of the selection pressure on helping must vary with increasing group size. The first component is the marginal benefit of helping to group members, which determines both direct fitness benefits to the actor and indirect fitness benefits to recipients. While this is often assumed to be independent of group size, marginal benefits are in practice likely to be maximal at intermediate group sizes for many types of collective action problems, and will eventually become very small in large groups due to the law of decreasing returns. The second component is the response of social partners on the past play of an actor, which underlies conditional behaviour under repeated social interactions. We argue that under realistic conditions on the transmission of information in a population, this response on past play decreases rapidly with increasing group size so that reciprocity alone (whether direct, indirect, or generalised) cannot sustain cooperation in very large groups. The final component is the relatedness between actor and recipient, which, according to the rules of inheritance, again decreases rapidly with increasing group size. These results explain why helping behaviours in very large social groups are limited to cases where the number of reproducing individuals is small, as in social insects, or where there are social institutions that can promote (possibly through sanctioning) large-scale cooperation, as in human societies. Finally, we discuss how individually devised institutions can foster the transition from small-scale to large-scale cooperative groups in human evolution.

Group testing based spectrum hole search using a simple sub-nyquist sampling scheme

In this paper, we consider the problem of finding a spectrum hole of a specified bandwidth in a given wide band of interest. We propose a new, simple and easily implementable sub-Nyquist sampling scheme for signal acquisition and a spectrum hole search algorithm that exploits sparsity in the primary spectral occupancy in the frequency domain by testing a group of adjacent subbands in a single test. The sampling scheme deliberately introduces aliasing during signal acquisition, resulting in a signal that is the sum of signals from adjacent sub-bands. Energy-based hypothesis tests are used to provide an occupancy decision over the group of subbands, and this forms the basis of the proposed algorithm to find contiguous spectrum holes. We extend this framework to a multi-stage sensing algorithm that can be employed in a variety of spectrum sensing scenarios, including non-contiguous spectrum hole search. Further, we provide the analytical means to optimize the hypothesis tests with respect to the detection thresholds, number of samples and group size to minimize the detection delay under a given error rate constraint. Depending on the sparsity and SNR, the proposed algorithms can lead to significantly lower detection delays compared to a conventional bin-by-bin energy detection scheme; the latter is in fact a special case of the group test when the group size is set to 1. We validate our analytical results via Monte Carlo simulations.

Group Testing-Based Spectrum Hole Search for Cognitive Radios

This paper investigates the use of adaptive group testing to find a spectrum hole of a specified bandwidth in a given wideband of interest. We propose a group testing-based spectrum hole search algorithm that exploits sparsity in the primary spectral occupancy by testing a group of adjacent subbands in a single test. This is enabled by a simple and easily implementable sub-Nyquist sampling scheme for signal acquisition by the cognitive radios (CRs). The sampling scheme deliberately introduces aliasing during signal acquisition, resulting in a signal that is the sum of signals from adjacent subbands. Energy-based hypothesis tests are used to provide an occupancy decision over the group of subbands, and this forms the basis of the proposed algorithm to find contiguous spectrum holes of a specified bandwidth. We extend this framework to a multistage sensing algorithm that can be employed in a variety of spectrum sensing scenarios, including noncontiguous spectrum hole search. Furthermore, we provide the analytical means to optimize the group tests with respect to the detection thresholds, number of samples, group size, and number of stages to minimize the detection delay under a given error probability constraint. Our analysis allows one to identify the sparsity and SNR regimes where group testing can lead to significantly lower detection delays compared with a conventional bin-by-bin energy detection scheme; the latter is, in fact, a special case of the group test when the group size is set to 1 bin. We validate our analytical results via Monte Carlo simulations.

Beluga, Delphinapterus leucas, Group Sizes in Cook Inlet, Alaska, Based on Observer Counts and Aerial Video

Belugas, Delphinapterus leucas, groups were videotaped concurrent to observer counts during annual NMFS aerial surveys of Cook Inlet, Alaska, from 1994 to 2000. The videotapes provided permanent records of whale groups that could be examined and compared to group size estimates ade by aerial observers.Examination of the video recordings resulted in 275 counts of 79 whale groups. The McLaren formula was used to account for whales missed while they were underwater (average correction factor 2.03; SD=0.64). A correction for whales missed due to video resolution was developed by using a second, paired video camera that magnified images relative to the standard video. This analysis showed that some whales were missed either because their image size fell below the resolution of hte standard video recording or because two whales surfaced so close to each other that their images appeared to be one large whale. The correction method that resulted depended on knowing the average whale image size in the videotapes. Image sizes were measured for 2,775 whales from 275 different passes over whale groups. Corrected group sizes were calcualted as the product of the original count from video, the correction factor for whales missed underwater, and the correction factor for whales missed due to video resolution (averaged 1.17; SD=0.06). A regression formula was developed to estimate group sizes from aerial observer counts; independent variables were the aerial counts and an interaction term relative to encounter rate (whales per second during the counting of a group), which were regressed against the respective group sizes as calculated from the videotapes. Significant effects of encounter rate, either positive or negative, were found for several observers. This formula was used to estimate group size when video was not available. The estimated group sizes were used in the annual abundance estimates.

Animal group forces resulting from predator avoidance and competition minimization

A new model to explain animal spacing, based on a trade-off between foraging efficiency and predation risk, is derived from biological principles. The model is able to explain not only the general tendency for animal groups to form, but some of the attributes of real groups. These include the independence of mean animal spacing from group population, the observed variation of animal spacing with resource availability and also with the probability of predation, and the decline in group stability with group size. The appearance of "neutral zones" within which animals are not motivated to adjust their relative positions is also explained. The model assumes that animals try to minimize a cost potential combining the loss of intake rate due to foraging interference and the risk from exposure to predators. The cost potential describes a hypothetical field giving rise to apparent attractive and repulsive forces between animals. Biologically based functions are given for the decline in interference cost and increase in the cost of predation risk with increasing animal separation. Predation risk is calculated from the probabilities of predator attack and predator detection as they vary with distance. Using example functions for these probabilities and foraging interference, we calculate the minimum cost potential for regular lattice arrangements of animals before generalizing to finite-sized groups and random arrangements of animals, showing optimal geometries in each case and describing how potentials vary with animal spacing. (C) 1999 Academic Press.</p>

Perceptions of Gender Group Variability in Majority and Minority Contexts Two Field Studies with Nurses and Police Officers

Two field studies demonstrated that majority and minority size moderate perceived group variability. In Study 1 we found an outgroup homogeneity (OH) effect for female nurses in the majority, but an ingroup homogeneity (IH) effect for a token minority of male nurses. In Study 2 we found similar effects in a different setting - an OH effect for policemen in the majority and an IH effect for policewomen in the minority. Although measures of visibility, status, and, especially, familiarity tended to show the same pattern as perceived variability, there was no evidence that they mediated perceived dispersion. Results are discussed in terms of group size, rather than gender, being moderators of perceived variability, and with reference to Kanter's (1977a, 1977b) theory of group proportions.

Seasonal patterns of body temperature daily rhythms in group-living cape ground squirrels Xerus inauris

Organisms respond to cyclical environmental conditions by entraining their endogenous biological rhythms. Such physiological responses are expected to be substantial for species inhabiting arid environments which incur large variations in daily and seasonal ambient temperature (T). We measured core body temperature (T) daily rhythms of Cape ground squirrels Xerus inauris inhabiting an area of Kalahari grassland for six months from the Austral winter through to the summer. Squirrels inhabited two different areas: an exposed flood plain and a nearby wooded, shady area, and occurred in different social group sizes, defined by the number of individuals that shared a sleeping burrow. Of a suite of environmental variables measured, maximal daily T provided the greatest explanatory power for mean T whereas sunrise had greatest power for T acrophase. There were significant changes in mean T and T acrophase over time with mean T increasing and T acrophase becoming earlier as the season progressed. Squirrels also emerged from their burrows earlier and returned to them later over the measurement period. Greater increases in T, sometimes in excess of 5°C, were noted during the first hour post emergence, after which T remained relatively constant. This is consistent with observations that squirrels entered their burrows during the day to 'offload' heat. In addition, greater T amplitude values were noted in individuals inhabiting the flood plain compared with the woodland suggesting that squirrels dealt with increased environmental variability by attempting to reduce their T-T gradient. Finally, there were significant effects of age and group size on T with a lower and less variable T in younger individuals and those from larger group sizes. These data indicate that Cape ground squirrels have a labile T which is sensitive to a number of abiotic and biotic factors and which enables them to be active in a harsh and variable environment.

Five-day plan for smoking cessation using group behaviour therapy.

The "Five-Day Plan to Stop Smoking" (FDP) is an educational group technique for smoking cessation. We studied a cohort of 123 smokers (55 men, 68 women, mean age 42 years) who participated in 11 successive FDP sessions held in Switzerland between 1995 and 1998 and who were followed up for at least 12 months by telephone or direct interview. Overall, 102 of the 123 subjects (83%) had stopped smoking by the end of the FDP, and self-declared smoking cessation rate was 25% after one year. The following factors potentially associated with outcome were studied: age, sex, smoking habit duration, cigarettes per day, Fagerström Test for Nicotine Dependence (FTND), group size, and medical presence among the group leaders. Smoking habit duration was the only variable which showed a statistically significant association with success: the rate of smoking cessation was higher among patients who had smoked for less than 20 years (34.7% vs. 18.9%, p = 0.049). Stress was the most common cause of relapse. The FDP appears to be an effective smoking cessation therapy. Propositions are made in order to improve the success rate of future sessions.

Extensive Social Choice and the Measurement of Group Fitness in Biological Hierarchies

Extensive social choice theory is used to study the problem of measuring group fitness in a two-level biological hierarchy. Both fixed and variable group size are considered. Axioms are identified that imply that the group measure satisfies a form of consequentialism in which group fitness only depends on the viabilities and fecundities of the individuals at the lower level in the hierarchy. This kind of consequentialism can take account of the group fitness advantages of germ-soma specialization, which is not possible with an alternative social choice framework proposed by Okasha, but which is an essential feature of the index of group fitness for a multicellular organism introduced by Michod, Viossat, Solari, Hurand, and Nedelcu to analyze the unicellular-multicellular evolutionary transition. The new framework is also used to analyze the fitness decoupling between levels that takes place during an evolutionary transition.

Behavioral suites mediate group-level foraging dynamics in communities of tropical stingless bees

Competition for floral resources is a key force shaping pollinator communities, particularly among social bees. The ability of social bees to recruit nestmates for group foraging is hypothesized to be a major factor in their ability to dominate rich resources such as mass-flowering trees. We tested the role of group foraging in attaining dominance by stingless bees, eusocial tropical pollinators that exhibit high diversity in foraging strategies. We provide the first experimental evidence that meliponine group foraging strategies, large colony sizes and aggressive behavior form a suite of traits that enable colonies to improve dominance of rich resources. Using a diverse assemblage of Brazilian stingless bee species and an array of artificial ""flowers"" that provided a sucrose reward, we compared species` dominance and visitation under unrestricted foraging conditions and with experimental removal of group-foraging species. Dominance does not vary with individual body size, but rather with foraging group size. Species that recruit larger numbers of nestmates (Scaptotrigona aff. depilis, Trigona hyalinata, Trigona spinipes) dominated both numerically (high local abundance) and behaviorally (controlling feeders). Removal of group-foraging species increased feeding opportunities for solitary foragers (Frieseomelitta varia, Melipona quadrifasciata and Nannotrigona testaceicornis). Trigona hyalinata always dominated under unrestricted conditions. When this species was removed, T. spinipes or S. aff. depilis controlled feeders and limited visitation by solitary-foraging species. Because bee foraging patterns determine plant pollination success, understanding the forces that shape these patterns is crucial to ensuring pollination of both crops and natural areas in the face of current pollinator declines.

Food Competition in a Semi-Free-Ranging Cebus apella Group

The competitive regime faced by individuals is fundamental to modelling the evolution of social organization. In this paper, we assess the relative importance of contest and scramble food competition on the social dynamics of a provisioned semi-free-ranging Cebus apella group (n=18). Individuals competed directly for provisioned and clumped foods. Effects of indirect competition were apparent with individuals foraging in different areas and with increased group dispersion during periods of low food abundance. We suggest that both forms of competition can act simultaneously and to some extent synergistically in their influence on social dynamics; the combination of social and ecological opportunities for competition and how those opportunities are exploited both influence the nature of the relationships within social groups of primates and underlie the evolved social structure. Copyright (c) 2008 S. Karger AG, Basel

Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.