Truncated power-law distribution of group sizes in antelope

Quantifying and understanding group size distributions can be useful for understanding group behaviour in animal populations. We analysed group size data of the blackbuck, Antilope cervicapra, from six different field sites to estimate the group size distribution of this antelope. We used likelihood based methods (AICs and likelihood ratios) to show that an exponentially truncated power law is the distribution that best describes blackbuck group data, outperforming a simple power-law, an exponential distribution, and a lognormal distribution. Our results show that distribution parameters can be used to draw novel insights regarding group dynamics, and we demonstrate this by investigating how habitat openness affects group size distributions.

The robust beauty of the majority rule by a small number of selected members

The principle of majority rule is a major decision-making strategy widely used in human and animal society. While majority rule yields highly accurate performance compared to individuals in the same situation, its performance is strongly undermined by a small correlation among individual judgments. We focus on the alternative, the selected majority rule, which is the majority rule by a small number of comities selected from the large group. The present study investigated relative advantages of a smaller group of selected majority rule with computer simulation, systematically controlling 4 parameters—group size, distribution of individual performance (mean and variance), and correlation among decisions. The result showed that compared to simple majority rule and the single expert, the selected majority rule robustly yields higher performance against changes in these parameter values. Further, the absolute number of committee members contributes to robustness against the influence of group size. This robustness is undermined if the number of committee members increases proportionally to the number of total members, even though the committee members are a minority. Thus, absolute number of group size is more critical than the proportion of selected members. This study indicates that the rationale for the majority decision of smaller committees is often fixed against the total number of members in the organization in terms of decision accuracy.

Truncated power-law distribution of group sizes in antelope

SummaryGroup size distributions are instrumental in understanding group behaviour in animal populations. We analysed group size data of the blackbuck, Antilope cervicapra, from six different field sites to estimate the group size distribution of this antelope. We show that an exponentially truncated power law (called the polylog distribution in this paper) is the best fitting distribution, against the simple power law and lognormal distributions as other contenders, and the exponential distribution as a control. To show this, we use two likelihood based methods (AICs and likelihood ratios). Finally, we show that polylog distribution parameters can be used to better understand group dynamics, by using them to explore how habitat openness affects group behaviour.

Comparing radio-tracking and visual detection methods to quantify group size measures

Abstract1. Average values of animal group sizes are prone to be overestimated in traditional field studies because small groups and singletons are easier to overlook than large ones. This kind of bias also applies for the method of locating groups by tracking previously radio-collared individuals in the wild. If the researcher randomly chooses a collared animal to locate a group to visit, a large group has higher probability to be selected than a small one, simply because it has more members.2. The question arises whether location of groups by means of finding collared animals has smaller or greater bias than searching for groups by visual observation. If the bias is smaller or same, this method can be recommended for finding groups. However, such a comparison cannot be made by speculation, only by empirical investigation.3. The present study compares the two methods empirically, by statistically comparing group size measures (mean, median, quantiles, frequency distribution, and ‘typical group size’) between two data sets. These data sets comprise of Rocky Mountain mule deer group size values collected in the same area during the same period of time, referring either to groups located by the traditional ‘search and observe method’ or located by tracking formerly collared individuals.4. All group size measures are statistically similar in the two samples, thus we conclude that the two methods yielded similar biases. Although the true group size measures are not known, we presume that both methods have overestimated them. We propose that these results do not necessary apply to other species, thus cannot be generalized. The reason for this is that bias may depend on factors specific to the species: bias of visual observation may depend on how well the species conceals itself in the existing habitat, and the bias associated with finding groups using collared animals is likely dependent on group size distribution and also on the proportion of collared animals in the population.

Variability in group size and the evolution of collective action

Models of the evolution of collective action typically assume that interactions occur in groups of identical size. In contrast, social interactions between animals occur in groups of widely dispersed size. This article models collective action problems as two-strategy multiplayer games and studies the effect of variability in group size on the evolution of cooperative behavior under the replicator dynamics. The analysis identifies elementary conditions on the payoff structure of the game implying that the evolution of cooperative behavior is promoted or inhibited when the group size experienced by a focal player is more or less variable. Similar but more stringent conditions are applicable when the confounding effect of size-biased sampling, which causes the group-size distribution experienced by a focal player to differ from the statistical distribution of group sizes, is taken into account.