Models in animal collective decision-making: information uncertainty and conflicting preferences

Abstract

Collective decision-making plays a central part in the lives of many social animals. Two important factors that influence collective decision-making are information uncertainty and conflicting preferences. Here, I bring together, and briefly review, basic models relating to animal collective decision-making in situations with information uncertainty and in situations with conflicting preferences between group members. The intention is to give an overview about the different types of modelling approaches that have been employed and the questions that they address and raise. Despite the use of a wide range of different modelling techniques, results show a coherent picture, as follows. Relatively simple cognitive mechanisms can lead to effective information pooling. Groups often face a trade-off between decision accuracy and speed, but appropriate fine-tuning of behavioural parameters could achieve high accuracy while maintaining reasonable speed. The right balance of interdependence and independence between animals is crucial for maintaining group cohesion and achieving high decision accuracy. In conflict situations, a high degree of decision-sharing between individuals is predicted, as well as transient leadership and leadership according to needs and physiological status. Animals often face crucial trade-offs between maintaining group cohesion and influencing the decision outcome in their own favour. Despite the great progress that has been made, there remains one big gap in our knowledge: how do animals make collective decisions in situations when information uncertainty and conflict of interest operate simultaneously?

Keywords: collective decisions; game-theory models; self-organizing systems.

Figure 1.

Example of a quorum response. Grey line shows the quorum response (with m = 5, B = 10); black symbols are simulated data assuming a simple step response by animals (i.e. p = 0 for A < 10 and p = 1 for A > 10) and that animals estimate the size of A with a normal-distributed error (with μ = 0 and σ = 2; note that the error was bounded so that the estimate cannot become negative).

Figure 2.

Accuracy with which the self-organized group moves in the profitable direction as a function of the number of informed animals within the group. The black solid lines in both graphs show the simulated accuracy in self-organized movements by groups of size (a) n = 200 and (b) n = 10 (after Couzin et al. [10]; note that their measure of accuracy has been rescaled to render possible comparisons with Condorcet accuracy). The grey lines give Condorcet accuracies for juries with the same number of jurors as there were informed animals in the group (note that the slight oscillations arise because juries with odd and even numbers of jurors are included), whereby the dashed grey lines assume an individual juror accuracy equivalent to the effective accuracy of a group in which only one individual is informed ((a) p = 0.53; (b) p = 0.68; lower boundary of comparable Condorcet jury accuracies) and the solid grey lines assume an individual juror accuracy that best fits the simulated group accuracy when there are many informed individuals ((a,b) p = 0.83 in both cases; upper boundary of comparable Condorcet jury accuracies). If the number of informed individuals within a group is very low, the decision accuracy of the self-organized group is poor (solid black line). However, decision accuracy increases much more steeply with the number of informed individuals than does the accuracy in comparable Condorcet juries. Therefore, already from a relatively moderate number of informed individuals onwards (6+ in groups of 200; 2+ in groups of 10), the self-organized groups make decisions that are similar in accuracy to those of Condorcet juries, which consist of relatively well-informed individuals.

Figure 3.

Illustration of a collective consensus decision about the timing of a group activity change. Time runs from left to right on the axis. A group of size n starts a group activity at time t = 0. Each individual group member has its own personal optimal time t_i for changing activity. The group changes activity collectively at one time. If the decision about this time is made unshared by a single dictator (e.g. the dominant), the group changes group activity at the time that is optimal to the dictator (t_dictator). If the decision is made shared (by a ‘majority vote’), the group changes activity when the majority of animals prefer to do so (i.e. at time t(n + 1)/2). The ‘consensus cost’ to an individual (which arises if the individual changes activity at a time that is different from its personal optimal time) increases with the difference between its optimal time and the actual time at which the group (including the individual) changes activity (indicated here by arrows for individual 2). The expected net costs to a group in a dictatorial decision are: and in a shared decision: whereby f(Δt) are the fitness costs to an individual of changing activity at a time that is different by Δt from its own optimal time.

Figure 4.

Predictions of the behaviour of two foragers as a function of their energy reserves according to the leader–follower model (after Rands et al. [33]).

Figure 5.

Best mutual strategies of individuals in pair synchronizations depending on the synchronization costs relative to grouping benefits (horizontal axis) and whether the costs are higher for departing too early or too late (vertical axis; after Dostálková & Špinka [27]). If the synchronization costs are large relative to grouping benefits, full synchronization might no longer be the best strategy. If departing too early is less costly than departing too late, animals should be ready to depart before their optimal time but not wait beyond it. If departing too late is less costly than departing too early, animals should be ready to depart before their optimal time but also to wait beyond it.

Figure 6.

Phenotypic evolution of decision-making about activity synchronization in groups of three (after Conradt & Roper [78]). Each trilinear coordinate system (TCS) represents populations consisting of three different phenotypes. Different TCSs are shown closely together to indicate the overall dynamics. Arrows show the directions in which the system evolves. Broken arrows indicate where the system evolves from one TCS to another. For clarity, in shaded areas, the direction of evolution is not shown, and the dynamics shown are not exhaustive (e.g. substituting ‘sub-majority’ for ‘super-majority’ phenotypes leads to similar dynamics).

Figure 7.

Schematic of the predictions following from the group-of-three model on synchronisation of movement destinations (after Conradt & Roper 2009 [80]). The area above the dotted line refers to groups that are above optimal group size; the area below the dotted line refers to groups of suboptimal group size.

Figure 8.

The proportion of birds in a flock that have landed as a function of time and of interdependence between neighbouring birds (after Bhattacharya & Vicsek [83]). If the interdependence factor between birds J is zero, all birds land independently of each other at their optimal times (solid line). If the interdependence factor is medium (dashed line) or large (dotted line), the landing slope is steeper and the flock's landing is much more synchronized. However, the larger the interdependence factor J, the later the average landing time (see main text for further details).