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A simple threshold rule is sufficient to explain sophisticated collective decision-making.

Robinson EJ, Franks NR, Ellis S, Okuda S, Marshall JA - PLoS ONE (2011)

Bottom Line: This highlights the need to carefully design experiments to detect individual comparison.We present empirical data strongly suggesting that best-of-n comparison is not used by individual ants, although individual sequential comparisons are not ruled out.This parsimonious mechanism could promote collective rationality in group decision-making.

View Article: PubMed Central - PubMed

Affiliation: School of Biological Sciences, University of Bristol, Bristol, United Kingdom. Elva.Robinson@yccsa.org

ABSTRACT
Decision-making animals can use slow-but-accurate strategies, such as making multiple comparisons, or opt for simpler, faster strategies to find a 'good enough' option. Social animals make collective decisions about many group behaviours including foraging and migration. The key to the collective choice lies with individual behaviour. We present a case study of a collective decision-making process (house-hunting ants, Temnothorax albipennis), in which a previously proposed decision strategy involved both quality-dependent hesitancy and direct comparisons of nests by scouts. An alternative possible decision strategy is that scouting ants use a very simple quality-dependent threshold rule to decide whether to recruit nest-mates to a new site or search for alternatives. We use analytical and simulation modelling to demonstrate that this simple rule is sufficient to explain empirical patterns from three studies of collective decision-making in ants, and can account parsimoniously for apparent comparison by individuals and apparent hesitancy (recruitment latency) effects, when available nests differ strongly in quality. This highlights the need to carefully design experiments to detect individual comparison. We present empirical data strongly suggesting that best-of-n comparison is not used by individual ants, although individual sequential comparisons are not ruled out. However, by using a simple threshold rule, decision-making groups are able to effectively compare options, without relying on any form of direct comparison of alternatives by individuals. This parsimonious mechanism could promote collective rationality in group decision-making.

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Comparison between empirical and simulated recruitment latency results where new nests are equidistant.Empirical and simulated recruitment latencies (solid line = good nest; dashed line = poor nest). The latency between entry and recruitment (mean ± SD), and the number of ants analysed, are shown next to the corresponding survivorship curve. (A–F) Empirical results with nests presented separately, reproduced from Figure 4, Mallon et al. [20] with permission of Springer Science and Business Media. Recruitment latencies to the poor nest are significantly greater in four of six colonies (generalised logrank test). (G–L) Simulated recruitment latencies, nests presented separately. Recruitment latencies to the poor nest are significantly greater. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with significant differences between recruitment latencies in 95% (Colony 5) or 100% (Colonies 1–4 and 6) of simulations. (M–R) Simulated recruitment latencies, nests presented together. There are no longer any significant differences between recruitment latencies. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with no significant difference between recruitment latencies in 96% (Colony 1), 93% (Colony 2), 90% (Colony 3) 90% (Colony 4), 96% (Colony 5) 93% (Colony 6) of simulations.
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pone-0019981-g005: Comparison between empirical and simulated recruitment latency results where new nests are equidistant.Empirical and simulated recruitment latencies (solid line = good nest; dashed line = poor nest). The latency between entry and recruitment (mean ± SD), and the number of ants analysed, are shown next to the corresponding survivorship curve. (A–F) Empirical results with nests presented separately, reproduced from Figure 4, Mallon et al. [20] with permission of Springer Science and Business Media. Recruitment latencies to the poor nest are significantly greater in four of six colonies (generalised logrank test). (G–L) Simulated recruitment latencies, nests presented separately. Recruitment latencies to the poor nest are significantly greater. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with significant differences between recruitment latencies in 95% (Colony 5) or 100% (Colonies 1–4 and 6) of simulations. (M–R) Simulated recruitment latencies, nests presented together. There are no longer any significant differences between recruitment latencies. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with no significant difference between recruitment latencies in 96% (Colony 1), 93% (Colony 2), 90% (Colony 3) 90% (Colony 4), 96% (Colony 5) 93% (Colony 6) of simulations.

Mentions: For the Monte-Carlo simulations, we model nest quality acceptance thresholds in the colony as a normally distributed random variable A, with some mean and variance. An individual simulated ant has a quality acceptance threshold a drawn at random from this distribution. It discovers its next nest by sampling from a probability distribution specified by its current nest, arena size and shape, and the proximities of other available nest sites (Table 1); part of this distribution is determined by the probability r that a randomly searching scout rediscovers the site it has just been in. On discovering a site, the scout evaluates the quality of the current nest site with some error ε added, sampled from a standard normal distribution (mean 0; standard deviation 1); this corresponds to error in the scout's quality assessment. If this sampled quality exceeds the scout's acceptance threshold then it becomes committed to the site, otherwise it continues searching (Fig. 2). Acceptance threshold distributions and nest qualities are given arbitrary values (Table 1), because individual probabilities of becoming committed to a nest are hard to estimate empirically, due to the difficulties in accurately identifying commitment and in eliminating the effects of interactions between ants. In the model, travel times between sites are sampled from normal distributions. By parameterizing this model to empirical ant movement speed and specific experimental arenas (Table 1), we can approximate the expected time for each simulated ant to find each nest, and the time from first finding a nest to becoming committed to it (the ant may visit other nests in between, or visit the same nest many times before committing to it). This allows us to calculate recruitment latencies for comparison with empirical data. In the empirical studies, recruitment latency concerns the time from discovering a nest to first recruiting to that nest. We do not include recruitment in the model, so modelled recruitment latency concerns the time from discovering a nest to ‘accepting’ that nest. For real ant colonies, searching behaviour is much reduced when quorum is achieved; we truncate the simulated data at the time at which quorum was achieved in the real experiment, to increase comparability (see Text S1).


A simple threshold rule is sufficient to explain sophisticated collective decision-making.

Robinson EJ, Franks NR, Ellis S, Okuda S, Marshall JA - PLoS ONE (2011)

Comparison between empirical and simulated recruitment latency results where new nests are equidistant.Empirical and simulated recruitment latencies (solid line = good nest; dashed line = poor nest). The latency between entry and recruitment (mean ± SD), and the number of ants analysed, are shown next to the corresponding survivorship curve. (A–F) Empirical results with nests presented separately, reproduced from Figure 4, Mallon et al. [20] with permission of Springer Science and Business Media. Recruitment latencies to the poor nest are significantly greater in four of six colonies (generalised logrank test). (G–L) Simulated recruitment latencies, nests presented separately. Recruitment latencies to the poor nest are significantly greater. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with significant differences between recruitment latencies in 95% (Colony 5) or 100% (Colonies 1–4 and 6) of simulations. (M–R) Simulated recruitment latencies, nests presented together. There are no longer any significant differences between recruitment latencies. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with no significant difference between recruitment latencies in 96% (Colony 1), 93% (Colony 2), 90% (Colony 3) 90% (Colony 4), 96% (Colony 5) 93% (Colony 6) of simulations.
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pone-0019981-g005: Comparison between empirical and simulated recruitment latency results where new nests are equidistant.Empirical and simulated recruitment latencies (solid line = good nest; dashed line = poor nest). The latency between entry and recruitment (mean ± SD), and the number of ants analysed, are shown next to the corresponding survivorship curve. (A–F) Empirical results with nests presented separately, reproduced from Figure 4, Mallon et al. [20] with permission of Springer Science and Business Media. Recruitment latencies to the poor nest are significantly greater in four of six colonies (generalised logrank test). (G–L) Simulated recruitment latencies, nests presented separately. Recruitment latencies to the poor nest are significantly greater. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with significant differences between recruitment latencies in 95% (Colony 5) or 100% (Colonies 1–4 and 6) of simulations. (M–R) Simulated recruitment latencies, nests presented together. There are no longer any significant differences between recruitment latencies. Empirical number of ants is matched for each colony. Sample graphs are shown; running 100 replicates of each gives the same pattern of results, with no significant difference between recruitment latencies in 96% (Colony 1), 93% (Colony 2), 90% (Colony 3) 90% (Colony 4), 96% (Colony 5) 93% (Colony 6) of simulations.
Mentions: For the Monte-Carlo simulations, we model nest quality acceptance thresholds in the colony as a normally distributed random variable A, with some mean and variance. An individual simulated ant has a quality acceptance threshold a drawn at random from this distribution. It discovers its next nest by sampling from a probability distribution specified by its current nest, arena size and shape, and the proximities of other available nest sites (Table 1); part of this distribution is determined by the probability r that a randomly searching scout rediscovers the site it has just been in. On discovering a site, the scout evaluates the quality of the current nest site with some error ε added, sampled from a standard normal distribution (mean 0; standard deviation 1); this corresponds to error in the scout's quality assessment. If this sampled quality exceeds the scout's acceptance threshold then it becomes committed to the site, otherwise it continues searching (Fig. 2). Acceptance threshold distributions and nest qualities are given arbitrary values (Table 1), because individual probabilities of becoming committed to a nest are hard to estimate empirically, due to the difficulties in accurately identifying commitment and in eliminating the effects of interactions between ants. In the model, travel times between sites are sampled from normal distributions. By parameterizing this model to empirical ant movement speed and specific experimental arenas (Table 1), we can approximate the expected time for each simulated ant to find each nest, and the time from first finding a nest to becoming committed to it (the ant may visit other nests in between, or visit the same nest many times before committing to it). This allows us to calculate recruitment latencies for comparison with empirical data. In the empirical studies, recruitment latency concerns the time from discovering a nest to first recruiting to that nest. We do not include recruitment in the model, so modelled recruitment latency concerns the time from discovering a nest to ‘accepting’ that nest. For real ant colonies, searching behaviour is much reduced when quorum is achieved; we truncate the simulated data at the time at which quorum was achieved in the real experiment, to increase comparability (see Text S1).

Bottom Line: This highlights the need to carefully design experiments to detect individual comparison.We present empirical data strongly suggesting that best-of-n comparison is not used by individual ants, although individual sequential comparisons are not ruled out.This parsimonious mechanism could promote collective rationality in group decision-making.

View Article: PubMed Central - PubMed

Affiliation: School of Biological Sciences, University of Bristol, Bristol, United Kingdom. Elva.Robinson@yccsa.org

ABSTRACT
Decision-making animals can use slow-but-accurate strategies, such as making multiple comparisons, or opt for simpler, faster strategies to find a 'good enough' option. Social animals make collective decisions about many group behaviours including foraging and migration. The key to the collective choice lies with individual behaviour. We present a case study of a collective decision-making process (house-hunting ants, Temnothorax albipennis), in which a previously proposed decision strategy involved both quality-dependent hesitancy and direct comparisons of nests by scouts. An alternative possible decision strategy is that scouting ants use a very simple quality-dependent threshold rule to decide whether to recruit nest-mates to a new site or search for alternatives. We use analytical and simulation modelling to demonstrate that this simple rule is sufficient to explain empirical patterns from three studies of collective decision-making in ants, and can account parsimoniously for apparent comparison by individuals and apparent hesitancy (recruitment latency) effects, when available nests differ strongly in quality. This highlights the need to carefully design experiments to detect individual comparison. We present empirical data strongly suggesting that best-of-n comparison is not used by individual ants, although individual sequential comparisons are not ruled out. However, by using a simple threshold rule, decision-making groups are able to effectively compare options, without relying on any form of direct comparison of alternatives by individuals. This parsimonious mechanism could promote collective rationality in group decision-making.

Show MeSH
Related in: MedlinePlus