Research Article

Ecology

Naïve individuals promote collective exploration in homing pigeons

Arizona State University, School of Earth and Space Exploration, United States
Arizona State University, School of Life Sciences, United States
Arizona State University, Beyond Center for Fundamental Concepts in Science, United States
Arizona State University, School of Computing and Augmented Intelligence, United States
Arizona State University, School of Sustainability, United States
Arizona State University, School of Complex Adaptive Systems, United States
Arizona State University, ASU–SFI Center for Biosocial Complex Systems, United States
Santa Fe Institute, United States
University of Oxford, Department of Zoology, United States
University of Rochester, Department of Brain and Cognitive Sciences, United States
University of Georgia, Odum School of Ecology, United States

Dec 20, 2021

https://doi.org/10.7554/eLife.68653

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Figures
Tables
Additional files

10 figures, 9 tables and 1 additional file

Figures

Figure 1

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Illustration of the methodological approach.

The spatial trajectories of an experienced (E) and a naïve (N) bird (point 1) are encoded as clockwise and counterclockwise rotations (point 2) which we represent as discrete time series (point 3). The combination of rotations encoded in both series (point 4) is used to estimate the probabilities required to compute transfer entropy (point 5) and to determine the influence of one individual over the future behaviour of the other (point 6). This example illustrates transfer entropy from experienced to naïve, but we also computed it for the opposite direction.

Figure 2

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Predictive power of birds over generations.

Panel (a) shows the net predictive power of the two birds over generations; it measures the excess predictive information within the pair and highlights which of the two birds is more informative (purple for the experienced bird, green for the naïve bird). The red line corresponds to a linear fit over generations using the Theil–Sen estimator. Panel (b) shows the predictive power of naïve and experienced birds separately from each other as a function of generations. The predictive power of a bird with respect to the other is measured in terms of the percentage reduction in uncertainty, and it has been computed on the basis of transfer entropy as detailed in Materials and methods.

Figure 3

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Predictive power of birds as a function of relative distance.

Panel (a) shows sample flight trajectories for a number of different releases, r, of the same pair of birds. Colours highlight which bird is ahead of the other during different segments of the route. Panel (b) shows the local transfer of information (mean and 95% confidence interval) between the experienced bird and the naïve one as a function of their relative distance (colours represent the direction of information transfer) estimated from generations 2–5 using smoothed conditional means.

Figure 4

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Analysis of exploration and exploitation.

Panel (a) shows the proportion of exploration over releases for the experimental group (the red dotted vertical line separates solo flights at generation 1 from paired flights at generations 2–5), the solo control, and the fixed-pairs control. Smoothed lines are computed using generalized additive models using shrinkage cubic regression splines (mean and standard error); points represent averages for individual releases. Panel (b) shows the proportion of a flight led by each bird during phases of exploration and exploitation in the experimental treatment. Darker colours correspond to exploitation, lighter colours to exploration; purple represents the experienced bird, green the naïve one; red lines represent linear fits to data pooled from both birds using the Theil–Sen estimator (slopes and p-values: respectively, 0.0203, p<0.001 for exploitation and –0.0171, p=0 for exploration). Panel (c) shows the probability for the naïve individual to initiate phases of exploration over releases (exact binomial test, p<0.01 for release 1). The dotted vertical line separates the first release, where the naïve bird was significantly more likely to initiate, from the successive releases 2–12 showing no significant difference between the two birds; the red line provides a visual reference indicating an equal likelihood between the two birds to initiate exploration.

Appendix 1—figure 1

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Landscape of information transfer as a function of the history length, k = ∈ {1, ... ,17}, and of the sampling period, {0.2, 0.4, ... , 4.0} s.

Panel (a) shows the total transfer of information between the pair of birds, $T_{E \to N} + T_{N \to E}$ , averaged over all releases and generations. Panel (b) shows the net transfer of information between thepair of birds, $T_{E \to N} - T_{N \to E}$ , averaged over all releases and generations. Positive (respectively, negative) values represent configurations where the experienced (naïve) bird is more informative than the naïve (experienced) one. The triangle represents the configuration with maximum total transfer of information.

Appendix 1—figure 2

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Probability density function of the duration of flight segments with either the experienced or the naïve bird at the front of the pair.

Panel (a) shows the results aggregated over all generations. Panel (b) shows the results separately for each generation.

Appendix 1—figure 3

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Distribution of minimum distances between the pairs of consecutive flights.

Panel (a) shows the results for the trained birds during the first generation of the experiment. Panel (b) shows the results for the pair of birds during all remaining generations of the experiments. Vertical lines highlight the division of the probability mass between exploitation (left) and exploration (right) defined by a 300 m threshold.

Appendix 1—figure 4

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Illustration of the distribution of point-to-point distances between pairs of consecutive flights highlighting the 300 m threshold that demarks the end of exploitation and the beginning on exploration.

Panel (a) reports the results for experimental pairs over generations 2–5, panel (b) reports those for the fixed-pairs control, and panel (c) those for the solo control. Panel (d) shows the proportion of times experienced (purple) and naïve (green) birds are leading the flock as a function of the distance between the current and the previous trajectory. The red line indicates an equal likelihood between the two birds to lead the flock.

Appendix 1—figure 5

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Illustration of the distribution of point-to-point distances between each flight of a generation (focal trajectories) and the last flight of the previous generation (baseline trajectory).

Colors and vertical lines highlight the 300 meter threshold that demarks the end of exploitation and the beginning of exploration. Panel (a) reports the results for experimental pairs over generations 2–5, panel (b) reports those for the fixed pairs control, and panel (c) those for the solo control.

Appendix 1—figure 6

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Illustration of the proportion of exploration (respectively, one minus the proportion of exploitation) over releases when considering the last release at the previous generation as the baseline trajectory.

Results are shown for the experimental group, the solo control, and the fixed pairs control. The red dotted vertical line delineates the end of the experimental group’s training phase. Smoothed lines are computed with generalized additive models using shrinkage cubic regression splines (mean and standard error); points represent averages for individual releases.

Tables

Appendix 1—table 1

Statistical comparison of information transfer between the original and the surrogate dataset over all generations and over separate generations.

Column 1 reports the generation and sample sizes. Columns 2 and 4 report the differences between the mean value of transfer entropy of the original dataset and that of the surrogate dataset. Columns 3 and 5 report the results of one-sided two-sample Whitney–Mann–Wilcoxon rank-sum tests with continuity correction (p-value and W statistic) testing if the original dataset has significantly higher transfer entropy than the surrogate one. Significant p-values are reported in bold.

Original vs. surrogate dataset
Generation	$T_{E \to N} - T_{E \to N}^{s}$	$H_{1} : T_{E \to N} §amp;gt; T_{E \to N}^{s}$	$T_{N \to E} - T_{N \to E}^{s}$	$H_{1} : T_{N \to E} §amp;gt; T_{N \to E}^{s}$
$A l l (n = 343, n^{s} = 29035)$	$μ = 0.0089$	$p < .001 (W = 6145522)$	$μ = 0.0088$	$p < .001 (W = 6126284)$
$2 (n = 94, n^{s} = 7912)$	$μ = 0.0062$	$p < .001 (W = 445262)$	$μ = 0.0074$	$p < .001 (W = 452733)$
$3 (n = 99, n^{s} = 9801)$	$μ = 0.0094$	$p < .001 (W = 615721.5)$	$μ = 0.0119$	$p < .001 (W = 645665.5)$
$4 (n = 81, n^{s} = 6561)$	$μ = 0.0071$	$p = .006 (W = 308433.5)$	$μ = 0.0057$	$p = .015 (W = 303085.5)$
$5 (n = 69, n^{s} = 4761)$	$μ = 0.0111$	$p < .001 (W = 214258.5)$	$μ = 0.0075$	$p = .002 (W = 197618.5)$

Appendix 1—table 2

Statistics for the duration of flight segments with either the experienced or the naïve bird at the front of the pair.

Column 1 reports the generation and sample sizes. Columns 2 and 3 give the mean duration and the standard deviation of segments for the experienced and the naïve bird. Column 4 reports the results of two-sided two-sample Whitney–Mann–Wilcoxon rank-sum tests with continuity correction (p-value and W statistic) testing differences between the distribution D of the duration of flight segments for the two birds. Significant p-values are reported in bold.

Generation	Experienced	Naïve	$H_{1} : D_{E} \neq D_{N}$
$A l l (n^{E} = 10725, n^{N} = 10773)$	$μ = 7.93, σ = 12.92$	$μ = 8.23, σ = 14.12$	$p = .047 (W = 56865638)$
$2 (n^{E} = 2512, n^{N} = 2492)$	$μ = 8.89, σ = 17.51$	$μ = 8.81, σ = 13.55$	$p = . 13 (W = 3052262)$
$3 (n^{E} = 3690, n^{N} = 3737)$	$μ = 6.83, σ = 9.08$	$μ = 7.96, σ = 14.51$	$p < .001 (W = 6588674)$
$4 (n^{E} = 2297 n^{N} = 2283)$	$μ = 8.63, σ = 13.65$	$μ = 8.55, σ = 14.23$	$p = . 86 (W = 2630132)$
$5 (n^{E} = 2226, n^{N} = 2261)$	$μ = 7.98, σ = 11.23$	$μ = 7.73, σ = 13.93$	$p = . 23 (W = 2568854)$

Appendix 1—table 3

Statistics for the proportion of a flight with either the experienced or the naïve bird at the front of the pair.

Column 1 reports the generation and sample size. Columns 2 and 3 give the mean and the standard deviation of the proportion of a flight with either the experienced or the naïve bird at the front of the pair. Column 4 reports the results of two-sided paired Wilcoxon signed-rank tests with continuity correction (p-value and V statistic) testing differences between the distribution of the proportion P of a flight for the two birds. Significant p-values are reported in bold.

Generation	Experienced	Naïve	$H_{1} : P_{E} \neq P_{N}$
$A l l (n = 341)$	$μ = 0.49, σ = 0.2$	$μ = 0.51, σ = 0.2$	$p = . 46 (V = 27817.5)$
$2 (n = 92)$	$μ = 0.51, σ = 0.23$	$μ = 0.49, σ = 0.23$	$p = . 69 (V = 2243)$
$3 (n = 99)$	$μ = 0.46, σ = 0.17$	$μ = 0.54, σ = 0.17$	$p = .03 (V = 1851)$
$4 (n = 81)$	$μ = 0.5, σ = 0.2$	$μ = 0.5, σ = 0.2$	$p = . 84 (V = 1705)$
$5 (n = 69)$	$μ = 0.49, σ = 0.2$	$μ = 0.51, σ = 0.2$	$p = . 95 (V = 1219)$

Appendix 1—table 4

Statistical comparison of mean proportions of a flight spent exploring versus exploiting across treatments (experimental pairs, solo, and fixed-pairs controls) for the first 12 releases (generation 1) and for releases 13–60 (generation 2–5).

Entries report the proportion of exploration vs. exploitation for pairs of treatments as well as the results of two-sided two-sample Whitney–Mann–Wilcoxon rank-sum tests with continuity correction (p-value and W statistic) for differences in proportion of exploration. Significant p-values are reported in bold. Results of testing for the proportion of exploitation are equivalent and not repeated below.

Releases	Dataset	Solo control	Fixed-pairs control
1–12	Experimental (generation 1)	Row: 36.7% vs. 63.3%Col: 34.2% vs. 65.8%	Row: 36.7% vs. 63.3%Col: 51.7% vs. 48.3% p <. 001 (W = 2230)
1–12	Solo control	–	Row: 36.7% vs. 63.3%Col: 34.2% vs. 65.8% p <.001 (W=1837)
13–60	Experimental (generations 2–5)	Row: 32.9% vs. 67.1%Col: 15.7% vs. 84.3%	Row: 32.9% vs. 67.1%Col: 29.3% vs. 70.7% p=.0456 (W=50472)
13–60	Solo control	–	Row: 15.7% vs. 84.3%Col: 29.3% vs. 70.7% p<.001 (W=31517)

Appendix 1—table 5

Statistical comparison of mean proportions of a flight spent exploring versus exploiting across treatments (experimental pairs, solo and fixed pairs controls) for the first 12 releases (generation 1) and for releases 13–60 (generation 2–5) when considering the last release at the previous generation as the baseline trajectory.

Entries report the proportion of exploration vs exploitation for pairs of treatments as well as the results of two-sided two-sample Whitney–Mann–Wilcoxon rank-sum tests with continuity correction (-value and statistic) for differences in proportion of exploration. Significant -values are reported in bold. Results of testing for the proportion of exploitation are equivalent and not repeated below.

Releases	Dataset	Solo control	Fixed pairs control
1–12	Experimental (gen. 1)	Row: 61.5 % vs 38.5%Col: 55.8 % vs 44.2%	Row: 61.5 % vs 38.5%Col: 82.9 % vs 17.1%
1–12	Solo control	–	Row: 55.8 % vs 44.2%Col: 82.9 % vs 17.1%
13–60	Experimental (gen. 2–5)	Row: 46.6 % vs 53.4%Col: 18.9 % vs 81.1%	Row: 46.6 % vs 53.4%Col: 32.4 % vs 67.6%
13–60	Solo control	–	Row: 18.9 % vs 81.1%Col: 32.4 % vs 67.6%

Appendix 1—table 6

Proportion of a flight led by each of the two birds, calculated separately for exploration and exploitation phases.

Column one reports the generation and sample size. Columns 2 and 3 give the mean and the standard deviation of the proportion of a flight led, respectively, by the experienced and the naïve bird for the case of exploration. Columns 4 and 5 give the mean and the standard deviation of the proportion of a flight led, respectively, by the experienced and the naïve bird for the case of exploitation.

	Exploration		Exploitation
Generation	Experienced	Naïve	Experienced	Naïve
$A l l (n = 341)$	$μ = 0.17, σ = 0.15$	$μ = 0.16, σ = 0.13$	$μ = 0.32, σ = 0.18$	$μ = 0.35, σ = 0.2$
$2 (n = 92)$	$μ = 0.2, σ = 0.17$	$μ = 0.17, σ = 0.14$	$μ = 0.31, σ = 0.2$	$μ = 0.32, σ = 0.21$
$3 (n = 99)$	$μ = 0.16, σ = 0.13$	$μ = 0.19, σ = 0.13$	$μ = 0.3, σ = 0.16$	$μ = 0.36, σ = 0.17$
$4 (n = 81)$	$μ = 0.18, σ = 0.16$	$μ = 0.16, σ = 0.13$	$μ = 0.32, σ = 0.18$	$μ = 0.34, σ = 0.22$
$(n = 69)$	$μ = 0.13, σ = 0.13$	$μ = 0.1, σ = 0.1$	$μ = 0.37, σ = 0.17$	$μ = 0.4, σ = 0.21$

Appendix 1—table 7

Statistical comparison of leadership by experienced vs. naïve birds, tested separately for exploration and exploitation over all generations and over separate generations.

Column one reports the generation and sample size. Columns 2 and 3 report the results of two-sided paired Wilcoxon signed-rank tests with continuity correction (-value and statistic) for differences in proportion of flight led between experienced and naïve birds for exploration and exploitation, respectively. Significant -values are reported in bold.

	Experienced vs naïve
Generation	Exploration	Exploitation
$A l l (n = 341)$	$p = . 44 (V = 28820)$	$p = . 13 (V = 26240)$
$2 (n = 92)$	$p = . 17 (V = 2490)$	$p = . 71 (V = 2048)$
$3 (n = 99)$	$p = . 08 (V = 1891)$	$p = .035 (V = 1871)$
$4 (n = 81)$	$p = . 36 (V = 1767)$	$p = . 79 (V = 1603)$
$5 (n = 69)$	$p = . 22 (V = 1187)$	$p = . 8 (V = 1131)$

Appendix 1—table 8

Statistical comparison of the proportion of transitions from exploitation to exploration and from exploration to exploitation led by the experienced and by the naïve bird over generations.

Column one reports the generation number. Columns 2 and 4 report the estimated probabilities that transitions are led by the experienced bird,, and by the naïve bird,, for transitions, respectively, from exploitation to exploration and from exploration to exploitation. Columns 3 and 5 give the results of exact binomial tests (-value and sample size) of the null hypothesis that the probability that transitions are led by the experienced bird equals 0.5. Significant -values are reported in bold.

	Exploitation → Exploration		Exploration → Exploitation
Generation	$P_{E}$ versus $P_{N}$	$H_{1} : P_{E} \neq 0.5$	$P_{E}$ versus $P_{N}$	$H_{1} : P_{E} \neq 0.5$
All	$P_{E} = 0.467, P_{N} = 0.533$	$p = .042 (n = 964)$	$P_{E} = 0.513, P_{N} = 0.487$	$p = . 42 (n = 966)$
2	$P_{E} = 0.494, P_{N} = 0.506$	$p = . 9 (n = 247)$	$P_{E} = 0.52, P_{N} = 0.48$	$p = . 56 (n = 244)$
3	$P_{E} = 0.432, P_{N} = 0.568$	$p = .02 (n = 301)$	$P_{E} = 0.483, P_{N} = 0.517$	$p = . 6 (n = 300)$
4	$P_{E} = 0.5, P_{N} = 0.5$	$p = 1 (n = 216)$	$P_{E} = 0.539, P_{N} = 0.461$	$p = . 28 (n = 219)$
5	$P_{E} = 0.45, P_{N} = 0.55$	$p = . 18 (n = 200)$	$P_{E} = 0.522, P_{N} = 0.478$	$p = . 57 (n = 203)$

Appendix 1—table 9

Statistical comparison of the proportion of transitions from exploitation to exploration and from exploration to exploitation led by the experienced and by the naïve bird over releases.

Column one reports the release number. Columns 2 and 4 report the estimated probabilities that transitions are led by the experienced bird,, and by the naïve bird,, for transitions, respectively, from exploitation to exploration and from exploration to exploitation. Columns 3 and 5 give the results of exact binomial tests (-value and sample size) of the null hypothesis that the probability that transitions are led by the experienced bird equals 0.5. Significant -values are reported in bold.

	Exploitation → Exploration		Exploration → Exploitation
Release	$P_{E}$ versus $P_{N}$	$H_{1} : P_{E} \neq 0.5$	$P_{E}$ versus $P_{N}$	$H_{1} : P_{E} \neq 0.5$
1	$P_{E} = 0.295, P_{N} = 0.705$	$p < .01 (n = 44)$	$P_{E} = 0.477, P_{N} = 0.523$	$p = . 88 (n = 44)$
2	$P_{E} = 0.478, P_{N} = 0.522$	$p = . 81 (n = 69)$	$P_{E} = 0.522, P_{N} = 0.478$	$p = . 81 (n = 67)$
3	$P_{E} = 0.519, P_{N} = 0.481$	$p = . 83 (n = 81)$	$P_{E} = 0.575, P_{N} = 0.425$	$p = . 22 (n = 80)$
4	$P_{E} = 0.576, P_{N} = 0.424$	$p = . 27 (n = 66)$	$P_{E} = 0.6, P_{N} = 0.4$	$p = . 14 (n = 65)$
5	$P_{E} = 0.487, P_{N} = 0.513$	$p = . 91 (n = 76)$	$P_{E} = 0.519, P_{N} = 0.481$	$p = . 82 (n = 77)$
6	$P_{E} = 0.54, P_{N} = 0.46$	$p = . 48 (n = 100)$	$P_{E} = 0.465, P_{N} = 0.535$	$p = . 55 (n = 99)$
7	$P_{E} = 0.443, P_{N} = 0.557$	$p = . 34 (n = 88)$	$P_{E} = 0.494, P_{N} = 0.506$	$p = 1.0 (n = 89)$
8	$P_{E} = 0.409, P_{N} = 0.591$	$p = . 18 (n = 66)$	$P_{E} = 0.597, P_{N} = 0.403$	$p = . 14 (n = 67)$
9	$P_{E} = 0.438, P_{N} = 0.562$	$p = . 22 (n = 112)$	$P_{E} = 0.496, P_{N} = 0.504$	$p = 1 (n = 115)$
10	$P_{E} = 0.422, P_{N} = 0.578$	$p = . 17 (n = 90)$	$P_{E} = 0.522, P_{N} = 0.478$	$p = . 75 (n = 92)$
11	$P_{E} = 0.391, P_{N} = 0.609$	$p = . 053 (n = 87)$	$P_{E} = 0.453, P_{N} = 0.547$	$p = . 45 (n = 86)$
12	$P_{E} = 0.541, P_{N} = 0.459$	$p = . 52 (n = 85)$	$P_{E} = 0.482, P_{N} = 0.518$	$p = . 83 (n = 85)$

Additional files

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Gabriele Valentini
Theodore P Pavlic
Sara Imari Walker
Stephen C Pratt
Dora Biro
Takao Sasaki

(2021)

Naïve individuals promote collective exploration in homing pigeons

eLife 10:e68653.

https://doi.org/10.7554/eLife.68653

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Illustration of the methodological approach.

Predictive power of birds over generations.

Predictive power of birds as a function of relative distance.

Analysis of exploration and exploitation.

Landscape of information transfer as a function of the history length, k = ∈ {1, ... ,17}, and of the sampling period, {0.2, 0.4, ... , 4.0} s.

Probability density function of the duration of flight segments with either the experienced or the naïve bird at the front of the pair.

Distribution of minimum distances between the pairs of consecutive flights.

Illustration of the distribution of point-to-point distances between pairs of consecutive flights highlighting the 300 m threshold that demarks the end of exploitation and the beginning on exploration.

Illustration of the distribution of point-to-point distances between each flight of a generation (focal trajectories) and the last flight of the previous generation (baseline trajectory).

Illustration of the proportion of exploration (respectively, one minus the proportion of exploitation) over releases when considering the last release at the previous generation as the baseline trajectory.

Statistical comparison of information transfer between the original and the surrogate dataset over all generations and over separate generations.

Statistics for the duration of flight segments with either the experienced or the naïve bird at the front of the pair.

Statistics for the proportion of a flight with either the experienced or the naïve bird at the front of the pair.

Statistical comparison of mean proportions of a flight spent exploring versus exploiting across treatments (experimental pairs, solo, and fixed-pairs controls) for the first 12 releases (generation 1) and for releases 13–60 (generation 2–5).

Proportion of a flight led by each of the two birds, calculated separately for exploration and exploitation phases.

Statistical comparison of leadership by experienced vs. naïve birds, tested separately for exploration and exploitation over all generations and over separate generations.

Statistical comparison of the proportion of transitions from exploitation to exploration and from exploration to exploitation led by the experienced and by the naïve bird over generations.

Statistical comparison of the proportion of transitions from exploitation to exploration and from exploration to exploitation led by the experienced and by the naïve bird over releases.

Transparent reporting form

Downloads (link to download the article as PDF)

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Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)