Cognitive simplicity drives collective route improvements in homing pigeons
- Department of Biology, University of Massachusetts Boston, United States
Figures
Figure 1
Schematic illustration of the experimental design used in the original study.
(A) In each generation, birds were flown either individually or in pairs for a total of 12 releases. In the experimental condition, partners were replaced in each generation (except the first), whereas in the control conditions, birds were flown either individually or as fixed pairs for a total of 60 releases. (B) Variation in route efficiency in each condition across generations. Route efficiency was calculated from the final flight of each generation (release 12) for the experimental condition, and from releases 12, 24, 36, 48, and 60 for the solo and fixed controls. Panel A and B are adapted from Figure 1 and 2 from Sasaki and Biro, 2017.
Figure 2
Illustration of the hypothesized social learning strategies.
At the center, we depict an example of a simulated averaged bird trajectory (which becomes the experienced bird’s route for the next generation) created using an experienced bird (E) and a naïve bird (N) trajectory. The strategies can be organized into three types based on the kind of information that is required to execute the strategy: (A) (red; requiring no information)—the simple process of equally averaging the two bird routes. (B) (green; requiring individuals to recognize relative experience levels)—strategies that optimize the weight of the experienced bird either to maximize performance in the final generation (experienced bird weighting) or in each generation (maximize generation). (C) (blue; requiring individuals to compare the relative path length of flights)—strategies where birds assess paired performance, either by assigning greater social weight to the better-performing bird (better bird weighting and all-or-nothing) or by fine-tuning local aspects of the flight (maximize flights and maximize time steps).
Figure 3
Results of mixed model analysis comparing the route efficiency of the hypothesized strategies to the experimental data.
(A) The odds ratio for each strategy relative to the experimental data after adjusting for generation, with the gray dotted line representing the null odds ratio of 1. (B) The route efficiency of each hypothesized strategy and the experimental data (black) across generations. The shaded confidence bands indicate the 95% confidence intervals for the model predictions and reflect the biological uncertainty in the empirical dataset, not simulation noise. Statistical significance levels are denoted as follows: *p<0.05, **p<0.01, ***p<0.001. The general color scheme in the plots matches that used in Figure 2 to highlight different strategy types.
Figure 4
Results of mixed model analysis for the social weighting of the experienced bird.
(A) The mean difference for each strategy relative to the experimental data after adjusting for generation, with the gray dotted line representing the mean difference of 0 between the datasets. (B) The variation of the social weighting assigned to the experienced bird for each strategy across generations. The shaded confidence bands indicate the 95% confidence intervals for the model predictions and reflect the biological uncertainty in the empirical dataset, not simulation noise. Statistical significance levels are denoted as follows: *p<0.05, **p<0.01, ***p<0.001. The color scheme in the plots is the same as in Figure 2.
Figure 5
The effective group size achieved by each strategy and the experimental data across generations.
The predicted mean route efficiency from each strategy is mapped onto a curve modeling the relationship between the route mean route efficiency and simulated flock sizes. The inset provides the curve, illustrating how route efficiency scales with flock size. The dashed orange line shows the 1:1 between the two variables. Shaded confidence bands denote the 95% confidence intervals for the estimated effective group sizes.
Appendix 1—figure 1
The figure illustrates various functional models fitted to the mean route efficiency values for a given group size.
A post hoc model comparison was conducted using AIC to determine the best-fitting model: hyperbolic (df = 3, AIC = –189.8), logistic (df = 3, AIC = –114.6), power law (df = 3, AIC = –113.5), and asymptotic (df = 3, AIC = –110.5). Among these, the hyperbolic model provided the best fit. Note that the power law and logistic curves in the figure are nearly identical.
Tables
Appendix 1—table 1
Route efficiency data model comparison.
| Model | df | AIC |
|---|---|---|
| Linear Model | 41 | –2141657 |
| Linear Mixed Effect Model (random effect bird ID) | 42 | –2280167 |
| Linear Mixed Effect Model (random effect bird ID and Generation) | 42 | –2281106 |
| Beta Regression Model | 41 | –2388197 |
| Beta Regression Model (random effect bird ID) | 42 | –2526965 |
| Beta Regression Model (random effect bird ID and Generation) | 42 | –2527103 |
Appendix 1—table 2
Model variance components and R2 values.
| Metric | Value |
|---|---|
| Fixed Effect Variance | 0.0425 |
| Random Variance | 0.1080 |
| Residual Variance | 0.00048 |
| Marginal R2 | 0.2815 |
| Conditional R2 | 0.9968 |
| Intraclass Correlation Coefficient (ICC) | 0.7154 |
Appendix 1—table 3
Social weight model comparison.
| Model | df | AIC |
|---|---|---|
| Linear Model | 21 | –18914.90 |
| Linear Mixed Effect Model (random effect bird ID) | 22 | –81533.43 |
| Linear Mixed Effect Model (random effect bird ID and Generation) | 22 | –81967.68 |
Appendix 1—table 4
Social weight model variance components and R2 values.
| Metric | Value |
|---|---|
| Fixed Effect Variance | 0.0038 |
| Random Variance | 0.0257 |
| Residual Variance | 0.0429 |
| Marginal R2 | 0.0527 |
| Conditional R2 | 0.4075 |
| Intraclass Correlation Coefficient (ICC) | 0.3548 |
Appendix 1—table 5
Contrasts between estimated route efficiencies of each strategy and the experimental data holding generation constant (at its mean value).
Contrasts were conducted on the log odds ratio scale relative to the experimental data. Confidence intervals (CIs) were calculated at the 95% interval. Dunnett’s correction was applied to both CIs and p-values to account for multiple comparisons. Significance levels: *p<0.05. **p<0.01. ***p<0.001.
| Contrast | Odds ratio | SE | 95% CI | p-value | |
|---|---|---|---|---|---|
| Averaging | 1.05 | 0.07 | [0.88, 1.25] | 0.93 | |
| Experienced Bird Weighting | 1.13 | 0.08 | [0.94, 1.34] | 0.34 | |
| Maximize Generation | 1.15 | 0.08 | [0.96, 1.37] | 0.19 | |
| Better Bird Weighting | 1.37 | 0.09 | [1.15, 1.63] | <0.001*** | *** |
| All-or-Nothing | 0.99 | 0.07 | [0.84, 1.19] | 1.00 | |
| Maximize Flight | 1.55 | 0.11 | [1.30, 1.86] | <0.001*** | *** |
| Maximize Time Steps | 1.26 | 0.08 | [1.06, 1.51] | <0.01** | ** |
Appendix 1—table 6
Contrasts between estimated social weights of the experienced bird for each strategy and the experimental data holding generation constant (at its mean value).
Contrasts were conducted on the response scale relative to the experimental data. CIs were calculated at the 95% interval. Dunnett’s correction was applied to both CIs and p-values. Significance levels: *p<0.05. **p<0.01. ***p<0.001.
| Contrast | Mean difference | SE | 95% CI | p-value |
|---|---|---|---|---|
| Averaging | 0.003 | 0.03 | [–0.08, 0.09] | 0.99 |
| Experienced Bird Weighting | 0.14 | 0.03 | [0.05, 0.23] | <0.001*** |
| Maximize Generation | 0.18 | 0.04 | [0.09, 0.27] | <0.001*** |
| Better Bird Weighting | 0.17 | 0.04 | [0.06, 0.29] | <0.001*** |
| All-or-Nothing | 0.23 | 0.04 | [0.11, 0.34] | <0.001*** |
| Maximize Flight | 0.23 | 0.04 | [0.11, 0.34] | <0.001*** |
| Maximize Time Steps | 0.12 | 0.04 | [0.00, 0.23] | 0.04* |
Appendix 1—table 7
Contrasts derived from the estimated marginal means (EMMs) of the beta regression model applied to the route efficiency data.
Contrasts were conducted on the log odds ratio scale relative to the experimental data. CIs were calculated at the 95% interval. Dunnett’s correction was applied to both CIs and p-values. Significance levels: *p<0.05. **p<0.01. ***p<0.001.
| Contrast | Generation | Odds ratio | SE | 95% CI | p-value |
|---|---|---|---|---|---|
| Averaging | 1 | 1.12 | 0.17 | [0.75, 1.67] | 0.91 |
| 2 | 0.98 | 0.14 | [0.67, 1.43] | 1.00 | |
| 3 | 1.29 | 0.18 | [0.90, 1.85] | 0.30 | |
| 4 | 0.90 | 0.14 | [0.60, 1.35] | 0.94 | |
| 5 | 1.05 | 0.16 | [0.70, 1.58] | 0.99 | |
| Experienced Bird Weighting | 1 | 1.12 | 0.17 | [0.75, 1.67] | 0.91 |
| 2 | 0.98 | 0.14 | [0.67, 1.43] | 1.00 | |
| 3 | 1.37 | 0.19 | [0.95, 1.96] | 0.13 | |
| 4 | 1.02 | 0.16 | [0.68, 1.53] | 1.00 | |
| 5 | 1.23 | 0.19 | [0.82, 1.86] | 0.60 | |
| Maximize Generation | 1 | 1.12 | 0.17 | [0.75, 1.67] | 0.91 |
| 2 | 0.98 | 0.14 | [0.67, 1.43] | 1.00 | |
| 3 | 1.40 | 0.19 | [0.97, 2.03] | 0.08 | |
| 4 | 1.08 | 0.17 | [0.71, 1.63] | 0.74 | |
| 5 | 1.36 | 0.21 | [0.89, 2.07] | 0.22 | |
| Better Bird Weighting | 1 | 1.12 | 0.17 | [0.75, 1.67] | 0.91 |
| 2 | 1.15 | 0.16 | [0.78, 1.69] | 0.83 | |
| 3 | 1.66 | 0.23 | [1.16, 2.39] | <0.01 ** | |
| 4 | 1.27 | 0.20 | [0.84, 1.90] | 0.48 | |
| 5 | 1.57 | 0.24 | [1.05, 2.37] | 0.02 * | |
| All-or-Nothing | 1 | 1.12 | 0.17 | [0.75, 1.67] | 0.91 |
| 2 | 0.94 | 0.13 | [0.64, 1.38] | 1.00 | |
| 3 | 1.23 | 0.17 | [0.85, 1.78] | 0.14 | |
| 4 | 0.88 | 0.14 | [0.58, 1.34] | 0.89 | |
| 5 | 1.06 | 0.16 | [0.70, 1.61] | 0.99 | |
| Maximize Flight | 1 | 1.12 | 0.17 | [0.75, 1.67] | 0.91 |
| 2 | 1.23 | 0.18 | [0.83, 1.79] | 0.54 | |
| 3 | 1.89 | 0.26 | [1.32, 2.72] | <0.001 *** | |
| 4 | 1.51 | 0.23 | [1.00, 2.27] | 0.046 * | |
| 5 | 1.96 | 0.30 | [1.30, 2.94] | <0.001 *** | |
| Maximize Time Steps | 1 | 1.12 | 0.17 | [0.75, 1.67] | 0.91 |
| 2 | 1.07 | 0.15 | [0.73, 1.57] | 0.76 | |
| 3 | 1.54 | 0.21 | [1.07, 2.22] | 0.01 * | |
| 4 | 1.18 | 0.18 | [0.79, 1.78] | 0.76 | |
| 5 | 1.49 | 0.23 | [0.99, 2.24] | 0.06 |
Appendix 1—table 8
Contrasts derived from the estimated marginal means (EMMs) of the linear mixed model applied to the social weights of the experienced bird.
Contrasts were conducted on the response scale with mean difference relative to the experimental data. CIs were calculated at the 95% interval. Dunnett’s correction was applied to both CIs and p-values. Significance levels: *p<0.05. **p<0.01. ***p<0.001.
| Contrast | Generation | Mean difference | SE | 95% CI | p-value |
|---|---|---|---|---|---|
| Averaging | 2 | –0.03 | 0.06 | [–0.19, 0.14] | 0.98 |
| 3 | 0.05 | 0.06 | [–0.12, 0.22] | 0.92 | |
| 4 | –0.05 | 0.07 | [–0.24, 0.14] | 0.95 | |
| 5 | 0.04 | 0.08 | [–0.17, 0.24] | 0.98 | |
| Experienced Bird Weighting | 2 | 0.11 | 0.06 | [–0.05, 0.28] | 0.38 |
| 3 | 0.19 | 0.06 | [0.02, 0.38] | 0.02 * | |
| 4 | 0.09 | 0.07 | [–0.09, 0.28] | 0.64 | |
| 5 | 0.17 | 0.08 | [–0.03, 0.38] | 0.13 | |
| Maximize Generation | 2 | –0.03 | 0.06 | [–0.20, 0.14] | 0.98 |
| 3 | 0.22 | 0.06 | [0.04, 0.39] | <0.01 ** | |
| 4 | 0.20 | 0.08 | [0.01, 0.39] | 0.03 * | |
| 5 | 0.33 | 0.08 | [0.13, 0.54] | <0.001 *** | |
| Better Bird Weighting | 2 | –0.03 | 0.08 | [–0.23, 0.17] | 0.99 |
| 3 | 0.22 | 0.08 | [0.00, 0.44] | 0.05 * | |
| 4 | 0.19 | 0.09 | [–0.04, 0.43] | 0.17 | |
| 5 | 0.29 | 0.09 | [0.05, 0.54] | 0.01 * | |
| All-or-Nothing | 2 | –0.03 | 0.08 | [–0.26, 0.20] | 0.99 |
| 3 | 0.26 | 0.08 | [0.03, 0.48] | 0.01 * | |
| 4 | 0.26 | 0.09 | [0.02, 0.49] | 0.02 * | |
| 5 | 0.39 | 0.09 | [0.14, 0.64] | <0.001 *** | |
| Maximize Flight | 2 | –0.03 | 0.09 | [–0.26, 0.20] | 0.99 |
| 3 | 0.27 | 0.08 | [0.04, 0.49] | 0.01 * | |
| 4 | 0.26 | 0.09 | [0.05, 0.49] | 0.03 * | |
| 5 | 0.39 | 0.09 | [0.14, 0.63] | <0.001 *** | |
| Maximize Time Steps | 2 | –0.03 | 0.09 | [–0.26, 0.20] | 0.99 |
| 3 | 0.17 | 0.08 | [–0.05, 0.39] | 0.23 | |
| 4 | 0.14 | 0.09 | [–0.10, 0.37] | 0.48 | |
| 5 | 0.26 | 0.09 | [0.00, 0.50] | 0.04 * |
Appendix 1—table 9
Bootstrap contrasts for different strategies relative to the experimental control for the route efficiency data.
The table reports odds ratios, 95% CIs and adjusted p-values. Multiple comparison adjustments were made using Dunnett’s method. Significance levels: *p<0.05. **p<0.01. ***p<0.001.
| Contrast | Generation | Odds ratio | 95% CI | p-value |
|---|---|---|---|---|
| Averaging | 1 | 1.09 | [0.51, 2.35] | 1.0 |
| 2 | 1.01 | [0.49, 2.07] | 1.0 | |
| 3 | 1.47 | [0.72, 3.00] | 0.53 | |
| 4 | 0.86 | [0.45, 1.65] | 0.95 | |
| 5 | 1.01 | [0.48, 2.17] | 1.0 | |
| Experienced Bird Weighting | 1 | 1.08 | [0.51, 2.33] | 1.0 |
| 2 | 0.97 | [0.46, 2.04] | 1.0 | |
| 3 | 1.54 | [0.76, 3.09] | 0.42 | |
| 4 | 0.97 | [0.54, 1.76] | 1.0 | |
| 5 | 1.21 | [0.61, 2.39] | 0.92 | |
| Maximize Generation | 1 | 1.09 | [0.51, 2.34] | 1.0 |
| 2 | 1.01 | [0.49, 2.06] | 1.0 | |
| 3 | 1.58 | [0.79, 3.14] | 0.35 | |
| 4 | 1.02 | [0.58, 1.79] | 1.0 | |
| 5 | 1.32 | [0.70, 2.50] | 0.71 | |
| Better Bird Weighting | 1 | 1.09 | [0.51, 2.34] | 1.0 |
| 2 | 1.20 | [0.60, 2.43] | 0.93 | |
| 3 | 1.96 | [1.08, 3.55] | 0.01 * | |
| 4 | 1.26 | [0.83, 1.91] | 0.52 | |
| 5 | 1.61 | [0.96, 2.69] | 0.08 | |
| All-or-Nothing | 1 | 1.09 | [0.51, 2.35] | 1.0 |
| 2 | 0.99 | [0.52, 1.89] | 1.0 | |
| 3 | 1.44 | [0.82, 2.51] | 0.38 | |
| 4 | 0.87 | [0.61, 1.22] | 0.74 | |
| 5 | 1.07 | [0.69, 1.65] | 0.99 | |
| Maximize Flight | 1 | 1.09 | [0.51, 2.34] | 1.0 |
| 2 | 1.12 | [0.62, 2.65] | 0.85 | |
| 3 | 2.21 | [1.19, 4.12] | <0.01 ** | |
| 4 | 1.51 | [1.00, 2.27] | 0.047 * | |
| 5 | 2.01 | [1.26, 3.23] | <0.001 *** | |
| Maximize Time Steps | 1 | 1.09 | [0.51, 2.34] | 1.0 |
| 2 | 1.16 | [0.55, 2.27] | 0.99 | |
| 3 | 1.80 | [0.96, 3.36] | 0.08 | |
| 4 | 1.16 | [0.74, 1.80] | 0.87 | |
| 5 | 1.49 | [0.89, 2.50] | 0.20 |
Appendix 1—table 10
Bootstrap mean difference contrasts for different strategies relative to the experimental control for the social weights data.
The table reports mean differences, 95% CIs, and adjusted p-values using Dunnett’s method. Significance levels: **p<0.05. **p<0.01. ***p<0.001.
| Contrast | Generation | Mean difference | 95% CI | p-value |
|---|---|---|---|---|
| Averaging | 2 | –0.03 | [–0.24, 0.18] | 0.99 |
| 3 | 0.05 | [–0.14, 0.23] | 0.93 | |
| 4 | –0.05 | [–0.34, 0.24] | 0.98 | |
| 5 | 0.04 | [–0.24, 0.31] | 0.99 | |
| Experienced Bird Weighting | 2 | 0.11 | [–0.10, 0.32] | 0.58 |
| 3 | 0.19 | [0.01, 0.37] | 0.041 * | |
| 4 | 0.09 | [–0.20, 0.38] | 0.88 | |
| 5 | 0.18 | [–0.10, 0.45] | 0.37 | |
| Maximize Generation | 2 | –0.03 | [–0.24, 0.18] | 0.99 |
| 3 | 0.22 | [0.03, 0.49] | 0.01 * | |
| 4 | 0.20 | [–0.08, 0.49] | 0.29 | |
| 5 | 0.34 | [0.06, 0.61] | <0.01 ** | |
| Better Bird Weighting | 2 | –0.03 | [–0.36, 0.31] | 1.00 |
| 3 | 0.22 | [0.00, 0.49] | 0.16 | |
| 4 | 0.19 | [–0.13, 0.52] | 0.47 | |
| 5 | 0.30 | [0.06, 0.61] | <0.01 ** | |
| All-or-Nothing | 2 | –0.03 | [–0.52, 0.47] | 1.00 |
| 3 | 0.26 | [–0.17, 0.68] | 0.44 | |
| 4 | 0.26 | [–0.21, 0.73] | 0.53 | |
| 5 | 0.40 | [–0.04, 0.84] | 0.09 | |
| Maximize Flight | 2 | –0.03 | [–0.32, 0.26] | 1.00 |
| 3 | 0.27 | [0.01, 0.53] | 0.04 * | |
| 4 | 0.26 | [–0.07, 0.59] | 0.21 | |
| 5 | 0.39 | [0.08, 0.70] | <0.01 ** | |
| Maximize Time Steps | 2 | –0.03 | [–0.35, 0.29] | 1.00 |
| 3 | 0.16 | [–0.12, 0.45] | 0.46 | |
| 4 | 0.14 | [–0.23, 0.50] | 0.82 | |
| 5 | 0.26 | [–0.10, 0.61] | 0.28 |
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Cognitive simplicity drives collective route improvements in homing pigeons
eLife 14:RP108054.
https://doi.org/10.7554/eLife.108054.3
