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) T1 (red; requiring no information) — the simple process of equally averaging the two bird routes. (B) T2 (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) T3 (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).

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. Statistical significance levels are denoted as follows: * p < 0.05, ** p < 0.01, *** p < 0.001. The general color scheme in the plots match that used in Fig. 1 to highlight different strategy types.

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. Statistical significance levels are denoted as follows: * p < 0.05, ** p < 0.01, *** p < 0.001. The color scheme in the plots are same as in Fig. 1.

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.