Fig. 6: Computer simulations of insect migrations.

a Example simulation of a monarch butterfly (Danaus plexippus) during its autumn migration, using a clockwise (CW) hour-angle model (blue) and complete model (yellow). Haversine distance: 3303.01 km. The red dashed arrow illustrates the straight line between the start and goal locations. b Examples of similar migrations that start from different locations along the Canadian border and California. c Haversine distance (km) between the butterflies' search centroid and the migration’s destination point for each model and starting location. Variability comes from spatial (± 5°) and temporal (± 72 h) variations at the beginning of the migration. d Similar example simulation for the Bogong moth (Agrotis infusa) during its autumn migration, using a counter-clockwise (CCW) hour angle and complete models. Haversine distance: 1114.65 km. e Other examples of the same migration, starting from different locations in Australia. f Haversine distance between the moths' search centroid and the migration’s target location (similar to c, but for the moths). g Example simulation of a globe skimmer dragonfly (Pantal flavescens) during its spring migration, using the horizontal (east-west) component of the hour-angle model (vertical is set to zero) and the complete model. Haversine distance: 4859.20 km. h Similar simulations start from different locations on the east African coast. i The Haversine distance (km) of the dragonflies' search centroid from the target migration’s target location (similar to c and f, but for the dragonflies). j Sensitivity analysis of the complete model to disturbances in estimating the sun’s azimuth (grey; dashed: noise in the one-dimensional angle, solid: noise in the eight-dimensional neural representation of the angle), hour angle (blue) and magnetic inclination (yellow), pooled across the different migrations. In c, f and i each box shows the quartiles of the data (n = 10 samples); the whiskers extend to show the rest of the distribution except for points that exceed 1.5 × the inter-quartile range, which are marked as outliers. In j the sample size is n = 15 per 10% noise and the shaded areas are the 95% confidence interval. In a-i, there is 20% added noise in both sensing and processing. All maps were drawn with permission using the Contextly Python package with the CartoDB provider option.