Which dance indicates a nectar source that is between 15 yards to 4 miles away?

The waggle dance is used by honeybees to communicate the location of food sources, specifically nectar and pollen, that are situated between 15 yards and up to 4 miles away from the hive. This dance involves a distinctive movement pattern where the bee performs a series of straight runs followed by a waggle phase, where it shakes its body to convey information about the direction and distance of the resource in relation to the hive.

The duration of the waggle phase correlates with the distance to the food source; a longer waggle indicates a farther distance, while the angle of the waggle relative to the vertical comb indicates the direction in relation to the sun. This sophisticated form of communication allows for efficient foraging, enabling other bees to locate the source of nectar precisely.

For distances closer than 15 yards, the round dance is typically employed, which does not provide directional information but indicates that there is food nearby. The circle dance is also associated with close food sources, while the shivering dance is related to temperature regulation, not foraging. Hence, the waggle dance is the appropriate choice to signify a nectar source that lies within the range specified in the question.