Which group is responsible for modifying the rate and depth of breathing by receiving external input?

The correct answer is the dorsal respiratory group (DRG). This group of neurons, located in the medulla oblongata, plays a crucial role in the modulation of breathing patterns. The DRG receives sensory input from peripheral chemoreceptors and mechanoreceptors, which provide information about the levels of oxygen and carbon dioxide in the blood, as well as the lung inflation status. Based on this external input, the DRG adjusts the rate and depth of breathing to maintain homeostasis in the body's respiratory needs.

Furthermore, while the other groups mentioned—such as the ventral respiratory group, pneumotaxic center, and apneustic center—are all involved in regulating respiration, they serve different functions. The ventral respiratory group primarily facilitates rhythmic breathing and contributes to increases in ventilation during active states. The pneumotaxic center helps control the rhythm of breathing and can inhibit inspiration, ensuring that breathing is not excessively prolonged. The apneustic center stimulates prolonged inspiratory efforts but does not integrate external sensory input for modification. Thus, it's the DRG that specifically modifies the rate and depth of breathing based on external stimuli, making it the key group for this particular function.