Jellyfishes have functionally replaced several overexploited commercial stocks of planktivorous fishes. This is paradoxical, because they use a primitive prey capture mechanism requiring direct contact with the prey, whereas fishes use more efficient visual detection. We have compiled published data to show that, in spite of their primitive life-style, jellyfishes exhibit similar instantaneous prey clearance and respiration rates as their fish competitors and similar potential for growth and reproduction. To achieve this production, they have evolved large, water-laden bodies that increase prey contact rates. Although larger bodies are less efficient for swimming, optimization analysis reveals that large collectors are advantageous if they move through the water sufficiently slowly.