The macroscopic emergent behavior of social animal groups is thought to arise from the local interactions between individuals. We proposed a model of acoustic interaction within insect swarms that resemble gravitational attraction. Unlike gravity, the interactions between the insects are adaptive. Sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the sensitivity of the signal produced by the sensor is adapted to the overall amplitude of the signal. Adaptivity reduces the sensitivity in the presence of strong background stimulus, while increasing it when the background is weak. We find that in particular adaptivity is responsible for pairwise interaction that are characterized by higher-frequency nearly harmonic oscillations conducted by two synchronized insects. By comparison, the capture of pairs under normal gravity is extremely rare. We show that such pairs are created in simulations of the "adaptive gravity" model and compare them with pairs that were found in measurements of laboratory midge swarms. In addition we show similarities in density distributions between the simulations and laboratory measurements.