Many debris discs reveal a two-component structure , with a cold outer and a warm inner component . While the former are likely massive analogues of the Kuiper belt , the origin of the latter is still a matter of debate . In this work we investigate whether the warm dust may be a signature of asteroid belt analogues . In the scenario tested here the current two-belt architecture stems from an originally extended protoplanetary disc , in which planets have separating it into the outer and inner discs which , after the gas dispersal , experience a steady-state collisional decay . This idea is explored with an analytic collisional evolution model for a sample of 225 debris discs from a Spitzer/IRS catalogue that are likely to possess a two-component structure . We find that the vast majority of systems ( 220 out of 225 , or 98 % ) are compatible with this scenario . For their progenitors , original protoplanetary discs , we find an average surface density slope of -0.93 \pm 0.06 and an average initial mass of \left ( 3.3 ^ { +0.4 } _ { -0.3 } \right ) \times 10 ^ { -3 } solar masses , both of which are in agreement with the values inferred from submillimetre surveys . However , dust production by short-period comets and — more rarely — inward transport from the outer belts may be viable , and not mutually excluding , alternatives to the asteroid belt scenario . The remaining five discs ( 2 % of the sample ) harbour inner components that appear inconsistent with dust production in an ‘ ‘ asteroid belt. ’ ’ Warm dust in these systems must either be replenished from cometary sources or represent an aftermath of a recent rare event , such as a major collision or planetary system instability .