Hypermetry of the tracheal system - lab results:
Theoretical considerations show that the tracheal system has to take up more room in larger insects. When scientists study the relationship between dimensions of a structure and dimensions of body size, like body length or body mass, they call this scaling or allometric analysis.
The Harrison lab did several studies on allometric scaling of tracheael structures in insects of varying sizes. And most of the insects investigated revealed that investment in the tracheal system increased with body size. As the scaling relationship is higher than expected from isometry, it is called Hypermetry.
If this trend of increased tracheal investment continues unabated, the tracheal system would compete with other tissues and finally will limit insct size.
When grasshoppers grow, air sacs develop:
In 1957, Clarke found out that the tracheal system occupies more space in the body, when grasshoppers grow from instar to instar. But air sacs not only develop in the body core! The Harrison lab found that even in the leg, air sacs grew during development and that they took up more space as grashoppers got larger and older.
Images from Hartung et al. (2004) Journal of Morphology, volume 262, pages 800–812
The two images above show sections through the leg - and more specific, the femur - of the grasshopper Schistocerca americana in two different stages of development. Left is the second instar larvae, right is the adult. Comparison of both images demonstrates, how the tracheal system grows from small tubes (T) to large tubes and how the air sacs occupy most of the space of an adult leg.
The following image is from Kaiser et al. (2007) Proceedings of the National Society
Grasshoppers are not the only insects, where the tracheal system takes more space in larger animals. With x-ray images from Argonne National Laboratories, we found that the tracheal tube (yellow lines) that runs down the leg (blue line) of darkling beetles takes up mores space in larger beetles (from 1 to 4).
But how does this hypermetry affect insect size?