While your survey design is not the best, it does not produce an overestimate of population density. Distance sampling estimation used the encounter rate (number of detections per unit of survey effort) in the estimation of density. View the standard density
estimation formula this way:
The middle term on the right hand side is encounter rate.
Pretend there is one animal within the covered region of your transect, which is 1km long. You detect that animal on your outbound leg of your walk: encounter rate from that walk would be 1 detection per kilometer. Pretend you also detect that animal on your
return leg: encounter rate for the round trip is 2 detections per 2 kilometers.
Two issues in your design are of greater concern for the integrity of your work:
- by walking the same transect twice, you are not increasing spatial replication of your sampling. It is spatial replication that strengthens your inference when making inference from the area you sampled to the entire study area; more spatial replicates
- you mention walking trails. This also compromises the strength of your inference because trails are unlikely to be representative of the study area. Trails are not randomly distributed on the landscape. In addition, the animals you are studying know
of these trails and are either attracted or repelled by them. In either case, bias in your estimates can result.
If possible, try not to place your transects on trails and attempt to increase the spatial replication to make your inference stronger.