The consequences of using indirect signs that decay to determine species' occupancy

Statistical models of species' distributions rely on data on species' occupancy, or use, of sites across space and/or time. For rare or cryptic species, indirect signs, such as dung, may be the only realistic means of determining their occupancy status across broad spatial extents. However, the consequences of sign decay for errors in estimates of occupancy have not previously been considered. If signs decay very rapidly, then false-negative errors may occur because signs at an occupied site have decayed by the time it is surveyed. On the other hand, if signs decay very slowly, false-positive errors may occur because signs remain present at sites that are no longer occupied. We addressed this issue by quantifying, as functions of sign decay and accumulation rates: 1) the false-negative error rate due to sign decay and, 2) the expected time interval prior to a survey within which signs indicate the species was present; as this time interval increases, false-positives become more likely. We then applied this to the specific example of koala Phascolarctos cinereus occupancy derived from faecal pellet surveys using data on faecal pellet decay rates. We show that there is a clear trade-off between false-negative error rates and the potential for false-positive errors. For the koala case study, false-negative errors were low on average and the expected time interval prior to surveys that detected pellets indicate the species was present within less than 2-3 yr. However, these quantities showed quite substantial spatial variation that could lead to biased parameter estimates for distribution models based on faecal pellet surveys. This highlights the importance of observation errors arising from sign decay and we suggest some modifications to existing methods to deal with this issue.