The results confirm previous studies that dogs are able to determine the direction of a trail (Steen and Wilson, 1990
; Wells and Hepper, 2003) and this is achieved using an odour cue (Wells and Hepper, 2003). This study extends these findings by demonstrating that footsteps provide sufficient olfactory information for the determination of direction and that five sequential footsteps are required to enable these dogs to determine directionality.
In this study dogs used an odour left by an individual's footstep to determine direction. Air scent cues were not available as the individual laying the trail was not at either end of the trail. Two odour cues may be left as an individual walks: a direct contact cue that arises from the bottom of the shoe touching the ground; and a more indirect cue from body odour that falls to the ground (Szinak, 1985; Fenton, 1992) around the individual. Clifford (1958) suggests such indirect odour may spread out 
5 yards for ‘heavy particles of scent’ and 25 yards for ‘medium particles of scent’ from the body. Pearsall and Verbruggen (1982) argue that this indirect body odour is important for enabling the dog to track. However, the dogs in experiment 2 were unable to determine direction where cues from this general body odour deposition were available but footsteps were not. This supports the suggestion of Budgett (1933) that it is contact odour cues that are important for determining direction. When the individual odour was removed from the odour trail (experiment 3), but contact/disturbance odour was left, the dogs were unable to determine direction. Thus dogs in this study were using the individual odour cue deposited by a footstep to determine direction.
The study found that five sequential footsteps were needed to determine direction. This corresponds with the observation of Thesen et al. (1993), who reported dogs sniffed at 2–5 footprints when making a decision about directionality, although more footsteps were available.
How the dog determines directionality is unknown. Direct comparison with studies of navigation in an odour plume (see Introduction) may be inappropriate due to differences in the olfactory signal and species under question.
Footsteps provide a series of discrete odour cues that differ in time of deposition and hence may form a reasonably uniform stepwise olfactory gradient. Observations of the dogs' performance here, and by others (Steen and Wilsson, 1990; Thesen et al., 1993; Wells and Hepper, 2003), indicate that dogs perform this task with their nose just above the ground and not in the air. This suggests they are using the ground-based olfactory cues rather than airborne scents subject to turbulence. Previous observations (Steen and Wilsson, 1990) suggest that dogs are unable to determine direction from a continuous olfactory trail but can do so when discrete separate olfactory stimuli are present, e.g. footsteps. Studies of insect navigation in odour plumes have found that some moths require intermittency in the olfactory plume and are unable to locate the odour source in a continuous odour plume (Justus and Cardé, 2002). It has been suggested that the internal fine structure of an odour plume provides an important source of information regarding direction. A footstep may also provide some information regarding direction. In a normal footstep the heel touches the ground before the toe and potentially provides an internal cue to direction. However, dogs in this study did not appear to use this information as they were unable to determine direction with the 3 footstep sequence – where heel–toe information would be present.
It should also be noted that the ‘cognitive processing’ capacity of the dog is different to that of the insects and crustaceans previously studied and this may have implications for how direction is determined. It is most likely that the dog determines direction, in this task, through processing elements of the olfactory signal contained within a footstep. Flow may be unimportant as dogs here were able to determine direction upwind, downwind and crosswind.
Two possible mechanisms would allow the dog to determine directionality. Firstly, the odour cue(s) somehow encode absolute information about time. This would be the equivalent of a time code stamped on a photograph. Dogs would then ‘read’ this information from each footstep, compare the absolute times of different steps and then determine direction. This is most unlikely and it is virtually impossible to envisage a mechanism for this level of time encoding in an olfactory cue. Secondly, and much more likely, the dog compares the cues offered by each individual footstep which differ systematically with direction. Footsteps present a number of possibilities for an odour gradient to be followed. The individual odour may smell stronger with more recent footsteps, and thus the dog has to determine the strongest smell, which equates to the most recent, and move in that direction. Alternatively, it could be a product of decay that provides the relative information. With time, as decay increases, this provides a stronger smell and thus, comparatively, the more recent footstep smells less decayed that the preceding footstep. To determine direction the dog moves in the direction of least decay. The fact that discrete patches of olfactory information may be required to determine direction supports further the possibility of a comparative process.
Having detected the direction of the trail, what causes the dog to move towards the source is unknown. It may be the result of an innate response; however, these were trained dogs and so it may represent a result of their training.
Recording the time taken to complete the 21 footsteps enables an estimate of the time, and hence olfactory decay rate, between steps to be made. The time taken to complete 100 trails of 21 footsteps reveals an average time between footsteps of 0.486 s (SD ± 0.25). For 5 footsteps there is a time difference of 1.9 s between the first footstep and the fifth, whereas for 3 footsteps the time difference is 0.9 s. Thus, in this study, a time of 1–2 s is required for the olfactory information contained in a footstep to change on exposure to the environment to provide a sufficient difference in its olfactory signature for the dog to determine the trail's direction. Interestingly lobsters also take about 1–2 s to make a decision about which direction to turn when tracking a plume (Atema, 1996).
The dog has two pieces of information which it uses to determine the direction of a trail: (i) a number of discrete pieces of information, i.e. the number of footsteps; and (ii) the difference in the odour cue due to time. The interaction between these on the ability of the dog to determine direction has yet to be fully explored. For example, walking more slowly would increase the time difference between steps and may reduce the amount of discrete pieces of information required by the dog to determine direction. If time difference were the only factor involved, it should be theoretically possible for a dog to determine direction from 2 footsteps separated in their deposition by 2 s. However, the determination of direction is not just reliant on a difference in cues as provided by a difference in time. The dog also has to make a comparison between the different sources of information and it may be that a certain number are required (e.g. 5 footsteps in this study) for an accurate comparison to be made. Indeed pilot studies exploring this reveal that both the time difference between footsteps and the number of footsteps is important. Despite increasing time between footsteps we have been unable to observe dogs determining direction correctly from just 2 footsteps.
Caution must be expressed in reaching these conclusions. The influence of training on the dog's performance cannot be underestimated (cf. Schoon and De Bruin, 1994). The dogs used in this study were trained to determine directionality on 100 m tracks laid in grass, thus providing a large amount (for the dog) of olfactory information. Although dogs were able to perform the task in this study, specific training on the above task may reduce the amount of information required to make a determination of direction. Environmental conditions will influence the change in olfactory stimuli over time. The experiments here were conducted in the absence of strong winds on days, which were dull, not sunny and not raining (a typical Belfast day!). Differences in wind, humidity and temperature could all be expected to change the rate, and perhaps the way, that the olfactory information present in a footstep changes with time. Hence both training and environment may influence the dog's performance.
In summary, dogs trained to determine directionality required 5 sequential footsteps, i.e. discrete pieces of information, to determine the direction of an odour trail. It is likely that dogs use a comparative process comparing the odours of discrete footsteps to determine direction and require a 1–2 s time difference to ‘decay’ or change the odour within a footstep to provide the dog with an olfactory gradient it can use to determine direction. Further work is underway to explore the interaction between time and the amount of discrete information on the dog's ability to determine direction.
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