Fig 1.
A-D: Various arrangements of traps in an 11 x 11 cell block at the middle of a map of 71 x 71 cells.
The separation distance shown for each arrangement is the distance between a trap and its closest neighbour. That distance is half the greatest distance between traps in present arrangements. Arrows in D show what is meant in the main text by the “orthogonal” and “diagonal” directions of movement away from the central cell.
Fig 2.
Hypothetical circular areas sampled around traps in various arrangements.
A: single trap operated for several days. B: five traps placed in a roughly circular pattern but separated by a few kilometres and operated for only a few days, so that the areas sampled around each trap do not overlap; areas z and a-e are discussed in the main text. C: five traps placed in a line, separated by at least a few kilometres and operated for no more than a few days. D: five traps separated by a few kilometres and operated for many days, so that there is extensive overlap in the sampled areas. In A to D, the territory within the circles formed by solid lines indicates the areas needed to embrace the origin of all flies caught by the trap(s). Territory within dotted lines indicate smaller areas embracing the origin of only a proportion of the catch. One of the main aims of present work was to estimate the percentage of the catch originating from various sizes of such smaller areas.
Fig 3.
Numbers of flies per cell at different distances in orthogonal and diagonal directions from the cell of origin, after various days of movement.
There were 100 flies at the origin before movement began. Fig 1D exemplifies what is meant by orthogonal and diagonal directions of movement.
Fig 4.
Percentage of the catch originating from various circular areas around a single trap after different numbers of days of trapping.
Table 1.
The percentage of the cumulative catch originating from within given circular areas around a single trap, when various values were ascribed to the parameters Mnat (natural morality), Mcon (control morality) and E (catching efficiency), in five or 30 days of trapping.
Fig 5.
Percentage of the catch originating from areas of various radii around a single trap after different numbers of days of trapping.
The radii are expressed as multiples of the mean distance D between the start and end points of the flies’ movements during the whole duration of various trapping periods, from 5–30 days. Data are extracted from the studies of Fig 4, in which the natural daily death rate, Mnat, was 0.03, and the daily death rate due to control, Mcon, was zero, and the catching efficiency, E, was 0.10.
Fig 6.
Percentage of the total catch of five traps that was regarded as originating from various circular areas around the central trap, when the other traps in the group were at various distances from the central trap, as shown in the maps of Fig 1B–1D.
The inter-trap distance shown on each of the charts (A-C) of the present figure is the distance between a trap and its closest neighbour. The red plot on each chart indicates the estimated area needed to account for 100% of the catch after any number of days, as calculated by the method of De Meeûs et al. [1]. In chart C, the sampled area for five days of trapping is not shown since the separation between adjacent traps (inter-trap distance) is greater than the maximum possible distance that the flies could have moved in that time, i.e., there was no substantial overlap in the situations sampled by adjacent traps. Without such overlap, the notion of a pooled area of sampling is an excessive abstraction.