Proceedings of the First Symposium on Marsupials in New Zealand
A New Model
A New Model
Criticism of our change from daily assessment (Bamford's (1970) recommendation) to assessment over two nights at a time led to our including time in the basic model. The density should remain constant from night to night (or at least vary randomly) so it was possible to demonstrate (Appendix) a Poisson process where:
Relative density dt = - 1/t (loge (1-ft))
Where t is the time interval from the first assessment and
ft is the frequency of baits taken at time t.
When this model was tested with several sets of available data dt remained relatively stable.
Table 2 shows a typical data set from N.Z. Forest Products Ltd. for their 1974 poison area, and an un-poisoned control area. In column (4) dt can be seen to vary considerably and yet shows no systematic variation. The break at the poison date is sharp and results in a new level being established.
page 188POISONED AREA | NON-POISONED AREA | ||||||||
---|---|---|---|---|---|---|---|---|---|
DAYS | BAITS TAKEN % | Relative Density | BAITS TAKEN % | Relative Density | INTERVAL | ||||
t | f | d | dt | DI | f | d | dt | DI | i |
1 | 1 | 1.08 | 1.08 | 1.08 | 5 | 5.13 | 5.13 | 5.13 | 1 |
2 | 4 | 4.08 | 2.04 | 2.04 | 5 | 5.13 | 2.56 | 2.56 | 2 |
3 | 9 | 9.43 | 3.14 | 3.14 | 7 | 7.26 | 2.42 | 2.42 | 3 |
4 | 11 | 11.65 | 2.91 | 2.91 | 14 | 15.08 | 3.77 | 3.77 | 4 |
36 | 44 | 57.80 | 1.61 | 11.60 | 43 | 56.21 | 1.56 | 11.24 | 5 |
38 | 63 | 99.43 | 2.62 | 16.57 | 57 | 84.40 | 2.22 | 14.07 | 6 |
41 | 49 | 65.33 | 1.64 | 9.62 | 50 | 69.31 | 1.69 | 9.90 | 7 |
42 | 82 | 171.48 | 4.04 | 21.42 | 67 | 110.87 | 2.64 | 13.86 | 8 |
48 | 43 | 56.21 | 1.17 | 6.20 | 57 | 84.40 | 1.76 | 9.38 | 9 |
49 | 54 | 77.65 | 1.58 | 7.76 | 51 | 71.33 | 1.46 | 7.13 | 10 |
Poison | Drop | ||||||||
56 | 30 | 35.67 | 0.64 | 3.24 | 62 | 96.76 | 1.73 | 8.80 | 11 |
57 | 29 | 34.25 | 0.60 | 2.85 | 62 | 1.07.88 | 1.89 | 8.95 | 12 |
63 | 32 | 28.57 | 0.61 | 2.97 | 85 | 119.71 | 3.01 | 14.59 | 13 |
64 | 41 | 52.76 | 0.82 | 3.77 | 90 | 230.26 | 3.60 | 16.45 | 14 |
70 | 54 | 77.65 | 1.11 | 5.18 | 79 | 156.08 | 2.32 | 10.40 | 15 |
Kill % | Av. Max. | 33 54 |
69 | 45 |
Three estimators of relative density were calculated from the % of baits taken:
d = -100 loge (1-f/100)
dt = -100/t loge (1-f/100); t = time interval (column 1)
di = -100/i loge (1-f/100); i = no. of baitings (column 10)
Av. is the kill % from the average of baits taken before and after poisoning
Max. is the kill % from density on days 49 and 56 only (immediately before and after poisoning).
page 189Table 3 from 1972 data shows a similar pattern in the poisoned area data but in the control area dt falls sharply after day 2 and even more sharply after each break in baitings. Examination of the data on interference frequency (column 4) shows that almost all baits were taken from the fourth baiting onwards however and so a limit had soon been reached. Data from this point onwards should be excluded from analysis as it is no longer possible to estimate dt.
Further analysis of the 1976 Kaingaroa and Western Bays data (Table 4) showed difficulties with this model since dt (middle columns) fell rapidly, with a large decline after the poison date - yet at Western Bays dt rose again over the February baitings. If only the number of nights (i) over which the lines were baited are accumulated, then the new estimate di is a good fit and the estimate of kill in better agreement with that obtained from trapping.
page 190 page 191When di is calculated for N.Z. Forest Products data (Table 2) the fit was not good; there tended to be a rise in baits taken at the beginning of each baiting session followed by a decline. However at Kaingaroa and Western Bays baits were removed from bait stations between assessments, but at N.Z. Forest Products Ltd. baits were left and hence the total number of baited nights approximated the total time lapse. Finally it was found after analysis that at the last assessment at Western Bays baits were not removed from the bait stations between assessments and so i (the time interval) was not 10 but 8 + 14 = 22 days (as shown in Table 4 where the revised estimates of di are given in parentheses).