Proceedings of the First Symposium on Marsupials in New Zealand
Modelling the Effects of Control Operations on Possum Trichosurus Vulpecula Populations
Modelling the Effects of Control Operations on Possum Trichosurus Vulpecula Populations
Abstract
To model the effects of control operations on possum populations it was first necessary to determine the basic parameters on which the model could be based. In the absence of definitive field data, a range of parameters was used to simulate the growth of possum populations at various rates of increase. The theoretical effects of different levels of control by sterilisation and conventional killing were then calculated. The modelling shows that permanent sterilisation of both sexes is more effective than killing the same proportion of the population. Temporary sterilisation is not as effective as killing. The implications of these findings are discussed in relation to future control of possums.
Introduction
The objective of this paper is to model the effects of control by reproductive inhibition (conveniently called sterilization) compared to conventional control (killing) of the common brushtail possum Trichosurus vulpecula. The model used is developed from that given by Knipling and McGuire (1972), who presented a theoretical appraisal of the potential role of sterilization in suppressing rat populations.
The Basic Model
A population's pattern of growth is typically sigmoid, and may be represented by the following:
where
- N = the number in the population
- t = time
- e = the base of the natural logarithm
- r = the exponential rate of increase.
The rate of increase (e^{r}) is a function of reproduction and survival, and it is necessary to separate these functions when modelling reproductive inhibition of part of a population. Thus Knipling & McGuire (1972) expanded expression (1) as follows:
page 224where
- R = the size of the adult breeding population
- e^{S} = adult survival rate from t-1 to t
- e^{I} = the rate of recruitment to the adult population (in terms of animals recruited per adult female) and describes both birth and death rates of juveniles.
The exponents S and I are linear functions of the number in the population, so that:
To calculate the impact of reproductive inhibition it is necessary to further expand expression (2) (after Knipling & McGuire 1972) as follows:
where
Parameters for the Model
To model the rate at which a population will build up following a reduction in numbers it is first necessary to determine the parameters which could be used in the models.
To use expression (1), it is necessary to estimate the maximum rate of increase (e^{rm }), which is observed when population numbers are minimal, by measuring the rate of increase of either
i. | a newly established population, or |
ii. | an artificially reduced asymptotic population (and then extrapolating backward to minimal population size; see Caughley and Birch 1971). |
Neither of these measurements has been made for possum populations. Bamford (1972, 1973) calculated a maximum rate of increase from a translation of the time taken to disperse a certain distance; for possums in a part of the Taramakau Valley this rate was 1.41 (i.e. a 41% increase). While there may be some dispute with the derivation of this figure, and some doubt about page 225 liberation points and dispersal in the Taramakau Valley, a figure of 1.40 has been used as the maximum rate of increase for the model population in this paper.
To use expression (2) it is necessary to know adult survival and recruitment rates for
i. | an increasing population, and |
ii. | an asymptotic population. |
There are some data available for the latter but not for the former. Therefore, it was necessary to consider potential derivations of the maximum rate of increase.
The maximum annual adult survival is 100%, and the maximum annual recruitment to the adult possum population is 2 per adult female. When these are combined the maximum rate of increase is 2.0 (Table 1, Fig. 1). That is, the population doubles annually. Such a rate of increase is unlikely ever to have been reached. Some other potential rates of increase for possums are shown in Fig. 1, and their derivations in Table 1.
The maximum annual survival rate recorded for adults 1 year old and over (derived from stable age distributions presented by Bamford 1972 and Boersma 1974) is 80%. It is likely that survival rates would be higher in low density, increasing populations.
The maximum recorded rate of recruitment to an adult population (one year old and over) is 0.77 per adult female (derived from an age distribution of a harvested population as presented by Warburton 1977). This population had a fecundity or birth rate of 0.84 per female. Kean (1971) stated that double breeding (birth rate in excess of 1.0) occurs in low density populations with a good food supply. The maximum recorded birth rate (and therefore the maximum potential recruitment rate given 100% survival) is 1.8 births/female/year, recorded by Jolly (1976) on Banks Peninsula. The next highest recorded birth rates are 1.75 on Mt Egmont (Kean 1971), 1.5 on Banks Peninsula (Gilmore 1966), 1.4 on Kapiti Island (Kean 1971), and 1.2 in the Whitcombe Valley (Boersma 1974). All other birth rates recorded in New Zealand are less than 1.0 (e.g. Tyndale-Biscoe 1955, Bamford 1972, Crawley 1973, Boersma 1974, Bell this symposium).
If the maximum rate of increase of a population is 1.4, and the annual adult survival rate is in excess of 0.8, then the annual rate of recruitment to the adult population must be less than 1.2 per adult female (Table 1).
page 226ADULT SURVIVAL RATE | RATE OF ADULT RECRUITMENT PER FEMALE | POPULATION RATE OF INCREASE |
---|---|---|
1.00 | 2.00 | 2.00 |
.90 | 2.00 | 1.90 |
.90 | 1.80 | 1.80 |
.90 | 1.60 | 1.70 |
.90 | 1.40 | 1.60 |
.90 | 1.20 | 1.50 |
.90 | 1.00 | 1.40 |
.90 | .80 | 1.30 |
.90 | .60 | 1.20 |
.80 | 1.80 | 1.70 |
.80 | 1.60 | 1.60 |
.80 | 1.40 | 1.50 |
.80 | 1.20 | 1.40 |
.80 | 1.00 | 1.30 |
.80 | .80 | 1.20 |
.80 | .60 | 1.10 |
.74 | .52 | 1.00^{*} |
The Model Population
For the purposes of this paper the model population is assumed to have a maximum rate of increase of 1.4, in which maximum adult survival is 90% and recruitment to the adult population is 1.0 per adult female. The population prior to control is assumed:
i. | to be a stable population of 10 000 adult possums (1 year old and over) capable of breeding, with a sex ratio of 1:1; |
ii. | to be at the maximum sustainable density for the habitat; |
iii. | to be capable of breeding when 1 year old (and hence the adult population is 1 year old and over); |
iv. | to be isolated and not subject to emigration or immigration; |
v. | to have an annual adult survival of 74%, and an annual rate of recruitment to the adult population of 0.52 (adults recruited per adult female) which balances mortality (26%). |
The figure for adult survival is taken from live-trapping studies by Crawley (1973) in the Orongorongo Valley and Jolly (1976) in Birdlings Valley. Re-working of age distributions presented by Bamford (1972) in the Taramakau Valley and Boersma (1974) in the Hokitika River catchment provide estimates of adult survival ranging from 70% to 80%.
Effect of Different Control Operations
Killing removes a percentage of possums from the population. Possum numbers are reduced immediately. The survivors will have an increased reproductive and survival rate immediately after the numbers are reduced because of a reduction in density-dependent regulating factors. To calculate the theoretical rate at which a population will build up it is necessary only to impose the basic rate of increase curve on the remnant population. Following a 70% kill, a population with a maximum rate of increase of 1.4 will take a minimum of 10 years to return to 90% of its former level (Fig. 2). The increase in the first year after killing 70% of the population will be only 25% (or a rate of increase of 1.25). The maximum rate of increase of 1.40 will not be reached because population numbers have not been reduced to minimal. If the kill is 90%, the period of recovery is extended to 14 years. If the maximum rate of increase is only 1.2, the recovery time is much longer.
Inhibition of reproduction (or sterilisation) of both sexes leaves animals alive to compete for mates, food, nesting sites, and other resources, and therefore does not result in increased reproductive and survival rates of non-sterilised animals. If the sterilised animals are fully competitive and equally distributed they are theoretically capable of suppressing reproduction in non-sterilised members of the population to a degree equal to the percentage of the population sterilised. This will still apply even though possums may be polygamous, provided the same proportion of dominant individuals is sterilised as for the population as a whole.
Temporary sterilisation (i.e. sterilisation effective for only one breeding season) of 70% of the population reduces numbers only by suppression of reproduction for one breeding season. It will take a population with a maximum rate of increase of 1.4 only 3 years to reach 90% of its former level (Fig. 2).
Fig. 3. Theoretical response of possum populations to 70 percent control for three successive years.
The degree of sterilisation required to exterminate a population using expression (3) is 97% for a population with a maximum rate of increase of 1.4. This may be achieved by sterilisation of 70% of the population for three successive years (Fig. 3); i.e. 70% in the first year, 70% of the remainder in the second year, and 70% of the remainder in the third year. In practice the time to reach 90% of the population's former level as in Fig. 2, and to reach extinction as in Fig. 3, should both be shorter than shown. This is because the term for survival of sterile males and females does not take account of the increasing age of the sterilised animals. The term needs to be age specific.
Discussion
Some of the assumptions on which the modelling is based are unrealistic but necessary to compare the effect of control by killing versus reproductive inhibition. In fact, invalidity of some of the assumptions is likely to affect the modelling of control by conventional means more than sterilisation. Thus, the impact of immigration is likely to be felt immediately following reduction of numbers by conventional control, but not following any sterilisation which leaves animals to compete for resources. Furthermore, it is unlikely that a kill of 70% could be obtained for three successive years (because of the likely reduced acceptance of baits by a decreased population), but it is more reasonable, provided members of a population accept baits equally, to expect baits carrying a permanent sterilant to be accepted by 70% of the population for three successive years. (Bait shyness may affect acceptance of repeated applications of temporary chemosterilants but not permanent sterilants).
The pattern of results is the same for possum populations with other maximum rates of increase (and is the same as shown by Knipling and McGuire (1972) for rats). The slower the rate of increase of a possum population the more effective a control operation will be (i.e. the longer it will take the population to recover).
A maximum rate of increase of 1.4 is likely to be in excess of what a possum population would reach in today's modified New Zealand habitats page 231 (although it is quite possible that in the early days of colonisation such rates were reached). Starting with a population of 30 possums with a maximum rate of increase of 1.4, a colonising population is estimated (by the model) to take 23 years to reach 90% of its maximum density for the habitat. In fact populations typically over-shoot the maximum density, modify the habitat, and crash from this peak to a lower level. Pracy (1977) has noted that no population has yet stabilised in New Zealand.
Most of the early large-scale poison operations were aimed at peak or near peak possum populations (rather than stable asymptotic ones). If these populations would have naturally crashed to 50% of their peak level, then a kill of 50% only achieves what would have happened naturally. Such an example appears to have occurred in the Kokatahi (Boersma 1974). This may partially explain why no monitored populations are known to have increased significantly following large-scale poisoning operations (see also Bamford 1973).
The advantage of killing is that it gives immediate results. However, with the current use of poisons there are also problems with poisoning non-target species. Temporary sterilisation has no immediate or marked effect on a population, but is the safest for non-target species. However, it is unlikely that a temporary, moderate reduction in the numbers of a pest species will ever be required. Permanent sterilisation of one sex has no theoretical advantage over killing both sexes (Knipling and McGuire 1972). Permanent sterilisation of both sexes (whether by the same compound for both sexes or different compounds for each sex) is the most effective way of controlling population numbers. It is equally dangerous to target and non-target species. Thus, if permanent sterilants are to be used they will need to be highly specific or in a highly specific carrier-bait, and this is probably the main reason why they are not more widely used at present (see also Jackson 1972). Even then, a permanent sterilant will not give immediate results, and may need to be combined with conventional killing.
References
Bamford, J.M. 1972. The dynamics of possum (Trichosurus vulpecula Kerr) populations controlled by aerial poisoning. Unpublished Ph.D. thesis, University of Canterbury.
Bamford, J.M. 1973. Population statistics and their relation to the control of opossums in indigenous forests. In Assessment and management of introduced animals in New Zealand forests. N.Z. Forest Service, Forest Research Institute Symposium No. 14: 38–43.
page 232Bell, B.D. 1981. Breeding and condition of possums Trichosurus vulpecula in the Orongorongo Valley, near Wellington, New Zealand, 1966–1975 . In Bell, B.D. (Ed.). Proceedings of the first symposium on marsupials in New Zealand. Zoological Publications from Victoria University of Wellington 74: 87–139.
Boersma, A. 1974. Opossums in the Hokitika River catchment. N.Z. Journal of Forestry Science 4: 64–75.
Caughley, G. & Birch, L.C. 1971. Rate of increase. Journal of Wildlife Management 35: 658–663.
Crawley, M.C. 1973. A live-trapping study of Australian brush-tailed possums, Trichosurus vulpecula (Kerr) in the Orongorongo Valley, Wellington, New Zealand. Australian Journal of Zoology 21: 75–90.
Gilmore, D.P. 1966. Studies on the biology of Trichosurus vulpecula Kerr. Unpublished Ph.D. thesis, University of Canterbury.
Jackson, W.B. 1972. Biological and behavioural studies of rodents as a basis for control. Bulletin of the World Health Organisation 47: 281–286.
Jolly, J.N. 1976. Movements, habitat use and social behaviour of the opossum, Trichosurus vulpecula in a pastoral habitat. Unpublished M.Sc. thesis, University of Canterbury.
Kean, R.I. 1971. Selection for melanism and for low reproductive rate in Trichosurus vulpecula (Marsupialia). Proceedings of the N.Z. Ecological Society 18: 42–47.
Knipling, E.F. & McGuire, J.U. 1972. Potential role of sterilisation for suppressing rat populations. A theoretical appraisal. U.S. Department of Agriculture, Agricultural Research Service, Technical Bulletin No. 1455.
Pracy. L. 1977. Notes on opossums in New Zealand. New Zealand Institute of Foresters Newsletter 9(1): 10–14.
Tyndale-Biscoe, C.H. 1955. Observations on the reproduction and ecology of the brush-tailed possum, Trichosurus vulpecula Kerr (Marsupialia), in New Zealand. Australian Journal of Zoology 3: 162–184.
Warburton, B. 1977. Ecology of the Australian brush-tailed possum (Trichosurus vulpecula Kerr) in an exotic forest. Unpublished M.Sc. thesis, University of Canterbury.
General Discussion
WODZICKI. What do you call temporary sterilisation?
SPURR. Temporary sterilisation is preventing the breeding of a female for one year only i.e. in subsequent years she can join the breeding population again.
CLOUT. You have not taken any account of immigration in your model. Immigration could have a major impact. Certainly I found in my studies of possums that dispersal of animals into an area that had been poisoned could raise the population level quite rapidly after control. So you present a rather simplified view.
SPURR. Yes, typically the situation will be that you have both immigration and emigration. Only if the poisoned area was sufficiently large or sufficiently isolated would you have a situation where such movements were less important.
CLOUT. It would have to be very isolated since possums can move vast distances during the dispersal phase.
KEBER. If the animals have an average life-span of say 4 years and you permanently sterilise them, then you still have them doing potential damage for several years. In my particular area of exotic forest this could mean the difference between a crop harvested or not.
SPURR. Yes, I said killing gives the only immediate relief from damage. The purpose of the whole paper was to see if there was any advantage in searching for a chemo-sterilant.
page 234^{*} Stable population