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^r_m ), 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).

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Table 1. Derivation of different rates of increase

ADULT 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*