The intrinsic rate of increase of reindeer and caribou populations in arctic environments

The intrinsic rate of increase of an animal population, r , is specific to the environment in which it is measured. Previous estimates of maximum growth rates for reindeer and caribou Rangifer tarandus populations were based on introductions to islands with cool oceanic climates. The mean intrinsic rate of increase of 6 populations was 0.26 ranging from 0.21 on St Paul Island in the Bering Sea to 0.29 in the Barff herd on South Georgia. I calculated rmfor two Rangifer populations introduced to arctic environments to determine the effect of environmental severity on the intrinsic rate of increase. Reindeer on the Belcher islands increased at r m = 0.28 and caribou on Southampton Island increased at r m = 0.23 (mean = 0.26). The lower primary productivity and longer duration of snow cover in arctic environments did not affect the intrinsic rate of increase.


Introduction
The intrinsic rate of increase of an animal population, r m , is worth knowing for a variety of practical and fundamental purposes e.g., to compare the favourability of different environments (Begon et al. 1986), to estimate sustained yield hunting limits (Caughley and Birch 1971), and to indicate potential population regulation mechanisms (Bergerud 1980, 1983, Caughley and Krebs 1983, Tanner 1975).r m is best estimated by measuring the growth of a newly established population increasing from minimal density with unlimited resources (Caughley and Birch 1971).
Because birth rates and survival rates are unlikely to be the same everywhere an organism lives, r relates only to the environment whithin " m ' which it was measured (Birch 1948).Published estimates of maximum population growth rates in Rangifer have all been from island environments with cool oceanic climates (ie., 4-5 months with snow cover).In this paper I present data on the growth rates of two Rangifer populations introduced to islands with arctic climates (ie., 8-9 months with snow cover) and compare the intrinsic rates of increase in the two environments.Native caribou disappeared from the Belcher islands in the late 1800's (Ferguson 1985).

Methods
The intrinsic rate of increase can be calculated only when a population has a stable age and sex distribution (Caughley and Birch 1971 Calf survival (from birth to age one) was varied as required, to achieve the final population size.
The model was based on the following assumptions; 1) there was an equal sex ratio at birth, 2) calf survival was equal in both sexes, 3) adult survival was 100% in both sexes, 4) all adult

Results
The number of caribou on Southampton Island was estimated at 1200 ± 340, 11 years after they were introduced and at 5400 ±1130 nine years later (Heard unpublished).The actual rate of growth (r) was 0.25 and the intrinsic rate of increase was 0.23.
In March 1982, four years after the introduction, the number of reindeer on the Belchers was estimated at 287 (Ferguson 1985), an observed growth rate of r = 0.39 and r was 0.28.

Discussion
The mean intrinsic rate of increase of the two Rangifer populations introduced into arctic environments was 0.26; the same as the mean intrinsic rate of increase of 6 populations introduced to islands with cool oceanic climates (Table 1).Therefore lower primary productivity and the longer duration of snow cover in the arctic environments did not affect the intrinsic rate of increase, suggesting that reindeer and caribou can do well as long as the energetic costs of obtaining food (e.g., cratering) are compensated for by the energy derived from their forage.
The theoretical maximum rate that caribou can increase is 0.31 given a litter size that is al-  and Krebs 1983, Leader-WUliams 1988).
When introduced cohorts are biased toward adult females, r is always greater than r m and the difference is usually substantial (Table 1).
On St Mathew I for example, 24 yearling females and 5 yearling males were introduced in 1944.By 1957 they had increased to 1350 (Klein 1968), an actual rate of increase of 0.30.
Correcting for the distorted sex ratio indicates that the herd grew from 24 females to 685 females, a rate of increase of 0.26, assuming an even sex ratio of recruits (1350-29 = 1321 recrutis; 1321 x0.5 = 661 female recruits; 661 + 24 = 685 females).After correcting for the unstable age distribution using the simulation model, the estimate of r was further refined 7 m to 0.25 (Table 1).Bergerud (1971) adjusted for the distorted sex ratio of caribou introduced to Brunette Island by assuming that population composition would approach the mean sex ratio for the species at equilibrium which is only 56 males: 100 females (Bergerud 1971).My model of the Brunette population indicated that mortality was only 5%/yr for all ages and both sexes combined, providing little room for substantial differential mortality between the sexes.Therefore I believe Bergerud should have assumed an even sex ratio.
Again, no recolonization of caribou occurred and in March 1978, 60 semi-domestic reindeer (R. t. tarandus, 50 adult cows and 10 adult bulls) were taken from Tulctoyaktuk, NWT and released on Flaherty I, the largest island in the archipelago.Those animals were allowed to range freely.There are no wolves on the Belcher island and no animals were shot.

(
yearling and older) females produced one calf each year, and 5) all rates were constant through time.Data from Southampton Island were consistent with those assumptions.All 44 females (including 10 yearlings) in 1988 and 1989 collections were pregnant.Equal survival of the Sexes can be inferred from the even sex ratio found in 1987 (104 adult males: 100 adult females; Heard unpublished); Simulation was continued until the age distribution stabilized at which time lambda, the finite rate of population change, was determined as N c /N tl .The log e lambda for each population was considered an estimate of the intrinsic rate of increase for Rangifer.When more than two population estimates were available, I calculated the final population size and the actual growth rate from a linear regression of log e population size on time where the line was constrained to pass through the known number introduced.I considered the period of increase on St Paul and St George islands from the time of introduction until hunting began.

Table 1 .
Maximum rates of increase for reindeer and caribou populations where r is the actual rate of increase and r m is the intrinsic rate of increase; the rate at which the population would have increased if it had had a stable sex and age distribution.
(Reimers 1972)e birth to twins (Godkin 1986) and calves can become pregnant(Reimers 1972).The theoretical maximum rate of increase of