Density dependence, prey dependence, and population dynamics of martens in Ontario

Ecology, June, 1999 by John M. Fryxell, J. Bruce Falls, E. Ann Falls, Ronald J. Brooks, Linda Dix, Marjorie A. Strickland

INTRODUCTION

It has long been appreciated that interactions between predators and their prey could destabilize community dynamics, inducing population oscillations over time (Lotka 1925, Volterra 1928, Rosenzweig 1971, Gilpin 1972, May 1972, Murdoch and Oaten 1975, Tanner 1975). Such mechanisms have been invoked to explain well-documented cycles in a variety of systems, including snowshoe hares and lynx in the Canadian arctic (Sinclair et al. 1993, Krebs et al. 1995), moose and wolves on Isle Royale (McLaren and Peterson 1994, Messier 1994), and communities of microtine mammals and mustelid predators in northern Europe (Hanski et al. 1991, 1993, Hanski and Korpimaki 1995).

These apparent examples of predator-prey cycles are especially intriguing because they involve carnivores with a territorial social structure. Theory suggests that territoriality should itself lend a stabilizing influence (Rosenzweig and MacArthur 1963, DeAngelis et al. 1975, Schoener 1987, Fryxell and Lundberg 1997), if the rate of carnivore population growth is adversely affected by aggressive interactions among territory holders. This implies that the rate of carnivore population growth should be dependent on both the density of prey (hereafter termed prey dependence) as well as on the density of conspecifics (hereafter termed density dependence). Our ability to test this hypothesis is usually compromised, however, by scarcity of long-term demographic data on both predators and their prey. In this paper, we analyze 20 yr of time series data for a territorial carnivore, the marten (Martes americana), in relation to temporal fluctuations of small mammals in southern Ontario. We test whether the Algonquin marten population varies cyclically or unpredictably over time as well as test whether rates of marten population growth depend on densities of prey, predators, or both. This information provides the basis for simple models summarizing our current understanding of food chain dynamics of the Algonquin assemblage of small mammals.

METHODS

Data

Age data from a sample of the commercial marten harvest during 1972-1991 in the Bracebridge District adjoining Algonquin Provincial Park, Ontario (48 [degrees] 30 [minutes] N, 78 [degrees] 40 [minutes] W) were used to estimate population abundance via cohort analysis. Harvesting in this district is regulated by trapline quotas issued by the Ontario Ministry of Natural Resources and trappers were asked to voluntarily submit their marten carcasses. On average, 53% of the carcasses were turned in for aging each year, forming the age distribution used in cohort analysis. The sealing of marten fur was mandatory and the total harvest of marten in the Bracebridge District was obtained from the sealing records. We therefore corrected for the 47% of carcasses that were not turned in, by multiplying the proportion of each age group obtained from the carcass sample by the total harvest in each year. Trapline quotas fluctuated annually and were greatly reduced in the early 1970s, at the beginning of this study, following a long period of decline in trapping success in the Bracebridge District. Counts of cementum annuli in premolar teeth and/or radiographs of the canines were used to assess age (Dix and Strickland 1986, Strickland and Douglas 1987).

Marten population estimates were derived using cohort analysis (Ricker 1940, Fry 1949). The principle behind this population estimator is based on use of a backward recursion formula to reconstruct specific contemporaneous cohorts of harvested animals to estimate minimum population abundance at various points in time. When the harvest period is short, as was the case for the trapping data used in our study, one estimates the number of individuals (N) of age i in year t by

[N.sub.i,t] = [N.sub.i 1,t 1] / p [K.sub.i,t] (1)

where p = the annual survival rate and [K.sub.i,t] = the number of animals of age i harvested in year t. This formula estimates the number of individuals present in the population immediately preceding the harvest period. Based on Hodgman et al.'s (1994) radiotelemetry data for an intensively trapped marten population in Maine, we estimated annual survival as 87%.

Application of cohort analysis to more recent cohorts that have not completely passed through the population requires estimation of age-specific abundance in the last year from harvest data only. We used Baranov's (1918) random catch equation to estimate age-specific abundance in the terminal year:

[N.sub.i,t] = [K.sub.i,t] / 1 - exp(-[q.sub.i]) (2)

with [q.sub.i] estimated from completed cohorts (Fryxell et al. 1988, 1991). As with any population estimator, cohort analysis involves several assumptions, including an important assumption that trapping methods and trapping effort have remained constant over time (Pope 1972, Ulltang 1977, Fryxell et al. 1988). There was little change in trapping technology or pelt prices over the study period, so we think that these assumptions are wellfounded.

Live-trapping of small mammals was conducted in a standardized manner over the same 20-yr period (1972-1991) at the Algonquin Park Wildlife Research Station (Fryxell et al. 1998), [approximately] 40 km from the border of the Bracebridge District from which marten data were obtained. Although we don't know whether rodent population dynamics are synchronized over such a broad spatial scale, there is evidence from Scandinavia that this can be the case (Steen et al. 1996). At each of 10-15 forested sites, a 90-m trapline was established with either one or two Sherman traps at stations 10 m apart. The physical dimensions of the Sherman traps were 7.5 x 7.5 x 30.5 cm, of sufficient size to catch even large rodents, such as red or flying squirrels. Single lines had 10 traps in total, whereas double lines had 20 traps. Lines were sampled either once or twice a month for three nights from mid-May until the end of August or September, yielding a maximum of 10 trapping periods per year. A few lines were abandoned or moved, but otherwise the trapping protocol was quite consistent from year-to-year.