Dynamics of a harvested moose population in a variable environment


Erling Johan Solberg, Norwegian Institute for Nature Research, Tungasletta 2, N-7005 Trondheim, Norway Tel. 47 73 80 14 68 Fax: 47 73 80 14 01 E-mail: erling.solberg@ninatrd.ninaniku.no


1. Population size, calves per female, female mean age and adult sex ratio of a moose (Alces alces) population in Vefsn, northern Norway were reconstructed from 1967 to 1993 using cohort analysis and catch-at-age data from 96% (6752) of all individuals harvested.

2. The dynamics of the population were influenced mainly by density-dependent harvesting, stochastic variation in climate and intrinsic variation in the age-structure of the female segment of the population.

3. A time delay in the assignment of hunting permits in relation to population size increased fluctuations in population size.

4. Selective harvesting of calves and yearlings increased the mean age of adult females in the population, and, because fecundity in moose is strongly age-specific, the number of calves per female concordantly increased. However, after years with high recruitment, the adult mean age decreased as large cohorts entered the adult age-groups. This age-structure effect generated cycles in the rate of recruitment to the population and fluctuations introduced time-lags in the population dynamics.

5. An inverse relationship between recruitment rate and population density, mediated by a density-dependent decrease in female body condition, could potentially have constituted a regulatory mechanism in the dynamics of the population, but this effect was counteracted by a density-dependent increase in the mean age of adult females.

6. Stochastic variation in winter snow depth and summer temperature had delayed effects on recruitment rate and in turn population growth rate, apparently through effects on female body condition before conception.


The population dynamics of ungulates may be influenced by a combination of predation (e.g. Messier & Crète 1985; Boertje, Valkenburg & McNay 1996), density-dependent food limitation and stochastic environmental variation (review in Srther 1997). In addition, several ungulate species are subject to intense human exploitation (Renecker & Hudson 1991). Moreover, because of a long life and age-dependent variation in several demographic variables (e.g. Srther & Haagenrud 1983), cohort effects and delayed responses to density and environmental variation are expected (Srther 1997; Clutton-Brock et al. 1997; Gaillard et al. 1998). Hence, the dynamics of ungulate populations can be complex, including cyclic populations (Soay sheep Ovis aries on St Kilda, Clutton-Brock et al. 1997; mouflon Ovis ammon in Kerguelen, Bousses et al. 1994), relatively stable population (red deer Cervus elaphus on Rum, Clutton-Brock et al. 1997) and weakly regulated populations (moose Alces alces, Srther et al. 1996).

While several studies have attempted to tease apart the effects of predation, density dependence and climate on ungulate population dynamics (e.g. Messier 1991, 1994; Post & Stenseth 1998), less effort has been devoted to assess the role of harvesting together with density-dependent and density-independent factors (but see Fryxell, Mercer & Gellately 1988; Fryxell et al. 1991). In particular, we lack information on the responses of different demographic variables to changes in population density due to changes in the harvest rate. Hunters may not only affect the population dynamics of ungulates directly by increasing mortality, but also by selective hunting of certain sex- and age-classes (Caughley 1977; Renecker & Hudson 1991), although the long-term population-dynamical consequences of such harvesting are poorly understood (e.g. Srther 1987). Theoretical studies have suggested that changes in age structure may have considerable dynamical effects, for instance by introducing delays into the population dynamics (Caswell et al. 1997). Thus, harvested populations may be well-suited to study the pattern and magnitude of such delayed responses in the population dynamics of ungulates.

Here, we investigate the dynamics of a population of moose almost free of natural predation, but subjected to human harvesting during a 27-year period. We particularly wanted to examine to what extent fluctuations in this population resulted from direct or delayed responses to harvesting or to density-dependent effects and stochastic variation in climate (Solberg & Srther 1994). Srther et al. (1996) suggested that a stable high-density equilibrium between moose and their food resources was unlikely without the influence of predation, because stochastic variation in fecundity would generate delayed responses in the dynamics of the population. Similarly, human harvesting has been suggested to cause cycles in moose populations as a result of time delayed density-dependent harvesting (Ferguson & Messier 1996). However, few studies have compared the effects of both harvesting and natural processes simultaneously on the dynamics of moose populations.

We based our study on cohort analysis (Hilborn & Walters 1992), which is a retrospective analysis of abundance based on age-specific data from harvested individuals (catch-at-age data). Analyses based on catch-at-age data are among the most important methods of assessing temperate fish stocks (Hilborn & Walters 1992), and they have a long history within fisheries management (Ricker 1940; Fry 1949). However, cohort analysis has also been used in studies of the population dynamics of moose (Fryxell, Greever & Sinclair 1988; Ferguson 1993; Ferguson & Messier 1996), as well as red deer (Lowe 1969), white-tailed deer Odocoileus virgianus (McCullough 1979; Fryxell et al. 1991), and reindeer Rangifer tarandus (Eberhardt & Pitcher 1992). From the reconstructed population, we used time-series analysis to reveal time-lags in the population fluctuations, and then attempted to disentangle the effects of density-dependent and density-independent factors Typesetter: insert Fig. 1 near here(Fig. 1) on the dynamics of the population.

Figure 1.

Flow diagram showing the predicted influence of density-dependent and density-independent harvest and recruitment rates on the rate of population growth. The dashed arrows illustrate the influence of selective harvesting on the sex- and age-structure of the population. The potential direct influences of climate and density on growth rate through adult mortality or winter mortality of calves are not shown as natural mortality is assumed constant in the model.


Study area, data collection and measurements

The data were collected in the municipalities of Vefsn, Grane and Hattfjelldal in southern Nordland county in northern Norway (65°20′– 66°00′) from 1967 to 1995. The study area has been described in Srther (1985) and Solberg & Srther (1994).

In co-operation with the local wild game authorities, hunters recorded date, locality, sex and carcass mass, and collected the lower jawbone of each moose harvested. Carcass mass (Langvatn 1977) was measured to the nearest kilogram. For calves and yearlings, the ontogenetic development and the pattern of tooth replacement in the lower jaw determined age. In older individuals, age was determined in the laboratory by counting the number of layers in the secondary dentine of the incisors (Haagenrud 1978). Because of a small number of weighed females within the different age groups and years we restricted the analyses of annual body mass variation to three age-groups: calves, yearlings, and females Р3 years old. For yearlings and females Р3 years old, the annual number of weighed individuals always exceeded 10 (range: 10–82), except during 5 years for yearlings (range 6–8) and 1 year for the oldest age-group (9). Excluding these years from the analyses did not lead to qualitatively different results. Because of the low number of calves harvested in the first part of the period, samples of weighed female calves were small (< 6) or absent during the 1960s and 1970s. We therefore only used mean body mass from calves harvested after 1980.

During the study period, 6996 moose were harvested in the population. Jawbones were collected from and age was determined for 6752 (96·5%) moose. The annual proportion of aged animals within different sex and age groups (calves, yearlings and adults) ranged between 87% and 100%. To correct for missing individuals, the annual number of moose within each sex and age group was multiplied with a factor correcting for the number of missing individuals in the data. For instance, in 1975 only 45 out of 49 adult females harvested were aged. The number of females within each adult (> 1-year-old) age-group for 1975 were therefore multiplied by 49/45 = 1·09 to correct for this deviation.

Harvest system

During the study, two different harvest practices were used. From 1967 to 1972, hunting permits were specified only for males, females and ‘free’ animals (male or female). After 1973, quotas have specified calves and yearlings (juveniles), adult males (> 1·5 years), and adult females (> 1·5 years). In general, juveniles formed the largest proportion of the quotas, followed by adult males, and adult females. Accordingly, a large proportion of the harvest comprised yearlings (mean = 32%, sd = 7), whereas the proportion of calves was lower (annual mean = 12%, sd = 7) than in most Scandinavian moose populations (Østgaard 1987).

Cohort analysis

From catch-at-age data, the minimum number of individuals alive in a specific year can be reconstructed, provided that data have been collected long enough to allow several of the cohorts to pass completely through the population. The population size immediately prior to the hunt in year t (Nt) will then be:

image(eqn 1)

where ni,t = the number of age i individuals present prior to the hunt in year t. ni,t is calculated as:

image(eqn 2)

where Di,t is the number of age i individuals killed in year t, and pi,t is the probability that an individual of age i alive after the hunting season will survive to year t + 1. The starting value for ni,t+1 is the number of individuals in the oldest age-class present. In practice, it is convenient to determine the terminal age beyond which only a small fraction of individuals survive the hunt as a starting value (Fryxell et al. 1988; Hilborn & Walters 1992). The terminal age was chosen at which only 1% of the individuals initially present in the cohort survived the hunt: 14 years in females and 7 years in males. Hence, based on the completed cohorts, the male segment of the population could be reconstructed from 1967 until 1988, and the female segment until 1981.

Cohort analysis requires independent estimates of natural mortality (pi), but as no estimates of age-dependent mortality are currently available for Norwegian populations we used data from radio-collared female moose with low exposure to wolves and bears in the Kenai Peninsula, Alaska (Bangs, Bailey & Portner 1989). In this study, annual survival rates were estimated as 0·97, 0·91, and 0·90 in 1–5, 6–10 and 11–15-year-old moose, respectively. These values fit well within the rates of survival observed among adult moose in Norway (Srther et al. 1992), as could be expected based on the almost absence of large carnivores predating on moose in Norway. Calf survival was set at 0·95 (see Srther et al. 1996). Varying the survival rates from 0 to 10% within the different age and sex-groups resulted in only small changes in abundance, probably because of the large proportion of young individuals (calves, yearlings and 2-year-olds) harvested within each cohort. Ferguson (1993) found similar results in a study of Newfoundland moose with cohort analysis.

Estimation of incomplete cohorts

Reconstruction of the population size with cohort analysis can only be accomplished based on cohorts that have passed completely through the population. To reconstruct population size from cohorts with surviving members requires estimates of the number of age i individuals killed in year t, Di,t, in recent years (Fryxell et al. 1988, 1991; Hilborn & Walters 1992). Such estimates can be obtained by calculating the age-specific hunting vulnerability per unit effort from completed cohorts, and using hunting effort from recent years to estimate Di,t from unfinished cohorts (Ricker 1940; Fryxell et al. 1988, 1991; Hilborn & Walters 1992). In the present study we lacked reliable data on total hunting effort (total number of hunter-days) for the full period. However, from the relationship between hunter-days and population size from the period 1973 (change of hunting system) to 1979 (with complete data on total number of hunter-days), hunting effort apparently increased proportionally with population size (ln(hunter-days) = 1·11 ln(population size), SE = 0·24). Hence, Di,t of older age-groups in incomplete cohorts may be assumed to be proportional to the mean age-specific proportion of adult moose harvested in cohorts that have completely passed through the population Typesetter: insert Fig. 2 near here(Fig. 2). Hence, we estimated the size of Di,ts of incomplete cohorts from the size of the Di,ts already harvested from the cohort. For example, Fig. 2 indicates that on average 40% of all adult males (Ð2-years-old) within a cohort were harvested as 2-year-olds, and 70%– 40% = 30% of all adult males were harvested as 3-year-olds (Fig. 2). Hence, based on the number of males harvested at the age of 2 years (2 years), we estimated the harvested number of 3-year-olds (3 years) next year to be: 3 years = 2 years/40*30. The Di,ts of incomplete cohorts were subsequently included in eqn 1 to calculate ni,t.

Figure 2.

The cumulative mean harvest (with SE) of male cohorts (top) born in the period 1973–88, and the cumulative mean harvest (with SE) of female cohorts born between 1973 and 1981, in relation to age in the Vefsn moose population, Norway.


Estimation of population size by cohort analysis depends on the following assumptions.

1. The use of a terminal age beyond which only a negligible number of animals survive the hunt assumes that hunters do not avoid old animals (Fryxell et al. 1988), which we have no reason to believe they do.

2. Cohort analysis assumes no annual variation in cohort-specific natural mortality (pi), for instance due to fluctuations in weather and population density (Fryxell et al. 1988). This effect may be of minor importance in large mammals, because of their generally high and stable adult survival (Fowler 1987; Srther 1997; Gaillard, Festa-Bianchet & Yoccoz 1998). As long as the majority of individuals in each cohort die from hunting, the effect of annual variation in natural mortality will also have only minor influence on the population size estimated by cohort analysis (Fryxell et al. 1988).

3.abundance estimates based on cohort analysis assume a closed population, i.e. no emigration or net immigration during the study period (Hilborn & Walters 1992). As we possess no quantitative data on migration in the Vefsn population, this assumption cannot be evaluated, but there is no evidence that there has been large variation in net migration during the period.

4. Estimation of incomplete cohorts assumes no annual variation in age-specific harvest vulnerability, e.g. due to a change of hunting methods (Fryxell et al. 1988; Hilborn & Walters 1992). For instance, a decrease in the hunting vulnerability of the young age groups (e.g. due to increased hunter selection for old animals) in the incomplete cohorts will lead to an underestimation of population size. This effect may be particularly important in our study, as the high terminal age leads to a large number of incomplete cohorts. However, as we possess data until 1995, but reconstructed the population only to 1993, we ensured that all calves, yearlings and 2-year-olds (which constitute mean = 64%, sd = 7·58 of the annual harvest) have been harvested and therefore included in the analyses. Hence, even in the most recent cohorts, less than about 40% of the cohort had to be estimated, which suggests that erroneous estimation of incomplete age-groups have a limited influence on our estimate of total population size.

The assumptions regarding the estimation of incomplete cohorts were further supported by the fact that the reconstruction of the population with a terminal age of 3 and 5 years in males and females, respectively (84% of all individuals harvested, Typesetter: insert Fig. 3 near hereFig. 3), was very closely correlated with the population reconstructed based on a terminal age which included 99% of the harvest (r = 0·98). In addition, there was a close relationship between the calves per female rates (r = 0·91), and the males per female rates (r = 0·74) in the population reconstructed with different sets of terminal age. This suggests that our population estimate was not greatly biased by the inclusion of incomplete cohorts.

Figure 3.

The reconstructed moose population size (left axis) based on (a) female cohorts of 14 years and male cohorts of 7 years (99% of total harvest), and (b) the reconstructed population size based on female cohorts of 5 years and male cohorts of 3 years (84% of total harvest). The two bottom curves (right axis) show the annual variation in number of hunting permits (c) and the annual variation in harvest size (d) in the Vefsn moose population, Norway, during the study period 1967–93.

Comparison with other population estimates

The population size was estimated by aerial census twice during the study period (Sørvig 1986). An aerial survey in 1976 by fixed-wing aircraft indicated a population size between 720 and 873 before the hunting season in 1975, whereas cohort analysis estimated it at 801 individuals. Similarly, an aerial survey in 1986 (Sørvig 1986) concluded with between 1229 and 1447 moose before the hunting season in 1985, when the reconstructed estimate was 1319, thus indicating that the cohort analysis provided a reliable estimate of the actual population size.

Solberg & Srther 1998 ) examined data on the number, sex and age of moose observed by the hunters during the study period in relation to similar data from the reconstructed population (Solberg & Srther 1998). A close correlation existed between the number of moose observed per hunter day and the reconstructed population size (r = 0·76, n = 26, P < 0·001) and, although not that close, between the sex ratio based on observations and the sex ratio from the reconstructed population (r = 0·41, n = 26, P < 0·05). Similarly, the relationship between annual observations of calves per cow and the number of calves per female in the reconstructed population was strongly correlated (r = 0·80, n = 26, P < 0·001, Solberg & Srther in press). The large recruitment rate (above 2) in some years (Typesetter: insert Table 1 near hereTable 1, Fig. 7), however, makes it evident that some of the assumptions on which cohort analysis depends have been violated. The most probable explanation for this discrepancy is that there was biased sampling (Fryxell et al. 1988; Hilborn & Walters 1992) in relation to the average hunting vulnerability on which the estimation of incomplete cohorts depends. The extreme rates appeared to be a result of too few females rather than too many calves in the reconstructed population, as the adult sex ratio tended towards a male bias, whereas the observed sex ratio was close to its most female-biased values (Solberg & Srther in press). This indicates that the number of females harvested from the younger age groups (2-, 3- and 4-year-olds) in some years was less than expected from their hunting vulnerability, leading to an underestimation of the number of older females in the incomplete cohorts. Nevertheless, the observed recruitment rates were strongly correlated with the reconstructed recruitment rates (Solberg & Srther in press), suggesting that the reconstructed recruitment rates may constitute a reliable index of actual recruitment rates during the study period.

Table 1.  Annual variation in the demographic variables of the moose population in the Vefsn valley, Norway 1967–93. Calves per female = calves per adult female (Р2 years old) in the reconstructed population. Harvest ratet–1 = annual harvestt–1/nt–1. Population growth rate = nt/nt–1
YearTotal population abundanceCalves per femaleHarvest rate t–1Population growth rate
Figure 7.

Annual variation in the mean age of adult (Р2 years old) females after the harvest season in year t–1 (top curve, left axis), and the annual variation in the number of calves per female (bottom curve, right axis) in year t, in the Vefsn moose population, Norway, during the study period 1967–93.

Variables based on the reconstructed population, hunting records and moose observations

From the reconstructed population we calculated the following variables used in the subsequent analyses (all values are ln-transformed (ln = natural logarithm) to stabilize the variance): Annual population size (Xt = ln Nt) measured just before the harvest season. Population growth rate (Rt = Xt – Xt–1). Calves per adult: the number of calves per adult Р2 years old before the hunting season. Calves per female: the number of calves per female Р2 years old before the hunting season. Sex ratio: the number of adult males (Р2 years old) per adult female (Р2 years old) before the hunting season. Female mean age: the mean age of adult (Р2 years old) females in the reconstructed population just after the hunting season.

From the reconstructed population and harvest records we calculated the harvest rate: ln(annual harvest, Dt/Nt), and the hunting success: ln(Dt/the annual number of hunting permits).

The observation indices were estimated from moose observation forms completed by the leader of each team of moose hunters from 1968 to 1993. The number of moose observed and number of hunters in the team were reported for each day during the first 2 weeks of the hunting season. Moose were allocated to six different categories; calves, yearling + adult males, yearling + adult females without calf, females with one calf, females with twins, and individuals unidentifiable to sex or age.

From the annual moose observation records, we calculated the following population indices (all values are ln-transformed to stabilize the variance): Observed calves per adult: the total number of calves divided by the total number of yearling- and adults. Observed calves per female: the total number of calves divided by the total number of yearling- and adult females. Observed sex ratio: the total number of yearling and adult males divided by the total number of females (yearling and adult). Twinning rate: the mean number of calves per female recorded with one or two calves.

Data analyses

Direct and delayed density dependence in population size

The presence of time-lags in the dynamics of the population was first examined with partial autocorrelation functions between the population sizes at different times. To illustrate the time-lags in the population dynamics, we plotted the partial autocorrelation against the time-lag (a correlogram). As population size increased during the period, we detrended (i) by regressing the series on year and then subsequently using the residuals, and (ii) by taking the first difference, DXt = Xt – Xt-1 (Diggle 1990), which is equal to the population growth rate, Rt.

We tested for direct and delayed density dependence in the population abundance series by applying a first and second order autoregression model (Royama 1992). We tested the relationship between population growth rate and density based on ln-transformed values. Analysing the relationship between Rt and Nt (a Ricker (1954) population model) gave qualitatively similar results. The log-linear relationship between Rt and population size at previous time steps (Xt, Xt–1, . . .., Xt–d) can be described by:

image(eqn 3)

where ai are the auto-regressive coefficients (Box & Jenkins 1970) and ɛ the random noise assumed to have zero mean and a constant variance. The equation can also be expressed as an auto-regressive model in Xt (Royama 1992; Bjørnstad, Falck & Stenseth 1995; Stenseth, Bjørnstad & Falck 1996):

image(eqn 4)

We estimated the auto-regressive coefficients with the autoreg procedure using maximum likelihood estimation (SAS Institute 1993, see below) with lags from 1 to 3 years. The most parsimonious model was selected by the corrected Akaike information criterion, AICc (Hurvich & Tsai 1989; see Forchhammer et al. 1998 for similar use), the model with lowest AICc being considered most parsimonious (Sakamoto, Ishiguro & Kitagawa 1986). Because the series was positively correlated with time, we removed the trend by including ‘year’ as a covariate in the auto-regressive model (Forchhammer et al. 1998). Moreover, the effect of detrending with time was examined by estimating the auto-regressive coefficients using Rt as a substitute for Xt.

To check the robustness of our conclusions regarding density dependence, we also applied the direct density-dependent test of Dennis & Taper (1994), a likelihood ratio test, which obtains the distribution of the test statistic through parametric bootstrapping. We tested the hypothesis of direct density dependence against the null hypothesis that the population was undergoing stochastic exponential growth or decline, or a random walk. The number of bootstrap samples in the model was set to 2000. We refer to the original reference for further details about the test.

Direct and delayed density-dependent harvest

We used multiple regression to investigate the relative influence of harvest rate and recruitment rate on Rt. Next, to determine the potential density-dependent effect of harvesting, we regressed the annual harvest (the total response) on population size (both values ln-transformed). Regression coefficients greater than one imply density-dependent harvesting because the harvest numbers grow faster than the number of moose (Messier 1994). Moreover, as hunting quotas determined by local managers each year bound the annual harvest in Vefsn, lags in the effect of density on harvest rate may appear because managers are not able to respond immediately to changes in population size. We examined time-lags between population size and harvest and hunting quotas by using phase plots (Fryxell et al. 1988; Ferguson & Messier 1996) of annual harvest and hunting quotas on population size with the points joined in a temporal sequence. An anticlockwise relationship may be an indication of time-lags in the response of the hunters to changes in population density. We then used cross-correlation function analysis (e.g. Diggle 1990; Chatfield 1996) to identify the lags in the effect of population size on hunting quotas and harvest, and determined the relative influence of population size at specified lags in stepwise regression analyses with forward inclusion of variables. The lagged population size found to enter was considered the most important lag determining hunting quotas and harvest size.

Density and climate effects on recruitment rate and body mass

As illustrated by Fig. 1, we expected the recruitment rate to vary according to population density, climate (working through female body condition), female age and adult sex ratio.

This was examined first by investigating the relationship between recruitment rate, calves per female and adult sex ratio to determine to what extent the variation in proportion of females or variation in number of calves per female determined variation in recruitment rate. Thereafter, we examined the relationship between the mean age of adult females in year t–1 and calves per female to identify the relative influence of female mean age on recruitment. We used the mean age after harvesting in year t–1 in preference to mean age in the current year as the former reflects the adult female age structure at conception.

We then examined the potential direct and delayed effects of population density and climate on body mass of calves, yearlings and females Р3 years old. We quantified density as the number of adults (calves excluded) during winter because food limitation was assumed to be most severe during winter and because calves are found to consume less and are subdominant to adults (Andersen & Srther 1992). This density estimate was strongly correlated with other estimates of population density, such as number of adult females (r = 0·99, partial r = 0·98 controlling for time), and population abundance before harvest, nt (r = 0·93, partial r = 0·88 controlling for time). Climatic variables included in the analyses were restricted to variables similar or close to variables previously shown to affect body condition or recruitment rate in moose (e.g. Srther 1985; Mech et al. 1987; Solberg & Srther 1994; Crète & Courtois 1997): the mean of the monthly mean snow depths from December to April, the mean of the monthly mean temperatures from December to April, the mean temperature in June, the sum of the June precipitation, the mean of the monthly mean temperatures from July and August and the sum of the precipitation in July and August. We used cross-correlation analyses to determine the lag at which density affected body mass. Then we performed a multiple regression analysis with forward inclusion of density (with all significant lags) on body mass to determine the most influential lag. Next, the climatic variables were entered with backward exclusion of variables not found to contribute significantly to the model. All climatic variables were measured at the Majavatn meteorological station in the municipality of Grane in the Vefsn valley (Norwegian Meteorological Institute, Oslo, Norway).

To evaluate the effect of density at different lags on calves per female, we included density in the current and four previous years in combination with adult female mean age in year t–1 in a stepwise multiple regression model. We used forward inclusion of variables to select the lag of density with most effect. We then tested the effect of climate, age at time t–1, and population density (at most effective lag) on calves per female in a multiple regression model. We restricted the analyses to include only climatic variables found to significantly covary with body mass because these variables were most likely to affect fecundity and neonatal body condition of calves (e.g. Srther et al. 1996). To get independent tests of several of the above relationships, we also performed tests using the demographic variables based on hunter observations (e.g. observed calves per female, observed sex ratio, twinning rate) in place of the demographic variables from the reconstructed population.

The effect of climate at different lags on population dynamics may be incorporated in the auto-regressive model as part of the random noise ɛt (Forchhammer et al. 1998). Hence, we extended eqn 4:

image(eqn 5)

where Ut is the stochastic climatic term at different lags. From this model, we estimated the auto-regressive coefficients as well as the climatic terms based on the procedure described for the auto-regressive modelling (see also Royama 1992; Bjørnstad et al. 1995; Forchhammer et al. 1998) using maximum likelihood estimation (SAS Institute 1993). We tested all climatic terms at time t and t–1, only.

Effects of harvesting on the population sex- and age-structure

Since the early 1970s, selective harvesting has been performed in Norwegian moose populations to optimize the yield of moose (Østgaard 1987). From 1967 to 1972, hunting permits were allocated as males and females and ‘free’ animals, which led to a high harvest of prime age individuals of both sexes. Since 1973, however, quotas have been specified for calves, yearlings, adult males and adult females, respectively, with the main proportion of the quota comprising adult males and juveniles (calves and yearlings), to restrict the harvest on productive females.

To examine the effect of selective harvesting, we tested whether the female mean age and adult sex ratio in the population varied with the proportion of female calves and yearlings in the harvest and variation in the sex ratio of the harvest in previous years. Moreover, because large cohorts may have proportionally larger effects on female mean age a few years later (e.g. Bergerud 1971), we tested whether annual variation in the postharvest number of calves per female varied with the mean age of adult females in the year calves entered the adult age-groups. Similarly, as indicated by several simulation studies (e.g. Sylvèn, Cederlund, & Haagenrud 1987; Srther et al. 1992), the effect of sex-skewed harvesting on the population sex ratio varies depending on the harvest size in proportion to population size. Hence, in the multiple regression models testing the effects of sex-skewed harvesting, we also included the harvest rate in t–1.


In most cases we expected our time series to covary beyond displaying trends. Therefore, we presented relationships mainly between detrended variables. Detrending was accomplished either by including time in the analyses or by using residuals from the regression on time (Diggle 1990; Chatfield 1996). In most cases relationships based on detrended and not detrended variables gave qualitatively (statistically significant or not) similar results. However, in cases where they differed, we present the results based on both detrended and nondetrended variables. Most demographic variables from the reconstructed population, harvest records and moose observation records were significantly related with time, but not the climatic variables.

In the present study both the dependent and independent variables in several analyses displayed significant autocorrelation. We therefore corrected the degrees of freedom by a method proposed by Bartlett (1946), which has been used in several recent studies (Myers, Mertz & Barrowman 1995; Post et al. 1997; Post & Stenseth 1998). This method modifies the tests of significance by adjusting the degrees of freedom (d.f.): N′ = N (1 –a1a2)/(1 + a1a2), in which N′ is the adjusted d.f., N the number of paired observations and a1 and a2 are the first order auto-correlation coefficients for the two series. Furthermore, the method assumes a first order auto-regressive process and does not account for excess variability explained by longer lags (Myers et al. 1995). Hence, in the case of longer lags we may to some extent overestimate N′. All significant first order autocorrelations were positive.

In testing for significance of coefficients of multiple regression analyses with auto-correlated variables, we used partial correlation analyses with adjusted d.f. The d.f. and P-value of relationships based on auto-correlated variables are denoted d.f.adj and padj, respectively. First order autocorrelation was substantial in the demographic variables from the reconstructed population and the harvest records (0·6–0·87), moderate in the observed values (0·35–0·60), and not significant in the body mass and climatic variables (0·06–0·30).

Statistical analyses were done using Spss for Windows (SPSS 1996), SAS (SAS Institute 1995) and Resampling Stats (1997). Multiple regression analyses utilized forward inclusion and backward elimination of independent variables. Forward inclusion of significant variables was used to discriminate between the effect of several highly correlated independent variables (e.g. variables with different lags), whereas backward exclusion of variables was used to find the best combination of independent variables to explain the effect. Models were examined for multicolinearity as strong correlation between independent variables makes the interpretation of their separate effect difficult. No pairs of independent variable were correlated by more than r = 0·5 (which were our tolerance criteria). Stepwise forward entry of independent variables used α-to-enter < 0·05 and α-to-remove > 0·10. Stepwise backward exclusion of variables used α-to-remove > 0·10. If not stated, the multiple regression analysis used backward exclusion of variables. For the sake of comparison and simplicity, standardized regression coefficients (Beta) were presented. The level of significance was set at α = 0·05.


Direct and delayed density dependence in population size

The moose population before the hunting season increased from 434 to 1370 animals (0·07–0·21 moose km–2 or 0·25–0·79 moose km–2 forests and bogs; Fig. 3, Table 1) during the study period with two distinctive declines. During the period 1984–89, there was a strong decrease in population size. This period was followed by a rapid increase between 1989 and 1992. The population also decreased in number between 1967 and 1972 and between 1977 and 1980.

Partial autocorrelation coefficients of population size and Rt both showed significant positive coefficients for lag 1 and negative coefficients for lag 2 ypesetter: insert Fig. 4 near here(Fig. 4), suggesting that density the current year was dependent on density in the two previous years. However, according to the corrected Akaike (AICc) selection criterion, the detrended population estimates were most parsimoniously described by a first order auto-regressive process (although with small margins), whereas a second order auto-regressive process best described the variation in Rt (Typesetter: insert Table 2 near hereTable 2). Moreover, applying the bootstrapping test of Dennis & Taper (1994) did not confirm the presence of direct density dependence in the population abundance series (one-sided test, P > 0·10), although this does not exclude the presence of a higher order process. Assuming that the process was second order, the auto-regressive coefficients were, according to the parameter plane of Royama (1992; p. 63), in the region that predicts dampened oscillations, suggesting no strong regulation of this population.

Figure 4.

Correlograms showing the partial autocorrelation function of (a) population size (ln(nt) and detrended), and (b) population growth rate (ln (nt/nt–1)), against the time-lag. All correlation coefficients exceeding the expected 95% confidence interval (Bartlett band ≈ 2/Ür1T, 2/Ür1T in the correlogram, T is the length of the series) were considered significant.

Table 2.  Auto-regressive (AR) coefficient estimates (1 + β1 and β2) based on detrended time series. Detrending was achieved by (i) including time in the auto-regressive models (population size), and (ii) by using the first difference of Xt (DXt = Xt –Xt–1 = growth rate). All coefficients in bold are statistically significant (P < 0·05). Bold AICc values denote the most parsimonious models. (a) Auto-regressive models without climate. (b) Models including climate (Snowd. = mean snow depth in Dec–April, Junt. = mean June temperature). Only the most parsimonious models are shown in (b)
(a)   AR(2)-coef 
Dependent variablenAR(1)-coef. (1 + β1)b ± SE AICc(1 + β1)b± SEβ2a ± SE AICc
  1. a Two-tailed t-test, H0: β2 = 0.

  2. b Two-tailed t-test, H0: (1 + β1) = 1.

  3. c Two-tailed t-test, H0: ωk = 0.

Population size270·626 ± 0·173–61·181·559 ± 0·132–0·776 ± 0·133–59·45
Population DXt260·668 ± 0·151–53·421·017 ± 0·185–0·525 ± 0·184–55·65
bltl>a Two-tailed t-test, H0: β2 = 0.
b Two-tailed t-test, H0: (1 + β1) = 1.
(b) AR(2)-coef   
Dependent variablen(1 + β1)b ± SE β2a ± SE Snowd.t–1ω1c ± SE Junet.t–1ω2c ± SE AICc
Population size271·413 ± 0·118–0·694 ± 0·1120·001 ± 0·000–0·013 ± 0·007–65·45
Population DXt261·021 ± 0·165–0·578 ± 0·1650·001 ± 0·000 –60·41

Proximate causes of variation in population growth rate

The variation in population growth rate Rt was closely correlated to annual variation in harvest rate in year t–1 Typesetter: insert Fig. 5 near here(Fig. 5a, r = – 0·76, d.fadj = 9, padj < 0·05) and calves per adult (Fig. 5br = 0·62, d.fadj = 11, padj < 0·05). Harvest rate (Beta = – 0·65, P < 0·001, partial r = 0·94, d.fadj = 9, padj < 0·05) and calves per adult (Beta = 0·62, P < 0·001, partial r = 0·91, d.fadj = 8, padj < 0·05) explained combined 93% of the variation in Rt. Using the observed calves per adult as a measure of recruitment rate gave a similar, although weaker relationship with Rt (partial r = 0·71, d.fadj = 10, padj < 0·05).

Figure 5.

Population growth rate (nt/nt–1) of the Vefsn moose population, Norway 1967–93, in relation to (a) harvest rate (Dt–1/nt–1) and (b) calves per adult (Р2 years old). n = annual population size, D = annual harvest.

Direct and delayed density-dependent harvest

The regression coefficient (y) did not support the prediction that harvesting increased faster than population size (y = 1·16, SE = 0·11, P > 0·10). However, as shown by the phase plots Typesetter: insert Fig. 6 near here(Fig. 6a–c), there were some indications that a density-dependent process may have influenced the population at two different levels: first, in the early part of the study period before the change of harvest system (1973), and next, at a much higher population size after a period of large population growth (Table 1, Fig. 3). When we re-tested the prediction after excluding the data before 1973, annual harvest increased significantly faster than population size, indicating density-dependent harvesting (y = 1·56, SE = 0·21, P < 0·05).

Figure 6.

Annual variation in (a) the annual harvest, (b) the number of permits, (c) the harvest rate, and (d) the calves per adult female (Р2 years old) in successive years in relation to total population size (a,b,c), or number of adults (d). Data from the Vefsn moose population, Norway 1967–93.

The phase plots, displaying characteristic anticlockwise relationships, indicated a time-delay in the relationship between the annual harvest and population size, and the hunting quota and population size (Fig. 6a,b). This was supported by the regression models revealing that the annual variation in harvest size and hunting quotas was best explained by population size in year t–1 (detrended r = 0·91, d.f.adj = 6, padj < 0·05) and t−2 (detrended r = 0·85, d.f.adj = 6, padj < 0·05), respectively. The annual harvest was closely related to the size of the harvest quota (detrended r = 0·97, d.f.adj = 8 padj < 0·05) and constituted on average 73% (sd = 5·45) of the number of permits issued. Hence, apparently neither the managers nor the hunters were able to respond instantaneously to changes in moose abundance. On the other hand, hunter success (harvest size/hunting quota) increased significantly with population size (detrended r = 0·57, d.f.adj = 14, padj < 0·05), indicating that the hunters to some extent were able to compensate for the disparity between hunting quotas and population size, and thus reduce the time-lag in the system.

The influence of adult sex ratio on recruitment rate

The combined variation in adult sex ratio (Beta = – 0·15, P < 0·001, partial r = 0·99, d.f.adj = 12, padj < 0·001) and calves per female (Beta = 1·06, P < 0·001, partial r = – 0·68, d.f.adj = 14, padj < 0·01) contributed significantly to the variation in calves per adult. However, the effect of varying sex ratio was small compared to the effect of varying calves per female. Indeed, the univariate effect of calves per female on calves per adults was almost as large (R2 = 0·97) as the combined effect (R2 = 0·98). This was probably partly due to the positive correlation between calves per female and adult sex ratio (r = 0·43, d.f.adj = 11, padj > 0·10), i.e. the fecundity rate increased with the proportion of females in the population. When repeating the analyses with the observed calves per female and observed sex ratio as independent variables, only the observed calves per female contributed significantly to the variation in calves per adult (Beta = 0·70, P < 0·001, partial r = 0·72, d.f.adj = 15, padj < 0·01).

Female body mass and calves per female in relation to age, density and climate

A significantly higher number of calves per female (r = 0·71, n = 26, P < 0·001) and observed calves per female (r = 0·67, n = 26, P < 0·001) followed years with high postharvest mean age among adult females Typesetter: insert Fig. 7 near here(Fig. 7). However, when controlling for similarity in trend and autocorrelation only calves per female (detrended r = 0·67, d.f.adj = 14, padj < 0·05), but not observed calves per female (detrended r = 0·43, d.f.adj = 16, padj = 0·11), exhibited significant relationships with variation in adult female mean age in t–1. Twinning rate increased with mean age in t–1 (r = 0·71, n = 26, P < 0·001), but not significantly when controlling for time (detrended r = 0·30, n = 26, P = 0·13).

There was a positive relationship between the annual variation in mean body mass of female yearlings and females Р3-years old (r = 0·48, n = 27, P < 0·05), but not between female yearlings and female calves (r = 0·43, n = 14, P > 0·10) or females Р3 years old and female calves (r = 0·27, n = 14, P > 0·10). However, mean body mass of female yearlings was positively related to the body mass of female calves of the same cohort (r = 0·62, n = 14, P < 0·05) indicating that factors affecting calf body mass were long lasting.

Variation in mean body mass of calves and yearling females was most significantly related to the number of adults in year t–1 (r = – 0·60, n = 14, P < 0·05) and t−2 Typesetter: insert Fig. 8 near here(Fig. 8, r = – 0·53, n = 25, P < 0·01, detrended r = – 0·46, n = 25, P = 0·05), respectively, whereas body mass of females Р3 years old varied independently of population density (r = – 0·27, n = 27, P > 0·10). The mean body mass of female yearlings changed from 165 kg in 1968 to 124 kg in 1987, corresponding to a 25% drop in body mass, whereas the mean body mass of female calves dropped 16% from 73 kg in 1982 to 61 kg in 1987. In addition, annual variation in body mass was related to variation in climate (Typesetter: insert Table 3 near hereTable 3). Large female calves and yearlings occurred after cool early summers when simultaneously accounting for population size, and large body mass was found among yearlings and females Р3 years old after snow-rich winters (Table 3).

Figure 8.

Body mass of female yearlings in relation to the number of adults (Р2 years old) in year t–2 in the Vefsn moose population, Norway, during the study period 1967–93.

Table 3.  Standardized regression coefficients (Beta) for models describing the relationship between population density (number of adults) and climate, and body mass of female calves, yearlings, and adult females (Р3 years) of moose in the Vefsn population, Norway 1967–93
Detrended variables
Dependent variableIndependent variableBetapR2BetapR2
Mean calf body massPopulation density t–1
June temp.
June prec.
Mean yearling body massPopulation density t–2
June temp.
Snow depth
0·54 0·44
Р3-year-old female mean body mass Snow depth 0·450·0250·20   

When accounting for the change in age structure, there was a negative effect of population density in year t–2 on the number of calves per female. Winter snow depth in year t–1 was positively related to the number of calves per female when controlling for female mean age and population density (Typesetter: insert Table 4 near hereTable 4). This result was also significant after accounting for similarity in trend, whereas the effect of density was not significant after adjusting for auto-correlation in the dependent and independent variables (Table 4). However, the weak partial correlation between density and calves per female could to some extent be due to the close relationship between age and density in year t–1 (detrended r = – 0·47). Moreover, accounting for trend and auto-correlation, variation in the observed calves per female was positively related to winter snow depth in year t–1, while twinning rate was positively affected by both winter snow depth and adult female mean age in year t–1. The effects of climate in the current year were not significant, suggesting that climate influenced recruitment indirectly through body condition of the mother before conception, but not during the period of gestation and lactation.

Table 4.  Standardized regression coefficients (Beta), and partial correlation coefficients for the combined effects of female age, population density (number of adults) and climate on recruitment rate. Recruitment rate is measured as calves per female from the reconstructed population, calves per female from observation records (observed calves per female), and twinning rate from observation records. Bold partial correlation coefficients (partial r) are found significant (P < 0·05) after correcting d.f. for autocorrelation
Detrended variables
Dependent variableIndependent variableBetap2Partial rBetapR2
Calves per femaleMean age t–1 0·860·0000·710·64 0·580·0010·62
density t–2
0·380·006 –0·440·340·038 
 snow depth
0·340·011 0·510·360·016 
Observed calves per femaleMean age t–1 0·770·0000·64 0·41 0·340·0570·61
density t–2
–0·270·066 –0·51–0·430·016 
 Snow depth
0·480·002 0·590·480·004 
Twinning rateMean age t–1 0·790·0000·680·56 0·540·0060·42
 Snow depth
0·300·035 0·440·390·040 
 June temp.
0·250·064 –0·37–0·320·091 

Including climate in the auto-regressive model

The second order auto-regressive process was the most parsimonious in describing the dynamics of both population size and Rt, when climate was included in the models (Table 2b). Snow depth in year t–1 explained a significant proportion of the variation in both population size and population growth rate, whereas June temperature was also entered in the model using population size, although the effect was only marginally significant (P = 0·07). This supports the previous observation that the dynamics of this population mainly exhibited delayed density dependence.

Interaction between harvesting and recruitment rate

On average, a significantly larger number of male than female calves were recruited to the population each year (males mean (sd) = 163 (62), female mean (sd) = 118 (53); paired t-test, t = 8·76, n = 27, P < 0·001). The sex ratio was male-biased among yearlings, but female-biased among adults (mean (sd) = 0·92 (0·09)). The harvest sex ratio was strongly male-biased (mean (sd) = 1·72 (0·34)) suggesting that the female-biased adult sex ratio resulted from selective hunting of males. Moreover, the adult sex ratio decreased with increasing harvest rate in year t–1 Typesetter: insert Fig. 9 near here(Fig. 9, r = – 0·73, n = 26, P < 0·001). Accordingly, the adult sex ratio was significantly affected by the annual variation in the harvest sex ratio in year t–2 (Beta = – 0·37, P < 0·01, partial r = – 0·55, d.f.adj = 9, padj = 0·10) as well as harvest rate in t–1 (Beta = – 89, P < 0·001, partial r = – 0·81, d.f.adj = 7, padj < 0·05). However, as suggested by the partial regression coefficients (Beta), the effect of harvest rate on the adult sex ratio in the remaining population was much larger than the effect of varying male-biased harvest alone. Moreover, harvest sex ratio was not significant after correcting for auto-correlation. When repeating the analyses with the observed sex ratio as the dependent variable, only harvest rate in year t–1 was significant (Beta = – 0·59, P < 0·01), but not after correcting for auto-correlation (partial r = 0·45, d.f.adj = 8, P > 0·10). Hence, the population sex ratio was apparently most affected by sex-skewed harvesting during years of high harvest rate, although the power of the tests was weak due to strong autocorrelation.

Figure 9.

Time series of harvest sex ratio (males: females), adult sex ratio in the population (males: females) and harvest rate in year t–1 (annual harvest, Dt–1/population size, nt–1) in the Vefsn moose population, Norway 1967–93.

The mean age of adult (Р2-year-old) females increased during the study period (Fig. 7, r = 0·75, n = 27, P < 0·001). A similar increase occurred in the proportion of calves + yearlings in the female harvest (r = 0·68, n = 27, P < 0·001), suggesting that the increase in female age was due to higher calf and yearling hunting mortality. However, after removing the trend and adjusting for autocorrelation, no correlation remained between the two variables (r = 0·04).

Fluctuations in adult female mean age (Fig. 7) could be due to the large variation in recruitment rate (Fig. 7) if hunters were unable to dampen the annual variation in recruitment rate by harvesting proportionally more yearling females in large cohorts compared to small cohorts. Indeed, in a multiple regression analysis, the calves per female after harvest in year t−2 (Beta = – 0·53, P < 0·01), and the annual proportion of calves and yearling females harvested (Beta = – 0·49, P < 0·05) explained a significant proportion of the variation in the adult female mean age. However, after removing the trend and adjusting for auto-correlation, only calves per female after harvest in year t–2 explained a significant proportion of the variation in the adult female mean age (partial r = – 0·67, d.f.adj = 9, padj < 0·05).


Our study corresponds with several recent studies of longer time series on ungulates demonstrating influences of both density-dependent and density-independent processes on population dynamics (reviewed in Srther 1997; Forchhammer et al. 1998; Gaillard et al. 1998; Post & Stenseth 1998). However, in contrast to most others, our study population was also influenced by intensive human exploitation (Fig. 1), by which ≈ 25% of the autumn population was harvested annually (Table 1). This introduced complexity to the dynamics of the population because selective harvesting indirectly affected recruitment rate and because harvest rate was density-dependent only part of the time. The latter was indicated by the strong effects of harvesting in the early phase of the time series at densities much lower than at densities that later exhibited population decrease due to harvesting (Fig. 3, Table 1). Hence, apparently there were two periods of strong density dependence separated by a period of weak or even inverse density dependence. This could have been caused by the introduction of a new harvest policy in the early seventies (e.g. Østgaard 1987), in which the focus changed from harvesting mainly adult moose to a more balanced system including more calves and yearlings in the harvest. As indicated by the present study, this change led to a more productive population, which may have given the moose population the ability to increase despite an increasing annual harvest (Fig. 3). This scenario is similar to models showing multiple stable states caused by density-dependent predation at low density and food limitation at high density (e.g. Fryxell, Greever & Sinclair 1988; Sinclair 1989, 1996; Messier 1994), except that in the present case both states apparently were caused by the predator, the hunters. However, this does not exclude the possibility that other causes may have operated simultaneously (Sinclair 1989). For instance, in the present study, periods of population decline were also associated with low recruitment rates (Figs 3 and 6), suggesting that variation in female age or density (see below) may have slowed growth simultaneously with intensive harvesting.

The harvest rate also showed a time-lag in relation to population fluctuations, probably because managers did not respond immediately to changes in the moose population. This corresponds with several predator–prey models (e.g. May 1981; Sinclair & Pech 1996), where time delays in the functional and numerical response of the predator to variation in the population size of the prey generates fluctuations in the prey species. However, the total response (numerical + functional) of the hunters was also dependent on population density, as hunting success increased with density. Hence, hunters were able to compensate by shooting a relatively larger proportion of their quota during years of high density, and less during years of low density when quotas tended to reflect high density. As a consequence, the time-lag in the effect of harvesting on the dynamics of the population was reduced, which probably prevented larger population fluctuations caused by harvesting. These results were also most consistent with the auto-regressive model, indicating that the Vefsn moose population mainly showed delayed density dependence. Moreover, the results support previous studies showing that harvesting indeed has a strong impact on the dynamics of moose populations (Fryxell et al. 1988) and may also cause recurrent population fluctuations due to delayed density-dependent harvesting (Ferguson & Messier 1996).

The main cause of variation in recruitment rate appeared to be variation in the age of breeding females (Table 4, Fig. 7). In female moose, a close relationship exists between the probability of ovulation and age (Srther & Haagenrud 1983; Srther & Heim 1993). Early maturation also seems to be associated with an early onset of twin production (Srther & Haagenrud 1983). This is in accordance with theoretical models predicting that allocation of energy to reproduction should increase with age (e.g. Gadgil & Bossert 1970) as the cost of reproduction is generally higher among young compared to old animals (Clutton-Brock 1991). Accordingly, both the calving rate and the twinning rate increased with the mean age of the adult females during the period. This pattern contrasts with other cervids where females regularly produce only a single calf (monotocous), e.g. in red deer and reindeer (Rangifer tarandus, Clutton-Brock, Guinness & Albon 1982; Skogland 1983, 1985, 1989; but see Bergerud 1971), or in polytocous species such as roe deer (Capreolus capreolus) where the lack of pronounced age-dependent variation in fecundity after the second year of life (Gaillard et al. 1992) prevents any strong effects of variation in age structure. Because of the often large increase in fecundity with age in female moose (Srther & Haagenrud 1983), variation in the female age structure may have a particularly strong influence on the recruitment rate in this species. Indeed, the effect of age on recruitment rate may be even larger than reflected by the age-specific fecundity rates alone, as early juvenile survival may improve with maternal age and experience (Clutton-Brock 1984). Similar effects may also reduce the effect of reproductive senescence on the recruitment rate.

There was also a negative feedback between the recruitment rate and the female mean age because hunters were not able to increase the harvest of calves in years with high recruitment rates. This was related to a reluctance among the hunters to shoot calves (calves constitute on average 12% (sd = 7) of the annual harvest). As a consequence, the variable female cohorts that entered the breeding population generated annual variation in recruitment to the population, causing time-lags in the population dynamics. This exemplifies how selective harvesting may generate time-lags and complex dynamics in an age-structured population.

Variation in the adult sex ratio exerted little influence on the population growth rate. This was contrary to our expectations and in contrast to Cederlund & Sand (1991), who observed that changes in sex ratio were more important to population growth rate than changes in female age-structure in a Swedish moose population. However, their study population contrasted with ours having less variation in fecundity rates among age-classes, and greater variation in the proportion of females. Despite the large variation in harvest sex ratio in Vefsn, the adult sex ratio was quite stable (Fig. 9). Indeed, sex-skewed harvesting had its main effect on adult sex ratio during years of high harvest rate even when the harvest was only moderately sex-biased. This was particularly apparent during years of intensive harvesting in the late eighties, during which both the population sex ratio and harvest sex ratios were low. This supports previous simulation studies (Sylvèn et al. 1987; Srther et al. 1992) showing that sex-skewed harvesting has its most significant effects on the population sex-structure when a large proportion is culled.

A decrease in the recruitment rate through density-dependent food limitation may act as a regulatory mechanism on the growth of the population (Sinclair 1989; Royama 1992). In moose, increasing population density may affect both age at maturity and twin production. For instance, age at maturity in moose is size-dependent (Srther & Haagenrud 1983, 1985; Srther & Heim 1993; Srther et al. 1996), as in several other large ungulates (Albon, Mitchell & Staines 1983; White 1983; Srther 1997), and some evidence also exists for a size-dependent fecundity rate in moose (Franzmann & Schwarts 1985; Sand 1996). However, the twinning rate did not decrease with increasing density, and no density-dependent decrease in body mass of adult females was detected during the period, although the latter could be the result of delayed age at maturity and thus prolonged time for high body growth (Gadgil & Bossert 1970). For instance, density-dependent decrease in the mean yearling body mass found in the present study may have increased the age at maturity and caused the inverse relationship between population density and recruitment rate indicated by the study. However, as the mean age of adult females increased with population density (and year), the effect of density on recruitment did not regulate the population. In other words, density-dependent reduction in recruitment may have been counteracted by an increase in the mean age of the female population.

Whether population density could lead to a more stable population size in the absence of the effect of increasing female age depends on the form of the regulatory mechanism (Srther 1997). For instance, a time-delay in the density-dependent effect on recruitment may amplify, rather than dampen population fluctuations (May 1981). Such time-lags in recruitment could result from density-dependent effects on early growth and subsequently on later reproduction (Fryxell et al. 1991; Sand 1996). In the present study, calves born after years of high population density tended to be small, and their relatively small size persisted among yearlings of the same cohort (see Solberg & Srther 1994 for similar effects on males). Initially, small calves may have been the result of mothers in poor condition, as has been observed in other cervids (Skogland 1985; Albon, Clutton-Brock & Guinness 1987; Albon, Clutton-Brock & Langvatn 1992). Alternatively, the density-dependent decline in recruitment could be the result of larger neonatal mortality of calves, as has been observed among several ungulates (review in Gaillard et al. 1998). However, the time delay in the density-dependent response strongly indicates that the change in fecundity (age at first reproduction, twinning rate), through the effect of body condition rather than mortality, was the main reason for the change in recruitment rate. Moreover, in an extensive study based on radio-collared animals, Srther et al. (1996) found no evidence of density-dependent summer mortality of moose calves in Norway. In the absence of other regulatory factors, such time-lags may lead to long return time in the population dynamics and large fluctuations in population size, which makes a stable equilibrium between the moose and its resource supply less likely (Srther et al. 1996; Srther 1997).

Based on previous work (Srther 1985; Solberg & Srther 1994), we were particularly interested in whether stochastic variation in climate influenced female body mass and in turn the population dynamics. The influence of summer temperature on calf and yearling female body mass, and the potential effect of female body condition on recruitment, may support such an expectation. Indeed, June temperature also showed a tendency to affect the twinning rate the year after. It is commonly accepted that weather conditions during the vegetative season affects the quality and quantity of forage (Riley & SkjelvaÅg 1984; Albon & Langvatn 1992; Sand 1996) and summer climate has previously been shown to explain significant proportions of the variance in body mass of other temperate (White 1983; Albon et al. 1987; Albon & Langvatn 1992; Gaillard et al. 1996; Langvatn et al. 1996) and subtropical ungulates (Owen-Smith 1990). In the present study, the negative relationship between body mass and early summer temperature was presumably related to climatic effects on the phenological stage of the plants important in the diet of moose (Bø & Hjeljord 1991). Stochastic variation in summer weather conditions may consequently affect female body mass and subsequently the age at maturity and the frequency of females producing twins. Moreover, calf body mass was correlated with yearling body mass in next year as well as June temperature the current year. Apparently, the effect of summer temperature may have immediate effects on female body condition and delayed effects on calf production, which support similar conclusions by Srther et al. (1996), and by Crète & Courtois (1997) for moose in Canada.

Winter snow depth also affected female body mass, and was even more influential than summer temperature on recruitment rate. However, the overall positive influence on both body mass and recruitment rate was contrary to the prediction that snow depth increases energetic expenditure during winter, which in turn reduces body condition and subsequently the recruitment rate (Mech et al. 1987; Crète & Courtois 1997; Post & Stenseth 1998). This also contrasts with Srther's (1985) result, which showed negative effects of snow depth on body condition of moose in southern-and central Norway, whereas Solberg & Srther (1994) found no such effects in Vefsn & Sand (1996) in Sweden. This was not because of shallow snow depths in the Vefsn area. Mech et al. (1987) found the critical value of annual snow accumulation (the sum of monthly maximum snow depths) to be 361 cm, which was in fact exceeded in the Vefsn valley in 17 of 26 winters.

We suggest two possible explanations for the positive effect of snow depth in the present study. First, deep snow may have positive effects on the phenology of plant species important in the moose diet. Deep snow in winter was related to deep snow in May (r = 0·85, n = 26, P < 0·0001), which in turn may prolong the period of freshly exposed vegetation in the early summer. Because early stages of plant growth are associated with peak protein levels (Van Soest 1983), this may have positive effects on moose body condition. This may be particularly important in mountainous areas such as Vefsn, where the start of the growing season may differ by a month between the valley floor and timber line, giving rise to a long period of high-quality fodder for moose during summer. Similar mechanisms have been suggested to explain part of the variation in body mass of red deer (Langvatn & Albon 1986; Albon & Langvatn 1992) in Norway. Secondly, deep snow may increase the availability of winter food because thick snow layers that carry a moose may enable browsing on taller trees and bushes. The unstable climate in northern Norway, often changing between mild and cold weather, may make the snow less penetrable due to the formation of several layers of ice. Therefore, moose may be able to manage even thick snow layers without much conditional costs under such favourable conditions. Assuming this hypothesis is right, we would expect that the effect of snow depth on moose condition would depend on local climatic conditions shaping the texture of the snow, and less on the depth of the snow layers.

The pattern in the auto-correlations suggested that fluctuations in the time series could be best described as a cyclic model (Royama 1992; page 134). Although the short duration of the time series seriously reduces the probability of successfully detecting regulation (Royama 1992; Turchin 1995), this suggests that delay in the response of hunters to changes in population size, and changes in recruitment rate induced by changes in age-composition are sufficient to counteract the regulatory effects of the density-dependent decrease in recruitment. Such fluctuations have strong implications for the management of this population. For instance, time delays in the population dynamics will impose problems in correctly predicting the population size, which should influence the choice of harvest strategy (Engen, Lande & Srther 1997). Furthermore, calculating the correct quotas for such a population will in itself be difficult. Thus, provided that the management aim is to prevent wide oscillations in population size, a management system should be developed that facilitates a more rapid response in the harvest rate to changes in population size.


We wish to thank all the hunters in the Vefsn valley who made this study possible through their sampling and preparation of the data from the moose harvested. We are also grateful to H. Haagenrud who initiated the study, and to M. HaÅker who organized the collection of data. The comments of Eric Post, John Fryxell and Nigel G. Yoccoz greatly improved the manuscript. The study was funded by the Norwegian Research Council (Use and management of outlying fields), the Directorate for Nature Management (DN) and the Norwegian Institute for Nature Research (NINA).

Received 19 September 1997;revisionreceived 13 May 1998