• Alces alces;
  • climate;
  • population dynamics;
  • recruitment;
  • ungulate nutrition


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

1. Better understanding of the mechanisms affecting demographic variation in ungulate populations is needed to support sustainable management of harvested populations. While studies of moose Alces alces L. populations have previously explored temporal variation in demographic processes, managers responsible for populations that span large heterogeneous landscapes would benefit from an understanding of how demography varies across biogeographical gradients in climate and other population drivers. Evidence of thresholds in population response to manageable and un-manageable drivers could aid resource managers in identifying limits to the magnitude of sustainable change.

2. Generalized additive models (GAMs) were used to evaluate the relative importance of population density, habitat abundance, summer and winter climatic conditions, primary production, and harvest intensity in explaining spatial variation in moose vital rates in Ontario, Canada. Tree regression was used to test for thresholds in the magnitudes of environmental predictor variables that significantly affected population vital rates.

3. Moose population growth rate was negatively related to moose density and positively related to the abundance of mixed deciduous habitat abundant in forage. Calf recruitment was negatively related to a later start of the growing season and calf harvest. The ratio of bulls to cows was related to male harvest and hunter access, and thresholds were evident in predictor variables for all vital rate models.

4. Findings indicate that the contributions of density-dependent and independent factors can vary depending on the scale of population process. The importance of density dependence and habitat supply to low-density ungulate populations was evident, and management strategies for ungulates may be improved by explicitly linking forest management and harvest. Findings emphasize the importance of considering summer climatic influences to ungulate populations, as recruitment in moose was more sensitive to the timing of vegetation green-up than winter severity. The efficacy of management decisions for harvested ungulates may require regional shifts in targets where populations span bioclimatic gradients. The use of GAMs in combination with recursive partitioning was demonstrated to be an informative analytical framework that captured nonlinear relationships common in natural processes and thresholds that are relevant to population management in diverse systems.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Key questions in the study of herbivore population ecology include the mechanisms responsible for variability in vital rates and the contributions of density-dependent and density-independent factors (Sæther 1997; Gaillard, Festa-Bianchet & Yoccoz 1998). Predation, harvest, density-dependent forage competition and climate have been shown to significantly affect vital rates of northern ungulates (Messier 1994; Solberg et al. 1999; Patterson & Power 2002; Garrott et al. 2003). While studies have identified the effects of a variety of individual climate variables on animal growth, body condition and survival (Pettorelli et al. 2007; Mysterud et al. 2008), it is rare to find a comprehensive analysis that explicitly compares the relative contributions of geographic, climatic and biological variables, including hunter harvest. This is particularly relevant for managed populations that span broad biogeographical gradients and for which knowledge of the most sensitive indicators and drivers of population change can be informative for population status assessment and management decision-making.

Annual stochastic variation in climate can be an important driver of ungulate population dynamics (Sæther 1997), affecting the quality of summer forage available to ungulates (Chapin et al. 1995) and potentially having complex interactions with other limiting factors (Post et al. 1999). Large herbivores inhabiting seasonal environments are adapted to give birth during the period of vegetation green-up to maximize access to highly nutritious forage. Annual variation in weather patterns and geographic variation in climate regime that affect the timing of vegetation green-up or delay the deterioration in plant nutritional value may thus affect juvenile growth and survival (Langvatn et al. 1996; Pettorelli et al. 2007). While the effects of climate in highly seasonal environments has been demonstrated in alpine areas (Pettorelli et al. 2007) or northern boreal communities (Herfindal et al. 2006), the importance of vegetation onset and plant phenology to large herbivores in warm summer continental climates is not well understood. Anticipating the effects of global warming to ungulate populations will require improved understanding of the influence of landscape-scale variation in climate and the relative importance of winter versus summer climatic variation in vital rates. Mechanisms including biotic effects, such as changes in trophic interactions, as well as direct abiotic effects may be influential, and Lenarz et al. (2009) found that survival of moose at the southern limit of their circumpolar range in Minnesota, USA, was negatively correlated with the frequency and magnitude by which temperature exceeded an upper heat stress threshold (Renecker & Hudson 1986). The importance of heat stress to moose populations that span climatic gradients across southern to core range limits in eastern North America has not been examined.

Government agencies responsible for sustaining healthy ungulate populations would benefit from an understanding of the relative importance of more easily controllable factors, such as ungulate harvest and land management that affect the availability of preferred habitat, in relation to climate-related effects on vital rates. Of particular value would be an understanding of the interactions among limiting factors and identification of thresholds in drivers that negatively affect populations. For example, identification of ungulate harvest levels that can be sustained at a particular population density and habitat supply could aid resource managers in balancing multiple management objectives.

Here, the dynamics of a harvested moose population exposed to natural predation and forest management in Ontario, Canada, were investigated. Population growth rate (GR), calf recruitment into the winter population [calves per 100 cows (CPC)] and the bull/cow ratio were used as key parameters to evaluate population drivers. The population dynamics of moose were examined across spatial gradients in hypothesized population drivers as means to understand the mechanisms responsible for variation in vital rates. The objectives were (i) to determine the relative importance of population density, habitat abundance, summer and winter climatic conditions, rate of change in primary production and harvest intensity in explaining spatial variation in moose vital rates and (ii) to identify potential thresholds in predictor variables that affect moose population vital rates. A broad suite of climate and vegetation indices were examined to clarify the relative contribution of summer versus winter bioclimatic effects, including winter severity (snow depth), the timing and change in vegetation phenology, and indices for heat stress. This comprehensive approach, combined with objective (ii) to identify thresholds, was intended to identify the most sensitive indicators useful for monitoring populations of relevance to sustainable resource management.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Study Area

The study was conducted in the province of Ontario, Canada, where managed forests overlap the population range of moose (Fig. 1). The study area encompassed diverse vegetation communities, reflecting a transition zone between the southern deciduous forest of eastern North America and the northern boreal forest. Detailed descriptions of forest community species composition for the study area, corresponding to the Boreal and Great Lakes – St Lawrence Forest Regions can be found in Rowe (1972).


Figure 1.  The study area in Ontario, Canada, showing the population growth rate for selected wildlife management units.

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The study area encompassed a north–south gradient in mean annual temperature, and moist conditions were more prevalent in the south and east because of the moderating effects of the Great Lakes. In the most southerly portion of the study area, mean annual temperature was approximately 2–6 °C, mean length of the growing season (GS) was 168–189 days and mean annual precipitation was 673–838 mm (MacKey et al. 1996). In the north-west, mean annual temperature was 0–2 °C, mean length of the GS was 146–170 days and mean annual precipitation was 550–785 mm.

Moose in Ontario share their range with white-tailed deer Odocoileus virginianus Zimmermann in the southern portions of their range, woodland caribou Rangifer tarandus caribou Gmelin in the north, and small, isolated populations of re-introduced elk Cervus elaphus L. in north-western and south-central Ontario. The most important predators of moose include wolves Canis lupus L. and black bears Ursus americanus Pallas and humans.

Moose Population Data

Moose population data employed in the study were collected by the Ontario Ministry of Natural Resources (OMNR) during standardized aerial population surveys conducted between 1997 and 2005 (McLaren 2006). Ontario is divided into discrete wildlife management units (WMUs) for the purpose of conducting population surveys and administration of management activities for moose and other wildlife. Population GR for each WMU was calculated as:

  • image

where N was measured as the population density in each WMU estimated from aerial surveys (Fig. 1). Winter recruitment was measured as the number of CPC, based on the mean number of adult females and calves observed in the surveyed plots for each WMU. To reduce potential bias in the estimation of the CPC and the adult sex ratio, estimates were only used for further analysis if the percentage of unknown adults recorded during aerial surveys was <20% of the total number of observed animals among all plots surveyed for the WMU.

Moose Harvest Data

Moose harvest data were collected annually by OMNR for each WMU using a postcard questionnaire survey mailed to all hunters who received a bull or cow tag and to a sample of tag applicants who did not receive a tag (unsuccessful applicants eligible to harvest a calf). For the data employed in this study, the average return rate of questionnaires among WMUs was 58% and ranged from 41% to 79%. The estimated kill of bulls, cows and calves in each WMU was used to calculate the proportion of moose harvested each fall during the years of the study. Proportion of animals harvested was calculated as:

  • image

where the number of animals in the postharvest population for each WMU was determined using abundance estimates from the aerial inventory conducted during the winter immediately following the fall harvest.

Habitat Data

Habitat attributes for each WMU were derived from the Ontario land cover classification (Anonymous 2004) and the provincial road layer maintained by the OMNR. Evidence from Brown, Rettie & Mallory (2006) suggested that this classification was effective for wildlife-habitat assessment based on field verification in the north-eastern portion of the study area. The coverage was derived from Landsat-7 Thematic Mapper (TM) satellite data frames recorded between 1999 and 2002, and a supervised maximum-likelihood algorithm was used to classify the imagery (25 m by 25 m pixel size) using bands TM 1–TM 7 (Anonymous 2004). The land cover classification was used to generate three habitat variables: the percentage cover of depletions, mixed-deciduous forest and coniferous forest within each WMU. Depletions included the sum total extent of forest cutovers (<10 years in age), recent burns (<10 years in age) and regenerating depletions (old burns >10 years in age supporting sparse vegetation), while mixed-deciduous forest included both mixed forest and deciduous forest as identified in the original land cover classification (Anonymous 2004). The age thresholds of depletions were approximate, and the actual classification was based on spectral reflectance characteristics dictated by the independent classification source. The classification may not have captured subtle variations in forage for moose or predatory black bear that varied in shorter time frames. These three habitat classes were chosen as evidence elsewhere has shown that moose populations benefit from early seral forest depletions and mixed deciduous forest for foraging opportunities and conifer cover as shelter from snow and predators during winter (Dussault, Courtois & Ouellet 2006). Annual forest harvest and natural disturbance spatial layers available from the OMNR were used to update the land cover classification to ensure it accurately reflected habitat conditions for each WMU in corresponding years of the study. Road density (km of road per 100 km2) in each WMU was included as a covariate because of the potential for road access to augment opportunities for hunter harvest. All spatial analyses were conducted using ArcGIS desktop 9.2 (ESRI Inc., Redlands, California, USA).

Climate Data

Spatial grids of historical climate data were obtained from Natural Resources Canada (McKenney et al. 2007), and the resolution of grids was 150 arc second (approximately 4·5 km). Details of the methodology are described elsewhere (McKenney et al. 2006, 2007) and used point estimates from approximately 471 meteorological stations and the ANUSPLIN model (Hutchinson 1995) to develop spatially continuous climate layers. Three summer bioclimatic variables were used for subsequent moose population modelling: mean temperature of the warmest quarter (sTemp), precipitation of the warmest quarter (sPrecip) and the Julian day number of the start of the GS. These variables were intended as indicators of the potential limiting effects of spring and summer climate on forage availability and quality. The GS was defined as starting when the mean daily temperature was ≥5 °C for 5 consecutive days beginning March 1 of each year (MacKey et al. 1996). Climate layers were superimposed on each WMU to obtain mean values for each combination of WMU and year of the study.

To evaluate heat stress effects on moose population rates, the methods and key findings for the sensitivity of indices reported by Lenarz et al. (2009) were used with the spatial climate data available for Ontario. A winter heat stress index (HSIw) was calculated as the sum of °C above – 5 °C during January (Julian day 1–31) when daily maximum ambient air temperature exceeded the threshold. Late spring heat stress indices, when moose may still have remnant winter coat, included the sum of °C above threshold during April–May (Julian days 92–152) when daily maximum ambient air temperature exceeded 14 °C (HSIsp14) and 20 °C (HSIsp20), respectively. Maximum daily temperatures were estimated for each WMU using spatial grids (150 arc second) of daily maximum temperature provided by Natural Resources Canada (Hutchinson et al. 2009) and generating mean values for each WMU and Julian day.

Potential winter constraints on moose energetics and foraging were assessed using snow accumulation data available from the OMNR snow course network (Smith, Voigt & Bisset 1989). Details of the sampling methods and locations are described by Smith, Voigt & Bisset (1989), and data from 33 snow stations from across the province were used in the analysis. Most WMUs had 1–3 snow course sites, and the nearest adjacent snow station was used for WMUs lacking a station. The snow depth index (SDI) for each site in each year is the weekly snow depth values summed for the entire season. For WMUs with more than one snow course, the snow depth indices were averaged to generate a single value for each WMU for each year. These values were then averaged for the three years proceeding the year of the respective moose population survey for each WMU. Snow course data were not available in all three preceding years for all WMUs; in which case, the average value used in the present analysis was based on the number of years available (range 1–3 years).


The normalized difference vegetation index (NDVI) was used to generate an index of rate of change in vegetation phenology that may affect forage quality. NDVI data processed by the GIMMS group were obtained form the University of Maryland Global Land Cover Facility (Tucker et al. 2005). NDVI is the difference in reflectance (light reflected by vegetation) between the near-infrared and visible bands divided by the sum of these two bands. The NDVI was derived from data collected from the advanced very high-resolution radiometer instruments on board the National Oceanic and Atmospheric Administration satellites (NOAA). NDVI time-series data were available on a bimonthly basis at a spatial resolution of 64 km2. Each bimonthly time step is a maximum value composite from days 1–15 of the month and days 16 through to the end of the month. The NDVI pixels overlapping each WMU boundary were pooled to calculate a mean NDVI value for each WMU for each year and bimonthly time step corresponding to the moose population data. Following methods described by Pettorelli et al. (2007), the rate of change in plant productivity during the spring period of rapid plant growth (green-up) was defined as the maximal slope between any two consecutive bimonthly NDVI values between May 1 and August 15. Higher maximal increases in NDVI were assumed to reflect more rapid changes in vegetation growth.

Data Analysis

Generalized additive models (GAMs) were constructed to test the hypotheses that rates of population growth, calf recruitment and the bull/cow ratio were negatively related to population density, summer and winter climatic conditions, hunter harvest and habitat supply. GAMs automatically allow nonlinear response shapes by fitting smoothed functions for the predictor variables (Guisan, Edwards & Hastie 2002) and have the potential to better represent the underlying ecological data (Pearce & Ferrier 2000). To avoid over-fitting and to retain more easily interpretable relationships in the GAM smoothing functions (thin plate regression spline), an upper of limit of 3 degrees of freedom was set for each explanatory variable when fitting the models.

The predictor variables used for model fitting for each response variable are listed in Table 1. Values of each climatic variable and NDVI were averaged among the three years prior to each aerial survey to provide a generalized representation of potential climatic influences on vital rates across the bioclimatic gradient and for consistency with the 3-year interval of the population GR data. Owing to the absence of vital rate information between years of aerial surveys, vital rate measures from the previous survey were used to measure the potential effects of endogenous population drivers on vital rates in the most recent survey years (i.e. years in which values of the response variable were calculated). Only biologically meaningful interaction terms were included in the model fitting for each response variable. Predictor variables were standardized to zero mean and unit variance to minimize the differences in measurement scale.

Table 1.   Predictor variables used to model moose population growth rate (GR), calves per 100 cows (CPC) and the bull/cow ratio (BCR)
VariablesDescriptionResponse variable model
  1. HSI, heat stress index; NDVI, normalized difference vegetation index.

Population predictors
 DensityNo. of moose per km2 as estimated in the preceding surveyGR, CPC, BCR
 CPCCalves per 100 cowsGR
 BCRBull/cow ratioGR
Harvest predictors
 HarvallProportion of moose (all age and sex classes) harvested in the autumn preceding the surveyGR
 HarvmProportion of adult male moose harvested in the autumn preceding the surveyBCR
 HarvfProportion of adult female moose harvested in the autumn preceding the surveyBCR
 HarvcProportion of calf (both sexes) moose harvested in the autumn preceding the surveyCPC
Habitat predictors
 Road densityKm of road per 100 km2 within each wildlife management unitGR, CPC, BCR
 DepletionsPercentage cover of forest cutovers, recent burns and regenerating depletionsGR, CPC, BCR
 MixedPercentage cover of mixed-deciduous forestGR, CPC, BCR
 ConiferPercentage cover of coniferous forestGR, CPC, BCR
 NDVIMaximal slope between two consecutive bimonthly NDVI values between May and AugustGR, CPC, BCR
Climate predictors
 HSIwWinter heat stress index for January (−5 °C threshold)GR, CPC, BCR
 HSIsp14Late spring (April–May) heat stress index (14 °C threshold)GR, CPC, BCR
 HSIsp20Late spring (April–May) heat stress index (20 °C threshold)GR, CPC, BCR
 sTempMean temperature of warmest quarterGR, CPC, BCR
 sPrecipTotal precipitation of the warmest quarterGR, CPC, BCR
 Growing seasonJulian day number of the start of the growing seasonGR, CPC, BCR
 SDISnow depth indexGR, CPC, BCR

The time interval between consecutive population surveys varied among WMUs (2–6 years) and averaged three years. Owing to the sensitivity of the GR model to the time interval between repeat surveys, only WMUs with a three-year interval were included in building the model. This constraint was relaxed for the calf recruitment and the bull/cow ratio models to take advantage of the greater sample size, and evidence that density in the previous survey was not a significant variable regardless of whether only WMUs with a 3-year interval were used.

Parsimonious model fitting was accomplished using forward-backward variable selection, in which each forward step was followed by a backward step to remove any variables in the model that were no longer significant (Pearce & Ferrier 2000). Variables were retained in the model if their removal caused a significant increase in model deviance based on F-tests with = 0·05 (Crawley 2007). Owing to the small sample size, lack of available independent data, and emphasis on explanatory as opposed to predictive ability, I used leave-one-out cross-validation to assess the accuracy of fitted models. To evaluate the prediction accuracy of fitted models, the following distance measures of the relationship between observed and predicted values were calculated: the mean bias error (MBE), root-mean-square error (RMSE) normalized by the range in observed response values and Willmot’s index of agreement (D) (Willmott 1982).

Tree regression was used to identify potential thresholds in predictor variables that were retained in the final GAMs. Records for each response variable (GR, CPC and bull/cow ratio) were recursively partitioned into groupings that were as homogeneous as possible using the multidimensional space defined by the predictor variables (Rejwan et al. 1999). The location of each sample unit (WMU) in a group was determined by repeatedly dividing the data set into two groups and calculating the variance of the response variable for each group. The procedure was repeated for all possible values of all the predictor variables. The predictor variable and split-point that resulted in the smallest summed variance for the two groups were used to divide the data set into the regression tree. Separate tree models were created for each predictor variable retained in the final GAMs, and bivariate tree models were created for all interaction terms. The maximum possible number of nodes was restricted to one node for univariate models and three nodes for bivariate models to accommodate interactions. A bagging approach to building the tree regression models was used to minimize the identification of spurious thresholds (Breiman 1996). For each response variable, 100 trees were independently constructed using a bootstrap sample of the data set. Threshold values for predictor variables were calculated as the average split-point value at the node location. For bivariate models, the predictor variables at secondary nodes were discarded if it was the same variable that occupied the root node for that tree. Mean values of the response variable for each terminal branch of the final plotted regression tree were calculated using the raw data for each response variable model and the average split-point value at each respective node location that was retained using the above selection criteria. The split-points for each predictor variable were used to partition the raw data for each set of models, and independent sample t-tests were used to test for significant differences in the response variable between groupings. All statistical analyses were conducted using R version 2.8.1 (R Development Core Team 2008), GAMs were constructed using the mgcv package (Wood & Augustin 2002) and tree regression was conducted using the ipred package (Peters & Hothorn 2009).


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Population Growth Rate

The predictor variables selected using forward-backward selection in the GAM for population GR were density in the preceding survey (Density) and the percentage of mixed-deciduous forest (Mixed) (Table 2). The proportion of the null deviance explained by the final model was 79·7% (inline image = 0·76), and the omission of each term from the model resulted in a 61·2% (Density) and 16·9% (Mixed) decrease in explained deviance.

Table 2.   Fitted generalized additive models of moose population growth rate (GR), calves per 100 cows (CPC), and the bull/cow ratio (BCR) using thin plate regression splines
ModelLinear termsSmoothed terms
GR (N = 32)
 Density    2·88724·391<0·001
 Mixed    2·2796·5560·003
CPC (N = 40)
 Growing season−10·4501·343−7·783<0·001   
BCR (N = 38)
 Road density−0·0960·026−3·706<0·001   
 Harvm    2·2108·843<0·001

Visual inspection of the response curves for smoothed predictor variables in the GAM indicated a negative nonlinear relationship between density and moose population GR (Fig. 2). Tree regression suggested that population GR was stable to decreasing when density was >0·13 moose per km2 (Table 3), and partitioning of the raw data indicated that GR was significantly lower where density was greater than this threshold (= 4·515, d.f. = 30, < 0·001). The percentage of mixed-deciduous forest exhibited an approximately quadratic relationship to population GR (Fig. 2), but a prominent threshold was not evident (Table 3). Although a significant interaction between Density and Mixed was evident during the model building process, the more parsimonious model favoured the individual additive terms. Tree regression to explore the interaction between Density and Mixed suggested that population GR generally shifted from increasing to decreasing where moose density was >0·13 moose per km2, but GR was only stable above the moose density threshold where the percentage of mixed-deciduous forest was >47% (Table 3).


Figure 2.  Generalized additive model response curves for population growth rate. The predictor variables include (a) population density (moose per km2) and (b) the percentage cover of mixed-deciduous forest. The y-axis is centred on the response scale by subtracting a weighted mean to ensure valid pointwise 95% confidence intervals (Hastie & Tibshirani 1990). Zero on the y-axis corresponds to no effect of the predictor variable. Solid curves are the thin plate regression spline fits for the predictor variable. The broken lines correspond to 95% Bayesian confidence limits for the smooth. Ticks on the x-axis indicate the locations of observations.

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Table 3.   Thresholds in predictor variables retained in final generalized additive models for moose population growth rate (a), calves per 100 cows (b), and the bull/cow ratio (c) and the mean response values generated for partitions of the raw data at each threshold. Thresholds were identified using bootstrapped regression tree analysis
Primary nodeSecondary nodeThreshold (95% CI)naSplitResponse (SE, n)P
  1. a= the number of trees, of 100 bootstrapped samples, where each predictor occurred at the specified location, and for bivariate models, in the variable combination specified for primary and secondary nodes. Only variables that occurred at a particular node location in at least 25% of the 100 bootstrapped samples are reported.

(a) Growth rate model
Density 0·13 (0·12–0·13)100<0·22 (0·06, 9)<0·001
    −0·004 (0·02, 23) 
Mixed 46 (43–50)100<0·01 (0·04, 13)0·162
    0·09 (0·04, 19) 
Density 0·13 (0·12–0·13)95   
 Density < 0·13Terminal 95 0·22 (0·06, 9) 
 Density ≥ 0·13Mixed47 (44–51)57<−0·06 (0·04, 8)0·058
    0·03 (0·02, 15) 
(b) Calves per 100 cows model
Growing season 120 (119–121)100<42 (2, 23)<0·001
    28 (3, 17) 
Harvc 0·15 (0·14–0·15)100<40 (3, 19)0·057
    32 (3, 21) 
(c) Bull/cow model
Harvm 0·09 (0·09–0·10)100<0·76 (0·07, 10)0·001
    0·55 (0·02, 28) 
Road density 18·5 (17·2–19·9)100<0·71 (0·05, 16)0·003
    0·53 (0·03, 22) 
Harvm 0·08 (0·07–0·08)77   
 Harvm < 0·08Terminal 76   
 Harvm ≥ 0·08Road density23·4 (22·5–24·4)71<0·64 (0·03, 12)<0·001
    0·48 (0·02, 17) 

Calves per 100 Cows

The predictor variables selected in the GAM for CPC were the Julian date of the start of the GS and the proportion of calves harvested (Harvc) (Table 2). The proportion of the null deviance explained by the final model was 62·9% (inline image = 0·61). The date of the start of GS explained the greatest proportion of observed variation in CPC, with a 60·8% decrease in explained deviance when GS was omitted from the final model. Omission of Harvc resulted in a 11·8% decrease in explained deviance.

The final model indicated a negative linear relationship between GS and the number of CPC (Fig. 3). Tree regression and partitioning of the raw data indicated that the CPC were significantly greater (= 3·903, d.f. = 38, < 0·001) where the start of the GS was before Julian day 120 (Table 3). The proportion of calves harvested had a negative linear effect on recruitment (Fig. 3); however, a distinct threshold was not apparent from the tree regression analysis (= 1·967, d.f. = 38, < 0·057) (Table 3). Data points were sparse and the confidence limits wide for Harvc at values >0·20 (Fig. 3), indicating uncertainty in the effects of Harvc at higher values.


Figure 3.  Generalized additive model response curves for the CPC. The predictor variables include (a) the Julian day number of the start of the growing season (GS) and (b) the proportion of calves harvested (Harvc). The y-axis is centred on the response scale by subtracting a weighted mean to ensure valid pointwise 95% confidence intervals (Hastie & Tibshirani 1990). Zero on the y-axis corresponds to no effect of the predictor variable.

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Univariate models revealed significant relationships between the CPC and the heat stress index HSIsp14 (inline image = 0·41, = 10·180, smoothed d.f. = 2·306, < 0·001), HSIsp20 (inline image = 0·38, = 9·378, smoothed d.f. =2·112, < 0·001), HSIw (inline image = 0·24, = 6·163, smoothed d.f. = 1·617, = 0·004), NDVI (inline image = 0·23, =4·504, smoothed d.f. = 2·478, = 0·009) and SDI (inline image = 0·15, = 5·164, smoothed d.f. = 1, = 0·017). However, their lower explanatory power and, in the case of the heat stress indices, collinearity with GS resulted in their exclusion from the final model. The NDVI and SDI exhibited negative relationships, and HSIw, HSIsp14 and HSIsp20 were positively related to the CPC. Based on average conditions across each WMU and the 3 years preceding each survey, mean HSI per day was 2·6 °C above the 14 °C threshold and 0·7 °C above the 20 °C threshold during late spring (April–May). During the cold season (January), mean HSI per day was 1·3 °C above the −5 °C threshold. Mean annual HSIs were 160 (HSIsp14), 40 (HSIsp20) and 42 (HSIw).

Ratio of Bulls to Cows

The final GAM for the ratio of bulls to cows (BCR) included the proportion of adult male moose harvested (Harvm) and road density (Table 2). The proportion of the null deviance explained by the final model was 61·2% (inline image = 0·57). Removal of Harvm from the full model resulted in a 26·6% decrease in explained deviance, while omission of road density resulted in a decrease of 26·7% in explained deviance.

The GAM response curves indicated negative relationships between the ratio of BCR and both Harvm and road density (Fig. 4). Univariate tree regression (Table 3) indicated that the ratio of BCR was significantly lower where Harvm was >0·09 (= 3·539, d.f. = 36, = 0·001) and where road density was >18·5 km of road per 100 km2 (= 3·139, d.f. = 36, = 0·003). Although a significant interaction between Harvm and road density was evident during the model selection process, the more parsimonious model favoured the individual additive terms. Even so, a positive correlation existed between the proportion of males harvested and road density (= 0·59, = 38, < 0·001), suggesting that hunter access may have augmented harvest pressure. Tree regression for the interaction between Harvm and road density suggested that the bull/cow ratio was significantly lower where Harvm was >0·08 and road density was >23·4 km of road per 100 km2 (= 4·014, d.f. = 27, < 0·001).


Figure 4.  Response curve of the predictor variables for the ratio of bulls to cows. The predictor variables on the x-axis include (a) the proportion of adult male moose harvested (thin plate regression spline) and (b) road density (km of road per 100 km2) (linear term). The broken lines correspond to 95% Bayesian confidence limits for the smooth.

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Error estimators of the cross-validation test indicated good predictive performance for each of the final models for GR, CPC and BCR. The moderate to high values for Willmott’s D suggested general agreement of all models with the observed values (GR: 0·88, CPC: 0·86, BCR: 0·77). The MBE was close to zero (min.:−0·06, CPC model; max. 0·002, GR model), indicating the absence of skew in the distribution of residuals. The residuals were not correlated with the predictor variables or the geographic coordinates of the centroid of each WMU (min.: = −0·219, BCR model-Northing; max.: r = 0·132 BCR model-Easting), indicating that the error was randomly distributed. The mean difference in the units of observed and predicted values (RMSE) was smallest for the GR model (0·117 of the range of the observed values) and largest for the CPC model (0·179).


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Both density-dependent and density-independent processes affected moose population dynamics with their contributions evident at different scales of population rate assessment. Evidence suggested that density-dependent effects on population GR operated through natural predation and possibly habitat supply. Moose densities were below values expected to constrain numerical growth through forage competition and within the range where predation may suppress ungulate population growth and have a density-dependent regulatory effect (Messier 1994; Wilmers, Post & Hastings 2007). The shift from negative density dependence to apparent density independence in population GR (GAM response curve, Fig. 2a) is consistent with Messier’s (1994) suggestion that moose in a predation-dominated system may stabilize at a low-density equilibrium between approximately 0·2 and 0·4 moose per km2. Wolf predation is expected to have a reduced impact as moose density increases because of the functional and numerical response of wolves characterized by an asymptotic relationship between kill rate and the ratio of prey to predators (Vucetich, Peterson & Schaefer 2002; Jost et al. 2005). Saturation of predator functional response may be affected by prey handling time, group hunting, territoriality, and changes in the relative availability and kill rate of old and young moose (Vucetich, Peterson & Schaefer 2002; Wilmers, Post & Hastings 2007). In contrast to a predation-based explanation of moose population GR, negative density dependence operating through forage competition is not expected to diminish as moose density increases.

Here I provide evidence that density-dependent processes involving predation explained more variation in population GR than abiotic processes across spatial environmental gradients and in an open system. This contrasts with evidence for drivers of interannual variation in population GR for the closed wolf-moose system on Isle Royale, where Vucetich & Peterson (2004) concluded that abiotic processes followed by bottom-up processes explained more of the interannual variation in moose population GR than predation. The absence of an effect of climate on moose population GR in this study is consistent with Wilmers et al.’s (2006) finding that predation can dampen the effects of climate on ungulate populations. On Isle Royale, climate shifted from having a weak effect to a highly significant effect on moose population GR following a pathogen-mediated shift from top-down to bottom-up control of the moose population (Wilmers et al. 2006). Clarifying these contrasts in the role of biotic and abiotic process to populations is particularly relevant in managed systems that span bioclimatic gradients, providing insight into appropriate management policies for both spatial and temporal dynamics.

Despite evidence for the importance of density-dependent predation, the positive effect of forage-rich habitat on moose population GR is not consistent with a predation-only regulation model (Messier 1994). The significant additive effects of mixed forest but inconsistency of population GR models with density-dependent forage competition calls for alternative explanations, such as a density-independent bottom-up process. This is supported by the importance of GS, a surrogate for bottom-up effects on calf recruitment and evidence elsewhere that habitat quality can affect twinning rates in moose (Franzmann & Schwartz 1985). The mixture of forest habitat elements selected by moose should reflect trade-offs in meeting life-history requirements, and these relationships should scale to influence population level patterns in relation to habitat. For example, the inverted u-shape relationship between mixed-deciduous forest and population GR may reflect the importance of conifer as shelter habitat for moose from both predators and severe winter weather, placing an upper limit on the value of mixed forests with an abundance of forage (Dussault, Courtois & Ouellet 2006). The roles of top-down and bottom-up forces warrant further study to improve understanding of the mechanisms driving variation in large herbivore population dynamics.

Density-independent environmental stochasticity, operating through climatic variation, was an important factor affecting spatial variation in moose calf recruitment. While previous studies of ungulate populations have documented the important effects of temporal variation in winter climate (e.g. North American Oscillation Index) in closed populations, where dynamic fluctuations are driven by the combined effects of predation, density dependence and climate (Vucetich & Peterson 2004; Wilmers & Getz 2005; Wilmers, Post & Hastings 2007), and in ungulates that inhabit extreme environments (e.g. alpine goats)(Pettorelli et al. 2007), this study provides evidence for the important limiting effects of spatial variation in summer climate for an open ungulate population inhabiting a continental climatic. Winter is considered an energetic bottleneck for many ungulates in northern latitudes, and studies of climate-related effects on ungulate demography have frequently emphasized the importance of severe winter weather (Post & Stenseth 1998; Solberg et al. 1999; Garrott et al. 2003). In contrast, this study found that winter severity was less important than indicators of summer climate in affecting calf recruitment. Evidence from this study suggests that variation in summer climate, hypothesized to operate through effects on plant phenology and summer nutrition, may have demographic consequences in populations that are below ecological carrying capacities. During summer, female ungulates in northern climates have high daily metabolizable energy requirements in relation to lactation and recovering from the previous winter weight loss (Cook et al. 2004) and summer climate may affect body mass and reproductive performance of ungulates (Gaillard et al. 1996; Solberg et al. 1999; Pettorelli et al. 2007). In contrast to the findings by Pettorelli et al. (2007), the early onset of vegetation growth was a better predictor of population recruitment than the rate of change in vegetation phenology. Earlier access to highly nutritious forage was evidently more important in this system than phenological changes in forage quality. This finding is consistent with evidence elsewhere that early born offspring are able to enter the winter period of resource limitation with greater body mass and likelihood of survival compared with later born offspring (Clutton-Brock et al. 1987; Festa-Bianchet 1988). It is possible that the sensitivity of NDVI as an indicator of forage phenology may have been diminished in this system because of the higher saturation potential of NDVI in heavily forested areas (Pettorelli et al. 2006). The use of the maximum rate of change as opposed to a seasonal average or maximum should have reduced this problem. Findings highlight the variable mechanisms by which climate may affect ungulate population dynamics in different systems, reinforcing the need for additional research to clarify general mechanisms and to test recent model advances (Wilmers, Post & Hastings 2007) with data from a range of natural conditions.

In contrast to findings by Lenarz et al. (2009), the heat stress index was positively correlated with recruitment in moose inhabiting southern periphery and core portions of range in eastern North America, suggesting cold climate effects were more limiting to moose. The use of spatially continuous climate grids in this study across a broad climatic gradient may account for the difference in findings from those reported by Lenarz et al. (2009), where temperature monitoring was localized within a smaller study area at the southern extent of moose range. In this study, annual heat stress indices were lower than reported by Lenarz et al. (2009), but still included values indicative of days above critical temperatures. Behavioural responses including selection of canopy cover shelter from wind or solar radiation may be sufficient to reduce both heat stress and cold stress in many species, including moose. Alternatively, moose may be more resilient to heat stress than previously suggested (Renecker & Hudson 1986). In core areas of moose range, evidence in this study suggests that climate-related effects on vegetation onset and calf recruitment may provide a more sensitive indicator for monitoring the long-term effects of climate change on moose populations. Global warming is expected to be highly influential to ungulate population dynamic because of the close alignment of life-history patterns of ungulates in northern latitudes with annual cycles in climate and primary productivity.

The negative relationships identified between population vital rates and harvest is consistent with other jurisdictions (Solberg et al. 1999; Patterson & Power 2002) and supports the importance of managing harvest allocation in relation to ungulate population targets. Calf harvest appeared to be additive (as opposed to compensatory) to other limiting factors, as evidenced by the negative linear relationship with recruitment and absence of distinct thresholds across the range of harvest rates observed (Williams, Nichols & Conroy 2002). In relation to the effects of climate on recruitment, managers should not assume that harvesting of calves removes a constant proportion of the calf population. Assuming that harvest is compensatory to other factors affecting survival of ungulates for purposes of harvest management may be misleading, and growing evidence indicates its additive effects (Bender et al. 2004). The absence of a significant effect of harvest on population GR may reflect the spatial nature of the present analysis and consistent implementation of harvest policy among WMUs. Harvest management in Ontario typically involves reducing hunting tag allocation at low moose densities to stimulate growth and increasing tags in response to increased densities of moose and public desire for hunting opportunities. The relationship between GR and harvest is expected to be more apparent within a time-series analysis that captures management response to population change across multiple cycles of population surveys and hunter tag allocation (Solberg et al. 1999). The impact of harvest may also vary depending on predation rates, but such relationships could not be resolved because of the absence of predation information for this analysis.

Managers of ungulate populations must often address multiple management objectives that permit consumptive use by the public while still ensuring population sustainability. The importance of hunter harvest and habitat variables in population rate models suggests that sustainable management strategies for harvested ungulates may be improved by explicitly linking harvest strategies, forest management policy with respect to habitat targets and access (i.e. roads), for example, a lower harvest rate may be necessary where suitable habitat is less abundant. Further, knowledge of the relative contributions of population drivers beyond the scope of management intervention can improve assessment of the feasibility of alternative management tools. Where managers are responsible for ungulate populations that span broad biogeographical gradients, the identification of shifts in climatic patterns that affect demographic potential (e.g. recruitment) could aid mangers in identifying regional differences in the prioritization of management actions.

The unexplained variation in population rate models may be attributable to factors such as predation, parasites, variation in forage quality, nonlicensed aboriginal harvest and age structure of the populations, but data were unavailable for these factors at the geographic and temporal scales employed in the study. The importance of predation rates by wolves and other non-human predators on moose population vital rates has been well documented (Hayes et al. 2003; Jost et al. 2005). An additional factor not considered in this study was the expansion of deer range associated with climate change that may augment mortality risk to moose through brainworm infestation. Incidental reports for Ontario document an expansion of deer northward into moose range in relation to mild winters that may potentially induce increased infection rates. Data were not available to include in the present analysis, and incidental information is limited to localized portions of the study area. Understanding the impacts of global warming to moose populations will need to consider long-term changes in brainworm infestation.

Studies of ungulate density dependence often focus on either predation or food limitation; however, findings highlight that observed low ungulate densities do not exclude the possibility that bottom-up and top-down processes may operate simultaneously on populations. As evidenced here, populations assumed to be suppressed by predation exhibited negative GRs at higher moose densities, but were stable where forage-rich habitat was more abundant. Likewise, GS onset, a surrogate for bottom-up effects, significantly affected calf recruitment for populations below ecological carrying capacities. Sustainable harvest of ungulates may be dependent on harvest strategies that incorporate the effects of environmental stochasticity, and failing to consider summer nutritional effects may lead to incomplete understanding of the range of climatic effects on populations. This study identified thresholds in drivers of moose population vital rates, providing a useful analytical framework to support evaluation of the viability of alternative management options.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

I thank the staff of the Ontario Ministry of Natural Resources responsible for conducting the moose population aerial surveys, snow surveys and hunter questionnaire surveys used for this project. Dan McKenney (Natural Resources Canada) provided the spatial climate data and Lyle Walton, Brent Patterson, anonymous reviewers and editors provided valuable comments on the manuscript.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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