Characterizing demographic parameters across environmental gradients: a case study with Ontario moose (Alces alces)

Population-level demographic characteristics as estimated by standard logistic growth models (i.e., carrying capacity and intrinsic growth rate) should vary with changes in habitat quality and availability of resources. However, few published studies have tested this hypothesis by comparing population growth rates across broad bioclimatic gradients, and fewer still the carrying capacities of those populations. We used time series data on moose (Alces alces) population densities based on aerial census and hunter harvest data for 34 management units across Ontario to estimate local carrying capacities and intrinsic growth rates. These population parameters were then regressed against associated habitat covariates for each management unit to assess how moose demography changes across a broad gradient of productivity, habitat abundance, and timber harvest. Moose carrying capacity was found to increase with increasing forest productivity as measured by ΔNDVI and the proportion of mixedwood stands in the forest. Both variables are plausibly indicative of high quality forage abundance for moose. Moose carrying capacity decreased with the proportion of forest stands harvested for timber annually, suggesting that immediate removal of forest stands and increased access by hunters temper maximum population size. Maximum rates of population growth by Ontario moose did not vary predictably with any of the landscape covariates tested. These findings contribute to our understanding of changes in demography across broad geographic and bioclimatic gradients and suggest that crude population estimators may be derived based on known habitat preferences and resource availability without a priori knowledge of animal abundance.


INTRODUCTION
That population size is related to resource availability is well established in the ecological literature.Space and resources are finite in ecological systems, and organisms should distribute themselves such that they maximize access to and use of these resources.This should lead to higher local animal densities with increasing quality of habitat (Fretwell and Lucas 1970).This relationship should also hold across spatial scales.Within an individual's home range, high quality habitats should be occupied most frequently, while lower quality areas should be avoided or occupied only briefly before individuals move on to better areas (Fretwell andLucas 1970, Benhamou 1992).At the population scale, this would produce changes in localized density where individual home ranges overlap (Mladenoff and Sickley 1998), and multiple populations would exhibit variation in average density based on differences in relative abundance of resources and habitat types (Caughley et al. 1988, Curnutt et al. 1996).This process should ultimately lead to a gradient of animal density across a species' range, wherein populations at the center of the range (i.e., where important niche factors converge) tend to have the highest density, and those at the periphery of the range the lowest density, as has been demonstrated in kangaroos (Macropus spp.; Caughley et al. 1988) and multiple species of grassland sparrow (Curnutt et al. 1996).
From a population modeling perspective, these differences in average density across space should be relatable to key demographic parameters, such as carrying capacity (K ) and intrinsic growth rate (r max ).However, few studies have actually compared variation in these demographic parameters across broad spatial gradients (but see Saether et al. 2008).This is at least partly attributable to the relative difficulty of obtaining sufficient time series data on abundance across large areas, which limits most studies of demography to a single population or a small number of discrete subpopulations in a relatively small area (e.g., Clutton-Brock et al. 1996, MacCracken et al. 1997, Post and Stenseth 1998, Coulson et al. 2001, Stephenson et al. 2006).Those few studies with sufficient data have often focused on characterizing spatial variation in temporal population dynamics (i.e., cyclic vs. non-cyclic populations) rather than sources of spatial variation in key demographic parameters (e.g., Caughley et al. 1984, Forchhammer et al. 1998, Stenseth et al. 2002, Lima et al. 2003).Identifying how and why basic demographic parameters change over space could be useful for a wide variety of practical applications in conservation biology and wildlife management (Saether et al. 2008).Specifically, considering the prevalence of habitat selection analysis in wildlife management, there remains a need to better understand how variation in habitat composition might influence the carrying capacity and/or maximum growth rates of populations.
We addressed this question using time series data on population abundance and harvest of moose (Alces alces) occurring in central and northern Ontario.Since 1980, Ontario moose populations have been surveyed every 3-5 years within each Wildlife Management Unit (WMU) across the province beginning in 1980 (McLaren 2006).These time series data span a wide spatial gradient of primary productivity that generally increases from north to south and east to west (Carleton 2000), and the frequency and size of forest fires follows a similar trend.Management units also vary in the proportion of timber harvest that has occurred over the past 40 years.The abundance of deciduous forest stands within management units varies with natural and anthropogenic disturbance frequency, and stochastic forest successional pathways (Chapin et al. 2004, Beck et al. 2011).These landscape covariates (i.e., productivity, forest fire frequency, timber harvest, and foraging habitat) represent different environmental gradients that potentially influence the availability and quality of moose foraging habitat, which may in turn influence estimates of environmental carrying capacity and intrinsic growth rate of moose within management units.Physiologically based aspects of the maximum growth rate should be a fixed characteristic of a species' life history, yet it is conceivable that other aspects of maximum growth rates might vary with environmental features that influence energetic efficiency at low population densities, such as climatic conditions (Brown 2011) or forage availability under pristine conditions (Saether et al. 1996, Milner et al. 2013).An explicit evaluation of these key demographic parameters (K and r max ) and their responses to environmental conditions would thus be valuable to both our understanding of moose demography, and more generally, population ecology of any species that occurs across broad geographic and bioclimatic gradients.
Environmental contributors to moose carrying capacity have been studied for individual popu-lations of moose in numerous locations.For example, moose carrying capacity has been linked to abundance of birch (Betula spp.) in Scandinavia (Wam et al. 2010), willow (Salix spp.) in Alaska (Stephenson et al. 2006), and general deciduous cover in Quebec (Crête 1989).Similar differences exist with regard to the influence of hunting (Mercer andMcLaren 2002, Timmermann et al. 2002) and predation (Stephens and Peterson 1984, Gasaway et al. 1992, Dussault et al. 2005) on moose habitat selection and density across space.Though useful in their own right, such studies alone are insufficient to demonstrate how and why the carrying capacity of a generalist herbivore might vary across a broad geographic gradient.This requires a much more general (i.e., less biologically detailed) approach to classifying the land cover characteristics used by moose populations, and the disturbance regimes they experience, over a much broader expanse (e.g., the metapopulation range).These environmental characteristics may then be compared to variation in carrying capacity and intrinsic growth rate to assess how general habitat characteristics, rather than specific localized factors, influence patterns of variation in demography over space.
Here we estimated the intrinsic growth rate and carrying capacity for 34 subpopulations of Ontario moose across a broad latitudinal and environmental disturbance gradient.We then regressed these regional demographic parameters against landscape covariates derived from regional maps of forest cover and productivity to assess the influence of disturbance regimes and forage availability on demographic characteristics of moose across their Ontario range.Given that disturbance increases deciduous forage abundance (Peek et al. 1976, Stephenson et al. 2006), and increased forage availability improves moose survivorship and browsing efficiency (Peek 1974, MacCracken et al. 1997, Brown 2011), we predicted that moose demographic parameters should be positively influenced by increases in both of these landscape characteristics.This work builds upon previous findings that populations of numerous taxa respond to changes in environmental conditions across space (e.g., Caughley et al. 1984, Post and Stenseth 1998, Stenseth et al. 2002, Saether et al. 2008) and evaluates the commonly held but rarely tested assumption that demographic parameters of any population are largely dependent on associated bioclimatic gradients (Rempel 2011).

METHODS
This study was conducted across a large part of central and northern Ontario, Canada, encompassing approximately 46-508 N and 76-998 W. This area, ;438,000 km 2 , has been subject to varying levels of timber harvest based on unique management strategies set forth for each Forest Management Unit (FMU).Vegetation communities within the study area are diverse but generally shift from the predominately deciduous Great Lakes-St.Lawrence forests in the south to the predominately coniferous boreal forest matrix to the north (Rowe 1972).Natural disturbance is characterized by an annual fire season from April to October, with timber harvest the primary anthropogenic disturbance, representing roughly an order of magnitude greater frequency than fire in most parts of our study area (see below).
Ontario moose are generalist herbivores with known preferences for deciduous and seral forest habitat.Their range overlaps that of white-tailed deer (Odocoileus virginianus) to the south and woodland caribou (Rangifer tarandus caribou) to the north.Managed populations of elk (Cervus elaphus) occur at the southern and western extents of our study area and likely co-occur with moose in some regions.Predators of moose in Ontario include wolves (Canis lupus) and black bears (Ursus americanus), both of which have widespread distributions that span our study site.
Estimates of moose abundance were obtained from the Moose Aerial Inventory maintained by the Ontario Ministry of Natural Resources.Standardized aerial surveys have been conducted during the winter (December-March) every 3-5 years starting in 1981.We used these data to estimate the average exponential growth rate as the log-transformed ratio of abundance between surveys where N is a vector of densities (no.individuals/ km 2 ) within a management unit, t, the year in which a survey was flown, and x, the number of years between surveys.We thus defined each wildlife management unit as a spatially distinct subpopulation of moose.The boundaries of Ontario's wildlife management units are typically defined by landscape characteristics like river and lake systems, railroad lines, geologic differences, and administrative boundaries, hence management units do not necessarily correspond to biologically distinct subpopulations.However, the average area of our management units was 7,984.1 km 2 (min ¼ 832.1 km 2 , max ¼ 19259.0km 2 ), three orders of magnitude greater than the average home range typically reported for moose (e.g., Phillips et al. 1973, Cederlund andOkarma 1988).We are thus confident that moose mobility has little influence on population estimates at such a large spatial scale and that our WMUs adequately represent discrete samples of the moose population across Ontario.
Although individual surveys are flown with as much rigor as possible, the provincial guidelines for the Moose Aerial Inventory do not include protocols for incorporating habitat-specific sighting biases.Explicitly accounting for such bias in estimating the census would improve reliability of survey estimates, but we have no way to account for this in our dataset.Still, given that correction for sightability inflates the survey estimate, the inventory data may be thought of as a minimum density based on observation.Inventory estimates consistently underestimate the true population density, rendering our estimated carrying capacities conservative and, presumably, having no effect on intrinsic growth rate.
Moose in Ontario are subject to varying degrees of harvest across management units.Removal of individuals from the population could accordingly bias estimates of demographic parameters (Vucetich et al. 2005, Brown 2011).To evaluate the maximum potential for such bias, we adjusted the recorded moose abundance based on the moose harvest as recorded by management unit such that, given a continuous vector of harvested densities, H, the corrected density, N c , at time t þ x was calculated as Corrected estimates of density were then substituted into Eq. 1 to obtain the average exponential growth rate corrected for moose harvest (r 0 t ).These separate estimates of r encompass two possibilities: (1) that harvest mortality is compensatory and hence has no effect on population growth rates (i.e., harvested individuals would have been removed from the population anyway by, e.g., predators), and (2) that harvest mortality is completely additive.In reality, the contribution of harvest mortality to population growth rates is likely somewhere between these two extremes.The relationship between additive and compensatory mortality is often complex and difficult to isolate in wildlife studies, so we defer such issues to a separate study.For our purposes, using these extremes allowed us to bracket the range of demographic possibilities, allowing us to determine whether our findings were robust to the impact of potentially additive harvest mortality.Estimates of K and r max for each WMU were accordingly derived from simple linear regressions of both formulations of instantaneous growth rate as a function of density, with r max as the y-intercept, and K, the x-intercept of the regression line (Fig. 1).
We quantified moose habitat characteristics for each wildlife management unit using the Ontario Provincial Land Cover 2000 (OLC) database available from the Land Information Ontario data warehouse (LIO; https://www.appliometadata.lrc.gov.on.ca/geonetwork/srv/ en/main.home) at a 25-m resolution (Spectranalysis 2004).The Ontario Land Cover database represents a snapshot of a spatially explicit landscape that clearly will change over time, but given the slow rate of change likely associated with forest succession at the relevant spatial and temporal scales for this study, we assumed that the static OLC data adequately represents spatial variation in vegetation composition across the study area.Based on established relationships between forest cover types and moose forage availability (e.g., Peek et al. 1976, MacCracken et al. 1997, Stephenson et al. 2006, Wam et al. 2010), land cover classes characterizing different forest stands should be proportional to relative abundance of forage generally increasing with the proportion of deciduous coverage represented in each class.We subsequently identified six OLC forest stand classifi-cations (out of 29 classes available) that represent potential moose foraging habitat: depletion (cuts), depletion (burns), regenerating depletion, dense deciduous, dense mixedwood, and dense coniferous (Spectranalysis 2004).We calculated the proportional coverage of each habitat type within each wildlife management unit as a representation of relative abundance of moose foraging habitats.
Given the lack of temporally explicit land cover data, we were unable to directly address annual changes in cover by deciduous foraging habitat.We accommodated this by including seasonal changes in the Normalized Difference Vegetative Index (NDVI).Monthly NDVI data at a 1-km resolution were obtained from NASA's Land Processes Distributed Active Archive Center (NASA LP DAAC 2013) and averaged for summer (June-September) and winter (December-March).The difference in seasonal NDVI was calculated from 2000 to 2007 and averaged for each WMU (DNDVI ¼ NDVI summer À NDVI winter ) across the study area.NDVI has been demonstrated to covary with primary productivity (Birky 2001), and seasonal differences in NDVI should be proportional to the seasonal greenness of a landscape (i.e., coverage of deciduous foliage; Avgar et al. 2013), and also serves to correct the We hypothesized that moose demographic characteristics are governed in part by natural and anthropogenic disturbance regimes.Spatially explicit forest fire and timber harvest records were obtained from the Land Information Ontario data warehouse, and annual fire and harvest were separately calculated for each wildlife management unit as the proportion of the landscape disturbed by each source from 1981 to 2007.We then averaged these proportions for each management unit to obtain separate estimates of differences in fire and timber harvest frequency across our study area.This assumes a constant mean and variation in fire characteristics (i.e., severity and intensity) across the management units.This may be problematic from a continuous time perspective, as this mean may be influenced by climate and harvest regimes, but should not influence our results because of the static landscape methodology used here.
We evaluated spatial variation in moose demographic parameters using a model competition procedure.We estimated simple linear regressions of K and r max using a suite of biologically relevant models representing the contribution of different combinations of habitat and disturbance variables to demography (Table 1).Proportional coverage data were logit-trans-formed.Model comparison was conducted using Akaike's Information Criterion corrected for small sample size (AIC c ).However, each estimate of density per survey year is associated with a 90% confidence interval that represents 10-20% of the census estimate (McLaren 2006), which may influence the reliability of estimates of K and r max , and thus the estimated relationship between these demographic parameters and environmental covariates.To accommodate this, we generated 1000 bootstrapped time series using the 90% confidence interval for each survey year and estimated K and r max for each time series.We repeated our regressions for each demographic parameter using the most parsimonious model based on AIC c to evaluate how sensitive estimated slopes were to variation in the survey data.All analyses were performed using the core package in R (R Development Core Team 2013).

RESULTS
Regardless of the method used to estimate instantaneous growth rate, the most parsimonious model for carrying capacity (K) included DNDVI, the proportion of the landscape harvested for timber, and proportional coverage by mixedwood habitat (r: R 2 ¼ 0.46; r 0 : R 2 ¼ 0.43; Table 1).DNDVI and mixedwood coverage positively influenced carrying capacity by as much as 0.25 and 0.3 individuals per square v www.esajournals.orgkilometer, respectively.On the other hand, increasing timber harvest reduced moose carrying capacity by as much as 0.4 individuals per square kilometer at the highest timber harvest levels recorded (Fig. 2).Estimated slopes were robust to variation in the survey data based on sensitivity analysis of 1000 bootstrapped time series per management unit (Fig. 3).Moose carrying capacity thus increased with landscape covariates associated with increasing abundance of high quality foraging habitat and decreased with the anthropogenic removal of forested habitat in general (note that fire disturbance did not come out as an important predictor).When projected across the entire province, our model predicts that moose carrying capacity should generally increase from east to west and from south to north, tracking well the forest productivity gradient across Ontario (Fig. 4).
The most parsimonious model for r max was simply the average r max for the entire dataset (mean r ¼ 0.43, mean r 0 ¼ 0.53; Table 1).Intrinsic population growth rate thus varied little across Ontario, whereas carrying capacity was much more responsive to landscape covariates.This could be attributable to small sample sizes within WMUs, which would produce highly variable estimates of r max .The fact that spatial variation in estimates of moose carrying capacity was closely correlated with landscape variables suggests that this is not the case.It seems more likely that the available landscape variables simply have little impact on intrinsic population growth rates or that r max is an innate characteristic of populations or species (see Discussion).

DISCUSSION
We found that moose carrying capacity varied positively with changes in average productivity and the relative abundance of mixedwood habitat.These variables coincide with increases in deciduous foliage, which is widely recognized as the main source of moose forage (Peek et al. 1976, Belovsky 1981, Stephenson et al. 2006); thus maximum population size of moose increases with resource availability.That this occurs is unsurprising, given that population size is often associated with forage abundance and habitat availability.For example, populations of red and grey kangaroos (Macropus spp.) respond numer-Fig.2. Partial residual plot of K as a function of seasonal differences in productivity (DNDVI), proportional coverage of mixedwood habitat, and average proportion of the landscape harvested for timber per year.Open circles represent K as estimated using uncorrected instantaneous growth rate (r t ), and solid lines the trend in the associated partial residuals, whereas plus symbols and dashed lines the values and trends for K as estimated using instantaneous growth rates corrected for moose harvest (r t,c ).K increases with increases in foraging habitat and productivity, but declines with annual timber harvest (R 2 r ¼ 0.46, R 2 r,c ¼ 0.43).
v www.esajournals.orgically to changes in rainfall as it strongly influences forage abundance (Caughley et al. 1984), timber wolf population density tracks habitat characteristics associated with prey foraging requirements (Mladenoff and Sickley 1998), and the density of California gnatcatchers (Polioptila californica) declines with loss of sage scrub and increasing distance between habitat patches (Akçakaya and Atwood 1997).However, changes in density alone may be insufficient to assess the quality of a landscape for animal populations and can lead to inaccurate population projections without estimating associated demographic parameters (Van Horne 1983).To our knowledge, this represents one of the most rigorous demonstrations to date of changing environmental carrying capacity of a large mammal across a broad range of landscape characteristics, and our findings corroborate that population size is limited maximally by the availability of resources.
We found that increasing annual timber harvest negatively influenced moose carrying capacity (Fig. 2).This seems counterintuitive in that timber harvest resets forest stands to an early successional stage and has been demonstrated to increase the amount of deciduous forage available to moose following regrowth in Minnesota (Stephenson et al. 2006), Ontario (Carleton 2000), and Scandinavia (Wam et al. 2010).Timber harvest requires the creation of roads to transport lumber out of the forest, however, which when coupled to clear cuts improves access to moose populations by wolves as well as human hunters, thereby contributing to increased moose mortality (Rempel et al. 1997).Increased hunting pressure and efficiency depresses moose population size and may explain the negative relationship detected between timber harvest and carrying capacity.An explicit evaluation of hunter effort as it influences demography would be a worthwhile contribution to this work; however, the provincial data on moose harvests are not sufficiently detailed to permit estimation of effort, as single moose tags are often associated with hunting parties of variable size, which are not reported in our dataset.We note that timber harvest similarly affects moose carrying capacity even when human induced mortality is taken into account, indicating that hunting may be a less important determinant of moose carrying capacity than forage availability, as well as the potentially important role played by wolf predation.
We estimated average timber harvest from time series data of harvest for each management unit assuming variable annual harvests around a mean.Given discrete stages of forest succession (e.g., early, mid, and late) and constant rates of transition from one stage to the next, a forest v www.esajournals.orgstand removed for lumber may be simultaneously replaced elsewhere on the landscape by an early successional stand harvested previously, early stands will develop into late successional stands, and so on.This is an admittedly simple perspective on forest succession, but it serves to demonstrate that, operating from an average landscape composition perspective as we do here, increasing annual timber harvest may not coincide with an immediate increase in deciduous cover, but effectively immediate removal of forest habitat from the landscape.Given that all forested stands have at least some value to moose, for example as forage habitat (Peek et al. 1976, Stephenson et al. 2006), predatory cover (Stephens andPeterson 1984, Dussault et al. 2005), or thermal cover (Dussault et al. 2004, van Beest et al. 2012), it is reasonable that increasing the average annual timber harvest would depress estimated carrying capacity within wildlife management units.Timber harvest may thus depress moose abundance both indirectly through increased mortality due to improved hunting efficiency by humans and natural predators and directly through changes to the distribution and abundance of forest stands.
Although increasing the average area harvested for lumber in a landscape would reduce the total forested area at a given time, it would be expected to produce greater abundance of mixedwood habitat over time relative to an unmanaged forest (Carleton 2000).As such, we may expect moose carrying capacity to be highest in a landscape that experiences sufficient timber harvest to maximize the presence of mixedwood habitat while providing sufficient cover of other stand types.The question is, what is the optimum balance between these variables?That is, what level of timber harvest would ultimately result in the greatest average annual mixedwood abundance?This would depend primarily on the time lag from initial depletion to full regeneration, and on the pathways of succession.Use of a temporally explicit landscape would permit exploration of how quickly timber harvest produces new moose foraging habitat.Succession rates and stand composition post-harvest have been extensively studied in Ontario, and the boreal forest in general (i.e., Carleton 2000, Chapin et al. 2004, Drescher et al. 2008); however, how patterns of succession and temporal dynamics of vegetation composition influence utilization of clearcuts by moose remains unclear.Generally, we expect moose to begin utilizing clearcuts as early as one growing season following timber harvest as the understory regenerates, but few studies have examined over what duration such utilization improves foraging efficiency and how this improvement influences carrying capacity (but see Stephenson et al. 2006).Clearly additional work is needed to understand precisely how and over what duration timber harvest improves moose habitat configuration.
We failed to find a link between intrinsic population growth rates and landscape covariates.This could be attributable to r max being an innate characteristic of populations.Healthy populations of moose produce approximately one calf per adult female per year with a twinning rate of about 40% (Gasaway et al. 1992, Mac-Cracken et al. 1997), and deviation from this maximum should be a function of declines in density-independent juvenile survivorship and female fecundity.Forage availability should also influence these demographic parameters, as body condition and fecundity of moose is associated with seasonal range conditions that can have considerable impact on foraging efficiency (Saether et al. 1996, Milner et al. 2013).Nonetheless, our findings show that intrinsic growth rate estimates are not correlated with the landscape covariates we identified, suggesting that other factors (e.g., reproductive biology or landscape change over broad time periods) may be more important in predicting intrinsic growth rates.
Based on our findings, moose carrying capacity should be maximized in a landscape with high productivity and relative abundance of mixedwood, with minimal timber harvest (Fig. 2), and we can estimate changes in K across this gradient (Fig. 4).This suggests that a first order prediction of moose population size of moose at equilibrium can be derived for a landscape with known habitat characteristics and disturbance regimes.This is conceptually similar to Mladenoff and Sickley's (1998) procedure for estimating equilibrium abundance of reintroduced populations of wolves in the northeastern United States, based on known habitat preferences of wolves and densities of wolf prey, wherein it was assumed reintroduced wolf densities would correspond to densities in similar landscapes.However, this assumption may not hold for populations occurring along a range periphery (Caughley et al. 1988, Curnutt et al. 1996) or in novel environments where demographic parameters are unknown (Van Horne 1983).Moreover, wolf functional and numeric responses are well studied and provide a theoretical basis for predictive population estimates unavailable for other species.On the contrary, estimating demographic parameters simply requires a time series of abundance, and extending these estimates to v www.esajournals.orgnovel environments should be relatively simple given known predictors of carrying capacity across space and average intrinsic growth rate.This would permit us to predict not only abundance and distribution but also population dynamics of species occurring in reintroduced habitats or otherwise unsurveyed landscapes and could be particularly useful in estimating variation in demographic parameters of populations in response to anticipated changes in habitat configuration and environmental characteristics due to climate change.Whether such predictive population modeling would be a suitable alternative to the approach of Mladenoff and Sickley (1998) therefore remains to be demonstrated.
A thorough understanding of the factors influencing population dynamics across broad environmental gradients is vital to the conservation and management of widespread species (Avgar et al. 2013).However, demographic parameters as estimated from population models are often overlooked in studies of population demography.
Here we demonstrate that environmental carrying capacity of managed moose populations can be predicted using a suite of biologically relevant landscape covariates associated with forage abundance and habitat disturbance.This not only contributes to our understanding of habitat use and home range requirements of moose, but also provides a general framework for quantifying demographic variation in any given population with respect to changes in landscape configuration and human land use.Extension of these relationships into predictive population modeling may lead to more robust predictions of population viability over space and time, and thus better informed management practices for this and other species of concern.

Fig. 1 .
Fig.1.Regressions of instantaneous growth rate (r t ) as a function of moose density (no.individuals/km 2 ) by wildlife management unit (WMU).Estimates of K (the x-intercept) and r max (the y-intercept) vary markedly by WMU.

Fig. 3 .
Fig. 3. Kernel density estimates of the sensitivity analysis of estimated slopes of the most parsimonious model of carrying capacity (K ), based on the 90% confidence intervals of the moose aerial survey each year.Dashed lines represent instantaneous population growth corrected for hunting, and solid lines are uncorrected (i.e., pure survey data).The relationships between estimated carrying capacity and environmental covariates were robust to variation in the survey data based on 90% confidence intervals.

Fig. 4 .
Fig. 4. Map plate of study site, data, and results.(A) Location of Ontario study site (red outline) in Canada.(B) Wildlife management units in Ontario.Highlighted units had sufficiently lengthy time series (i.e., .10surveys) to estimate carrying capacity and maximum growth rate.(C-D) Average NDVI in September 2001 (C) and in March 2001 (D) demonstrating seasonal differences in deciduous cover.(E) The Ontario Land Cover 2000.For a complete legend of cover types, see Spectranalysis (2004).(F) Projection of the statistical model of carrying capacity across management units used in this study and smoothed using cubic splines.Carrying capacities range from a maximum of 49.0 moose per 100 km 2 (red) to a minimum of 16.2 moose per 100 km 2 (blue).

Table 1 .
Structure of competing models of carrying capacity (K ) and intrinsic growth rate (r max ) and associated DAIC values in ascending order of model complexity for both compensatory (r t ) and additive (r 0 t ) formulations of instantaneous growth rate.DNDVI was included in all models except the intercept only model.Cut, burn, regeneration, sparse, deciduous, and mixedwood are proportional land cover defined by the Provincial Land Cover.Fire and harvest are average annual proportional disturbance defined by yearly data available from 1981 to 2007 from the Ontario Ministry of Natural Resources.