Behavioral Timing without Clockwork: Photoperiod-Dependent Trade-Off between Predation Hazard and Energy Balance in an Arctic Ungulate.

Occurrence of 24-h rhythms in species apparently lacking functional molecular clockwork indicates that strong circadian mechanisms are not essential prerequisites of robust timing, and that rhythmical patterns may arise instead as passive responses to periodically changing environmental stimuli. Thus, in a new synthesis of grazing in a ruminant (MINDY), crepuscular peaks of activity emerge from interactions between internal and external stimuli that influence motivation to feed, and the influence of the light/dark cycle is mediated through the effect of low nocturnal levels of food intake on gastric function. Drawing on risk allocation theory, we hypothesized that the timing of behavior in ruminants is influenced by the independent effects of light on motivation to feed and perceived risk of predation. We predicted that the antithetical relationship between these 2 drivers would vary with photoperiod, resulting in a systematic shift in the phase of activity relative to the solar cycle across the year. This prediction was formalized in a model in which phase of activity emerges from a photoperiod-dependent trade-off between food and safety. We tested this model using data on the temporal pattern of activity in reindeer/caribou Rangifer tarandus free-living at natural mountain pasture in sub-Arctic Norway. The resulting nonlinear relationship between the phasing of crepuscular activity and photoperiod, consistent with the model, suggests a mechanism for behavioral timing that is independent of the core circadian system. We anticipate that such timing depends on integration of metabolic feedback from the digestive system and the activity of the glucocorticoid axis which modulates the behavioral responses of the animal to environmental hazard. The hypothalamus is the obvious neural substrate to achieve this integration.

Phenological mismatch with abiotic conditions implications for flowering in Arctic plants.

Although many studies have examined the phenological mismatches between interacting organisms, few have addressed the potential for mismatches between phenology and seasonal weather conditions. In the Arctic, rapid phenological changes in many taxa are occurring in association with earlier snowmelt. The timing of snowmelt is jointly affected by the size of the late winter snowpack and the temperature during the spring thaw. Increased winter snowpack results in delayed snowmelt, whereas higher air temperatures and faster snowmelt advance the timing of snowmelt. Where interannual variation in snowpack is substantial, changes in the timing of snowmelt can be largely uncoupled from changes in air temperature. Using detailed, long-term data on the flowering phenology of four arctic plant species from Zackenberg, Greenland, we investigate whether there is a phenological component to the temperature conditions experienced prior to and during flowering. In particular, we assess the role of timing of flowering in determining pre-flowering exposure to freezing temperatures and to the temperatures-experienced prior to flowering. We then examine the implications of flowering phenology for flower abundance. Earlier snowmelt resulted in greater exposure to freezing conditions, suggesting an increased potential for a mismatch between the timing of flowering and seasonal weather conditions and an increased potential for negative consequences, such as freezing 'damage. We also found a parabolic relationship between the timing of flowering and the temperature experienced during flowering after taking interannual temperature effects into account. If timing of flowering advances to a cooler period of the growing season, this may moderate the effects of a general warming trend across years. Flower abundance was quadratically associated with the timing of flowering, such that both early and late flowering led to lower flower abundance than did intermediate flowering. Our results indicate that shifting the timing of flowering affects the temperature experienced during flower development and flowering beyond that imposed by interannual variations in climate. We also found that phenological timing may affect flower abundance, and hence, fitness. These findings suggest that plant population responses to future climate change will be shaped not only by extrinsic climate forcing, but also by species' phenological responses.

The role of biotic interactions in shaping distributions and realised assemblages of species: implications for species distribution modelling.

Predicting which species will occur together in the future, and where, remains one of the greatest challenges in ecology, and requires a sound understanding of how the abiotic and biotic environments interact with dispersal processes and history across scales. Biotic interactions and their dynamics influence species' relationships to climate, and this also has important implications for predicting future distributions of species. It is already well accepted that biotic interactions shape species' spatial distributions at local spatial extents, but the role of these interactions beyond local extents (e.g. 10 km(2) to global extents) are usually dismissed as unimportant. In this review we consolidate evidence for how biotic interactions shape species distributions beyond local extents and review methods for integrating biotic interactions into species distribution modelling tools. Drawing upon evidence from contemporary and palaeoecological studies of individual species ranges, functional groups, and species richness patterns, we show that biotic interactions have clearly left their mark on species distributions and realised assemblages of species across all spatial extents. We demonstrate this with examples from within and across trophic groups. A range of species distribution modelling tools is available to quantify species environmental relationships and predict species occurrence, such as: (i) integrating pairwise dependencies, (ii) using integrative predictors, and (iii) hybridising species distribution models (SDMs) with dynamic models. These methods have typically only been applied to interacting pairs of species at a single time, require a priori ecological knowledge about which species interact, and due to data paucity must assume that biotic interactions are constant in space and time. To better inform the future development of these models across spatial scales, we call for accelerated collection of spatially and temporally explicit species data. Ideally, these data should be sampled to reflect variation in the underlying environment across large spatial extents, and at fine spatial resolution. Simplified ecosystems where there are relatively few interacting species and sometimes a wealth of existing ecosystem monitoring data (e.g. arctic, alpine or island habitats) offer settings where the development of modelling tools that account for biotic interactions may be less difficult than elsewhere.

Response of an arctic predator guild to collapsing lemming cycles.

Alpine and arctic lemming populations appear to be highly sensitive to climate change, and when faced with warmer and shorter winters, their well-known high-amplitude population cycles may collapse. Being keystone species in tundra ecosystems, changed lemming dynamics may convey significant knock-on effects on trophically linked species. Here, we analyse long-term (1988-2010), community-wide monitoring data from two sites in high-arctic Greenland and document how a collapse in collared lemming cyclicity affects the population dynamics of the predator guild. Dramatic changes were observed in two highly specialized lemming predators: snowy owl and stoat. Following the lemming cycle collapse, snowy owl fledgling production declined by 98 per cent, and there was indication of a severe population decline of stoats at one site. The less specialized long-tailed skua and the generalist arctic fox were more loosely coupled to the lemming dynamics. Still, the lemming collapse had noticeable effects on their reproductive performance. Predator responses differed somewhat between sites in all species and could arise from site-specific differences in lemming dynamics, intra-guild interactions or subsidies from other resources. Nevertheless, population extinctions and community restructuring of this arctic endemic predator guild are likely if the lemming dynamics are maintained at the current non-cyclic, low-density state.

The effects of landscape modifications on the long-term persistence of animal populations.

BACKGROUND: The effects of landscape modifications on the long-term persistence of wild animal populations is of crucial importance to wildlife managers and conservation biologists, but obtaining experimental evidence using real landscapes is usually impossible. To circumvent this problem we used individual-based models (IBMs) of interacting animals in experimental modifications of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of four species with contrasting life-history characteristics: skylark (Alauda arvensis), vole (Microtus agrestis), a ground beetle (Bembidion lampros) and a linyphiid spider (Erigone atra). This allows us to quantify the population implications of experimental modifications of landscape configuration and composition. METHODOLOGY/PRINCIPAL FINDINGS: Starting with a real agricultural landscape, we progressively reduced landscape complexity by (i) homogenizing habitat patch shapes, (ii) randomizing the locations of the patches, and (iii) randomizing the size of the patches. The first two steps increased landscape fragmentation. We assessed the effects of these manipulations on the long-term persistence of animal populations by measuring equilibrium population sizes and time to recovery after disturbance. Patch rearrangement and the presence of corridors had a large effect on the population dynamics of species whose local success depends on the surrounding terrain. Landscape modifications that reduced population sizes increased recovery times in the short-dispersing species, making small populations vulnerable to increasing disturbance. The species that were most strongly affected by large disturbances fluctuated little in population sizes in years when no perturbations took place. SIGNIFICANCE: Traditional approaches to the management and conservation of populations use either classical methods of population analysis, which fail to adequately account for the spatial configurations of landscapes, or landscape ecology, which accounts for landscape structure but has difficulty predicting the dynamics of populations living in them. Here we show how realistic and replicable individual-based models can bridge the gap between non-spatial population theory and non-dynamic landscape ecology. A major strength of the approach is its ability to identify population vulnerabilities not detected by standard population viability analyses.

Ecological dynamics across the Arctic associated with recent climate change.

At the close of the Fourth International Polar Year, we take stock of the ecological consequences of recent climate change in the Arctic, focusing on effects at population, community, and ecosystem scales. Despite the buffering effect of landscape heterogeneity, Arctic ecosystems and the trophic relationships that structure them have been severely perturbed. These rapid changes may be a bellwether of changes to come at lower latitudes and have the potential to affect ecosystem services related to natural resources, food production, climate regulation, and cultural integrity. We highlight areas of ecological research that deserve priority as the Arctic continues to warm.

The effects of spatial and temporal heterogeneity on the population dynamics of four animal species in a Danish landscape.

BACKGROUND: Variation in carrying capacity and population return rates is generally ignored in traditional studies of population dynamics. Variation is hard to study in the field because of difficulties controlling the environment in order to obtain statistical replicates, and because of the scale and expense of experimenting on populations. There may also be ethical issues. To circumvent these problems we used detailed simulations of the simultaneous behaviours of interacting animals in an accurate facsimile of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of skylarks Alauda arvensis, voles Microtus agrestis, a ground beetle Bembidion lampros and a linyphiid spider Erigone atra. This allows us to quantify and evaluate the importance of spatial and temporal heterogeneity on the population dynamics of the four species. RESULTS: Both spatial and temporal heterogeneity affected the relationship between population growth rate and population density in all four species. Spatial heterogeneity accounted for 23-30% of the variance in population growth rate after accounting for the effects of density, reflecting big differences in local carrying capacity associated with the landscape features important to individual species. Temporal heterogeneity accounted for 3-13% of the variance in vole, skylark and spider, but 43% in beetles. The associated temporal variation in carrying capacity would be problematic in traditional analyses of density dependence. Return rates were less than one in all species and essentially invariant in skylarks, spiders and beetles. Return rates varied over the landscape in voles, being slower where there were larger fluctuations in local population sizes. CONCLUSION: Our analyses estimated the traditional parameters of carrying capacities and return rates, but these are now seen as varying continuously over the landscape depending on habitat quality and the mechanisms of density dependence. The importance of our results lies in our demonstration that the effects of spatial and temporal heterogeneity must be accounted for if we are to have accurate predictive models for use in management and conservation. This is an area which until now has lacked an adequate theoretical framework and methodology.

Predation and fragmentation portrayed in the statistical structure of prey time series.

BACKGROUND: Statistical autoregressive analyses of direct and delayed density dependence are widespread in ecological research. The models suggest that changes in ecological factors affecting density dependence, like predation and landscape heterogeneity are directly portrayed in the first and second order autoregressive parameters, and the models are therefore used to decipher complex biological patterns. However, independent tests of model predictions are complicated by the inherent variability of natural populations, where differences in landscape structure, climate or species composition prevent controlled repeated analyses. To circumvent this problem, we applied second-order autoregressive time series analyses to data generated by a realistic agent-based computer model. The model simulated life history decisions of individual field voles under controlled variations in predator pressure and landscape fragmentation. Analyses were made on three levels: comparisons between predated and non-predated populations, between populations exposed to different types of predators and between populations experiencing different degrees of habitat fragmentation. RESULTS: The results are unambiguous: Changes in landscape fragmentation and the numerical response of predators are clearly portrayed in the statistical time series structure as predicted by the autoregressive model. Populations without predators displayed significantly stronger negative direct density dependence than did those exposed to predators, where direct density dependence was only moderately negative. The effects of predation versus no predation had an even stronger effect on the delayed density dependence of the simulated prey populations. In non-predated prey populations, the coefficients of delayed density dependence were distinctly positive, whereas they were negative in predated populations. Similarly, increasing the degree of fragmentation of optimal habitat available to the prey was accompanied with a shift in the delayed density dependence, from strongly negative to gradually becoming less negative. CONCLUSION: We conclude that statistical second-order autoregressive time series analyses are capable of deciphering interactions within and across trophic levels and their effect on direct and delayed density dependence.

Nonlinear effects of climate and density in the dynamics of a fluctuating population of reindeer.

Nonlinear and irregular population dynamics may arise as a result of phase dependence and coexistence of multiple attractors. Here we explore effects of climate and density in the dynamics of a highly fluctuating population of wild reindeer (Rangifer tarandus platyrhynchus) on Svalbard observed over a period of 29 years. Time series analyses revealed that density dependence and the effects of local climate (measured as the degree of ablation [melting] of snow during winter) on numbers were both highly nonlinear: direct negative density dependence was found when the population was growing (Rt > 0) and during phases of the North Atlantic Oscillation (NAO) characterized by winters with generally high (1979-1995) and low (1996-2007) indices, respectively. A growth-phase-dependent model explained the dynamics of the population best and revealed the influence of density-independent processes on numbers that a linear autoregressive model missed altogether. In particular, the abundance of reindeer was enhanced by ablation during phases of growth (Rt > 0), an observation that contrasts with the view that periods of mild weather in winter are normally deleterious for reindeer owing to icing of the snowpack. Analyses of vital rates corroborated the nonlinearity described in the population time series and showed that both starvation mortality in winter and fecundity were nonlinearly related to fluctuations in density and the level of ablation. The erratic pattern of growth of the population of reindeer in Adventdalen seems, therefore, to result from a combination of the effects of nonlinear density dependence, strong density-dependent mortality, and variable density independence related to ablation in winter.

Warming, plant phenology and the spatial dimension of trophic mismatch for large herbivores.

Temporal advancement of resource availability by warming in seasonal environments can reduce reproductive success of vertebrates if their own reproductive phenology does not also advance with warming. Indirect evidence from large-scale analyses suggests, however, that migratory vertebrates might compensate for this by tracking phenological variation across landscapes. Results from our two-year warming experiment combined with seven years of observations of plant phenology and offspring production by caribou (Rangifer tarandus) in Greenland, however, contradict evidence from large-scale analyses. At spatial scales relevant to the foraging horizon of individual herbivores, spatial variability in plant phenology was reduced--not increased--by both experimental and observed warming. Concurrently, offspring production by female caribou declined with reductions in spatial variability in plant phenology. By highlighting the spatial dimension of trophic mismatch, these results reveal heretofore unexpected adverse consequences of climatic warming for herbivore population ecology.

The influence of weather conditions on the activity of high-arctic arthropods inferred from long-term observations.

BACKGROUND: Climate change is particularly pronounced in the High Arctic and a better understanding of the repercussions on ecological processes like herbivory, predation and pollination is needed. Arthropods play an important role in the high-arctic ecosystem and this role is determined by their density and activity. However, density and activity may be sensitive to separate components of climate. Earlier emergence due to advanced timing of snowmelt following climate change may expose adult arthropods to unchanged temperatures but higher levels of radiation. The capture rate of arthropods in passive open traps like pitfall trap integrates density and activity and, therefore, serves as a proxy of the magnitude of such arthropod-related ecological processes. We used arthropod pitfall trapping data and weather data from 10 seasons in high-arctic Greenland to identify climatic effects on the activity pattern of nine arthropod taxa. RESULTS: We were able to statistically separate the variation in capture rates into a non-linear component of capture date (density) and a linear component of weather (activity). The non-linear proxy of density always accounted for more of the variation than the linear component of weather. After accounting for the seasonal phenological development, the most important weather variable influencing the capture rate of flying arthropods was temperature, while surface-dwelling species were principally influenced by solar radiation. CONCLUSION: Consistent with previous findings, air temperature best explained variation in the activity level of flying insects. An advancement of the phenology in this group due to earlier snowmelt will make individuals appear earlier in the season, but parallel temperature increases could mean that individuals are exposed to similar temperatures. Hence, the effect of climatic changes on the activity pattern in this group may be unchanged. In contrast, we found that solar radiation is a better proxy of activity levels than air temperature in surface-dwelling arthropods. An advancement of the phenology may expose surface-dwelling arthropods to higher levels of solar radiation, which suggest that their locomotory performance is enhanced and their contribution to ecological processes is increased.

Phenological sequences reveal aggregate life history response to climatic warming.

Climatic warming is associated with organisms breeding earlier in the season than is typical for their species. In some species, however, response to warming is more complex than a simple advance in the timing of all life history events preceding reproduction. Disparities in the extent to which different components of the reproductive phenology of organisms vary with climatic warming indicate that not all life history events are equally responsive to environmental variation. Here, we propose that our understanding of phenological response to climate change can be improved by considering entire sequences of events comprising the aggregate life histories of organisms preceding reproduction. We present results of a two-year warming experiment conducted on 33 individuals of three plant species inhabiting a low-arctic site. Analysis of phenological sequences of three key events for each species revealed how the aggregate life histories preceding reproduction responded to warming, and which individual events exerted the greatest influence on aggregate life history variation. For alpine chickweed (Cerastium alpinum), warming elicited a shortening of the duration of the emergence stage by 2.5 days on average, but the aggregate life history did not differ between warmed and ambient plots. For gray willow (Salix glauca), however, all phenological events monitored occurred earlier on warmed than on ambient plots, and warming reduced the aggregate life history of this species by 22 days on average. Similarly, in dwarf birch (Betula nana), warming advanced flower bud set, blooming, and fruit set and reduced the aggregate life history by 27 days on average. Our approach provides important insight into life history responses of many organisms to climate change and other forms of environmental variation. Such insight may be compromised by considering changes in individual phenological events in isolation.

Climate change reduces reproductive success of an Arctic herbivore through trophic mismatch.

In highly seasonal environments, offspring production by vertebrates is timed to coincide with the annual peak of resource availability. For herbivores, this resource peak is represented by the annual onset and progression of the plant growth season. As plant phenology advances in response to climatic warming, there is potential for development of a mismatch between the peak of resource demands by reproducing herbivores and the peak of resource availability. For migratory herbivores, such as caribou, development of a trophic mismatch is particularly likely because the timing of their seasonal migration to summer ranges, where calves are born, is cued by changes in day length, while onset of the plant-growing season on the same ranges is cued by local temperatures. Using data collected since 1993 on timing of calving by caribou and timing of plant growth in West Greenland, we document the consequences for reproductive success of a developing trophic mismatch between caribou and their forage plants. As mean spring temperatures at our study site have risen by more than 4 degrees C, caribou have not kept pace with advancement of the plant-growing season on their calving range. As a consequence, offspring mortality has risen and offspring production has dropped fourfold.

Inter-annual growth of Arctic charr (Salvelinus alpinus, L.) in relation to climate variation.

BACKGROUND: Major changes in climate have been observed in the Arctic and climate models predict further amplification of the enhanced greenhouse effect at high-latitudes leading to increased warming. We propose that warming in the Arctic may affect the annual growth conditions of the cold adapted Arctic charr and that such effects can already be detected retrospectrally using otolith data. RESULTS: Inter-annual growth of the circumpolar Arctic charr (Salvelinus alpinus, L.) was analysed in relation to climatic changes observed in the Arctic during the last two decades. Arctic charr were sampled from six locations at Qeqertarsuaq in West Greenland, where climate data have been recorded since 1990. Two fish populations met the criteria of homogeny and, consequently, only these were used in further analyses. The results demonstrate a complex coupling between annual growth rates and fluctuations in annual mean temperatures and precipitation. Significant changes in temporal patterns of growth were observed between cohorts of 1990 and 2004. CONCLUSION: Differences in pattern of growth appear to be a consequence of climatic changes over the last two decades and we thereby conclude that climatic affects short term and inter-annual growth as well as influencing long term shifts in age-specific growth patterns in population of Arctic charr.

Long-term patterns in European brown hare population dynamics in Denmark: effects of agriculture, predation and climate.

BACKGROUND: In Denmark and many other European countries, harvest records suggest a marked decline in European brown hare numbers, a decline often attributed to the agricultural practice. In the present study, we analyse the association between agricultural land-use, predator abundance and winter severity on the number of European brown hares harvested in Denmark in the years 1955 through 2000. RESULTS: Winter cereals had a significant negative association with European brown hare numbers. In contrast to this, root crop area was positively related to their numbers. Remaining crop categories were not significantly associated with the European brown hare numbers, though grass out of rotation tended to be positively related. The areas of root crop production and of grass out of rotation have been reduced by approximately 80% and 50%, respectively, while the area of winter cereals has increased markedly (>70%). However, European brown hare numbers were primarily negatively associated with the number of red fox. Finally, we also found a positive association between mild winters and European brown hare numbers. CONCLUSION: The decline of Danish European brown hare populations can mainly be attributed to predation by red fox, but the development in agricultural land-use during the last 45 years have also affected the European brown hare numbers negatively. Additionally, though mild winters were beneficial to European brown hares, the increasing frequency of mild winters during the study period was insufficient to reverse the negative population trend.

Spatial synchrony of local populations has increased in association with the recent Northern Hemisphere climate trend.

According to ecological theory, populations whose dynamics are entrained by environmental correlation face increased extinction risk as environmental conditions become more synchronized spatially. This prediction is highly relevant to the study of ecological consequences of climate change. Recent empirical studies have indicated, for example, that large-scale climate synchronizes trophic interactions and population dynamics over broad spatial scales in freshwater and terrestrial systems. Here, we present an analysis of century-scale, spatially replicated data on local weather and the population dynamics of caribou in Greenland. Our results indicate that spatial autocorrelation in local weather has increased with large-scale climatic warming. This increase in spatial synchrony of environmental conditions has been matched, in turn, by an increase in the spatial synchrony of local caribou populations toward the end of the 20th century. Our results indicate that spatial synchrony in environmental conditions and the populations influenced by them are highly variable through time and can increase with climatic warming. We suggest that if future warming can increase population synchrony, it may also increase extinction risk.

Synchronization of animal population dynamics by large-scale climate.

The hypothesis that animal population dynamics may be synchronized by climate is highly relevant in the context of climate change because it suggests that several populations might respond simultaneously to climatic trends if their dynamics are entrained by environmental correlation. The dynamics of many species throughout the Northern Hemisphere are influenced by a single large-scale climate system, the North Atlantic Oscillation (NAO), which exerts highly correlated regional effects on local weather. But efforts to attribute synchronous fluctuations of contiguous populations to large-scale climate are confounded by the synchronizing influences of dispersal or trophic interactions. Here we report that the dynamics of caribou and musk oxen on opposite coasts of Greenland show spatial synchrony among populations of both species that correlates with the NAO index. Our analysis shows that the NAO has an influence in the high degree of cross-species synchrony between pairs of caribou and musk oxen populations separated by a minimum of 1,000 km of inland ice. The vast distances, and complete physical and ecological separation of these species, rule out spatial coupling by dispersal or interaction. These results indicate that animal populations of different species may respond synchronously to global climate change over large regions.

Extrinsic Modification of Vertebrate Sex Ratios by Climatic Variation.

Evidence for the influences of climate on early development, maternal condition, and offspring viability in terrestrial vertebrates suggests that climatic change has the potential to induce variation in offspring sex ratios in such organisms. Using long-term data at individual and population levels, we investigated the influence of global climatic variation, as a result of the North Atlantic Oscillation (NAO), on offspring sex ratios of red deer in Norway. The state of the NAO during the fetal development of hinds influenced the mass of their sons, but not daughters, and increasingly warmer and snowy winters led to increasingly male-biased offspring sex ratios, independently of changes in the mean age of hinds. Moreover, hinds that were themselves born following warm, snowy winters were smaller as adults, produced significantly lighter sons, and tended to produce more sons than hinds born following cold, dry winters. In light of the fact that these observations defy explanation according to previous hypotheses of adaptive modification of offspring sex ratios, we present the extrinsic modification hypothesis, which suggests that sex ratios may evolve in variable environments through natural selection independently of maternal strategies of sex allocation.

Foraging strategies and seasonal diet optimization of muskoxen in West Greenland.

Various aspects of optimal foraging and seasonal diet composition of bulls (bachelor and dominant), cows, subadults, and yearlings of muskoxen Ovibos moschatus were investigated in West Greenland during the following seasons: calving, post-calving, summer, rut and mid-winter. The following hypotheses were tested: (1) muskoxen maximize daily energy intake during spring and summer, (2) dominant bulls monopolizing cows during the rutting season shift from an energy maximizing to a time minimizing foraging strategy in order to maximize the time available for reproductive activities, and (3) muskoxen employ a time minimizing foraging strategy during winter to conserve energy. As forage quality changed throughout the short Arctic growing season, muskoxen responded by changing the proportions of daily time spent feeding on graminoids (Cyperaceae, Poaceae) and dicots (Salix, Betula), respectively. This seasonal variation in the relative proportion of daily feeding time spent ingesting graminoids followed approximately the energy maximization prediction over the periods calving to rut. Neither time minimizing nor random foraging could explain the observed diets in this period, thus confirming hypothesis 1. Dominant bulls did not shift to the time minimizing strategy as predicted by hypothesis 2. However, during the pre-rutting and rutting seasons bulls deviated from the other sex/age classes by failing to obtain the daily maximum energy predicted by the model, as a result of a higher proportion of time allocated to agonistic and sexual behaviour. During winter, none of the sex/age classes employed a time minimizing strategy, so rejecting hypothesis 3. Instead, muskoxen were found to maximize Na intake, indicating that Na is of major importance for winter survival. The results emerging from a linear programming model with constraint settings varying over seasons confirm that the constraint parameters applied are indeed important limiting factors for muskoxen in natural populations.