Spatiotemporal dynamics of habitat use by koalas: the checkerboard model

Animal movement patterns and use of space depend upon food and nonfood resources, as well as conspecific and heterospecific interactions, but models of habitat use often neglect to examine multiple factors and rarely include marsupials. We studied habitat use in an Australian population of koalas (Phascolarctos cinereus) over a 6-year period in order to determine how koalas navigate their environment and partition limited patchy food and nonfood resources. Tree selection among koalas appears to be mediated by folar chemistry, but nonfood tree selection exerts a major impact on home range use due to thermoregulatory constraints. Koalas moved on a daily basis, during both day and night, but daytime resting site was not necessarily in the same location as nighttime feeding site. Koalas had substantial home range overlap in the near absence of resource sharing with less than 1% of trees located in areas of overlap used by multiple koalas. We suggest that koala spatiotemporal distribution and habitat use are probably based upon a community structure of individuals, with a checkerboard model best describing overlap in home range area but not in resource use. Nonfood refugia and social networks should be incorporated into models of animal range and habitat use.     

Analyzing animal movements using Brownian bridges

By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.     

Optimal movement strategies for social foragers in unpredictable environments

Spatial movement models often base movement decision rules on traditional optimal foraging theories, including ideal free distribution (IFD) theory, more recently generalized as density-dependent habitat selection (DDHS) theory, and the marginal value theorem (MVT). Thus optimal patch departure times are predicted on the basis of the density-dependent resource level in the patch. Recently, alternatives to density as a habitat selection criterion, such as individual knowledge of the resource distribution, conspecific attraction, and site fidelity, have been recognized as important influences on movement behavior in environments with an uncertain resource distribution. For foraging processes incorporating these influences, it is not clear whether simple optimal foraging theories provide a reasonable approximation to animal behavior or whether they may be misleading. This study compares patch departure strategies predicted by DDHS theory and the MVT with evolutionarily optimal patch departure strategies for a wide range of foraging scenarios. The level of accuracy with which individuals can navigate toward local food sources is varied, and individual tendency for conspecific attraction or repulsion is optimized over a continuous spectrum. We find that DDHS theory and the MVT accurately predict the evolutionarily optimal patch departure strategy for foragers with high navigational accuracy for a wide range of resource distributions. As navigational accuracy is reduced, the patch departure strategy cannot be accurately predicted by these theories for environments with a heterogeneous resource distribution. In these situations, social forces improve foraging success and have a strong influence on optimal patch departure strategies, causing individuals to stay longer in patches than the optimal foraging theories predict.     

Covariates affecting spatial variability in bison travel behavior in Yellowstone National Park.

Understanding mechanisms influencing the movement paths of animals is essential for comprehending behavior and accurately predicting use of travel corridors. In Yellowstone National Park (USA), the effects of roads and winter road grooming on bison (Bison bison) travel routes and spatial dynamics have been debated for more than a decade. However, no rigorous studies have been conducted on bison spatial movement patterns. We collected 121 380 locations from 14 female bison with GPS collars in central Yellowstone to examine how topography, habitat type, roads, and elevation affected the probability of bison travel year-round. We also conducted daily winter bison road use surveys (2003-2005) to quantify how topography and habitat type influenced spatial variability in the amount of bison road travel. Using model comparison techniques, we found the probability of bison travel and spatial distribution of travel locations were affected by multiple topographic and habitat type attributes including slope, landscape roughness, habitat type, elevation, and distances to streams, foraging areas, forested habitats, and roads. Streams were the most influential natural landscape feature affecting bison travel, and results suggest the bison travel network throughout central Yellowstone is spatially defined largely by the presence of streams that connect foraging areas. Also, the probability of bison travel was higher in regions of variable topography that constrain movements, such as in canyons. Pronounced travel corridors existed both in close association with roads and distant from any roads, and results indicate that roads may facilitate bison travel in certain areas. However, our findings suggest that many road segments used as travel corridors are overlaid upon natural travel pathways because road segments receiving high amounts of bison travel had similar landscape features as natural travel corridors. We suggest that most spatial patterns in bison road travel are a manifestation of general spatial travel trends. Our research offers novel insights into bison spatial dynamics and provides conceptual and analytical frameworks for examining movement patterns of other species.     

Energy gains predict the distribution of plains bison across populations and ecosystems

Developing tools that help predict animal distribution in the face of environmental change is central to understanding ecosystem function, but it remains a significant ecological challenge. We tested whether a single foraging currency could explain bison (Bison bison) distribution in dissimilar environments: a largely forested environment in Prince Albert National Park (Saskatchewan, Canada) and a prairie environment in Grasslands National Park (Saskatchewan, Canada). We blended extensive behavioral observations, relocations of radio-collared bison, vegetation surveys, and laboratory analyses to spatially link bison distribution in the two parks and expected gains for different nutritional currencies. In Prince Albert National Park, bison were more closely associated with the distribution of plants that maximized their instantaneous energy intake rate (IDE) than their daily intake of digestible energy. This result reflected both bison's intensity of use of individual meadows and their selection of foraging sites within meadows. On this basis, we tested whether IDE could explain the spatial dynamics of bison reintroduced to Grasslands National Park. As predicted, bison distribution in this park best matched spatial patterns of plants offering rapid IDE rather than rapid sodium intake, phosphorus intake, or daily intake of digestible energy. Because the two study areas have very different plant communities, a phenomenological model of resource selection developed in one area could not be used to predict animal distribution in the other. We were able, however, to successfully infer the distribution of bison from their foraging objective. This consistency in foraging currency across ecosystems and populations provides a strong basis for forecasting animal distributions in novel and dynamic environments.     

Modeling resource selection using polytomous logistic regression and kernel density estimates

Wildlife resource selection studies typically compare used to available resources; selection or avoidance occurs when use is disproportionately greater or less than availability. Comparing used to available resources is problematic because results are often greatly influenced by what is considered available to the animal. Moreover, placing relocation points within resource units is often difficult due to radiotelemetry and mapping errors. Given these problems, we suggest that an animal’s resource use be summarized at the scale of the home range (i.e., the spatial distribution of all point locations of an animal) rather than by individual points that are considered used or available. To account for differences in use-intensity throughout an animal’s home range, we model resource selection using kernel density estimates and polytomous logistic regression. We present a case study of elk (Cervus elaphus) resource selection in South Dakota to illustrate the procedure. There are several advantages of our proposed approach. First, resource availability goes undefined by the investigator, which is a difficult and often arbitrary decision. Instead, the technique compares the intensity of animal use throughout the home range. This technique also avoids problems with classifying locations rigidly as used or unused. Second, location coordinates do not need to be placed within mapped resource units, which is problematic given mapping and telemetry error. Finally, resource use is considered at an appropriate scale for management because most wildlife resource decisions are made at the level of the patch. Despite the advantages of this use-intensity procedure, future research should address spatial autocorrelation and develop spatial models for ordered categorical variables.     

Spatial and temporal patterns of habitat use by Eurasian oystercatchers (<Emphasis Type="Italic">Haematopus ostralegus</Emphasis>) in the eastern Wadden Sea revealed using GPS data loggers

Detailed knowledge on species–habitat relationships is of crucial importance for the understanding of processes in marine ecosystems. Being top-predators, birds are important bio-indicators for marine systems. The aim of this study was to elucidate precise information on foraging habitat use and foraging times of oystercatchers (Haematopus ostralegus) on wide tidal flats using global positioning system (GPS) data loggers. The study was conducted to collect hints for the negative population trends in oystercatchers in the Wadden Sea. It is the first time that GPS technique has been used in a shorebird species. Although oystercatchers are known to exhibit foraging site fidelity, a number of individuals visited multiple sites. Foraging trips at night were longer, and the targeted sites were further away than those used during the day. These patterns were likely to be caused by higher risks of clutch predation by avian predators during the day that led adults to reduce their absence to defend their clutches. Our methodological approach enabled the subtle spatio-temporal patterns of habitat use to be determined on a very fine spatio-temporal scale. We suggest further potential studies using GPS data loggers that may help to reveal the reasons for the current declines in oystercatcher populations in the German Wadden Sea.     

Social context influences cue-mediated recruitment in an invasive social wasp

Social insects often serve as model systems for communication and recruitment studies, and yet, it remains controversial whether social vespid wasps can reliably communicate resource information to nestmates. In this study, I present empirical evidence that foraging strategies depend on the initial assessment of resource size and potential competition by foraging yellowjackets. The context dependent foraging behavior of Vespula pensylvanica provides a potential explanation for the inconsistent reports of the existence of recruitment communication in vespid wasps. Furthermore, life history traits may influence yellowjacket foraging behavior; annual V. pensylvanica colonies, whose foragers routinely patrol near the nest, exhibited increased bait visitation in response to the return of successful foragers, whereas perennial colonies did not. These behavioral disparities provide insight into how foraging strategies and search patterns may shift with colony size and longevity. In experiments that investigate the effects of visual cues of conspecifics and bait dispersion, foraging decisions corresponded with expectations of yellowjackets integrating resource quantity and access into a perception of demand. When resource competition could be assessed as high, V. pensylvanica foragers quickly exploited the bait closest to their colony regardless of occupation by other wasps; however, foragers preferred visiting unoccupied baits in situations where competition could be perceived as low. Moreover, a meta-analysis revealed that context-dependent, cue-mediated recruitment was widespread in Vespidae, where such foraging behaviors changed with habitat and the potential for resource competition. Such plastic foraging strategies may contribute to the invasion success of some vespid wasps.     

Lek promiscuity in a semelparous mammal,Antechinus stuartii (Marsupialia: Dasyuridae)?

Summary All male Antechinus stuartii die following a brief rut towards the end of their first year of life. Outside the rutting period, both males and females forage in clearly-defined invidual home ranges, but neither sex is territorial. As temperatures drop during the winter, both sexes may leave their foraging range each day to spend the latter part of the night and most of the daylight hours in communal nests which may be used by fifteen animals simultaneously, and over forty individuals during one winter. These temporary movements away from the foraging range cause an increase in the daily home range revealed by radiotelemetry. When the mating season commences, males abandon their foraging range and aggregate in a few of the communal nest trees, where they spend most of the night. There is some movement between aggregations, but the movement appears to be rapid and direct. Females continue to use their foraging area, and nest solitarily. However, they make excursions to the male aggregations, and spend time in the nests with the males. By the third week of the mating season, immediately prior to male mortality, males move frequently from one aggregation to another, but are still confined to the aggregations and direct movements between those nests. By this time some females have ceased visiting the aggregations and nest solitarily within their foraging range. These data suggest that the mating system of A. stuartii is lek promiscuity, and support the hypothesis that the abrupt mortality of males is a cost of endocrine changes which facilitate gluconeogenic mobilisation of body protein, allowing the males to sustain their vigil at the leks.     

In situ measures of foraging success and prey encounter reveal marine habitat-dependent search strategies

Predators are thought to reduce travel speed and increase turning rate in areas where resources are relatively more abundant, a behavior termed "area-restricted search." However, evidence for this is rare, and few empirical data exist for large predators. Animals exhibiting foraging site fidelity could also be spatially aware of suitable feeding areas based on prior experience; changes in movement patterns might therefore arise from the anticipation of higher prey density. We tested the hypothesis that regions of area-restricted search were associated with a higher number of daily speed spikes (a proxy for potential prey encounter rate) and foraging success in southern elephant seals (Mirounga leonina), a species exhibiting both area-restricted searches and high interannual foraging site fidelity. We used onshore morphological measurements and diving data from archival tags deployed during winter foraging trips. Foraging success was inferred from in situ changes in relative lipid content derived from measured changes in buoyancy, and first-passage time analysis was used to identify area-restricted search behavior. Seals exhibited relatively direct southerly movement on average, with intensive search behavior predominantly located at the distal end of tracks. The probability of being in search mode was positively related to changes in relative lipid content; thus, intensively searched areas were associated with the highest foraging success. However, there was high foraging success during the outward transit even though seals moved through quickly without slowing down and increasing turning rate to exploit these areas. In addition, the probability of being in search mode was negatively related to the number of daily speed spikes. These results suggest that movement patterns represent a response to prior expectation of the location of predictable and profitable resources. Shelf habitat was 4-9 times more profitable than the other habitats, emphasizing the importance of the East Antarctic shelf for this and other predators in the region. We have provided rare empirical data with which to investigate the relationship between predator foraging strategy and prey encounter/ foraging success, underlining the importance of inferring the timing and spatial arrangement of successful food acquisition for interpreting foraging strategies correctly.     

Grizzly bear habitat selection is scale dependent.

The purpose of our study is to show how ecologists' interpretation of habitat selection by grizzly bears (Ursus arctos) is altered by the scale of observation and also how management questions would be best addressed using predetermined scales of analysis. Using resource selection functions (RSF) we examined how variation in the spatial extent of availability affected our interpretation of habitat selection by grizzly bears inhabiting mountain and plateau landscapes. We estimated separate models for females and males using three spatial extents: within the study area, within the home range, and within predetermined movement buffers. We employed two methods for evaluating the effects of scale on our RSF designs. First, we chose a priori six candidate models, estimated at each scale, and ranked them using Akaike Information Criteria. Using this method, results changed among scales for males but not for females. For female bears, models that included the full suite of covariates predicted habitat use best at each scale. For male bears that resided in the mountains, models based on forest successional stages ranked highest at the study-wide and home range extents, whereas models containing covariates based on terrain features ranked highest at the buffer extent. For male bears on the plateau, each scale estimated a different highest-ranked model. Second, we examined differences among model coefficients across the three scales for one candidate model. We found that both the magnitude and direction of coefficients were dependent upon the scale examined; results varied between landscapes, scales, and sexes. Greenness, reflecting lush green vegetation, was a strong predictor of the presence of female bears in both landscapes and males that resided in the mountains. Male bears on the plateau were the only animals to select areas that exposed them to a high risk of mortality by humans. Our results show that grizzly bear habitat selection is scale dependent. Further, the selection of resources can be dependent upon the availability of a particular vegetation type on the landscape. From a management perspective, decisions should be based on a hierarchical process of habitat selection, recognizing that selection patterns vary across scales.     

The establishment of foraging flocks in house sparrows: risk of predation and daily temperature

Summary The foraging decisions of animals often reflect a trade-off between the risk of predation and efficient foraging. One way an animal may reduce the risk of predation, and hence exploit a resource patch in relative safety, is by foraging in a group. Solitary pioneer sparrows often recruit others to a food source by making chirrup calls in order to establish foraging flocks. This study describes the decisions of house sparrows that arrive at food resources of different risks of predation. Four feeding sites at different distances from a perching site and from an observer were presented to sparrows. When the feeder was adjacent to the perching site and far from the observer, the pioneers chirruped less frequently and were more likely to forage alone than when the feeder was in the other three positions. There were differences in the scanning behaviour of sparrows at these sites, suggesting that they were responding to different risks of predation. Furthermore, the chirrup rates of pioneer sparrows in this study and a previous study were found to be negatively correlated with maximum daily temperature. This is consistent with the hypothesis that energy requirements may affect the flock establishment decisions of sparrows, and that the benefits of foraging in flocks may be greater at lower temperatures.     

Linking patch-use behavior, resource density, and growth expectations in fish

Optimality theory rests on the assumptions that short-term foraging decisions are driven by variation in environmental quality, and that these decisions have important implications for long-term fitness. These assumptions, however, are rarely tested in a field setting. We linked behavioral foraging decisions in food patches with measures of environmental quality covering larger spatial (resource density) or temporal (growth parameters) scales. In 10 lakes, we measured the food density at which benthic fish give up foraging in experimental food patches (giving-up density, GUD), quantified the biomass of benthic invertebrates, and calculated the maximum individual size (L(infinity)) of bream (Abramis brama L.), a typical benthivore in these lakes. We found positive relationships between resource density and both GUD and L(infinity), and a positive relationship between L(infinity) and GUD. Prey characterized as vulnerable to predation contributed most to the relationships between resource density and either GUD or L(infinity). A path analysis showed that resource density and L(infinity) directly explained 54% and 28%, respectively, of the variation in GUD, whereas 86% of the variation in L(infinity) was explained by resource density, with mostly indirect contribution from GUD. We conclude that the short-term foraging behavior of benthivores matched our expectations based on optimality theory by being positively linked to variables on environmental quality operating at both a larger spatial scale and a longer temporal scale.     

Pattern-oriented modeling of bird foraging and pest control in coffee farms

We develop a model of how land use and habitat diversity affect migratory bird populations and their ability to suppress an insect pest on Jamaican coffee farms. Bird foraging—choosing which habitat patch and prey to use as prey abundance changes over space and time—is the key process driving this system. Following the “pattern-oriented” modeling strategy, we identified nine observed patterns that characterize the real system's dynamics. The model was designed so that these patterns could potentially emerge from it. The resulting model is individual-based, has fine spatial and temporal resolutions, represents very simply the supply of the pest insect and other arthropod food in six habitat types, and includes foraging habitat selection as the only adaptive behavior of birds. Although there is an extensive heritage of bird foraging theory in ecology, most of it addresses only the individual level and is too simple for our context. We used pattern-oriented modeling to develop and test foraging theory for this across-scale problem: rules for individual bird foraging that cause the model to reproduce a variety of patterns observed at the system level. Four alternative foraging theories were contrasted by how well they caused the model to reproduce the nine characteristic patterns. Four of these patterns were clearly reproduced with the “null” theory that birds select habitat randomly. A version of classical theory in which birds stay in a patch until food is depleted to some threshold caused the model to reproduce five patterns; this theory caused lower, not higher, use of habitat experiencing an outbreak of prey insects. Assuming that birds select the nearby patch providing highest intake rate caused the model to reproduce all but one pattern, whereas assuming birds select the highest-intake patch over a large radius produced an unrealistic distribution of movement distances. The pattern reproduced under none of the theories, a negative relation between bird density and distance to trees, appears to result from a process not in the model: birds return to trees at night to roost. We conclude that a foraging model for small insectivorous birds in diverse habitat should assume birds can sense higher food supply but over short, not long, distances.     

Spatial organization and behaviour of badgers <Emphasis Type="Italic">(Meles meles)</Emphasis> in a moderate-density population

Badgers are carnivores that show considerable variation in their social and spatial organization. At the westernmost part of their range, in Britain and Ireland, variation in spatial organization appears to be determined by the availability of resources. However, the majority of studies has focussed at one end of the social/spatial spectrum, where population densities are high and adjacent territories are contiguous and non-overlapping. To examine whether the same limiting factors appear to apply across a wider range of badger densities, we established a study site in a predominantly coniferous habitat within an upland area of northeast England, where population densities were predicted to be low. Seasonal home ranges of individual badgers were largest in autumn, followed by summer and spring, then winter. This pattern is reflective of the likely seasonal changes in food availability within the area, as opposed to being related to breeding patterns. There were also significant correlations between territory size and the number of grassland patches (positive) and the proportion of grassland (negative), which are consistent with predictions from the Resource Dispersion Hypothesis. Although badgers at the site were living at low to moderate densities relative to many other studied populations in Britain, they showed patterns of spatial organization that were close to those of high-density populations. The nature of the relationship between resource availability and abundance patterns is likely to have important consequences for the conservation and management of badgers and other species that show flexible spatial organization.     

Costs and benefits of pocket gopher foraging: linking behavior and physiology

Animals can attain fitness benefits by maintaining a positive net energy balance, including costs of movement during resource acquisition and the profits from foraging. Subterranean rodent burrowing provides an excellent system in which to examine the effects of movement costs on foraging behavior because it is energetically expensive to excavate burrows. We used an individual-based modeling approach to study pocket gopher foraging and its relationship to digging cost, food abundance, and food distribution. We used a unique combination of an individual-based foraging-behavior model and an energetic model to assess survival, body mass dynamics, and burrow configurations. Our model revealed that even the extreme cost of digging is not as costly as it appears when compared to metabolic costs. Concentrating digging in the area where food was found, or area-restricted search (ARS), was the most energetically efficient digging strategy compared to a random strategy. Field data show that natural burrow configurations were more closely approximated by the animals we modeled using ARS compared to random diggers. By using behavior and simple physiological principles in our model, we were able to observe realistic body mass dynamics and recreate natural movement patterns.     

Integrated modelling of foraging behaviour, energy budget and memory properties

A predator's foraging performance is related to its ability to acquire sufficient information on environmental profitability. This process can be affected by the patchy distribution and clustering of food resources and by the food intake process dynamics.We simulated body mass growth and behaviour in a forager acting in a patchy environment with patchy distribution of both prey abundance and body mass by an individual-based model. In our model, food intake was a discrete and stochastic process and leaving decision was based on the estimate of net energy gain and searching time during their foraging activities. The study aimed to investigate the effects of learning processes and food resource exploitation on body mass and survival of foragers under different scenarios of intra-patch resource distribution.The simulation output showed that different sources of resource variability between patches affected foraging efficiency differently. When prey abundance varied across patches, the predator stayed longer in poorest patches to obtain the information needed and its performance was affected by the cost of sampling and the resulting assessment of the environment proved unreliable. On the other hand, when prey body mass, but not abundance, varied among the patches the predator was quickly able to assess local profitability. Both body mass and survival of the predator were greatly affected by learning processes and patterns of food resource distribution.     

Predator and prey space use: dragonflies and tadpoles in an interactive game

Predator and prey spatial distributions have important population and community level consequences. However, little is known either theoretically or empirically about behavioral mechanisms that underlie the spatial patterns that emerge when predators and prey freely interact. We examined the joint space use and behavioral rules governing movement of freely interacting groups of odonate (dragonfly) predators and two size classes of anuran (tadpole) prey in arenas containing two patches with different levels of the prey's resource. Predator and prey movement and space use was quantified both when they were apart and together. When apart from predators, large tadpoles strongly preferred the high resource patch. When apart from prey, dragonflies weakly preferred the high resource patch. When together, large prey shifted to a uniform distribution, while predators strongly preferred the high resource patch. These patterns qualitatively fit the predictions of several three trophic level, ideal free distribution models. In contrast, the space use of small prey and predators did not deviate from uniform. Three measures of joint space use (spatial correlations, overlap, and co-occurrence) concurred in suggesting that prey avoidance of predators was more important than predator attraction to prey in determining overall spatial patterns. To gain additional insight into behavioral mechanisms, we used a model selection approach to identify behavioral movement rules that can potentially explain the observed, emergent patterns of space use. Prey were more likely to leave patches with more predators and more conspecific competitors; resources had relatively weak effects on prey movements. In contrast, predators were more likely to leave patches with low resources (that they do not consume) and more competing predators; prey had relatively little effect on predator movements. These results highlight the importance of investigating freely interacting predators and prey, the potential for simple game theory models to predict joint spatial distributions, and the utility of using model choice methods to identify potential key factors that govern movement.     

Ranging behavior of the mountain gorillas (Gorilla beringei beringei) in Bwindi Impenetrable National Park, Uganda: a test of the ecological constraints model

The ecological constraints model predicts that daily travel distance and home range size of social animals will increase as group size increases in order to meet the dietary needs of additional group members. This theory has been supported more predominantly by studies of frugivorous primate species than by studies of folivorous species. We examined the ranging patterns of mountain gorillas in Bwindi Impenetrable National Park, Uganda, who include both herbaceous vegetation and fruit in their diet, to determine how ecological, behavioral, and social parameters influence movement patterns. Data were collected from three groups of gorillas with overlapping home ranges at a low-altitude location (1,450–1,800 m) and one group at a high-altitude location (2,100–2,500 m) in Bwindi from September 2001 to August 2002. We analyzed daily travel distance and home range size in relation to group size, while also considering patterns of frugivory, rainfall, and location (proxy for food availability) within the park. Both daily travel distance and home range size were positively related to group size. In addition, the degree of frugivory positively influenced daily travel distance and home range size, while rainfall negatively influenced daily travel distance only. Finally, groups at the low-altitude location, with higher fruit availability, traveled less than the group at the high-altitude location. These results demonstrate that mountain gorillas in Bwindi provide support for the ecological constraints model, but further studies are needed to determine how fine-scale spatial and temporal availability of food resources influence movement patterns. Ranging patterns of Bwindi gorillas are compared to those observed in other gorilla populations in the context of the ecological constraints model.Communicated by D. Watts