Spatial scaling of consumer-resource interactions in advection-dominated systems

Ecologists studying consumer-resource interactions in advection-dominated systems such as streams and rivers frequently seek to link the results of small-scale experiments with larger-scale patterns of distribution and abundance. Accomplishing this goal requires determining the characteristic scale, termed the response length, at which there is a shift from local dynamics dominated by advective dispersal to larger-scale dynamics dominated by births and deaths. Here, we model the dynamics of consumer-resource systems in a spatially variable, advective environment and show how consumer-resource interactions alter the response length relative to its single-species value. For one case involving a grazer that emigrates in response to high predator density, we quantify the changes using published data from small-scale experiments on aquatic invertebrates. Using Fourier analysis, we describe the responses of advection-dominated consumer-resource systems to spatially extended environmental variability in a way that involves explicit consideration of the response length. The patterns we derive for different consumer-resource systems exhibit important similarities in how component populations respond to spatial environmental variability affecting dispersal as opposed to demographic parameters.     

Integrodifference models for persistence in fragmented habitats

Integrodifference models of growth and dispersal are analyzed on finite domains to investigate the effects of emigration, local growth dynamics and habitat heterogeneity on population persistence. We derive the bifurcation structure for a range of population dynamics and present an approximation that allows straighforward calculation of the equilibrium populations in terms of local growth dynamics and dispersal success rates. We show how population persistence in a heterogeneous environment depends on the scale of the heterogeneity relative to the organism's characteristic dispersal distance. When organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence.     

Nonlinear Effect of Dispersal Rate on Spatial Synchrony of Predator-Prey Cycles

Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (<0.4% per prey generation) were capable of rapidly bringing initially anti-synchronous cycles into synchrony. Consistent with theory, ecologically-identical replicates exhibited very different levels of prey synchrony, especially at low to intermediate dispersal rates. Our results suggest that even the very low rates of dispersal observed in many natural systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.     

Evaluating within‐population variability in behavior and demography for the adaptive potential of a dispersal‐limited species to climate change

Multiple pathways exist for species to respond to changing climates. However, responses of dispersal‐limited species will be more strongly tied to ability to adapt within existing populations as rates of environmental change will likely exceed movement rates. Here, we assess adaptive capacity in Plethodon cinereus, a dispersal‐limited woodland salamander. We quantify plasticity in behavior and variation in demography to observed variation in environmental variables over a 5‐year period. We found strong evidence that temperature and rainfall influence P. cinereus surface presence, indicating changes in climate are likely to affect seasonal activity patterns. We also found that warmer summer temperatures reduced individual growth rates into the autumn, which is likely to have negative demographic consequences. Reduced growth rates may delay reproductive maturity and lead to reductions in size‐specific fecundity, potentially reducing population‐level persistence. To better understand within‐population variability in responses, we examined differences between two common color morphs. Previous evidence suggests that the color polymorphism may be linked to physiological differences in heat and moisture tolerance. We found only moderate support for morph‐specific differences for the relationship between individual growth and temperature. Measuring environmental sensitivity to climatic variability is the first step in predicting species' responses to climate change. Our results suggest phenological shifts and changes in growth rates are likely responses under scenarios where further warming occurs, and we discuss possible adaptive strategies for resulting selective pressures.     

Flexible dispersal strategies in native and non‐native ranges: environmental quality and the ‘good–stay,bad–disperse’ rule

Dispersal strategies are one of the most important determinants of range dynamics and a surrogate for invasiveness. We tested three inter‐related hypotheses derived from demographic and ecological models: (H₁) short‐distance dispersal strategies arise at native range margins due to their demographic advantage; (H₂) in non‐native areas a high diffusion rate is favoured at the advancing range front for niche filling; (H₃) environmental deterioration can increase dispersal and lead to a ‘good–stay, bad–disperse’ strategy. Spatially and temporally explicit rates of spread and dispersal kernels of the European starling Sturnus vulgaris were generated for its native range (Britain) using ringing records from 1909 to 2008, and for a non‐native area (South Africa) using ringing data and distributional records since its introduction in 1897. There was a marked spatial and temporal variation in the rate of spread within both native and non‐native ranges. In the native range the rate of spread declined with increasing distance from the species’ European distribution (contradicting H₁). In the non‐native range the rate of spread increased with distance from the introduction locality (supporting H₂). The annual rate of spread in the native range also increased significantly when environmental conditions were deteriorating as indicated by marked population declines and relatively low abundance (H₃), providing clear evidence for flexible dispersal strategies based on a ‘good–stay, bad–disperse’ rule. Starlings’ dispersal kernel followed an inverse power law and showed strong anisotropy and significant divergence between native and invasive populations, suggesting a flexible strategy comprising a dynamic response to spatial and temporal environmental variation with implications for predicting dispersal and range dynamics arising from environmental change.     

Estimating range expansion of wildlife in heterogeneous landscapes: A spatially explicit state‐space matrix model coupled with an improved numerical integration technique

Dispersal as well as population growth is a key demographic process that determines population dynamics. However, determining the effects of environmental covariates on dispersal from spatial‐temporal abundance proxy data is challenging owing to the complexity of model specification for directional dispersal permeability and the extremely high computational loads for numerical integration. In this paper, we present a case study estimating how environmental covariates affect the dispersal of Japanese sika deer by developing a spatially explicit state‐space matrix model coupled with an improved numerical integration technique (Markov chain Monte Carlo with particle filters). In particular, we explored the environmental drivers of inhomogeneous range expansion, characteristic of animals with short dispersal. Our model framework successfully reproduced the complex population dynamics of sika deer, including rapid changes in densely populated areas and distribution fronts within a decade. Furthermore, our results revealed that the inhomogeneous range expansion of sika deer seemed to be primarily caused by the dispersal process (i.e., movement barriers in fragmented forests) rather than population growth. Our state‐space matrix model enables the inference of population dynamics for a broad range of organisms, even those with low dispersal ability, in heterogeneous landscapes, and could address many pressing issues in conservation biology and ecosystem management.     

Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics

Aim The study and prediction of species–environment relationships is currently mainly based on species distribution models. These purely correlative models neglect spatial population dynamics and assume that species distributions are in equilibrium with their environment. This causes biased estimates of species niches and handicaps forecasts of range dynamics under environmental change. Here we aim to develop an approach that statistically estimates process‐based models of range dynamics from data on species distributions and permits a more comprehensive quantification of forecast uncertainties. Innovation We present an approach for the statistical estimation of process‐based dynamic range models (DRMs) that integrate Hutchinson's niche concept with spatial population dynamics. In a hierarchical Bayesian framework the environmental response of demographic rates, local population dynamics and dispersal are estimated conditional upon each other while accounting for various sources of uncertainty. The method thus: (1) jointly infers species niches and spatiotemporal population dynamics from occurrence and abundance data, and (2) provides fully probabilistic forecasts of future range dynamics under environmental change. In a simulation study, we investigate the performance of DRMs for a variety of scenarios that differ in both ecological dynamics and the data used for model estimation. Main conclusions Our results demonstrate the importance of considering dynamic aspects in the collection and analysis of biodiversity data. In combination with informative data, the presented framework has the potential to markedly improve the quantification of ecological niches, the process‐based understanding of range dynamics and the forecasting of species responses to environmental change. It thereby strengthens links between biogeography, population biology and theoretical and applied ecology.     

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature. Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.     

SpatialDemography: a spatially explicit,stage‐structured,metacommunity model

The responses of species and populations to changes in the environment (e.g. changes in climate and land use) are often complex and difficult to predict. We have created the SpatialDemography model (R package: spatialdemography). The model is a spatially explicit, stage‐structured, matrix‐based metacommunity model, with the potential for modeling species’ and populations’ potential responses to environmental heterogeneity and change. The SpatialDemography model assumes a cellular landscape populated by organisms with four life stages: a mobile dispersing stage, two sessile non‐reproductive stages, and a reproductive adult stage. Individuals are assumed to originate at the center of a given cell and disperse according to a specified dispersal kernel (e.g. log‐normal). All adult individuals are capable of producing offspring. The model approach and framework are described in the context of a hypothetical example with multiple competing species in a four cell landscape. In this example simulation, both spatial location and species interactions were important for understanding population dynamics. SpatialDemography can be applied to questions where an understanding of transient and long‐term demographic responses to spatiotemporal changes is desired. It is primarily applicable to metapopulations and metacommunities of organisms with early dispersal and sessile adults (i.e. modular organisms such as plants and some marine organisms). SpatialDemography differs from other population models in that it is spatially explicit, can incorporate biotic interactions, and is implemented in R.     

Demographic consequences of climate change and land cover help explain a history of extirpations and range contraction in a declining snake species

Developing conservation strategies for threatened species increasingly requires understanding vulnerabilities to climate change, in terms of both demographic sensitivities to climatic and other environmental factors, and exposure to variability in those factors over time and space. We conducted a range‐wide, spatially explicit climate change vulnerability assessment for Eastern Massasauga (Sistrurus catenatus), a declining endemic species in a region showing strong environmental change. Using active season and winter adult survival estimates derived from 17 data sets throughout the species' range, we identified demographic sensitivities to winter drought, maximum precipitation during the summer, and the proportion of the surrounding landscape dominated by agricultural and urban land cover. Each of these factors was negatively associated with active season adult survival rates in binomial generalized linear models. We then used these relationships to back‐cast adult survival with dynamic climate variables from 1950 to 2008 using spatially explicit demographic models. Demographic models for 189 population locations predicted known extant and extirpated populations well (AUC = 0.75), and models based on climate and land cover variables were superior to models incorporating either of those effects independently. These results suggest that increasing frequencies and severities of extreme events, including drought and flooding, have been important drivers of the long‐term spatiotemporal variation in a demographic rate. We provide evidence that this variation reflects nonadaptive sensitivity to climatic stressors, which are contributing to long‐term demographic decline and range contraction for a species of high‐conservation concern. Range‐wide demographic modeling facilitated an understanding of spatial shifts in climatic suitability and exposure, allowing the identification of important climate refugia for a dispersal‐limited species. Climate change vulnerability assessment provides a framework for linking demographic and distributional dynamics to environmental change, and can thereby provide unique information for conservation planning and management.     

Drivers of plant species’ potential to spread: the importance of demography versus seed dispersal

Understanding the ability of plants to spread is important for assessing conservation strategies, landscape dynamics, invasiveness and ability to cope with climate change. While long‐distance seed dispersal is often viewed as a key process in population spread, the importance of inter‐specific variation in demography is less explored. Indeed, the relative importance of demography vs seed dispersal in determining population spread is still little understood. We modelled species’ potential for population spread in terms of annual migration rates for a set of species inhabiting dry grasslands of central Europe. Simultaneously, we estimated the importance of demographic (population growth rate) versus long‐distance dispersal (99th percentile dispersal distance) characteristics for among‐species differences in modelled population spread. In addition, we assessed how well simple proxy measures related to demography (the number and survival of seedlings, the survival of flowering individuals) and dispersal (plant height, terminal velocity and wind speed during dispersal) predicted modelled spread rates. We found that species’ demographic rates were the more powerful predictors of species’ modelled potential to spread than dispersal. Furthermore, our simple proxies were correlated with modelled species spread rates and together their predictive power was high. Our findings highlight that for understanding variation among species in their potential for population spread, detailed information on local demography and dispersal might not always be necessary. Simple proxies or assumptions that are based primarily on species demography could be sufficient.     

Mating timing,dispersal and local adaptation in patchy environments

Dispersal is a life‐history trait that can evolve under various known selective pressures as identified by a multitude of theoretical and empirical studies. Yet only few of them are considering the succession of mating and dispersal. The sequence of these events influences gene flow and consequently affects the dynamics and evolution of populations. We use individual‐based simulations to investigate the evolution of the timing of dispersal and mating, i.e. mating before or after dispersal. We assume a discrete insect metapopulation in a heterogeneous environment, where populations may adapt to local conditions and only females are allowed to disperse. We run the model assuming different levels of species habitat tolerance, carrying capacity, and temporal environmental variability. Our results show that in species with narrow habitat tolerance, low to moderate dispersal evolves in combination with mating after dispersal (post‐dispersal mating). With such a strategy dispersing females benefit from mating with a resident male, as their offspring will be better adapted to the local habitat conditions. On the contrary, in species with wide habitat tolerance higher dispersal rates in combination with pre‐dispersal mating evolves. In this case individuals are adapted to the ‘average’ habitat where pre‐dispersal mating conveys the benefit of carrying relatives’ genes into a new population. With high dispersal rates and large population size, local adaptation and kin structure both vanish and the temporal sequence of dispersal and mating may become a (nearly) neutral trait.     

Spatial synchrony of recruitment in mountain-dwelling woodland caribou

Spatial synchrony in population dynamics is a ubiquitous feature across a range of taxa. Understanding factors influencing this synchrony may shed light on important drivers of population dynamics. Three mechanisms influence the degree of spatial synchrony between populations: dispersal, shared predators, and spatial environmental covariance (the Moran effect). We assessed demographic spatial synchrony in recruitment (calf:cow ratio) of 10 northern mountain caribou herds in the Yukon Territory, Canada (1982–2008). Shared predators and dispersal were ruled out as causal mechanisms of spatial recruitment synchrony in these herds and therefore any spatial synchrony should be due to the Moran effect. We also assessed the degree of spatial synchrony in April snow depth to represent environmental variability. The regional average spatial synchrony in detrended residuals of April snow depth was 0.46 (95% CI 0.37 to 0.55). Spatial synchrony in caribou recruitment was weak at 0.13 (95% CI −0.06 to 0.32). The spatial scale of synchrony in April snow depth and caribou recruitment was 330.2 km (95% CI 236.3 to 370.0 km) and 170.0 km (95% CI 69.5 to 282.8 km), respectively. We also investigated how the similarity in terrain features between herds influenced the degree of spatial synchrony using exponential decay models. Only the difference in elevation variability between herds during calving was supported by the data. Herds with more similar elevation variability may track snowmelt ablation patterns in a more similar fashion, which would subsequently result in more synchronized predation rates on calves and/or nutritional effects impacting juvenile survival. Interspecific interactions with predators and alternate prey may also influence spatial synchrony of recruitment in these herds.     

Assessing seasonal demographic covariation to understand environmental‐change impacts on a hibernating mammal

Natural populations are exposed to seasonal variation in environmental factors that simultaneously affect several demographic rates (survival, development and reproduction). The resulting covariation in these rates determines population dynamics, but accounting for its numerous biotic and abiotic drivers is a significant challenge. Here, we use a factor‐analytic approach to capture partially unobserved drivers of seasonal population dynamics. We use 40 years of individual‐based demography from yellow‐bellied marmots (Marmota flaviventer) to fit and project population models that account for seasonal demographic covariation using a latent variable. We show that this latent variable, by producing positive covariation among winter demographic rates, depicts a measure of environmental quality. Simultaneously, negative responses of winter survival and reproductive‐status change to declining environmental quality result in a higher risk of population quasi‐extinction, regardless of summer demography where recruitment takes place. We demonstrate how complex environmental processes can be summarized to understand population persistence in seasonal environments.     

The effects of small dispersal rates on extinction times in structured metapopulation models

Habitat destruction is a critical factor that affects persistence in several taxa, including Pacific salmon. Salmon are noted for their ability to home to their natal streams for reproduction. Since straying (i.e., spawners reproducing in nonnatal streams) is typically low in salmon, its effects have not been appreciated. In this article, we develop both a general analytical model and a simple simulation model describing structured metapopulations to study how weak connections between subpopulations affect the ability of a species to tolerate habitat destruction and/or declines in habitat quality. Our goals are to develop general principles and to relate these principles to salmon population dynamics. The analytical model describes the dynamics of two density-dependent subpopulations, connected by dispersal, whose growth rates fluctuate in response to environmental and demographic stochasticity. We find that, for moderate levels of environmental variability, small dispersal rates can significantly increase mean extinction times. This effect declines with increasing habitat quality, increasing temporal correlation, and increasing spatial correlation, but it is still significant for realistic parameter values. The simulation model shows there is a threshold rate of dispersal that minimizes extinction probabilities. These results cannot be seen in classical metapopulation models and provide new insights into the rescue effect.     

Disentangling the role of connectivity,environmental filtering,and spatial structure on metacommunity dynamics

Dispersal is a key process in metacommunity dynamics, allowing the maintenance of diversity in complex community networks. Geographic distance is usually used as a surrogate for connectivity implying that communities that are closely located are considered more prone to exchange individuals than distant communities. However, in some natural systems, organisms may be subjected to directional dispersal (air or water flows, particular landscape configuration), possibly leading close communities to be isolated from each other and distant communities to be connected. Using geographic distance as a proxy for realised connectivity may then yield misleading results regarding the role of dispersal in structuring communities in such systems. Here, we quantified the relative importance of flow connectivity, geographic distance, and environmental gradients to explain polychaete metacommunity structure along the coasts of the Gulf of Lions (northwest Mediterranean Sea). Flow connectivity was estimated by Lagrangian particle dispersal simulations. Our results revealed that this metacommunity is strongly structured by the environment at large spatial scales, and that both flow connectivity and geographic distance play an important role within homogeneous environments at smaller spatial scales. We thus strongly advocate for a wider use of connectivity measures, in addition to geographic distance, to study spatial patterns of biological diversity (e.g. distance decay) and to infer the processes behind these patterns at different spatial scales. Synthesis Everything is connected, but connections are seldom accurately quantified. Biological communities are often studied separately, using observations, experiments and models to unravel local dynamics of organisms interacting with each other. However, regional processes such as dispersal through ocean and air circulation, likely to connect distant communities and influence their local dynamics, are not always accounted for, or, at best, used as an homogeneous and distance‐related factor. Ocean models have being extensively developed and validated during the past decades with the increasing availability of accurate meteorological data. Using such model outputs, precise quantifi cation of exchange rates of organisms between communities was performed in a marine Mediterranean coastal area. Jointly with local environmental and biological data, these results were used to quantify the effects of realistic connectivity on local and regional polychaete community structure, and revealed that the environmental gradient, geographic distance, and connectivity were responsible for community structure at different spatial scales.     

Individual‐based modelling of resource competition to predict density‐dependent population dynamics: a case study with white storks

Density regulation influences population dynamics through its effects on demographic rates and consequently constitutes a key mechanism explaining the response of organisms to environmental changes. Yet, it is difficult to establish the exact form of density dependence from empirical data. Here, we developed an individual‐based model to explore how resource limitation and behavioural processes determine the spatial structure of white stork Ciconia ciconia populations and regulate reproductive rates. We found that the form of density dependence differed considerably between landscapes with the same overall resource availability and between home range selection strategies, highlighting the importance of fine‐scale resource distribution in interaction with behaviour. In accordance with theories of density dependence, breeding output generally decreased with density but this effect was highly variable and strongly affected by optimal foraging strategy, resource detection probability and colonial behaviour. Moreover, our results uncovered an overlooked consequence of density dependence by showing that high early nestling mortality in storks, assumed to be the outcome of harsh weather, may actually result from density dependent effects on food provision. Our findings emphasize that accounting for interactive effects of individual behaviour and local environmental factors is crucial for understanding density‐dependent processes within spatially structured populations. Enhanced understanding of the ways animal populations are regulated in general, and how habitat conditions and behaviour may dictate spatial population structure and demographic rates is critically needed for predicting the dynamics of populations, communities and ecosystems under changing environmental conditions.     

Dispersal of introduced house sparrows Passer domesticus: an experiment

An important issue concerning the introduction of non-indigenous organisms into local populations is the potential of the introduced individuals to spread and interfere both demographically and genetically with the local population. Accordingly, the potential of spatial dispersal among introduced individuals compared with local individuals is a key parameter to understand the spatial and temporal dynamics of populations after an introduction event. In addition, if the variance in dispersal rate and distance is linked to individual characteristics, this may further affect the population dynamics. We conducted a large-scale experiment where we introduced 123 house sparrows from a distant population into 18 local populations without changing population density or sex ratio. Introduced individuals dispersed more frequently and over longer distances than residents. Furthermore, females had higher probability of dispersal than males. In females, there was also a positive relationship between the wing length and the probability of dispersal and dispersal distance. These results suggest that the distribution and frequency of introduced individuals may be predicted by their sex ratio as well as their phenotypic characteristics.     

Restricted dispersal reduces the strength of spatial density dependence in a tropical bird population

Spatial processes could play an important role in density-dependent population regulation because the disproportionate use of poor quality habitats as population size increases is widespread in animal populations-the so-called buffer effect. While the buffer effect patterns and their demographic consequences have been described in a number of wild populations, much less is known about how dispersal affects distribution patterns and ultimately density dependence. Here, we investigated the role of dispersal in spatial density dependence using an extraordinarily detailed dataset from a reintroduced Mauritius kestrel (Falco punctatus) population with a territorial (despotic) breeding system. We show that recruitment rates varied significantly between territories, and that territory occupancy was related to its recruitment rate, both of which are consistent with the buffer effect theory. However, we also show that restricted dispersal affects the patterns of territory occupancy with the territories close to release sites being occupied sooner and for longer as the population has grown than the territories further away. As a result of these dispersal patterns, the strength of spatial density dependence is significantly reduced. We conclude that restricted dispersal can modify spatial density dependence in the wild, which has implications for the way population dynamics are likely to be impacted by environmental change.     

The numerical response: rate of increase and food limitation in herbivores and predators

Two types of numerical response function have evolved since Solomon first introduced the term to generalize features of Lotka-Volterra predator-prey models: (i) the demographic numerical response, which links change in consumer demographic rates to food availability; and (ii) the isocline numerical response, which links consumer abundance per se to food availability. These numerical responses are interchangeable because both recognize negative feedback loops between consumer and food abundance resulting in population regulation. We review how demographic and isocline numerical responses have been used to enhance our understanding of population regulation of kangaroos and possums, and argue that their utility may be increased by explicitly accounting for non-equilibrium dynamics (due to environmental variability and/or biological interactions) and the existence of multiple limiting factors. Interferential numerical response functions may help bridge three major historical dichotomies in population ecology (equilibrium versus non-equilibrium dynamics, extrinsic versus intrinsic regulation and demographic versus isocline numerical responses).