Study methodology impacts density-dependent dispersal observations: a systematic review

The relationship between animal dispersal and conspecific density has been explored in various study systems but results in terms of both the magnitude and the direction of density dependence are inconsistent. We conducted a thorough review of the literature (2000-2023) and found k = 97 empirical studies of birds, fishes, herpetofauna (amphibians and reptiles), invertebrates, or mammals that had tested for a correlation between conspecific density and animal dispersal. We extracted categorical variables for taxonomic group, sex, age, migratory behavior, study design, dispersal metric, density metric and variable type, as well as temporal and spatial scale, to test each of their correlation with the effect of density on dispersal (Pearson's r) using linear regressions and multilevel mixed-effect modelling. We found certain biases in the published literature, highlighting that the impact of conspecific density on dispersal is not as widespread as it is thought to be. We also found no predominant trend for density-dependent dispersal across taxonomic groups. Instead, results show that the scale and metrics of empirical observations significantly affected analytical results, and heterogeneity measures were high within taxonomic groups. Therefore, the direction and magnitude of the interaction between density and dispersal in empirical studies could partially be attributed to the data collection method involved. We suggest that the contradictory observations for density-dependent dispersal could be explained by dispersal-dependent density, where density is driven by movement instead, and urge researchers to either test this interaction when applicable or consider this perspective when reporting results.

Source-sink dynamics within a complex life history

Source-sink patch dynamics occur when movement from sources stabilizes sinks by compensating for low local vital rates. The mechanisms underlying source-sink dynamics may be complicated in species that undergo transitions between discrete life stages, particularly when stages have overlapping habitat requirements and similar movement abilities. In these species, for example, the demographic effects of movement by one stage may augment or offset the effects of movement by another stage. We used a stream salamander system to investigate patch dynamics within this form of complex life history. Specifically, we tested the hypothesis that the salamander Gyrinophilus porphyriticus experiences source-sink dynamics in riffles and pools, the dominant geomorphic patch types in headwater streams. We estimated stage-specific survival probabilities in riffles and pools and stage-specific movement probabilities between the two patch types using 8 years of capture-recapture data on 4491 individuals, including premetamorphic larvae and postmetamorphic adults. We then incorporated survival and movement probabilities into a stage-structured, two-patch model to determine the demographic interactions between riffles and pools. Monthly survival probabilities of both stages were higher in pools than in riffles. Larvae were more likely to move from riffles to pools, but adults were more likely to move from pools to riffles, despite experiencing much lower survival in riffles. In simulations, eliminating interpatch movements by both stages indicated that riffles are sinks that rely on immigration from pools for stability. Allowing only larvae to move stabilized both patch types, but allowing only adults to move destabilized pools due to the demographic cost of adult emigration. These results indicated that larval movement not only stabilizes riffles, but also offsets the destabilizing effects of maladaptive adult movement. Similar patch dynamics may emerge in any structured population in which movement and local vital rates differ by age, size, or stage. Addressing these forms of internal demographic structure in patch dynamics analyses will help to refine and advance general understanding of spatial ecology.

Does Population Size Drive Changes in Transatlantic Vagrancy for Gulls? A Study of Seven North Atlantic Species

European gulls Chroicocephalus ridibundus, Larus canus, and L. graellsii have dispersed to North America and C. ridibundus and L. graellsii have bred or attempted to breed. North American gulls L. delawarensis, Leucophaeus atricilla, Leucophaeus pipixcan, and Chroicocephalus philadelphia have dispersed to Europe, although no successful breeding by non-hybrid pairs has yet occurred. We hypothesized that as gull population sizes increase, the number of birds exploring potential new breeding sites also increases. To test our hypothesis, we compared the number of transatlantic vagrants to the population size on the previous year using generalized linear models. We found an increasing number of transatlantic vagrants moving in both directions, which suggests that vagrancy is not a random phenomenon driven by strong winds nor caused by reverse migration. Population size predicted transatlantic vagrancy in four of the seven species. However, our hypothesis that increases in population size drive increases in vagrancy was only supported in two of these instances. We further looked at sub-populations of L. delawarensis in North America and tested our hypothesis for each subpopulation. We found partial support for our hypothesis for these data. Even within one species, we observed multiple relationships between vagrancy and population size. Our results showed that size or trend in source population size—in some circumstances—is clearly a driver of vagrancy, but other factors must play an important role too. As anthropogenic development continues, and high-quality habitats become farther apart, it is important that we continue to investigate all drivers of vagrancy because the persistence of a species may depend crucially on its longest-distance dispersers.

Movement and dispersal of a habitat specialist in human-dominated landscapes: a case study of the red panda

BACKGROUND

Habitat specialists living in human-dominated landscapes are likely to be affected by habitat fragmentation and human disturbances more than generalists. But there is a paucity of information on their response to such factors. We examined the effect of these factors on movement patterns of red pandas Ailurus fulgens, a habitat and diet specialist that inhabits the eastern Himalaya.

METHODS

We equipped 10 red pandas (six females, four males) with GPS collars and monitored them from September 2019 to March 2020 in Ilam, eastern Nepal. We collected habitat and disturbance data over four seasons. We considered geophysical covariates, anthropogenic factors and habitat fragmentation metrics, and employed linear -mixed models and logistic regression to evaluate the effect of those variables on movement patterns.

RESULTS

The median daily distance travelled by red pandas was 756 m. Males travelled nearly 1.5 times further than females (605 m). Males and sub-adults travelled more in the mating season while females showed no seasonal variation for their daily distance coverage. Red pandas were relatively more active during dawn and morning than the rest of the day, and they exhibited seasonal variation in distance coverage on the diel cycle. Both males and females appeared to be more active in the cub-rearing season, yet males were more active in the dawn in the birthing season. Two sub-adult females dispersed an average of 21 km starting their dispersal with the onset of the new moon following the winter solstice. The single subadult male did not disperse. Red pandas avoided roads, small-habitat patches and large unsuitable areas between habitat patches. Where connected habitat with high forest cover was scarce the animals moved more directly than when habitat was abundant.

CONCLUSIONS

Our study indicates that this habitat specialist is vulnerable to human disturbances and habitat fragmentation. Habitat restoration through improving functional connectivity may be necessary to secure the long-term conservation of specialist species in a human-dominated landscape. Regulation of human activities should go in parallel to minimize disturbances during biologically crucial life phases. We recommend habitat zonation to limit human activities and avoid disturbances, especially livestock herding and road construction in core areas.

Individual differences in dominance-related traits drive dispersal and settlement in hatchery-reared juvenile brown trout

Effective management of exploited populations is based on an understanding of population dynamics and evolutionary processes. In spatially structured populations, dispersal is a central process that ultimately can affect population growth and viability. It can be influenced by environmental conditions, individual phenotypes, and stochastic factors. However, we have a limited knowledge of the relative contribution of these components and its interactions, and which traits can be used as reliable predictors of the dispersal ability. Here, we conducted a longitudinal field experiment aimed to identify traits which can be used as proxy for dispersal in juvenile brown trout (Salmo trutta L.). We measured body size and standard metabolic rates, and estimated body shapes for 212 hatchery-reared juvenile fish that were marked with individual codes and released in a small coastal stream in northwest Spain. We registered fish positions and distances to the releasing point after 19, 41, 60 and 158 days in the stream. We detected a high autocorrelation of dispersal distances, demonstrating that most individuals settle down relatively soon and then hold stable positions over the study period. Body size and fish shape were reliable predictors of dispersal, with bigger and more robust-set individuals being more likely to settle closer to the release site than smaller and more elongated fish. In addition, the analysis of spacing and spatial patterns indicated that the dispersal of introduced fish could affect the distribution of resident conspecifics. All together, these results suggest that stocking programs aimed to the enhancement of overexploited populations at fine spatial scales can be optimized by adjusting the size and shape of the introduced fish to specific management targets and environmental conditions.

Empirical tests of habitat selection theory reveal that conspecific density and patch quality, but not habitat amount, drive long-distance immigration in a wild bird

Individuals that disperse long distances from their natal site must select breeding patches with no prior knowledge of patch suitability. Despite decades of theoretical studies examining which cues dispersing individuals should use to select breeding patches, few empirical studies have tested the predictions of these theories at spatial scales relevant to long‐distance dispersal in wild animal populations. Here, we use a novel assignment model based on multiple intrinsic markers to quantify natal dispersal distances of Wood Thrush (Hylocichla mustelina) breeding in forest fragments. We show that long‐distance natal dispersal in this species is more frequent than commonly assumed for songbirds and that habitat selection by these individuals is driven by density‐dependence and patch quality but not the amount of habitat surrounding breeding patches. These results represent an important contribution to understanding habitat selection by dispersing individuals, especially with regards to long‐distance dispersal.

Modeling habitat connectivity in support of multiobjective species movement: An application to amphibian habitat systems

Reasoning about the factors underlying habitat connectivity and the inter-habitat movement of species is essential to many areas of biological inquiry. In order to better describe and understand the ways in which the landscape may support species movement, an increasing amount of research has focused on identification of paths or corridors that may be important in providing connectivity among habitat. The least-cost path problem has proven to be an instrumental analytical tool in this sense. A complicating aspect of such path identification methods is how to best reconcile and integrate the array of criteria or objectives that species may consider in traversal of a landscape. In cases where habitat connectivity is thought to be influenced or guided by multiple objectives, numerous solutions to least-cost path problems can exist, representing tradeoffs between the objectives. In practice though, identification of these solutions can be very challenging and as such, only a small proportion of them are typically examined leading to a weak characterization of habitat connectivity. To address this computational challenge, a multiobjective optimization framework is proposed. A generalizable multiobjective least-cost path model is first detailed. A non-inferior set estimation (MONISE) algorithm for identifying supported efficient solutions to the multiobjective least-cost path model is then described. However, it is well known that unsupported efficient solutions (which are equally important) can also exist, but are typically ignored given that they are more difficult to identify. Thus, to enable the identification of the full set of efficient solutions (supported and unsupported) to the multiobjective model, a multi-criteria labeling algorithm is then proposed. The developed framework is applied to assess different conceptualizations of habitat connectivity supporting amphibian movement in a wetland system. The results highlight the range of tradeoffs in characterizations of connectivity that can exist when multiple objectives are thought to contribute to movement decisions and that the number of unsupported efficient solutions (which are typically ignored) can vastly outweigh that of the supported efficient solutions.

Long-distance natal dispersal is relatively frequent and correlated with environmental factors in a widespread raptor

Dispersal is a critical process influencing population dynamics and responses to global change. Long-distance dispersal (LDD) can be especially important for gene flow and adaptability, although little is known about the factors influencing LDD because studying large-scale movements is challenging and LDD tends to be observed less frequently than shorter-distance dispersal (SDD). We sought to understand patterns of natal dispersal at a large scale, specifically aiming to understand the relative frequency of LDD compared to SDD and correlates of dispersal distances. We used bird banding and encounter data for American kestrels (Falco sparverius) to investigate the effects of sex, migration strategy, population density, weather, year and agricultural land cover on LDD frequency, LDD distance and SDD distance in North America from 1961 to 2015. Nearly half of all natal dispersal (48.9%) was LDD (classified as >30 km), and the likelihood of LDD was positively associated with the proportion of agricultural land cover around natal sites. Correlates of distance differed between LDD and SDD movements. LDD distance was positively correlated with latitude, a proxy for migration strategy, suggesting that migratory individuals disperse farther than residents. Distance of LDD in males was positively associated with maximum summer temperature. We did not find sex-bias or an effect of population density in LDD distance or frequency. Within SDD, females tended to disperse farther than males, and distance was positively correlated with density. Sampling affected all responses, likely because local studies more frequently capture SDD within study areas. Our findings that LDD occurs at a relatively high frequency and is related to different proximate factors from SDD, including a lack of sex-bias in LDD, suggest that LDD may be more common than previously reported, and LDD and SDD may be distinct processes rather than two outcomes originating from a single dispersal distribution. To our knowledge, this is the first evidence that LDD and SDD may be separate processes in an avian species, and suggests that environmental change may have different outcomes on the two processes.

Long-term survival probability, not current habitat quality, predicts dispersal distance in a stream salamander

Dispersal evolves as an adaptive mechanism to optimize individual fitness across the landscape. Specifically, dispersal represents a mechanism to escape fitness costs resulting from changes in environmental conditions. Decades of empirical work suggest that individuals use local habitat cues to make movement decisions, but theory predicts that dispersal can also evolve as a fixed trait, independent of local conditions, in environments characterized by a history of stochastic spatiotemporal variation. Until now, however, both conditional and fixed models of dispersal evolution have primarily been evaluated using emigration data (stay vs. leave), and not dispersal distances: a more comprehensive measure of dispersal. Our goal was to test whether conditional or fixed models of dispersal evolution predict variation in dispersal distance in the stream salamander Gyrinophilus porphyriticus. We quantified variation in habitat conditions using measures of salamander performance from 4 yr of spatially explicit, capture-mark-recapture (CMR) data across three headwater streams in the Hubbard Brook Experimental Forest in central New Hampshire, USA. We used body condition as an index of local habitat quality that individuals may use to make dispersal decisions, and survival probability estimated from multistate CMR models as an index of mortality risk resulting from the long-term history of environmental variation. We found that dispersal distances increased with declining survival probability, indicating that salamanders disperse further in risky environments. Dispersal distances were unrelated to spatial variation in body condition, suggesting that salamanders do not base dispersal distance decisions on local habitat quality. Our study provides the first empirical support for fixed models of dispersal evolution, which predict that dispersal evolves in response to a history of spatiotemporal environmental variation, rather than as a conditional response to current habitat conditions. More broadly, this study underscores the value of assessing alternative scales of environmental variation to gain a more complete and balanced understanding of dispersal evolution.

Parasite infection induces size-dependent host dispersal: consequences for parasite persistence

Host dispersal is now recognized as a key predictor of the landscape-level persistence and expansion of parasites. However, current theories treat post-infection dispersal propensities as a fixed trait, and the plastic nature of host's responses to parasite infection has long been underappreciated. Here, we present a mark-recapture experiment in a single host-parasite system (larval parasites of the freshwater mussel Margaritifera laevis and its salmonid fish host Oncorhynchus masou masou) and provide, to our knowledge, the first empirical evidence that parasite infection induces size-dependent host dispersal in the field. In response to parasite infection, large fish become more dispersive, whereas small fish tend to stay at the home patch. The observed plasticity in dispersal is interpretable from the viewpoint of host fitness: expected benefits (release from further infection) may exceed dispersal-associated costs for individuals with high dispersal ability (i.e. large fish) but are marginal for individuals with limited dispersal ability (i.e. small fish). Indeed, our growth analysis revealed that only small fish hosts incurred dispersal costs (reduced growth). Strikingly, our simulation study revealed that this plastic dispersal response of infected hosts substantially enhanced parasite persistence and occupancy in a spatially structured system. These results suggest that dispersal plasticity in host species is critical for understanding how parasites emerge, spatially spread, and persist in nature. Our findings provide a novel starting point for building a reliable, predictive model for parasite/disease management.

Local Adaptation Interacts with Expansion Load during Range Expansion: Maladaptation Reduces Expansion Load

The biotic and abiotic factors that facilitate or hinder species range expansions are many and complex. We examine the impact of two genetic processes and their interaction on fitness at expanding range edges: local maladaptation resulting from the presence of an environmental gradient and expansion load resulting from increased genetic drift at the range edge. Results from spatially explicit simulations indicate that the presence of an environmental gradient during range expansion reduces expansion load; conversely, increasing expansion load allows only locally adapted populations to persist at the range edge. Increased maladaptation reduces the speed of range expansion, resulting in less genetic drift at the expanding front and more immigration from the range center, therefore reducing expansion load at the range edge. These results may have ramifications for species being forced to shift their ranges because of climate change or other anthropogenic changes. If rapidly changing climate leads to faster expansion as populations track their shifting climatic optima, populations may suffer increased expansion load beyond previous expectations.

Spatial sorting promotes the spread of maladaptive hybridization

Invasive hybridization is causing loss of biodiversity worldwide. The spread of such introgression can occur even when hybrids have reduced Darwinian fitness, which decreases the frequency of hybrids due to low survival or reproduction through time. This paradox can be partially explained by spatial sorting, where genotypes associated with dispersal increase in frequency at the edge of expansion, fueling further expansion and allowing invasive hybrids to increase in frequency through space rather than time. Furthermore, because all progeny of a hybrid will be hybrids (i.e., will possess genes from both parental taxa), nonnative admixture in invaded populations can increase even when most hybrid progeny do not survive. Broader understanding of spatial sorting is needed to protect native biodiversity.

Physiological vagility and its relationship to dispersal and neutral genetic heterogeneity in vertebrates

Vagility is the inherent power of movement by individuals. Vagility and the available duration of movement determine the dispersal distance individuals can move to interbreed, which affects the fine-scale genetic structure of vertebrate populations. Vagility and variation in population genetic structure are normally explained by geographic variation and not by the inherent power of movement by individuals. We present a new, quantitative definition for physiological vagility that incorporates aerobic capacity, body size, body temperature and the metabolic cost of transport, variables that are independent of the physical environment. Physiological vagility is the speed at which an animal can move sustainably based on these parameters. This meta-analysis tests whether this definition of physiological vagility correlates with empirical data for maximal dispersal distances and measured microsatellite genetic differentiation with distance {[F(ST)/[1-F(ST))]/ln distance} for amphibians, reptiles, birds and mammals utilizing three locomotor modes (running, flying, swimming). Maximal dispersal distance and physiological vagility increased with body mass for amphibians, reptiles and mammals utilizing terrestrial movement. The relative slopes of these relationships indicate that larger individuals require longer movement durations to achieve maximal dispersal distances. Both physiological vagility and maximal dispersal distance were independent of body mass for flying vertebrates. Genetic differentiation with distance was greatest for terrestrial locomotion, with amphibians showing the greatest mean and variance in differentiation. Flying birds, flying mammals and swimming marine mammals showed the least differentiation. Mean physiological vagility of different groups (class and locomotor mode) accounted for 98% of the mean variation in genetic differentiation with distance in each group. Genetic differentiation with distance was not related to body mass. The physiological capacity for movement (physiological vagility) quantitatively predicts genetic isolation by distance in the vertebrates examined.

Immune response varies with rate of dispersal in invasive cane toads (Rhinella marina)

What level of immunocompetence should an animal maintain while undertaking long-distance dispersal? Immune function (surveillance and response) might be down-regulated during prolonged physical exertion due to energy depletion, and/or to avoid autoimmune reactions arising from damaged tissue. On the other hand, heightened immune vigilance might be favored if the organism encounters novel pathogens as it enters novel environments. We assessed the links between immune defense and long-distance movement in a population of invasive cane toads (Rhinella marina) in Australia. Toads were radio-tracked for seven days to measure their activity levels and were then captured and subjected to a suite of immune assays. Toads that moved further showed decreased bacteria-killing ability in their plasma and decreased phagocytic activity in their whole blood, but a heightened skin-swelling response to phytohemagglutinin. Baseline and post-stress corticosterone levels were unrelated to distance moved. Thus, long-distance movement in cane toads is associated with a dampened response in some systems and enhanced response in another. This pattern suggests that sustained activity is accompanied by trade-offs among immune components rather than an overall down or up-regulation. The finding that high mobility is accompanied by modification of the immune system has important implications for animal invasions.

Movement ecology of amphibians: from individual migratory behaviour to spatially structured populations in heterogeneous landscapes,

Both genetic cohesion among local populations of animals and range expansion depend on the frequency of dispersers moving at an interpatch scale. Animal movement has an individual component that reflects behaviour and an ecological component that reflects the spatial organization of populations. The total movement capacity of an individual describes maximum movement distance theoretically achievable during a lifetime, whereas its variation among the members of a local population determines the magnitude of interpatch movements and thus of gene flow between neighbouring patches within metapopulation or patchy population systems. Here, I review information on dispersal and migration as components of the movement capacity of juvenile and adult pond-breeding amphibians and discuss how these components inform the spatial structure of populations. Amphibians disperse as juveniles and adults, but movement distances detected in tracking or capture–mark–recapture studies are usually far below the corresponding estimates based on molecular gene-flow data. This discrepancy reflects the constraints of available tracking methods for free-ranging individuals leading to inappropriate surrogates of annual movement capacity, but can be resolved using probabilistic approaches based on dispersal functions. There is remarkable capacity for and plasticity in movements in amphibians. Annual within-patch movements (migrations) of individuals can be large and likely represent an underestimated capacity for movement at the interpatch scale. Landscape resistance may influence the paths of dispersing amphibians, but rarely impedes interpatch movements. Juveniles emigrating unpredictably far from the natal pond and adults switching from within-patch migrations to dispersal to another patch demonstrate the plasticity of individual movement behaviour. Three basic conclusions can be drawn with respect to the linkage of individual movement behaviour and spatial or genetic structure of local amphibian populations embedded in a heterogeneous landscape: (1) individual movements or consecutive short-term series of movements are misleading surrogate measures of total movement capacity; (2) probabilistic modelling of movement capacity is the best available behavioural predictor of interpatch gene flow; (3) connectivity of local populations in heterogeneous landscapes is less affected by landscape resistance than previously expected.

Retention time variability as a mechanism for animal mediated long-distance dispersal

Long-distance dispersal (LDD) events, although rare for most plant species, can strongly influence population and community dynamics. Animals function as a key biotic vector of seeds and thus, a mechanistic and quantitative understanding of how individual animal behaviors scale to dispersal patterns at different spatial scales is a question of critical importance from both basic and applied perspectives. Using a diffusion-theory based analytical approach for a wide range of animal movement and seed transportation patterns, we show that the scale (a measure of local dispersal) of the seed dispersal kernel increases with the organisms' rate of movement and mean seed retention time. We reveal that variations in seed retention time is a key determinant of various measures of LDD such as kurtosis (or shape) of the kernel, thinkness of tails and the absolute number of seeds falling beyond a threshold distance. Using empirical data sets of frugivores, we illustrate the importance of variability in retention times for predicting the key disperser species that influence LDD. Our study makes testable predictions linking animal movement behaviors and gut retention times to dispersal patterns and, more generally, highlights the potential importance of animal behavioral variability for the LDD of seeds.

Coexistence in streams: do source-sink dynamics allow salamanders to persist with fish predators?

Theory suggests that source-sink dynamics can allow coexistence of intraguild predators and prey, but empirical evidence for this coexistence mechanism is limited. We used capture-mark-recapture, genetic methods, and stable isotopes to test whether source-sink dynamics promote coexistence between stream fishes, the intraguild predator, and stream salamanders (Dicamptodon aterrimus), the intraguild prey. Salamander populations from upstream reaches without fish were predicted to maintain or supplement sink populations in downstream reaches with fish. We found instead that downstream reaches with fish were not sinks even though fish consumed salamander larvae-apparent survival, recruitment, and population growth rate did not differ between upstream and downstream reaches. There was also no difference between upstream and downstream reaches in net emigration. We did find that D. aterrimus moved frequently along streams, but believe that this is a response to seasonal habitat changes rather than intraguild predation. Our study provides empirical evidence that local-scale mechanisms are more important than dispersal dynamics to coexistence of streams salamanders and fish. More broadly, it shows the value of empirical data on dispersal and gene flow for distinguishing between local and spatial mechanisms of coexistence.

Explaining long-distance dispersal: effects of dispersal distance on survival and growth in a stream salamander

Long-distance dispersal (LDD) may contribute disproportionately to range expansions, the creation of new evolutionary lineages, and species persistence in human-dominated landscapes. However, because data on the individual consequences of dispersal distance are extremely limited, we have little insight on how LDD is maintained in natural populations. I used six years of spatially explicit capture-mark-recapture (CMR) data to test the prediction that individual performance increases with dispersal distance in the stream salamander Gyrinophilus porphyriticus. Dispersal distance was total distance moved along the 1-km study stream, ranging from 0 to 565 m. To quantify individual performance, I used CMR estimates of survival and individual growth rates based on change in body length. Survival and growth rates increased significantly with dispersal distance. These relationships were not confounded by pre-dispersal body condition or by ecological gradients along the stream. Individual benefits of LDD were likely caused by an increase in the upper limit of settlement site quality with dispersal distance. My results do not support the view that the fitness consequences of LDD are unpredictable and instead suggest that consistent evolutionary mechanisms may explain the prevalence of LDD in nature. They also highlight the value of direct CMR data for understanding the individual consequences of variation in dispersal distance and how that variation is maintained in natural populations.

Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers

Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population models predict that a species with a lower dispersal rate always drives a competing species to extinction in the presence of spatial variation of resources. However, the introduction of intrinsic demographic stochasticity can reverse this conclusion. We present a simple model in which competition between the exploitation of resources and stochastic fluctuations leads to victory by either the faster or slower of two species depending on the environmental parameters. A simplified limiting case of the model, analyzed by closing the moment and correlation hierarchy, quantitatively predicts which species will win in the complete model under given parameters of spatial variation and average carrying capacity.