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1.
Norman Owen‐Smith 《Oikos》2015,124(11):1417-1426
Simple models coupling the dynamics of single predators to single prey populations tend to generate oscillatory dynamics of both predator and prey, or extirpation of the prey followed by that of the predator. In reality, such oscillatory dynamics may be counteracted by prey refugia or by opportunities for prey switching by the predator in multi‐prey assemblages. How these mechanisms operate depends on relative prey vulnerability, a factor ignored in simple interactive models. I outline how compositional, temporal, demographic and spatial heterogeneities help explain the contrasting effects of top predators on large herbivore abundance and population dynamics in species‐rich African savanna ecosystems compared with less species‐diverse northern temperate or subarctic ecosystems. Demographically, mortality inflicted by predation depends on the relative size and life history stage of the prey. Because all animals eventually die and are consumed by various carnivores, the additive component of the mortality inflicted is somewhat less than the predation rate. Prey vulnerability varies annually and seasonally, and between day and night. Spatial variation in the risk of predation depends on vegetation cover as well as on the availability of food resources. During times of food shortage, herbivores become prompted to occupy more risky habitats retaining more food. Predator concentrations dependent on the abundance of primary prey species may restrict the occurrence of other potential prey species less resistant to predation. The presence of multiple herbivore species of similar size in African savannas allows the top predator, the lion, to shift its prey selection flexibly dependent on changing prey vulnerability. Hence top–down and bottom–up influences on herbivore populations are intrinsically entangled. Models coupling the population dynamics of predators and prey need to accommodate the changing influences of prey demography, temporal variation in environmental conditions, and spatial variation in the relative vulnerability of alternative prey species to predation. Synthesis While re‐established predators have had major impacts on prey populations in northern temperate regions, multiple large herbivore species typically coexist along with diverse carnivores in African savanna ecosystems. In order to explain these contrasting outcomes, certain functional heterogeneities must be recognised, including relative vulnerability of alternative prey, temporal variation in the risk of predation, demographic differences in susceptibility to predation, and spatial contrasts in exposure to predation. Food shortfalls prompt herbivores to exploit more risky habitats, meaning that top–down and bottom–up influences on prey populations are intrinsically entangled. Models coupling the interactive dynamics of predator and prey populations need to incorporate these varying influences on relative prey vulnerability.  相似文献   

2.
Spatial variation in ecological systems can arise both as a consequence of variation in the quality and availability of resources and as an emergent property of spatially structured interactions. We used a spatially explicit model to simulate populations of herbivore hosts and their parasitoids in landscapes with different levels of variance in plant patch quality and different spatial arrangements of high‐ and low‐quality plant patches. We found that even small variation in patch quality at a fine spatial scale decreased overall herbivore populations, as parasitoid populations on low‐quality plant patches were subsidized by those from high‐quality neighbors. On landscapes with large, homogeneous regions of high‐ and low‐quality plant patches, herbivore populations increased with variation in patch quality. Overall, our results demonstrate that local variation in resource quality profoundly influences global population dynamics. In particular, fine‐scale variation in plant patch quality enhanced biological control of herbivores by parasitoids, suggesting that adding back plant genetic variation into perennial production systems may enhance the biological control of herbivores by their natural enemies.  相似文献   

3.
Single-species populations of ciliates (Colpidium and Paramecium) experienced constant temperature or white or reddened temperature fluctuations in aquatic microcosms in order to test three hypotheses about how environmental colour influences population dynamics. (i) Models predict that the colour of population dynamics is tinged by the colour of the environmental variability. However, environmental colour had no effect on the colour of population dynamics. All population dynamics in this experiment were reddened, regardless of environmental colour. (ii) Models predict that populations will track reddened environmental variability more closely than white environmental variability and that populations with a higher intrinsic growth rate (r) will track environmental variability more closely than populations with a low r. The experimental populations behaved as predicted. (iii) Models predict that population variability is determined by interaction between r and the environmental variability. The experimental populations behaved as predicted. These results show that (i) reddened population dynamics may need no special explanation, such as reddened environments, spatial subdivision or interspecific interactions, and (ii) and (iii) that population dynamics are sensitive to environmental colour, in agreement with population models. Correct specification of the colour of the environmental variability in models is required for accurate predictions. Further work is needed to study the effects of environmental colour on communities and ecosystems.  相似文献   

4.
Understanding the ways that resource heterogeneity shapes the performance of individuals and the dynamics of populations offers a central challenge in contemporary ecology. Emerging evidence shows that herbivores track heterogeneity in nutritional quality of vegetation by responding to phenological differences in plants, differences that result from spatial and temporal variation in conditions favoring plant growth. Theory predicts that when spatial variation in temperature, nutrients, or moisture results in spatially asynchronous pulses of plant growth, herbivores are able to prolong the period during which they have access to forage of peak nutritional value. Although this idea has substantial support from observational and modeling studies, it has not been examined experimentally. We hypothesized that access to asynchronous resources enhances nutritional status and growth of herbivores and that the magnitude of this effect depends on the scale of access relative to the grain of resources. We tested these hypotheses in mesocosm experiment using the migratory grasshopper, Melanoplus sanguinipes, feeding on young wheat and protein-rich bran as a model system. We demonstrated access to asynchronous pulses in resources enhanced the efficiency of use of high quality resource use and increased growth of individuals by 13%. Disruption of this mechanism when landscapes were fragmented lowered efficiency of resource use and caused growth of individuals to decline by 15%. However, the strength of the effects of fragmentation on herbivore performance depended on the spatial extent of fragmentation relative to the spatial and temporal grain of resource emergence. Our findings add experimental support to modeling and observational studies that have linked herbivore performance to spatial and temporal variation in plant phenology. We also offer evidence that fragmentation can impair herbivore performance, even when the total amount and quality of resources on landscapes remains unchanged.  相似文献   

5.
Paul Glaum  John Vandermeer 《Oikos》2021,130(7):1116-1130
Demographic heterogeneity influences how populations respond to density dependent intraspecific competition and trophic interactions. Distinct stages across an organism's development, or ontogeny, are an important example of demographic heterogeneity. In consumer populations, ontogenetic stage structure has been shown to produce categorical differences in population dynamics, community dynamics and even species coexistence compared to models lacking explicit ontogeny. The study of consumer–resource interactions must also consider the ontogenetic stage structure of the resource itself, particularly plants, given their fundamental role at the basis of terrestrial food webs. We incorporate distinct ontogenetic stages of plants into an adaptable multi-stage consumer–resource modeling framework that facilitates studying how stage specific consumers shape trophic dynamics at low trophic levels. We describe the role of density dependent demographic rates in mediating the dynamics of stage-structured plant populations. We then investigate how these demographic rates interact with consumer pressure to influence stability and coexistence in multiple stage-specific consumer–resource interactions. Results detail how density dependent effects across distinct ontogenetic stages in plant development produce non-additivity in the drivers of dynamic stability both in single populations and in consumer–resource settings, challenging the ubiquity of certain traditional ecological dynamic paradigms. We also find categorical differences in the population variability induced by herbivores consuming separate plant stages. Consumer–resource models, such as plant–herbivore interactions, often average out demographic heterogeneity in populations. Here, we show that explicitly including plant demographic heterogeneity through ontogeny yields distinct dynamic expectations for both plants and herbivores compared to traditional consumer–resource formulations. Our results indicate that efforts to understand the demographic effect of herbivores on plant populations may need to also consider the effects of plant demographics on herbivores and the reciprocal relationship between them.  相似文献   

6.
Specialist herbivores are suggested to be unaffected by or attracted to the defense compounds of their host-plants, and can even prefer higher levels of certain chemicals. Abrostola asclepiadis is a specialist herbivore whose larvae feed on the leaves of Vincetoxicum hirundinaria, which contains toxic alkaloids and is unpalatable to most generalist herbivores. The food choice, leaf consumption and growth of A. asclepiadis larvae were studied to determine whether there is variation among and within host-plant populations in their suitability for this specialist herbivore. There was significant variation in food preference and leaf consumption among host-plant populations, but no differences were found in larval growth and feeding on different host-plant populations. A. asclepiadis larvae preferred host-plant populations with higher alkaloid concentrations, but did not consume more leaf material from plants originating from such populations in a no-choice experiment. There was also some variation in food preference of larvae among host-plant individuals belonging to the same population, suggesting that there was variability in leaf chemistry also within populations. Such variation in larval preference among host-plant genotypes and populations may create potential for coevolutionary dynamics in a spatial mosaic.  相似文献   

7.
Variation in the abundance of animals has traditionally been explained as the outcome of endogenous forcing from density dependence and exogenous forcing arising from variation in weather and predation. Emerging evidence suggests that the effects of density dependence interact with external influences on population dynamics. In particular, spatial heterogeneity in resources and the presence of capable predators may weaken feedbacks from density dependence to growth of populations. We used the Kalman filter to analyze 23 time series of estimates of abundance of northern ungulate populations arrayed along a latitudinal gradient (latitude range of 40°–70°N) to evaluate the influence of spatial heterogeneity in resources and predation on density dependence. We also used contingency tables to test whether density dependence was independent of the presence of carnivores (our estimate of predation) and multiple regressions to determine the effects of spatial heterogeneity in resources, predation, and latitude on the strength of density dependence. Our results showed that the strength of density dependence of ungulate populations was low in the presence of large carnivores, particularly at northern latitudes with low primary productivity. We found that heterogeneity in elevation, which we assume acted as a surrogate for spatial heterogeneity in plant phenology, also reduced effects of density dependence. Thus, we show that external forces created by heterogeneity in resources and predation interact with internal feedbacks from population density to shape dynamics of populations of northern ungulates.  相似文献   

8.
Fruit bats (Pteropodidae) have received increased attention after the recent emergence of notable viral pathogens of bat origin. Their vagility hinders data collection on abundance and distribution, which constrains modeling efforts and our understanding of bat ecology, viral dynamics, and spillover. We addressed this knowledge gap with models and data on the occurrence and abundance of nectarivorous fruit bat populations at 3 day roosts in southeast Queensland. We used environmental drivers of nectar production as predictors and explored relationships between bat abundance and virus spillover. Specifically, we developed several novel modeling tools motivated by complexities of fruit bat foraging ecology, including: (1) a dataset of spatial variables comprising Eucalypt‐focused vegetation indices, cumulative precipitation, and temperature anomaly; (2) an algorithm that associated bat population response with spatial covariates in a spatially and temporally relevant way given our current understanding of bat foraging behavior; and (3) a thorough statistical learning approach to finding optimal covariate combinations. We identified covariates that classify fruit bat occupancy at each of our three study roosts with 86–93% accuracy. Negative binomial models explained 43–53% of the variation in observed abundance across roosts. Our models suggest that spatiotemporal heterogeneity in Eucalypt‐based food resources could drive at least 50% of bat population behavior at the landscape scale. We found that 13 spillover events were observed within the foraging range of our study roosts, and they occurred during times when models predicted low population abundance. Our results suggest that, in southeast Queensland, spillover may not be driven by large aggregations of fruit bats attracted by nectar‐based resources, but rather by behavior of smaller resident subpopulations. Our models and data integrated remote sensing and statistical learning to make inferences on bat ecology and disease dynamics. This work provides a foundation for further studies on landscape‐scale population movement and spatiotemporal disease dynamics.  相似文献   

9.
Resource heterogeneity and ungulate population dynamics   总被引:9,自引:0,他引:9  
A. W. Illius  T. G. O'Connor 《Oikos》2000,89(2):283-294
It has been suggested that climatic variation has the effect on the dynamics of arid and semi-arid grazing systems of reducing animal numbers below the level at which they have much impact on vegetation or soils, and that spatial heterogeneity in resource availability serves to buffer herbivores against climatic variation. Modelling was used to test these hypotheses and to examine the interacting effects of temporal and spatial variability in plant production on animal population dynamics and defoliation intensity. The model distinguishes areas of the range that are accessible during wet and dry seasons, and examines the effect of seasonal restrictions in foraging area. It was established that the animal population is in long-term equilibrium with dry-season resources, on which it depends for survival; that dry season resource areas and outlying areas thus operate in a source-sink manner; and that the ratio of these areas determines the strength of consumer-resource coupling outside the dry-season range. A high ratio of dry season to wet season resources may support a sufficiently large animal population to impose non-trivial defoliation impacts on the outlying range. Increasing degrees of variability in primary production on areas used by animals for surviving the dry season increased the annual variation in animal abundance and reduced the mean. By comparison with a stable environment, for which the model predicts virtually stable animal numbers and constant, low defoliation intensity, variation in annual rainfall causes wide fluctuations in animal numbers and defoliation intensity. Under climatic variation, animal numbers can build up enough to impose much higher defoliation intensities than under a constant regime. Periodic intense defoliation is a consequence of climatic variability which is likely to make these environments more, not less, prone to ecological change.  相似文献   

10.
Helms SE  Hunter MD 《Oecologia》2005,145(2):196-203
In the attempt to use results from small-scale studies to make large-scale predictions, it is critical that we take into account the greater spatial heterogeneity encountered at larger spatial scales. An important component of this heterogeneity is variation in plant quality, which can have a profound influence on herbivore population dynamics. This influence is particularly relevant when we consider that the strength of density dependence can vary among host plants and that the strength of density dependence determines the difference between exponential and density- dependent growth. Here, we present some simple models and analyses designed to examine the impact of variable plant quality on the dynamics of insect herbivore populations, and specifically the consequences of variation in the strength of density dependence among host plants. We show that average values of herbivore population growth parameters, calculated from plants that vary in quality, do not predict overall population growth. Furthermore, we illustrate that the quality of a few individual plants within a larger plant population can dominate herbivore population growth. Our results demonstrate that ignoring spatial heterogeneity that exists in herbivore population growth on plants that differ in quality can lead to a misunderstanding of the mechanisms that underlie population dynamics.  相似文献   

11.
Natural populations of wild cabbage (Brassica oleracea) show significant qualitative diversity in heritable aliphatic glucosinolates, a class of secondary metabolites involved in defence against herbivore attack. One candidate mechanism for the maintenance of this diversity is that differential responses among herbivore species result in a net fitness balance across plant chemotypes. Such top-down differential selection would be promoted by consistent responses of herbivores to glucosinolates, temporal variation in herbivore abundance, and fitness impacts of herbivore attack on plants varying in glucosinolate profile. A 1-year survey across 12 wild cabbage populations demonstrated differential responses of herbivores to glucosinolates. We extended this survey to investigate the temporal consistency of these responses, and the extent of variation in abundance of key herbivores. Within plant populations, the aphid Brevicoryne brassicae consistently preferred plants producing the glucosinolate progoitrin. Among populations, increasing frequencies of sinigrin production correlated positively with herbivory by whitefly Aleyrodes proletella and negatively with herbivory by snails. Two Pieris butterfly species showed no consistent response to glucosinolates among years. Rates of herbivory varied significantly among years within populations, but the frequency of herbivory at the population scale varied only for B. brassicae. B. brassicae emerges as a strong candidate herbivore to impose differential selection on glucosinolates, as it satisfies the key assumptions of consistent preferences and heterogeneity in abundance. We show that variation in plant secondary metabolites structures the local herbivore community and that, for some key species, this structuring is consistent over time. We discuss the implications of these patterns for the maintenance of diversity in plant defence chemistry.  相似文献   

12.
Rios RS  Marquis RJ  Flunker JC 《Oecologia》2008,156(3):577-588
The benefits of ant–plant–herbivore interactions for the plant depend on the abundance of ants and herbivores and the selective pressures these arthropods exert. In plants bearing extrafloral nectaries (EFN), different mean trait values may be selected for by different populations in response to local herbivore pressure, ultimately resulting in the evolution of differences in plant traits that attract ants as defensive agents against herbivory. To determine if variation in traits that mediate ant–plant interactions reflect herbivore selective pressures, we quantified intra- and inter-population variation in plant traits for eight populations of the EFN-bearing annual Chamaecrista fasciculata (Michx.) (Fabaceae). Censuses in rural and urban areas of Missouri and Illinois (USA) showed population differences in ant attendance and herbivore pressure. Seeds were collected from each population, and plants were grown in a common greenhouse environment to measure sugar production, nectar volume and composition, EFN size and time of emergence, leaf pubescence, and leaf quality throughout plant development. Populations varied mainly in terms of nectary size, sugar production, and nectar volume, but to a lesser degree in leaf pubescence. Populations of C. fasciculata within urban areas (low in insect abundance) had small nectaries and the lowest nectar production. There was a positive correlation across populations between herbivore density and leaf damage by those herbivores on the one hand and sugar production and nectar volume on the other. These results, in conjunction with lack of evidence for maternally based environmental effects, suggest that population differences in herbivore damage have promoted differential evolution of EFN-related traits among populations. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.  相似文献   

13.
Kim TN  Holt RD 《Oecologia》2012,168(4):997-1012
Disturbance is a major source of spatial and temporal heterogeneity. In fire-maintained systems, disturbance by fire is often used as a management tool to increase biological diversity, restore degraded habitats, and reduce pest outbreaks. Much attention has been given to how plant communities recover from fire, but relatively few studies have examined post-fire responses of higher order species, such as insect herbivores. Because dynamic feedbacks occur between plants and their consumers, which can in turn influence the response of the entire ecosystem, incorporating higher trophic level responses into our understanding of the effects of fire is essential. In this study, we used structural equation modeling (SEM) to tease apart the direct and indirect effects of fire on insect herbivore assemblages found on three common oak species in the Florida scrub (Quercus inopina, Q. chapmanii, and Q. geminata). We investigated how fire affected herbivore abundance, richness, and community composition both directly and indirectly through environmental heterogeneity at different spatial scales (e.g., leaf quality, plant architecture, and habitat structure). We also investigated how seasonality and landscape heterogeneity influenced post-fire responses of insect herbivores and whether fire effects on herbivore assemblages varied among different host plants. Our general findings were that fire effects were (1) largely indirect, mediated through habitat structure (although direct fire effects were observed on Q. inopina herbivores), (2) non-linear through time due to self-thinning processes occurring in the scrub habitat, and (3) varied according to herbivore assemblage as a result of differences in the composition of species in each herbivore community. To the best of our knowledge, this is the first comprehensive study to examine how fire influences the assembly of insect herbivore communities through both direct and indirect pathways and at multiple spatial scales.  相似文献   

14.
Abstract Little attention has been paid to the impact that constitutive and inducible plant resistance traits will have on herbivore spatial dynamics. We investigate mathematical models in which herbivore demographic rates and movement rates respond to host plant quality, which in turn is determined by constitutive and inducible resistance. Models with and without induced resistance yield the same analytic expression for the asymptotic speed at which a herbivore population will spread through an initially uninduced plant population, suggesting that induced resistance will have no effect on the rate of invasion of herbivores that respond to plant resistance on small spatial scales. In contrast, constitutive resistance will influence the speed of an invasion. If herbivore movement is quite sensitive to plant quality, an increase in constitutive resistance can actually accelerate the rate of herbivore spread even while it reduces the herbivore's intrinsic rate of increase. In other scenarios, the rate of invasion attains a maximum at intermediate levels of constitutive resistance. These results argue that our view of plant resistance should be broadened to include herbivore movement if we are to understand fully the implications of differences in resistance for the dynamics of herbivore populations in natural and managed settings.  相似文献   

15.
Life-history theory suggests that iteroparous plants should be flexible in their allocation of resources toward growth and reproduction. Such plasticity could have consequences for herbivores that prefer or specialize on vegetative versus reproductive structures. To test this prediction, we studied the response of the cactus bug (Narnia pallidicornis) to meristem allocation by tree cholla cactus (Opuntia imbricata). We evaluated the explanatory power of demographic models that incorporated variation in cactus relative reproductive effort (RRE; the proportion of meristems allocated toward reproduction). Field data provided strong support for a single model that defined herbivore fecundity as a time-varying, increasing function of host RRE. High-RRE plants were predicted to support larger insect populations, and this effect was strongest late in the season. Independent field data provided strong support for these qualitative predictions and suggested that plant allocation effects extend across temporal and spatial scales. Specifically, late-season insect abundance was positively associated with interannual changes in cactus RRE over 3 years. Spatial variation in insect abundance was correlated with variation in RRE among five cactus populations across New Mexico. We conclude that plant allocation can be a critical component of resource quality for insect herbivores and, thus, an important mechanism underlying variation in herbivore abundance across time and space.  相似文献   

16.
Assessing risks of local extinction and shifts in species ranges are fundamental tasks in ecology and conservation. Most studies have focused either on the border of species’ range or on complex spatiotemporal dynamics of populations within the spatial distribution of species. The internal properties of species ranges, however, have received less attention due to a general lack of simple tools. We propose a novel approach within a metapopulation framework to study species ranges based on simple mathematical rules. We formulate and test a model of population fluctuations through space to identify key factors that regulate population density. We propose that spatial variability in species abundance reflects the interaction between temporal variability in population dynamics and the spatial variability of population parameters. This approach, that we call range structure analysis, integrates temporal and spatial properties to diagnose how each parameter contributes to species occupancy throughout its geographic range.  相似文献   

17.
The relative importance of extrinsic and intrinsic causes of variability is among the oldest unresolved problems in ecology. However, the interaction between large-scale intrinsic variability in species abundance and environmental heterogeneity is still unknown. We use a metacommunity model with disturbance-recovery dynamics to resolve the interaction between scales of environmental heterogeneity, biotic processes and of intrinsic variability. We explain how population density increases with environmental variability only when its scale matches that of intrinsic patterns of abundance, through their ability to develop in heterogeneous environments. Succession dynamics reveals how the strength of local species interactions, through its control of intrinsic variability, can in turn control the scale of metapopulation response to environmental scales. Our results show that the environment and species density might fail to show any correlation despite their strong causal association. They more generally suggest that the spatial scale of ecological processes might not be sufficient to build a predictive framework for spatially heterogeneous habitats, including marine reserve networks.  相似文献   

18.
Many animal species live in groups. Group living may increase exploitation competition within the group, and variation among groups in intra-group competition intensity could induce life-history variability among groups. Models of physiologically structured populations generally predict single generation cycles, driven by exploitation competition within and between generations. We expect that life-history variability and habitat heterogeneity induced by group living may affect such competition-driven population dynamics. In this study, we vary the gregariousness (the tendency to aggregate in groups) of a size-structured consumer population in a spatially explicit environment. The consumer has limited mobility, and moves according to a probabilistic movement process. We study the effects on the population dynamics, as mediated through the resource and the life-history of the consumer. We find that high gregariousness leads to large spatial resource variation, and highly variable individual life-history, resulting in highly stochastic population dynamics. At reduced gregariousness, life-history of consumers synchronizes, habitat heterogeneity is reduced, and single generation cycles appear. We expect this pattern to occur for any group living organism with limited mobility. Our results indicate that constraints set by population dynamical feedback may be an important aspect in understanding group living in nature.  相似文献   

19.
  1. Nearly 90% of the world's large herbivore diversity occurs in Africa, yet there is a striking dearth of information on the movement ecology of these organisms compared to herbivores living in higher latitude ecosystems.
  2. The environmental context for movements of large herbivores in African savanna ecosystems has several distinguishing features. African large herbivores move in landscapes with high spatiotemporal variability, low predictability, seasonal restrictions in surface water as well as food resources, and exposure to a diverse assemblage of competitors, predators, and pathogens. These features influence mobility, diel activity routines, home-range fidelity, and exposure to predation.
  3. We review the knowledge that has been gained about the movements of African herbivores from Global Positioning System (GPS) telemetry and identify important gaps in knowledge that exist. Topics addressed include seasonal movement patterns, daily activity schedules, space utilisation, water dependency, responses to risks of predation, pathogen transmission, social affiliations, and local population density determination.
  4. While the growing number of GPS telemetry studies has addressed a wide range of topics in Africa, they remain fragmentary in terms of places and species represented. Most research has been focussed on three species, and practices for data sharing and analysis should be improved. African landscapes are changing perhaps faster than any other region on Earth, with rapidly expanding human populations, massive infrastructure development projects, and changes in climatic regimes. There is a crucial need to establish relationships between herbivore movements and their changing environments, especially in Africa where most of the world's large herbivore diversity resides.
  相似文献   

20.
Spatial variations in the abundance of insect herbivores and in herbivore damage are both striking an commonplace. The standard explanations for heterogeneity in herbivore attack emphasize spatial variations in plant genetype, soils, or physical environment. Here I examine an alternative hypothesis-that heterogeneity arises in plant-herbivore systems, even in homogeneous environments, as a result of the direct coupling of herbivore movement to herbivore density and plant quality. Using a mathematical model for plant quality and herbivore growth and dispersal, I demonstrate how spatial instabilities about homogeneous steady state values result in both transient and stationary waves of damage to the plant. Key herbivore movement behaviors include the tendendy for herbivores to aggregate over a range of spatial scales for increased feeding efficiency and the tendency for herbivores to move up gradients in plant quality (herbivory-taxis). My approach translates the biased "random walk" behavior of individual herbivores into a continuum partial differential equation model. Analytical and numerical methods are used to demonstrate the nature of the spatio-temporal variations in plant quality and herbivore density.  相似文献   

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