Pattern Formation and the Spatial Scale of Interaction between Predators and Their Prey

Roos, André M. de; McCauley, Edward; Wilson, W. G.

doi:10.1006/tpbi.1997.1345

Cited by 133 publications

(124 citation statements)

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“…This can happen in two possible ways: if the predator migration rates are large, the prey in one patch can become extinct because of the flow of predators from another patch. This is the equivalent of the crystal lattice pattern observed in coupled map lattice models of host parasitoid dynamics (Hassell et al, 1991;Comins et al, 1992;Van der Laan and Hogeweg, 1995;De Roos et al, 1998). The other possibility for intermediate predator migration rates is that the periodic, quasi-periodic, or chaotic dynamics arise over which the amplitudes of the oscillations are reduced.…”

Section: Discussionmentioning

confidence: 81%

“…This seems to imply that no spatial pattern can be formed from equilibria but this is not the case: once the equilibrium E 22a has become unstable in a Hopf bifurcation this equilibria can go through a pitchfork bifurcation in which two new equilibria are formed, which then can regain stability. In this way the``crystal lattice'' type spatial patterns can form in simulations on large grids (Hassell et al, 1991;Van der Laan and Hogeweg, 1995;De Roos et al, 1998).…”

Section: Figmentioning

confidence: 99%

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The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

155

110

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I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator prey metapopulation or as a spatially explicit predator prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator prey populations can be regulated through the interplay of local dynamics and migration. ]

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Section: Discussionmentioning

confidence: 81%

Section: Figmentioning

confidence: 99%

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

155

110

View full text Add to dashboard Cite

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“…In recent years, a large number of theoretical studies have pointed to the possibility of self-organized spatial pat- terning in predator-prey systems (Hassell et al 1991;de Roos et al 1998;Gurney et al 1998). In spatially explicit models, predator-prey interactions may create large-scale coherent spatial structures that are either dynamic (e.g., spiral waves) or stable (e.g., stationary lattice or patchy patterns), starting from random initial conditions.…”

mentioning

confidence: 99%

“…In spatially explicit models, predator-prey interactions may create large-scale coherent spatial structures that are either dynamic (e.g., spiral waves) or stable (e.g., stationary lattice or patchy patterns), starting from random initial conditions. Spatial patterns may have important consequences by facilitating persistence of otherwise unstable predator-prey interactions, stimulating coexistence of competing species, and increasing stability on large spatial scales (Hassell et al 1994;Rohani et al 1997;de Roos et al 1998;Gurney et al 1998;Gurney and Veitch 2000).…”

mentioning

confidence: 99%

“…Strong predation leads to local depletion of the prey, invoking heterogeneity in the prey population. Depending on the relative dispersal rates of prey and predator, this leads to stable occurrence of prey patches (de Roos et al 1998) or to local collapse of the predator, which produces unstable wavelike spatial patterns in which the prey and predator are locked in an endless pursuit (Hassell et al 1991;Gurney et al 1998). Stable prey patches were predicted to occur if prey dispersal is much smaller than predator dispersal.…”

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confidence: 99%

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Scale‐Dependent Feedback and Regular Spatial Patterns in Young Mussel Beds

Koppel¹,

Rietkerk²,

Dankers³

et al. 2005

The American Naturalist

243

130

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In the past decade, theoretical ecologists have emphasized that local interactions between predators and prey may invoke emergent spatial patterning at larger spatial scales. However, empirical evidence for the occurrence of emergent spatial patterning is scarce, which questions the relevance of the proposed mechanisms to ecological theory. We report on regular spatial patterns in young mussel beds on soft sediments in the Wadden Sea. We propose that scale-dependent feedback, resulting from short-range facilitation by mutual protection from waves and currents and long-range competition for algae, induces spatial self-organization, thereby providing a possible explanation for the observed patterning. The emergent self-organization affects the functioning of mussel bed ecosystems by enhancing productivity and resilience against disturbance. Moreover, self-organization allows mussels to persist at algal concentrations that would not permit survival of mussels in a homogeneous bed. Our results emphasize the importance of self-organization in affecting the emergent properties of natural systems at larger spatial scales.

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Dissecting geographic variation in population synchrony using the common vole in central Europe as a test bed

Gouveia

Bjørnstad

Tkadlec

2015

Ecology and Evolution

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Spatial synchrony of population fluctuations is ubiquitous in nature. Theoretical models suggest that correlated environmental stochasticity, dispersal, and trophic interactions are important promoters of synchrony in nature to leave characteristic signatures of distance‐dependent decays in synchrony. Recent refinements of this theory have clarified how distance‐decay curves may steepen if local dynamics are governed by different density‐dependent feedbacks and how synchrony should vary regionally if the importance and correlation of environmental stochasticity is location‐specific. We analysed spatiotemporal data for the common vole, Microtus arvalis from 49 districts in the Czech Republic to examine the pattern of population synchrony between 2000 and 2014. By extending the nonparametric covariation function, we develop a quantitative method that allows a dissection of the effects of distance and additional variables such as altitude on synchrony. To examine the pattern of local synchrony, we apply the noncentered local‐indicators of spatial association (ncLISA) which highlights areas with different degrees of synchrony than expected by the region‐wide average. Additionally, in order to understand the obtained pattern of local spatial correlations, we have regressed LISA results against the proportion of forest in each district. The common vole abundances fluctuated strongly and exhibited synchronous dynamics with the typical tendency for a decline of synchrony with increasing distance but, not with altitude. The correlation between the neighbor districts decreases as the proportion of forest increases. Forested areas are suboptimum habitats and are strongly avoided by common voles. The investigation of spatiotemporal dynamics in animal populations is a key issue in ecology. Although the majority of studies are focused on testing hypotheses about which mechanisms are involved in shaping this dynamics it is crucial to understand the sources of variation involved in order to understand the underlying processes.

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Pattern Formation and the Spatial Scale of Interaction between Predators and Their Prey

Cited by 133 publications

References 30 publications

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Scale‐Dependent Feedback and Regular Spatial Patterns in Young Mussel Beds

Dissecting geographic variation in population synchrony using the common vole in central Europe as a test bed

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