Omnivory Creates Chaos in Simple Food Web Models

Tanabe, Kumi; Namba, Tsunehisa

doi:10.1890/05-0720

Cited by 140 publications

(105 citation statements)

References 27 publications

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“…Perhaps the work closest in nature to the one presented here can be found in [55]. Tanabe and Namba [55] numerically demonstrate that the addition of an omnivore (defined as feeding on more than one trophic level [43,44]) leads to a Hopf bifurcation and period doubling cascades.…”

Section: Introduction Pioneering Work By Lotkamentioning

confidence: 76%

Period Doubling Cascades in a Predator-Prey Model with a Scavenger

Previte¹,

Hoffman²

2013

SIAM Rev.

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Abstract. The dynamics of the classic planar two-species Lotka-Volterra predator-prey model are well understood. We introduce a scavenger species that scavenges the predator and is also a predator of the common prey. For this model, we analytically prove that all trajectories are bounded in forward time, and numerically demonstrate persistent bounded paired cascades of period-doubling orbits over a wide range of parameter values. Standard analytical and numerical techniques are used in the analysis of this model, making it an ideal pedagogical tool. We include exercises and an open-ended project to promote mastery of these techniques.

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Section: Introduction Pioneering Work By Lotkamentioning

confidence: 76%

Period Doubling Cascades in a Predator-Prey Model with a Scavenger

Previte¹,

Hoffman²

2013

SIAM Rev.

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“…The structural organization of species interactions is known (both theoretically and empirically) to influence the dynamics of relatively smaller-scale systems [106,183], and this connection has been extended to large communities with hundreds of species and thousands of interactions [55,140,171]. When such systems are composed of consumers and their resources, they are called food-webs.…”

Section: 77 33 Predator Dietary Specialization (✏) For Beringianmentioning

confidence: 99%

Dedication. Acknowledgments

2011

The Acquisition of German

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xvii Dedication xixAcknowledgments xx . See panel C. for a scenario where one prey is preferred over another. C. A tri-trophic system, where a top-predator consumes a meso-predator, which in turn consumes two prey. The sizes of the nodes denote relative abundance, and the thickness of the arrows denote the magnitude of the biomass flow. The top-predator in the leftmost network is relatively abundant, depressing the meso-predator population, thereby limiting the meso-predator's e↵ect on the two prey populations. The two rightmost networks (boxed) have reduced top-predator populations. In both cases, the meso-predator has greater abundance due to decreased predation pressure. However, in one scenario, both prey are preferred equally, resulting in apparent competition dynamics. In the second scenario, one prey is preferred over another, resulting in an asymmetric cascade. Such preferences could result from specific anatomical constraints of the meso-predator, a scenario explored in Chapter 4. C 1 and C 2 , and 4 prey: r 1 r 4 ) is represented by both pairwise interaction distributions for each link, and a network-level interaction distribution for the system. Link thickness represents the median link-strength, shown with the vertical bar in each pairwise interaction distribution. B-C. Both model food-webs X and Y have link-strengths drawn from the NLID. In model food-web X, the weights are distributed similar to the median weights of the empirical web (i.e. equivalent structure), but they are distributed di↵erently among nodes (i.e. alternative interactions). In model Y , the weight structure is di↵erent than that of the empirical web (i.e. alternative structure), and necessarily, the distribution of weights among nodes di↵ers as well (i.e. alternative interactions). Dotted nodes indicate those with link-strengths that di↵er from the median link-strengths of the empirical food-web. D-F. Given a single niche axis based on a continuous resource trait (e.g. body size) where prey are ranked from r 1 to r 4 , distributions of resource use are shown for the two consumers. Representations of dietary overlap illustrate higher similarity in diet between predators of the empirical system and model X, whereas the consumers in model Y have little dietary overlap, despite sharing the same NLID. 5 A-C. Sensitivity analyses of the Saskatchewan, Amboseli, and Lake Naivasha food-web ensembles, respectively. Similarity values for each cuto↵ (s i ) for Model 2 are on the y-axis, and the x-axis ranges from a lower standard deviation (SD) than the empirical SD to a higher SD (such that the empirical SD is central to the range; stippled vertical line). The colored data points represent the median similarity indices for each cuto↵ value (legend), while the top and bottom whiskers denote the 25 th and 75 th percentiles, respectively. The underlined values mark the standard deviation corresponding to the highest average similarity across cuto↵ values. For all systems, the highest average similarity is close to or exactly matches ...

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“…2d-f ). While omnivory has been studied quite extensively (e.g., Tanabe and Namba 2005, Stouffer et al 2007, Bascompte 2009), when considered in isolation it is only those systems in which the mid-trophic group outcompetes the omnivorous intra-trophic group that are stable (e.g., Holt andHuxel 2007, Kondoh 2008).…”

Section: Introductionmentioning

confidence: 99%

Relating food web structure to resilience, keystone status and uncertainty in ecological responses

et al. 2014

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Abstract. Food webs often include substructures that occur in much higher numbers than would be expected in random networks. These are referred to in the literature as network motifs. Here we explore how feedbacks within the most common food web motifs influence their responses to external factors such as environmental change or harvesting of species. We have used qualitative modelling approaches to demonstrate that simple three-and four-member motifs that include a closed feedback loop can exhibit a diverse range of qualitative responses, some of which are non-intuitive. The same outcomes are demonstrated to be emergent behaviors of larger food webs represented in complex ecosystem models. The sensitivity of ecological responses to small differences in food web motifs underlines the broader importance of structural uncertainty in ecological models. It is also argued that the resilience of species and their keystone status may be strongly influenced by their ecological role within particular motifs. Examples are provided from fisheries off southeastern Australian, where the slow recovery rates of some species have not previously been explained.

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Omnivory Creates Chaos in Simple Food Web Models

Cited by 140 publications

References 27 publications

Period Doubling Cascades in a Predator-Prey Model with a Scavenger

Period Doubling Cascades in a Predator-Prey Model with a Scavenger

Dedication. Acknowledgments

Relating food web structure to resilience, keystone status and uncertainty in ecological responses

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