Hydra effect and paradox of enrichment in discrete-time predator-prey models

Weide, Vinicius; Varriale, Maria Cristina; Hilker, Frank M.

doi:10.1016/j.mbs.2018.12.010

Cited by 35 publications

(30 citation statements)

References 31 publications

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“…Zhou et al (2013) suggested that such discrete-time systems with biomass conversion might be more stable because of the ordering of events, assuming that predation occurs before reproduction. However, even though event ordering (reproduction vs survival) can affect stability in these models, census timing may not: Weide et al (2018) show that, for models with explicit biomass conversion, census timing only imply minor quantitative differences in model outputs. For difference equations, major qualitative differences only occur between models that assume biomass conversion to happen before reproduction (more stable) or after (more oscillating), as shown by Weide et al (2018).…”

Section: Model Structurementioning

confidence: 99%

“…Aside from changing parameters, one neat way to produce wilder dynamics would be to allow for predation on adults -this can be done phenomenologically rather than mechanistically by simply having an adult prey survival rate that depends on predator (adult) density. Other options are proposed by Zhou et al (2013) and Weide et al (2018). This would allow for predator-prey cycles (we have seen this in explorations of the nonlinear matrix model), but we note that we would need to change the time-frames of simulation considered (e.g., 30 to 100 years) in order to see well these long-period cycles.…”

Section: More Intricate or Challenging Dynamicsmentioning

confidence: 99%

“…All events can be ordered on a time arrow by introducing an intermediate time t between t and t + 1 (see also Cooch et al 2003;Weide et al 2018). We consider first the post-breeding census scenario.…”

Section: E2 Order Of Events In the Stochastic Ibmmentioning

confidence: 99%

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Integrating multiple data sources to fit matrix population models for interacting species

Barraquand

Giménez²

2019

Preprint

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Inferring interactions between populations of different species is a challenging statistical endeavour, which requires a large amount of data. There is therefore some incentive to combine all available sources of data into a single analysis to do so. In demography and single-population studies, Integrated Population Models combine population counts, capturerecapture and reproduction data to fit matrix population models. Here, we extend this approach to the community level in a stage-structured predator-prey context. We develop Integrated Community Models (ICMs), implemented in a Bayesian framework, to fit multispecies nonlinear matrix models to multiple data sources. We assessed the value of the different sources of data using simulations of ICMs under different scenarios contrasting data availability. We found that combining all data types (capture-recapture, counts, and reproduction) allows the estimation of both demographic and interaction parameters, unlike count-only data which typically generate high bias and low precision in interaction parameter estimates for short time series. Moreover, reproduction surveys informed the estimation of interactions particularly well when compared to capture-recapture programs, and have the advantage of being less costly. Overall, ICMs offer an accurate representation of stage structure in community dynamics, and foster the development of efficient observational study designs to monitor communities in the field.L stages per species requires estimation of (S × L) 2 interaction parameters; this may be why unstructured statistical models for interaction between species have so far been preferred (Ives et al., 2003), at least when a single type of data is used (e.g., time series of counts, Dennis et al. 1995). Although nonlinear MPMs have many parameters, because of their internal age-structure, they also have advantages over unstructured discrete-time models currently fitted to data (i.e., discrete-time Lokta-Volterra or log-linear autoregressive modelling; Ives et al. 2008; Mutshinda et al. 2009; Hampton et al. 2013). Indeed, the survival rates expressed in MPMs are well estimated by capture-recapture techniques (Caswell, 2001; Lebreton et al., 2009). This opens new avenues tofit nonlinear matrix models for multiple species, by considering other types of data than just counts of species, such as data on survival and development rates, as well as reproduction. One approach to incorporate such demographic datasets, used in plant community dynamics, is to fit separate models for reproduction and survival components of the demography (Adler & HilleRisLambers, 2008;Chu & Adler, 2015), and then simulate the community-level model thus created, to evaluate its prediction of the counts and spatial structure. While this approach is sound, it does not take full advantage of opportunities to combine vital rate data with counts, which might be problematic for small datasets.Capture-recapture and reproduction data can be combined advantageously with counts within the Integrated Population ...

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Section: Model Structurementioning

confidence: 99%

Section: More Intricate or Challenging Dynamicsmentioning

confidence: 99%

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Integrating multiple data sources to fit matrix population models for interacting species

Barraquand

Giménez²

2019

Preprint

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“…In [28], the author analyzed a discrete predatorprey model with nonmonotonic functional response exhibit and proved the existence of fold bifurcation, transcritical bifurcation, flip bifurcation and Neimark-Sacker bifurcations (NSB). Similarly, some discrete-time predator-prey models and hydra effect and paradox of enrichment are studied in [29]. Furthermore, for several attracting findings associated to the qualitative analysis of difference equations, we refer to the work done by [30], [31].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Complexity in a Class of Novel Discrete-Time Predator-Prey Interaction With Cannibalism

et al. 2020

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Cannibalism is ubiquitous in natural communities and has the tendency to change the functional connection among prey-predator interactions. Keeping in view the inclusion of prey cannibalism, a novel discrete nonlinear predator-prey model is proposed. Asymptotic stability is carried out around biologically feasible equilibria of proposed model. Center manifold theorem and bifurcation theory of normal form ensure the existence of bifurcation in the system. Our study reveals that periodic outbreaks may result due to incorporation of cannibalism in prey population and this periodic outbreak is limited to prey population only without leaving an effect on predation. In order to control these periodic oscillations in prey population density and other bifurcating and fluctuating behavior of the system, various chaos control strategies are implemented. Ultimately, some extensive numerical simulations are elaborated to demonstrate the effectiveness of our acquired analytical and theoretical results.

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“…В мировой литературе широко представлены исследования динамических систем типа «хищник -жертва» или «паразит -хозяин» [1][2][3][4][5][6][7][8][9][10][22][23][24] модификациями классических моделей Лотки -Вольтерры [1] и Николсона -Бейли [2,3]. В непрерывной по времени модели Лотки -Вольтерры предполагается, что поколения взаимодействующих популяций полностью перекрываются и процессы рождаемости и смертности непрерывны.…”

Section: Introductionunclassified

Bistability and Bifurcations in Modified Nicholson-Bailey Model with Age-Structure for Prey

Revutskaya¹,

Кулаков²,

Frisman³

2019

Math.Biol.Bioinf.

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The paper investigates dynamic modes of the predator-prey model with age structure for prey. We use a slight modification of the Nicholson-Bailey model to describe the interaction between predator and prey. We assume the population size is regulated by decreasing juvenile survival rate with growth of age class sizes. Conditions for sustainable coexistence of interacting species are described. It is shown that the coexistence of species becomes possible if there are a transcritical or saddle-node (tangential) bifurcations. Due to the saddle-node bifurcation there is bistability in the system of interacting species: predator either coexists with prey or dies depending on the initial conditions. It is shown that the range of demographic parameters, for which the prey and predator coexist, can significantly increase with growth of survival of adult prey or the proportion of predators born or the prey consumption rate of the predator. We studied the oscillation scenarios of interacting population, influences of reproduction, survival and self-regulation rates of population prey and age-dependent predation as well as variations in the current number on transitions between different dynamic modes. It is shown that an increase in the birth rate of the prey under intraspecific competition can lead to a dynamics destabilization and to oscillations appearance in numbers. Age-dependent predation is shown to be a stabilizing influence. At the same time, with a high birth rate of the prey, the system stability is ensured by the high survival rate of adult prey. It was found that in the model parametric space, both bistability and multistability arises, which are not related to each other. Consequently, even a small variation of the current population size leads to more complex behavior of the interacting species, and can give a significant change in both the observed dynamic mode and the coexistence scenario of the species.

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Hydra effect and paradox of enrichment in discrete-time predator-prey models

Cited by 35 publications

References 31 publications

Integrating multiple data sources to fit matrix population models for interacting species

Integrating multiple data sources to fit matrix population models for interacting species

Dynamical Complexity in a Class of Novel Discrete-Time Predator-Prey Interaction With Cannibalism

Bistability and Bifurcations in Modified Nicholson-Bailey Model with Age-Structure for Prey

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