Testing a stochastic version of the Beddington–DeAngelis functional response in foraging shore crabs

Smallegange, Isabel M.; Meer, Jaap van der

doi:10.1007/s00227-009-1382-z

Cited by 6 publications

(5 citation statements)

References 39 publications

(48 reference statements)

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“…The probability that a continuous‐time Markov chain will be in state j at time t (generally) converges to a limiting value, or limiting probability, independent of the initial state (Ross 1989). Simulations showed that this condition holds for the 1‐ and 2‐predator Markov chains (Smallegange & van der Meer 2010) as well as for the 2‐patch‐2‐predator Markov chain (Supporting Information). Since the Markov chain represents a foraging process, the limiting probability of each state is the fraction of time that the foraging process is in that state.…”

Section: Methodsmentioning

confidence: 88%

‘Take‐away’ foraging spatially uncouples predator and prey‐attack distributions

Smallegange

Meer

Sabelis³

2010

Journal of Animal Ecology

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Summary1. Ideal-free distribution theory assumes that in a patchy environment foragers maximize fitness and hence their feeding rate by balancing gains from more food against losses from more competition. Ultimately, individuals cannot increase their feeding rate by moving to another patch and they distribute themselves over patches in proportion to prey density per patch. 2. In our experiments with shore crabs Carcinus maenas foraging on two adjacent patches with mussels Mytilus edulis, the implicit assumption of ideal-free distribution theory that catch should match time spent in a prey patch is not met, however. Despite aggregating their attack where it is most profitable shore crabs distributed themselves homogeneously across mussel patches: they 'take away' the prey caught and consume it elsewhere to reduce interference. 3. Thus, predator distributions can be quite different from prey-attack distributions. This is important because the latter is shown to be decisive for persistence of predator and prey populations in ecological models.

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Section: Methodsmentioning

confidence: 88%

‘Take‐away’ foraging spatially uncouples predator and prey‐attack distributions

Smallegange

Meer

Sabelis³

2010

Journal of Animal Ecology

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“…Software to estimate statistical ‘multi‐state models’ is available (e.g. Jackson ), which enables empirical analysis of transition rates between behavioural states as a function of food availability and the presence of group members (Smallegange & van der Meer ).…”

Section: Introductionmentioning

confidence: 99%

Moving on with foraging theory: incorporating movement decisions into the functional response of a gregarious shorebird

Gils

Geest

Meulenaer

et al. 2014

Journal of Animal Ecology

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Summary1. Models relating intake rate to food abundance and competitor density (generalized functional response models) can predict forager distributions and movements between patches, but we lack understanding of how distributions and small-scale movements by the foragers themselves affect intake rates. 2. Using a state-of-the-art approach based on continuous-time Markov chain dynamics, we add realism to classic functional response models by acknowledging that the chances to encounter food and competitors are influenced by movement decisions, and, vice versa, that movement decisions are influenced by these encounters. 3. We used a multi-state modelling framework to construct a stochastic functional response model in which foragers alternate between three behavioural states: searching, handling and moving. 4. Using behavioural observations on a molluscivore migrant shorebird (red knot, Calidris canutus canutus), at its main wintering area (Banc d'Arguin, Mauritania), we estimated transition rates between foraging states as a function of conspecific densities and densities of the two main bivalve prey. 5. Intake rate decreased with conspecific density. This interference effect was not due to decreased searching efficiency, but resulted from time lost to avoidance movements. 6. Red knots showed a strong functional response to one prey (Dosinia isocardia), but a weak response to the other prey (Loripes lucinalis). This corroborates predictions from a recently developed optimal diet model that accounts for the mildly toxic effects due to consuming Loripes. 7. Using model averaging across the most plausible multi-state models, the fully parameterized functional response model was then used to predict intake rate for an independent data set on habitat choice by red knot. 8. Comparison of the sites selected by red knots with random sampling sites showed that the birds fed at sites with higher than average Loripes and Dosinia densities, that is sites for which we predicted higher than average intake rates. 9. We discuss the limitations of Holling's classic functional response model which ignores movement and the limitations of contemporary movement ecological theory that ignores consumer-resource interactions. With the rapid advancement of technologies to track movements of individual foragers at fine spatial scales, the time is ripe to integrate descriptive tracking studies with stochastic movement-based functional response models.

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“…Dawes & Souza [21] analysed a Markov-chain model of a predator-prey system adapted from chemical reactions, and showed how Holling functional responses could emerge at the population level. Broom et al [22] and Smallegange & van der Meer [23] used a similar approach to derive a functional response in the specific cases of kleptoparasitism and a Beddington-DeAngelis functional response, respectively. Second, the development of stochastic models is needed for inferring functional responses from empirical data in order to clearly identify the processes and mechanisms underlying the variability of interaction rates, which appears to be large in experiments (e.g.…”

Section: Introductionmentioning

confidence: 99%

Rejuvenating functional responses with renewal theory

Billiard

Bansaye

Chazottes

2018

J. R. Soc. Interface.

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Functional responses are widely used to describe interactions and resource exchange between individuals in ecology. The form given to functional responses dramatically affects the dynamics and stability of populations and communities. Despite their importance, functional responses are generally considered with a phenomenological approach, without clear mechanistic justifications from individual traits and behaviours. Here, we develop a bottom-up stochastic framework grounded in renewal theory that shows how functional responses emerge from the level of the individuals through the decomposition of interactions into different activities. Our framework has many applications for conceptual, theoretical and empirical purposes. First, we show how the mean and variance of classical functional responses are obtained with explicit ecological assumptions, for instance regarding foraging behaviours. Second, we give examples in specific ecological contexts, such as in nuptial-feeding species or size-dependent handling times. Finally, we demonstrate how to analyse data with our framework, especially highlighting that observed variability in the number of interactions can be used to infer parameters and compare functional response models.

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Testing a stochastic version of the Beddington–DeAngelis functional response in foraging shore crabs

Cited by 6 publications

References 39 publications

‘Take‐away’ foraging spatially uncouples predator and prey‐attack distributions

‘Take‐away’ foraging spatially uncouples predator and prey‐attack distributions

Moving on with foraging theory: incorporating movement decisions into the functional response of a gregarious shorebird

Rejuvenating functional responses with renewal theory

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