Switching, Functional Response, and Stability in Predator-Prey Systems

Oaten, Allan; Murdoch, William W.

doi:10.1086/282999

Cited by 221 publications

(130 citation statements)

References 17 publications

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“…To construct a functional response that incorporates switching between multiple prey species, we follow Oaten and Murdoch (27) and Van Leeuwen et al (7) in modelling a predator's diet such that it incorporates the order in which it encounters and successfully attacks prey. As a simplifying assumption required for analytical tractability, only the last consumed prey is taken into account.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Once we know this equilibrium state for given states of the prey populations, we can derive the aggregated intakes of a predator and hence its functional response with respect to all these prey populations. Oaten and Murdoch (27) have proposed a model of multi-species functional responses based on similar ideas, but were unable to derive an explicit expression for the resulting functional response.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Building on earlier work by Oaten and Murdoch (27) and Van Leeuwen et al (7), we develop a generalized theory of predators that switch between multiple prey species. An important feature of this functional response is that it tracks the order in which prey are encountered and attacked and, therefore, allows the incorporation of behaviour based on dietary history.…”

Section: Introductionmentioning

confidence: 99%

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A generalized functional response for predators that switch between multiple prey species

Leeuwen

Brännström

Jansen

et al. 2013

Journal of Theoretical Biology

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ABSTRACT. We develop a theory for the food intake of a predator that can switch between multiple prey species. The theory addresses empirical observations of prey switching and is based on the behavioural assumption that a predator tends to continue feeding on prey that are similar to the prey it has consumed last, in terms of, e.g., their morphology, defences, location, habitat choice, or behaviour. From a predator's dietary history and the assumed similarity relationship among prey species, we derive a general closed-form multi-species functional response for describing predators switching between multiple prey species. Our theory includes the Holling type II functional response as a special case and makes consistent predictions when populations of equivalent prey are aggregated or split. An analysis of the derived functional response enables us to highlight the following five main findings.(1) Prey switching leads to an approximate power-law relationship between ratios of prey abundance and prey intake, consistent with experimental data. (2) In agreement with empirical observations, the theory predicts an upper limit of 2 for the exponent of such power laws. (3) Our theory predicts deviations from power-law switching at very low and very high prey-abundance ratios. (4) The theory can predict the diet composition of a predator feeding on multiple prey species from diet observations for predators feeding only on pairs of prey species. (5) Predators foraging on more prey species will show less pronounced prey switching than predators foraging on fewer prey species, thus providing a natural explanation for the known difficulties of observing prey switching in the field.

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Section: Model Descriptionmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A generalized functional response for predators that switch between multiple prey species

Leeuwen

Brännström

Jansen

et al. 2013

Journal of Theoretical Biology

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“…For instance, the most frequently used explanations of the sigmoid-like shape of the functional response are: (i) the existence of alternative food (Oaten and Murdoch, 1975b;Akre and Johnson, 1979;Gentleman et al, 2003;Elliott 2004), (ii) refuge for prey (Holling, 1966;Taylor, 1984;Poggiale, 1998;Wang et A c c e p t e d m a n u s c r i p t 21 al., 2009), (iii) learning in food searching by predator (Holling, 1965;Luck et al, 1979;Van Leeuwen et al, 2007). None of them is needed to provide a sigmoid response in model (6).…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling

Морозов

2010

Journal of Theoretical Biology

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Food-web population models are rather sensitive to parameterization of functional response in predation terms. Theoretical studies would predict enhancing of ecosystems' stability for a functional response of sigmoid type (Holling type III). The choice of a correct type of response is especially important for modelling outcome of grazing control of algal blooms by zooplankton in nutrient-rich ecosystems. Extensive experiments on zooplankton feeding in laboratories show non-sigmoid nature of response for most herbivorous zooplankton species.As a consequence, there is a strong opinion in the literature that the implementation of Holling III type grazing in plankton models is biologically meaningless. I argue, however, that such an 'evident' claim might be wrong and sigmoid functional responses in real plankton communities would emerge more often than it was suggested earlier. Especially, this concerns plankton models without vertical resolution, which ignore heterogeneity in species vertical distribution. By having conducted extensive literature search of data on zooplankton feeding in situ, I show that vertical heterogeneity in food distribution as well as active food searching behaviour of zooplankton can modify the type of functional response. A c c e p t e d m a n u s c r i p t 2In particular, the rate of food intake by the whole zooplankton population in the column, as a function of total amount of food, often exhibits a sigmoid behaviour, instead of a nonsigmoid one postulated previously based upon laboratory experiments. This conceptual discrepancy is due to the ability of zooplankton to feed mostly in layers with high algal density. I propose a generic model explaining the observed alteration of type between the overall and the local functional responses. I show that emergence of Holling type III in plankton systems is due to mechanisms different from those well known in the ecological literature (e.g. food search learning, existence of alternative food, refuge for prey).

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“…If we make the reasonable assumption that a search image would be formed for the more abundant prey type, this leads to a disproportionally high predation rate on the more abundant prey type and, thus, to prey switching (Murdoch, 1969;Oaten and Murdoch, 1975;Van Leeuwen et al, 2007). Search images cause prey switching by a predator, which leads to coexistence between prey species even if the prey species are in direct competition (Murdoch, 1969), such behaviour could also lead to polymorphism in prey species (Allen et al, 1998;Bond and Kamil, 2006).…”

Section: Introductionmentioning

confidence: 99%

Evolutionary consequences of a search image

Leeuwen

Jansen

2010

Theoretical Population Biology

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Many predators are able to become better at spotting cryptic prey by recognising specific clues, but by concentrating on one prey type they will become worse at spotting other prey types. This phenomenon is known as the formation of a search image for a certain prey by a predator and is related to apostatic selection. Here we study the evolution of a search image in the predator by formulating and analysing a mathematical model. The predator forages for two prey types and is able to form an independent search image for both prey. The results show that the evolutionary dynamics can be divided into two parts, a fast and a slow part. At first selection pressure will be strong towards a stable ratio of prey, which is the same as the ratio found for the unbeatable prey choice for predators with a Holling type II functional response. Following this the slow dynamics will keep this ratio constant independent of the trait values, but the predator will slowly evolve towards a stronger search image and ultimately become a specialist predator or slowly evolve towards generalist with a weak search image. In conclusion, the formation of a search image causes the predator to control the prey densities such that the ratio of available prey is kept constant by the predator.

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Switching, Functional Response, and Stability in Predator-Prey Systems

Cited by 221 publications

References 17 publications

A generalized functional response for predators that switch between multiple prey species

A generalized functional response for predators that switch between multiple prey species

Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling

Evolutionary consequences of a search image

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