Relating individual behaviour to population dynamics

Sumpter, David J. T.; Broomhead, D. S.

doi:10.1098/rspb.2001.1604

Cited by 64 publications

(56 citation statements)

References 30 publications

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“…In the absence of environmental stochasticity, we may also compare the results with those obtained when fitting a theoretically derived model. The model we consider is one of scramble competition for discrete resources, originally introduced by Sumpter & Broomhead (2001) for the parsitism of honey bee brood cells by Varroa mites.…”

Section: Testing the Modelsmentioning

confidence: 99%

Stochastic analogues of deterministic single-species population models

Brännström

Sumpter

2006

Theoretical Population Biology

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Section: Testing the Modelsmentioning

confidence: 99%

Stochastic analogues of deterministic single-species population models

Brännström

Sumpter

2006

Theoretical Population Biology

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“…This approach works even when the population dynamics are periodic or chaotic. Sumpter and Broomhead (2001) applied exactly this approach in predicting the population levels of a parasitic mite, Varroa in the Asian honey bee, which exhibited scramble competition. Data to parameterise interaction functions has also been collected, for example, for two species of bean bruchids: Callosobruchus analis which larvae exhibit contest competition and C. phaseoli which larvae exhibit scramble competition (Toquenaga and Fujii, 1991).…”

Section: Fitting Models To Field Datamentioning

confidence: 99%

“…(24), x Ã ¼ lnðrÞ: Unlike contest competition, where the population always reached a stable level, for scramble competition if lnðrÞ42 then the population will have periodic dynamics and, for even larger values of r; chaotic dynamics (Sumpter and Broomhead, 2001). Using Theorem 2, the estimated variance of the scramble site model defined by (23) is…”

Section: Scramble Competitionmentioning

confidence: 99%

“…Again the parameters in the individual-based model are linked to a 'top-down' model. In this case, the carrying capacity for the population is lnðB 0 Þ=ðrð1 À cÞÞ: Such a 'first principles' justification of the Ricker map can also be argued in terms of local competition between individuals distributed amongst a finite number of discrete resource sites (Sumpter and Broomhead (2001) and see later in this article). The method employed by Royama was also employed independently and greatly extended in a series of papers by Pacala on local plant interactions (Pacala and Silander, 1985), who added complexities such as more than one plant species (Pacala, 1986a), different seed dormancy times (Pacala, 1986b) and age and size structure.…”

Section: Introductionmentioning

confidence: 99%

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From local interactions to population dynamics in site-based models of ecology

Johansson

Sumpter

2003

Theoretical Population Biology

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A central problem in ecology is relating the interactions of individuals-described in terms of competition, predation, interference, etc.-to the dynamics of the populations of these individuals-in terms of change in numbers of individuals over time. Here, we address this problem for a class of site-based ecological models, where local interactions between individuals take place at a finite number of discrete resource sites over non-overlapping generations and, between generations, individuals move randomly between sites over the entire system. Such site-based models have previously been applied to a wide range of ecological systems: from those involving contest or scramble competition for resources to host-parasite interactions and meta-populations. We show how the population dynamics of site-based models can be accurately approximated by and understood through deterministic and stochastic difference equations. Conversely, we use the inverse of this approximation to show what implicit assumptions are made about individual interactions by modelling of population dynamics in terms of difference equations. To this end, we prove a useful and general theorem: that any model in our class of site-based models has a corresponding stochastic difference equation population model, by which it can be approximated. This theorem allows us to calculate long-term population dynamics, evolutionary stable strategies and, by extending our theory to account for large deviations, extinction probabilities for a wide range of site-based systems. Our methodology is then illustrated to various examples of between species competition, predator-prey interactions and co-operation. r

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“…Although initially developed to study distributed computer systems, more recently process algebras have been used to study biological systems [14,33]. In particular the process algebra Weighted Synchronous Calculus of Communicating Systems (WSCCS) [37] has proven useful in studying a wide range of biological systems [19,28,27,29,35,36]. Our group has established a rigorous method for deriving equations to describe the mean behaviour of an infectious disease system as a whole [28,26].…”

Section: Introductionmentioning

confidence: 99%

Using process algebra to develop predator–prey models of within-host parasite dynamics

McCaig

Fenton

Graham

et al. 2013

Journal of Theoretical Biology

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As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used functional response terms from the ecological literature.In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in previous models of immunemediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system.

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Relating individual behaviour to population dynamics

Cited by 64 publications

References 30 publications

Stochastic analogues of deterministic single-species population models

Stochastic analogues of deterministic single-species population models

From local interactions to population dynamics in site-based models of ecology

Using process algebra to develop predator–prey models of within-host parasite dynamics

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