Modelling Biological Populations in Space and Time

Renshaw, Eric

doi:10.1017/cbo9780511624094

Cited by 585 publications

(404 citation statements)

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“…Thus, at the end of the calculations, we take the time-step to zero, so time becomes continuous. We note that the models presented have close connections with `pure death' models of population biology (Renshaw, 1993).…”

Section: Appendix Bmentioning

confidence: 77%

Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model

Nouvellet¹,

Bacon²,

Waxman³

2010

Journal of Theoretical Biology

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. Testing the level of ant activity associated with quorum sensing; An empirical approach leading to the establishment and test of a null-model. Journal of Theoretical Biology, Elsevier, 2010, 266 (4) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractOn the basis of experimental observations, this paper develops two well-defined mathematical models for the level of activity of Pharaoh's ants within their nesting area, with the aim of providing a more general understanding of animal activity. Under specific conditions, we observe that the activity of ants within their nesting area appears to show no dependence on their density. Making the assumption that all ants move independently of one another, this behaviour can be mathematically modelled as a random process based on the binomial distribution. Developing the model on this basis allows an exponential distribution to be exposed that underlies the time-intervals between ants leaving the nesting area. Such a distribution is present, irrespective of whether the ant population in the nesting area remains constant or steadily depletes, and suggests that ant-ant interactions do not play any significant role in determining ant activity under these experimental conditions.The mathematical framework presented plays the role of a null model that will have a wide range of applications for detecting other determinants of activity-level (not addressed in this study) including environmental and social factors such as food availability, temperature, humidity, presence of pheromone trails, along with intraspecific and interspecific interactions outside the nest, and more generally. The null model should have applications to a range of organisms.Lastly, we discuss our data in relation to a recent study of ants leaving their nest (Richardson et al. 2010) in which the null model was rejected in favour of record dynamics, where ant-ant interactions were conjectured to play a role.Keywords: animal activity, movement, social insects, Pharaoh's ants, stochastic process, record dynamics. 3 IntroductionOrganisms frequently monitor the density of conspecifics in their immediate vicinity and modify their behaviour appropriately. For example, some bacteria secrete diffusible signals, for which they also express specific receptors, in order to signal and monitor their density.This mechanism was first discovered in the bacterium Vibrio fischeri; this species uses this technique to ensure that free-living bacteria, which are at low density in the sea, do not indulge in metabolically expensive luminescence, except when living symbiotically, at high density, in t...

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Section: Appendix Bmentioning

confidence: 77%

Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model

Nouvellet¹,

Bacon²,

Waxman³

2010

Journal of Theoretical Biology

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“…DISCUSSION Theories in conservation biology (Diamond 1975), metapopulation ecology (Hanksi 1999), population ecology (Haccou & Iwasa 1996;Matis & Kiffe 2000;Haccou & Vatunin 2003) and invasion biology (Leung et al 2004;MacIsaac et al 2004) have emphasized the importance of immigration for population persistence. Though the contribution of immigration to population growth rate is typically small, immigration is of considerable importance in stochastic models (Bailey 1964;Renshaw 1991;Matis & Kiffe 2000), and in nature, where rescue effects dramatically enhance growth of nearly extinct populations (Brown & Kodric-Brown 1977;Gotelli 1991).…”

Section: Results (A) Hypothesis 1: Realized Population Growth Ratementioning

confidence: 99%

Propagule pressure and persistence in experimental populations

2005

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Average inoculum size and number of introductions are known to have positive effects on population persistence. However, whether these factors affect persistence independently or interact is unknown. We conducted a two-factor experiment in which 112 populations of parthenogenetic Daphnia magna were maintained for 41 days to study effects of inoculum size and introduction frequency on: (i) population growth, (ii) population persistence and (iii) time-to-extinction. We found that the interaction of inoculum size and introduction frequency—the immigration rate—affected all three dependent variables, while population growth was additionally affected by introduction frequency. We conclude that for this system the most important aspect of propagule pressure is immigration rate, with relatively minor additional effects of introduction frequency and negligible effects of inoculum size.

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“…Despite what could be generally considered [6], deterministic models do not describe the average result obtained from an infinite number of stochastic simulations (see, for instance, [16]), and stochastic models result in lower epidemics than deterministic models. This observation, confirmed here (Fig.…”

Section: Discussionmentioning

confidence: 99%

A deterministic and stochastic simulation model for intra-herd paratuberculosis transmission

Pouillot¹,

Dufour²,

Durand³

2004

Vet. Res.

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-In France, the considerable economic losses due to paratuberculosis introduction in cattle herds may justify the development of a herd-level certification procedure. For a cost/benefit analysis purpose, a simple deterministic and stochastic simulation model for intra-herd paratuberculosis transmission has been developed to evaluate the economic consequences of the purchase of a single infected heifer in a French average herd. The values of the epidemiological parameters were provided by a panel of French paratuberculosis experts. The results were in adequacy with field observations. A sensitivity analysis was conducted. The model was however difficult to validate rigorously, since few data on the intra-herd paratuberculosis true prevalence level are currently available. paratuberculosis / stochastic model / deterministic model / sensitivity analysis

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Modelling Biological Populations in Space and Time

Cited by 585 publications

References 0 publications

Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model

Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model

Propagule pressure and persistence in experimental populations

A deterministic and stochastic simulation model for intra-herd paratuberculosis transmission

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